A Procedure to Convert Total Column Ozone Data to Numerical Weather Prediction Model Initializing Fields, and its Validation via Simulations of the 24-25 January 2000 East Coast Snowstorm
By
Dorothy A. Durnford
Department of Atmospheric and Oceanic Sciences McGill University Montreal
Submitted August 2007
A thesis submitted to McGill University in partial fulfilment of the requirements of the degree of Doctor of Philosophy.
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Abstract
Satellites provide uniform data coverage globally. Thus, their data have the potential to reduce analysis errors in data sparse areas significantly, thereby improving numerical weather prediction (NWP) model forecasts. We describe a previously-used methodology to generate NWP model initial conditions (ICs) from satellite total column ozone data based on three principal steps: 1) convert a chemical total column ozone field to a dynamical mean potential vorticity (MPV) field via linear regression, 2) convert the 2D MPV field to a 3D potential vorticity (PV) field via vertical mapping onto average PV profiles, 3) invert the 3D PV field to obtain model-initializing height, temperature and wind fields in the mid and upper troposphere. Our contribution to the discipline has been to increase significantly the overall accuracy of the process through a substantial reworking of the details of this previous version. For instance, in recognition of the fact that total column ozone ridges tend to be less reliable than troughs, the MPV field that is converted to a 3D PV field in the second step is a synthesis of ozone-derived MPV troughs and analysis MPV ridges. We also adjust the vertical mapping procedure of the second step so that the MPV field converts to a more realistic 3D PV field; unrealistic PV features appearing strongly at upper levels and decaying with decreasing altitude are no longer generated. As a result of these and other novel procedures, the previously-described conversion procedure produces a more realistic set of model upper-level initializing fields.
Using the 24-25 January 2000 east coast snowstorm as an example, we use the developed methodology to initialize the Mesoscale Compressible Community model (MC2). We find that ozone-influenced upper-level initializing fields improve the quantitative precipitation forecast for two of three (re)analyses. Furthermore, our best forecast of all utilizes ozone-influenced upper-level initializing fields. Finally, this novel procedure gives a quantitative precipitation forecast that is superior to an ozone-influenced four dimensional variational assimilation forecast of the same case.
The methodology presented, which generates NWP model ICs from total column ozone data, may be useful for the forecasting of weather systems originating in data sparse areas.
i Preliminaries
Resume
Les donnees meteorologiques acquises par satellite ont une resolution globale uniforme. Elles peuvent ainsi etre utilisees pour ameliorer les predictions par modele numerique (MN), en particulier, dans les regions ayant peu de stations d'observations meteorologiques. Nous decrirons une methodologie qui a deja ete presentee, qui produit des conditions initiales (CI) utilisables par les modeles numeriques. Cette methodologie utilise des donnees obtenues par satellite qui mesurent la quantite totale d'ozone dans une colonne verticale atmospherique. Ces CI sont obtenues en trois etapes. Premierement, un champ de la quantite d'ozone totale (un champ chimique) est converti en un champ dynamique de tourbillon potentiel moyen (TPM) par regression lineaire. Deuxiemement, le champ en deux dimensions de TPM est converti en un champ de trois dimensions de tourbillon potentiel (TP) par regression verticale basee sur les profils moyens de TP. Troisiemement, le dernier champ de TP est inverse afin d'obtenir les CI du MN, qui consistent de champs d'altitude, de temperature et de vent a la mi-troposphere et aux niveaux superieurs tropospheriques. Nous avons augmente la precision du processus d'une maniere significative en raffinant substantiellement les details de cette version anterieure, ce qui constitue notre contribution scientifique. Par exemple, comme les cretes d'ozone totale sont souvent moins fiables que les creux, le champ de TPM que nous convertissons en un champ de TP de trois dimensions pendant la deuxieme etape est une synthese des creux de TPM provenant d'ozone totale avec des cretes de TPM analysees. De plus, la regression verticale de la deuxieme etape est reglee afin de ne plus convertir des anomalies du champ de TMP en des anomalies de TP non realistes qui sont exagerees aux niveaux superieurs et qui diminuent avec 1'altitude. La methodologie de conversion mentionnee auparavant produit des CI de MN de niveaux superieurs qui sont plus realistes avec l'addition de ces processus et d'autres processus originaux.
En utilisant la tempete du 24-25 Janvier 2000, qui est associee a d'importantes accumulations de neige sur la cote est americaine, nous initialisons le Mesoscale Compressible Community Model (MC2) avec les CI produits par la methodologie developpee. Nous trouvons que les CI influencees par l'ozone sur les niveaux eleves ameliorent la prevision de precipitation quantitative pour deux des trois (re)analyses. De plus, la meilleure prevision utilise les CI influencees par l'ozone sur les niveaux eleves. Finalement, cette methodologie originale produit une prevision de precipitation quantitative qui est superieure a une prevision influencee par l'ozone de la meme tempete qui utilisait l'assimilation variationnelle en quatre dimensions.
La methodologie presentee, qui produit des CI de MN en utilisant les donnees de la quantite d'ozone totale, pourrait etre utile pour les previsions associees aux systemes meteorologiques qui proviennent des regions caracterisees par un manque de donnees.
ii Preliminaries
Statement of Originality
To our knowledge, the following aspects of this thesis are original:
1. Previously, ozone-derived fields, which are valid near local noon, were interpolated to the chosen universal time after both the performance of the total column ozone/Mean Potential Vorticity (MPV) regression and the conversion of the two-dimensional (2D) MPV field to a three-dimensional (3D) Potential Vorticity (PV) field (see Davis et al. 1999). This system is undesirable for two reasons: 1) the regression's ozone and MPV fields are valid at different times, and are, therefore, spatially misaligned, which reduces the accuracy of the regression, and 2) since pressure level winds are used as the advecting agent in the temporal interpolation of the 3D PV field, and since winds at different levels vary in strength and direction, the vertical alignment of PV features created by the vertical mapping of the MPV field onto carefully constructed average PV profiles is distorted by the temporal interpolation. The presented methodology addresses both of these issues by temporally interpolating the total column ozone field itself. The regression's fields are then spatially aligned, which increases its accuracy. Furthermore, the integrity of the 3D PV field's vertical alignments is preserved as pressure level winds no longer operate on this field. This advantageous temporal interpolation of the total column ozone field is made possible by our use of analysis dynamic tropopause winds as the advecting agent, which is appropriate owing to the fact that the majority of the ozone molecules contributing to the total column ozone field reside just above the tropopause (Salby and Callaghan 1993). No mention has been found in the literature of a temporal interpolation of total column ozone using dynamic tropopause winds.
2. The total column ozone/MPV regression has been performed in a variety of ways in the literature (see, e.g., Davis et al. 1999, Jang et al. 2003, Zou and Wu 2005), with no evidence provided as to the superiority of the selected method. This lack of justification is surprising, given that this regression is a necessary component of the assimilation of total column ozone data in NWP models, regardless of the assimilation system used, unless ozone is explicitly integrated by the model. In this research, instead of relying on a sophisticated assimilation technique to produce good results, we have re-examined the performance of this regression and have systematically established a methodology. For instance, we demonstrate that, for our domain and time period, a correlation coefficient of 0.89 describes the total column ozone and MPV fields when data points from all latitudes combined contribute to the calculation, while the average of the four coefficients calculated using sequential latitude bands falls to 0.80, where the highest individual coefficient is 0.86. Thus, we have provided the community with a systematically established technique, albeit possibly case-dependent, for the performance of this fundamental procedure.
in Preliminaries
3. Although it was previously known that diabatic processes are a source/sink for MPV but not for total column ozone, the development and extent of diabatically-caused discrepancies between the MPV and ozone fields has never been documented. In this study we provide evidence of diabatic heating and of the lack of response in the total column ozone field. We discuss the advection of such discrepancies, which further increases their spatial scale. We find that ozone-derived troughs tend to be more conserved than ozone-derived ridges, owing to the fact that ridges are often diabatically-generated. As a result of the severity of the discrepancies, we use only the ozone-derived MPV troughs. The use of only portions of an ozone or ozone-derived field, whether selected dynamically or not, has not been documented previously.
4. The vertical distribution of the total column ozone or ozone-derived increment in the assimilation of total column ozone is a known problem (Riish0jgaard 1996, Dethof and Holm 2004). When mapping the MPV field onto average profiles, two average profiles were previously provided, one each for ridges and troughs (Davis et al. 1999). In this study we provide 12 such profiles, so that a profile is available that is not only appropriate for the type but also the strength of the MPV field feature; ozone-influenced PV vertical profiles are more realistic when the difference between the MPV values of the average profile and of the ozone-influenced field is reduced. Furthermore, a constant mapping coefficient translates the MPV increment to a large PV feature at upper levels that decays with decreasing altitude, owing to the fact that, climatologically, PV increases with altitude; a constant factor multiplying larger PV values at upper levels yields the largest change in PV at those upper levels. This result is unphysical as PV disturbances maximize near the tropopause. In this research, we employ a level-varying mapping coefficient, which distributes the MPV increment predominantly to the upper troposphere/lower stratosphere. This creates more realistic vertical PV profiles. No mention of a level-varying mapping coefficient was found in the literature.
5. The PV inversion generated spurious dipoles in the inverted height fields of our 3626-grid point domain. As model grid-spacing decreases and the number of grid points in an inversion domain increases, such dipoles are likely to appear more frequently. We present a method of subdividing the inversion domain so that the subdomain boundary conditions can provide better guidance for the inversion, thereby preventing the generation of height field dipoles. The subdomains' inverted fields are subsequently recombined without leaving any trace of the subdomains' boundary conditions. To our knowledge, subdividing the PV inversion domain has not been documented previously.
IV Preliminaries
6. Jang et al. (2003) present the only published quantitative precipitation forecast (QPF) where total column ozone is assimilated and linked to model dynamical variables. However, despite the fact that our procedure is far less sophisticated than their four dimensional variational assimilation system, we have produced an ozone-influenced onshore accumulated precipitation forecast for the same event, the 24-25 January 2000 United States (U.S.) east coast snowstorm, that is superior to that of Jang et al. (2003), where the Brennan and Lackmann (2005) precipitation analysis constitutes the truth field; our precipitation forecast exhibits the greater degree of inland penetration, while omitting the unwanted North Carolina coastal maximum. Note that the model horizontal resolutions are virtually identical, although the Jang et al. (2003) simulation is initialized at the very start of the event at 1200 UTC on the 24*, six hours earlier than ours. One might expect the earlier initializing time to provide the Jang et al. (2003) simulation with an advantage, as our later initializing time precludes the generation of the precipitation from the event's first six hours. Thus, we have developed a methodology that produces a competitive onshore accumulated precipitation forecast for this snowstorm, but which is computationally less expensive.
7. The Jang et al. (2003) ozone-influenced onshore accumulated precipitation forecast of the 24-25 January 2000 U.S. east coast snowstorm was superior to their control forecast, in relation to the Brennan and Lackmann. (2005) precipitation analysis, in that the precipitation penetrated farther inland. However, South Carolina precipitation values unfortunately decreased in the ozone-influenced forecast, while a spurious maximum appeared over the northern coastal region of North Carolina. Thus, the effects of the ozone assimilation were mixed. In contrast, ozone-influenced upper-level initializing fields improved our GEM-initialized onshore accumulated forecast by pushing the precipitation farther inland and by generating an almost perfectly located self-contained onshore maximum across the border of the Carolinas. This subjective evaluation of the superiority of our ozone-influenced forecast is supported by the forecast's superior threat scores and biases for thresholds below 50 mm.
V Preliminaries
Acknowledgements
I am deeply indebted to my supervisor, Professor John Gyakum, who has taught me so much, both directly and indirectly. I appreciate his consistently high standards and his great expertise. His insights greatly improved the original version of this manuscript. As members of my supervisory committee, Professors Henry Leighton and Peter Yau also provided me with imaginative, constructive advice based on a deep understanding of meteorology.
I would like to express my sincere thanks to the following institutions for funding my PhD research: the Natural Sciences and Engineering Research Council of Canada, the Cooperative Program for Operational Meteorology, Education and Training, the Canadian Foundation for Climate and Atmospheric Sciences, and Environment Canada. Finally, I am indebted to the American Meteorological Society, which awarded me a student travel bursary.
Eyad Atallah at McGill University provided insightful comments on a regular basis. Marco Carrera provided the operational Eta analyses and forecasts. David Stephaniak at the University Corporation for Atmospheric Research (UCAR) made the ERA-40 fields available. Soundings were provided by the University of Wyoming. Rick Danielson provided me with the PV inversion program and detailed instructions on how to use it. The National Center for Atmospheric Research (NCAR) scientific computing division made available the streamfunction-calculating program. Environment Canada's Recherche en Prevision Numerique (RPN) made available their MC2 model and associated software, and permitted me to use their IBM supercomputers. Irena Paunova at McGill University along with Sylvie Gravel and Stephane Chamberland at RPN helped me to understand the details of the MC2 model. Julie Theriault checked my French translation of the abstract. I am grateful for all this help, which made my task considerably easier.
Finally, I would like to thank my family for being the best support group possible.
VI Preliminaries
Table of Contents
Abstract i Resume ii Statement of Originality iii Acknowledgements vi List of Figures ix List of Tables xx
Chapter 1 Introduction 1 1.1 Motivation 1 1.1.1 Quantitative precipitation forecasting 1 1.1.2 Initial conditions and numerical weather prediction model 4 forecast error 1.1.3 Initial conditions and satellite data 11 1.2 Objectives 16 1.3 Thesis overview 20
Chapter 2 The Conversion of Total Column Ozone Data to Numerical 21 Weather Prediction Model Initializing Fields, and its application to the 24-25 January 2000 East Coast Snowstorm 2.1 Total column ozone and its relationship to meteorological fields 23 2.1.1 The generation and behaviour of total column ozone 23 2.1.2 The generation and behaviour of potential vorticity 29 2.1.3 A description of mean potential vorticity 34 2.1.4 The correlation of ozone and dynamical variables 37 2.1.5 Ozone and numerical weather prediction models 41 2.2 Data sets 49 2.2.1 Technical details concerning the total column ozone data 49 2.2.2 Model analyses and forecasts 50 2.2.3 Precipitation analyses 52 2.2.4 Water vapour satellite imagery 52 2.3 The conversion of total column ozone data to model initializing fields 53 2.3.1 The conversion of total column ozone to mean potential 54 vorticity 2.3.1.1 Spatial interpolation of total column ozone 54 2.3.1.2 Temporal interpolation of total column ozone 56 2.3.1.3 Total column ozone / mean potential vorticity regression 63 scheme 2.3.1.4 Total column ozone regression 72 2.3.1.5 Synthesis of ozone-derived and analysis mean potential 77 vorticity 2.3.2 Mean potential vorticity to potential vorticity conversion 82
vn Preliminaries
2.3.2.1 Construction of average potential vorticity profiles 82 2.3.2.2 Vertical mapping 87 2.3.3 Potential vorticity inversion 92 2.3.3.1 Davis and Emanuel (1991) methodology 92 2.3.3.2 Modifications to the Davis and Emanuel (1991) 97 methodology 2.3.4 Summary 105
Chapter 3 The simulation of the 24-25 January 2000 East Coast 107 Snowstorm using ozone-influenced initial conditions 3.1 A synoptic overview of and previous research on the 24-25 January 109 2000 east coast snowstorm 3.1.1 A synoptic overview of the snowstorm and its forecasting 109 3.1.2 Previous research 131 3.2 Simulations of the 24-25 January 2000 East Coast 147 Snowstorm by the Mesoscale Compressible Community Model (MC2) 3.2.1 The numerical model and experimental setup 147 3.2.1.1 The Mesoscale Compressible Community Model 147 (MC2) 3.2.1.2 Experimental setup 148 3.2.2 Modeling results 153 3.2.2.1 Simulations initialized at 1800 UTC 24 January 2000 153 3.2.2.2 Simulations initialized at 1800 UTC 23 January 2000 187 3.2.3 Summary of modeling results 207
Chapter 4 Summary and Conclusions 211 4.1 Summary 211 4.1.1 Generation of model initializing fields from satellite total 211 column ozone data 4.1.2 Validation of the ozone-influenced model initializing fields 214 4.2 Conclusions 217 4.3 Future work 220
References 223
Vlll Preliminaries
List of Figures
1.1 : 2 Numerical model skill scores for 36-h 500-hPa geopotential height forecasts for North America and adjacent waters (open circles), and for 24-36-h probability of measurable precipitation forecast skill with respect to climatology at approximately 100 stations in the U.S. (solid circles; taken from Roebber and Bosart 1998).
1.2: 3 Annual threat scores for the NOAA Hydrometeorological Prediction Center for 24-h forecasts of 1.00 in. (25.4 mm) or more of precipitation (taken from Fritsch and Carbone 2004).
1.3: 3 Monthly threat scores for the NOAA Hydrometeorological Prediction Center for 24-h forecasts of 1.00 in. (25.4 mm) or more of precipitation for 1991-1999 (taken from Fritsch and Carbone 2004).
1.4: 7 North American rawinsonde stations (taken from University of Wyoming 2007).
1.5: 7 The North American distribution of aircraft meteorological observations for 0000 UTC 17 March 2006 (taken from Thepaut and Lalaurette 2007). Manually- transmitted aircraft (AIREP; red), Aircraft Meteorological Data Reporting (AMDAR; blue), Aircraft Communications Addressing and Reporting System (ACARS; green) reports are included.
1.6: 13 Meteosat water vapour imagery (grey shades) and 315-K isentropic surface PV (contour interval of 0.5 Potential Vorticity Units) at 0000 UTC 24 January 1996 (taken from Demirtas and Thorpe 1999).
1.7: 15 Total column ozone (solid, 15-DU contour interval, dashed 290-DU contour and shading for values greater than 350 DU), valid at local noon on the indicated date, and ERA-40 200-hPa heights (grey, 24-dam contour interval), valid at 1800 UTC.
2.1: 28 Total column ozone (15-DU contour interval, with the 290-DU contour dashed and values greater than 350 DU shaded), valid at local noon on the day indicated, and ERA-40 200-hPa heights (grey contours, with the 1152-dam contour wide and a 24-dam contour interval), valid at 1800 UTC. The red circles track the feature that evolves into the upper-level trough associated with the 24-25 January 2000 east coast snowstorm. Preliminaries
2.2: 32-33 ERA-40 dynamic tropopause potential temperatures (4-K contour interval, with the 316-K contour dashed and values less than 304 K shaded), valid at 1800 UTC. The red circles track the feature that evolves into the upper-level trough associated with the 24-25 January 2000 east coast snowstorm.
2.3: 35-36 ERA-40 Mean Potential Vorticity (MPV; calculated from the geopotential and streamfunction fields as per equation {2.23} in Section 2.3.3.1; 0.5-PVU contour interval, with the 5.5-PVU contour dashed and values greater than 7 PVU shaded). The red circles track the feature that evolves into the upper-level trough associated with the 24-25 January 2000 east coast snowstorm.
2.4: 52 The topography (m) of the operational Eta domain (taken from NARR 2007, where "NARR" represents the North American Regional Reanalysis).
2.5: 54 The topography (m, shaded) of the operational Eta domain has been interpolated from its native Lambert conic conformal grid to a Mercator grid. White regions are outside the native Eta grid. The computation region for the ozone to model initial conditions conversion is indicated by the black box. Also plotted are Eta subdomain 200-hPa temperatures (2-°C contour interval) embedded within the ERA-40 domain.
2.6: 55 Problematic spatially-interpolated total column ozone values (5-DU contour interval) bordering a) high-latitude and b) low-latitude data void regions (shaded) appear as bull's eyes.
2.7: 58 Correlation coefficients (dimensionless) calculated using various factors (dimensionless) to divide the ozone-advecting winds.
2.8: 61 Plotted for 24 January 2000 are a) the original total column ozone field valid at local noon with ERA-40 dynamic tropopause winds valid at 1800 UTC ((half) barb equals (2.5) 5ms", pennant equals 25 m s" ), and b) the temporally-mapped total column ozone field valid at 1800 UTC. The ozone fields are plotted with a contour interval of 25 DU, where smaller values are shown in lighter shades of grey, and shading from 350 DU.
2.9: 64-65 Total column ozone (DU)/MPV (PVU) data points from the indicated latitude bands are shown with the respective regressed lines. Available (filtered) points are plotted in black (grey). The heavy line along the abscissa is created by points from data void regions. Preliminaries
2.10: 66 Regression slopes (a) and intercepts (b) for the indicated latitude bands.
2.11: 68 Correlation coefficients (dimensionless) calculated using the indicated MPV upper and lower bounding pressure levels (hPa).
2.12: 69 Correlation coefficients (dimensionless) calculated using the indicated (re)analyses.
2.13: 71 Correlation coefficients (dimensionless) calculated using the indicated regression time periods (d).
2.14: 74 Plotted for 1800 UTC 24 January 2000 are: a) temporally-mapped total column ozone (contour interval of 25 DU with shading from 350 DU), and b) regressed MPV (contour interval of 1.2 PVU from 1.8 PVU with shading from 6.6 PVU). In both panels, paler shades of grey represent smaller values.
2.15: 75 Regressed and ERA-40 MPV valid at 1800 UTC 24 January 2000 are shown in panels a) and b), respectively. These fields are plotted using a contour interval of 1 PVU for solid lines (where smaller values are represented by paler shades of grey), a dashed line at 5.5 PVU and shading from 7 PVU. Note that the contour intervals of Figs. 2.14.b and 2.15.a are different.
2.16: 76 Shown for the indicated January 2000 day/UTC time are a), c) GEOS 10, and b), d) GOES 8 water vapour images.
2.17: 79 The a) regressed, b) synthesized, and c) ERA-40 MPV fields for 1800 UTC 24 January 2000 are shown, with a contour interval of 1 PVU for solid lines (where smaller values are represented by paler shades of grey), a dashed line at 5.5 PVU and shading from 7 PVU. The straight lines indicate the location of the cross sections of Figs. 2.21-2.24.
2.18: 80 Shown for the indicated dates, where "24/12" denotes 1200 UTC 24 January 2000 are a), c) MPV calculated from analysed rawinsonde data and b), d) ERA-40 MPV. The contour interval is 1 PVU for solid lines (where smaller values are represented by paler shades of grey), with a dashed line at 5.5 PVU and shading from 7 PVU. Triangles (squares) mark sounding stations contributing data at all (some of the) ten pressure levels contributing to the MPV calculation.
XI Preliminaries
2.19: 83 A Flow chart outlining the steps for the generation of a given grid point's average PV profile, using a hypothetical case as an example.
2.20: 86 Average PV vertical profiles (PVU) available at two latitudes and two longitudes. The legend indicates the range of MPV values (in terms of the number of standard deviations, a, from the mean MPV value) characterizing the subset of points - of the grid point's set of space/time points - that contributes to the corresponding average PV profile.
2.21: 89 For 1800 UTC 24 January 2000, cross sections of PV are shown along the line indicated in panel b) of Fig. 2.17, where the PV fields have been vertically mapped using a) a constant mapping coefficient, and b) a level-varying mapping coefficient. The PV fields are plotted every 1 PVU to 13 PVU and every 2 PVU from 13 PVU, with shading from 2-3 PVU.
2.22: 90 Cross sections of PV along the lines indicated in Fig. 2.17 are shown for 1800 UTC 24 January 2000 using: a) PV fields obtained by vertically mapping synthesized MPV using a level-varying mapping coefficient, and b) ERA-40 PV0F, 2.23: 96 Cross sections of PV along the line indicated in panel c) of Fig. 2.17 are shown for 1800 UTC 24 January 2000 using: a) EPV calculated from the original ERA- 40 fields, and b) EPV calculated from fields produced by inverting ERA-40 PVC^O). Full PV fields are plotted every 1 PVU to 13 PVU and every 2 PVU from 13 PVU. Panel a) also shows the difference of the two ERA-40 EPV fields (inverted-original; shading intervals of 0.5 PVU with a solid (dashed) contour at + (-) 0.5 PVU). 2.24: 100 Cross sections of PV for 1800 UTC 24 January 2000 along the lines indicated in Fig. 2.17 are presented from the following sources: a) vertical mapping of ozone- influenced MPV using a level-varying mapping coefficient, b) ERA-40 PV^,®), c) EPV calculated from ozone-influenced inverted fields, and d) ERA-40 EPV. The PV fields are plotted every 1 PVU to 13 PVU and every 2 PVU from 13 PVU, with shading from 2-3 PVU. 2.25: 101 Shown for 1800 UTC 24 January 2000 are a) inverted and b) ERA-40 500-hPa heights (12-dam contour interval, with a wider 540-dam contour) and winds ((half) barb equals (2.5) 5 m s"1, pennant equals 25 m s"1). Xll Preliminaries 2.26: 102 Shown at 500 hPa for the indicated dates, where "24/12" denotes 1200 UTC 24 January 2000, are a), c) analysed rawinsonde heights (6-dam contour interval, with a wider 540-dam contour) with observed heights (dam) and winds ((half) barb equals (2.5) 5 m s"1, pennant equals 25 m s"1), and b), d) ERA-40 heights and winds, plotted using the same conventions. 2.27: 103 Shown for 1800 UTC 24 January 2000 are a) inverted and b) ERA-40 200-hPa heights (18-dam contour interval, with a wider 1170-dam contour) and winds ((half) barb equals (2.5) 5 m s"1, pennant equals 25 m s"1). 2.28: 104 Shown at 200 hPa for the indicated dates, where "24/12" denotes 1200 UTC 24 January 2000, are a) c) analysed rawinsonde heights (12-dam contour interval, with a wider 1170-dam contour) with observed heights (dam) and winds ((half) barb equals (2.5) 5 m s"1, pennant equals 25 m s"1), and b), d) ERA-40 heights and winds, plotted using the same conventions. 3.1: 109 Accumulated liquid water equivalent precipitation for 24-26 January 2000 (contours at 5 mm and every 10 mm from 10 mm, with the 20-mm contour dashed, the 40-mm contour heavy, and light (dark) shading from 50 (80) mm; adapted from Brennan and Lackmann 2005). 3.2: 111 Accumulated liquid water equivalent precipitation (contours at 5 mm and every 10 mm from 10 mm, with the 20-mm contour dashed, the 40-mm contour heavy, and light (dark) shading from 50 (80) mm) for a) 24/12-25/12 and b) 24/18-25/12 from the operational Eta runs initialized at 23/18 and 24/18, respectively. 3.3: 114-115 Shown for the indicated January 2000 day/UTC time are GOES 8 water vapour images (left columns) and ERA-40 200-hPa height fields ( right columns, 12-dam contour interval, with the 1176-dam contour heavy). The red circles track the water vapour feature that evolves into the upper-level trough associated with the 24-25 January 2000 east coast snowstorm. 3.4: 115-116 ERA-40 sea level pressure (solid, 4-hPa contour interval) and 1000-500-hPa thickness fields (dot-dash, 6-dam contour interval with a wide, solid line for the 540-dam contour). Preliminaries 3.5: 117 ERA-40 sea level pressure (solid, 4-hPa contour interval), 850-hPa temperature (dash, 4-°C contour interval, 0-°C contour heavy) and 850-hPa mixing ratio fields (increasingly dark shading from 4-7 g kg~l). 3.6: 119 Eta operational forecasts initialized at 23/18 of sea level pressure (solid, 4-hPa contour interval) and 1000-500 hPa thickness (dot-dash, 6-dam contour interval with a wide, solid line for the 540-dam contour). 3.7: 120 Eta operational forecasts initialized at 24/18 of sea level pressure (solid, 4-hPa contour interval) and 1000-500 hPa thickness (dot-dash, 6-dam contour interval with a wide, solid line for the 540-dam contour). 3.8: 121 Eta operational forecasts initialized at 23/18 of sea level pressure (solid, 4-hPa contour interval), 850-hPa temperature (dash, 4-°C contour interval, 0-°C contour heavy) and 850-hPa mixing ratio (increasingly dark shading from 4-7 g kg"1). 3.9: 122 Eta operational forecasts initialized at 24/18 of sea level pressure (solid, 4-hPa contour interval), 850-hPa temperature (dash, 4-°C contour interval, 0-°C contour heavy) and 850-hPa mixing ratio (increasingly dark shading from 4-7 g kg"1). 3.10: 123 Eta operational forecasts initialized at 23/18 of dynamic tropopause potential temperature (lightly smoothed; 4-K contour interval with a dot-dash (dashed) contour for 304 (316) K). Also shown is the Eta and ERA-40 dynamic tropopause potential temperature difference field (Eta - ERA-40; 5-K shading interval from 5 to 20 K, with positive (negative) values surrounded by a solid (dotted) contour). 3.11: 124 Eta operational forecasts initialized at 24/18 of dynamic tropopause potential temperature (lightly smoothed; 4-K contour interval with a dot-dash (dashed) contour for 304 (316) K). Also shown is the Eta and ERA-40 dynamic tropopause potential temperature difference field (Eta - ERA-40; 5-K shading interval from 5 to 20 K, with positive (negative) values surrounded by a solid (dotted) contour). 3.12: 126 Dynamic tropopause potential temperatures (4-K contour interval, with the 316-K contour dashed and values less than 304 K shaded), and winds ((half) barb equals (2.5) 5 ms"1, pennant equals 25 m s"1) at 25/00 for a) the ERA-40, and for the XIV Preliminaries Eta runs initialized at b) 23/18 and c) 24/18. The triangle (square) marks the location of CHS (GSO), while the straight lines indicate the locations of the cross sections of Fig. 3.13. 3.13: 128 Vertical cross sections of PV (solid, 1-PVU contour interval, shaded from 2-3 PVU), equivalent potential temperature (dashed, 5-K contour interval), omega (grey solid (dashed) for positive (negative) values, 2xlO~3-hPa s~l contour interval, zero contour omitted). 3.14: 129 Skew-T log-p plots of temperature (°C, solid), dew point temperature (°C, dashed) and horizontal winds ((half) barb equals (2.5) 5 m s~l, pennant equals 25 m s-1) at 0000 UTC 25 January 2000 as observed (black), from the ERA-40 (red), and from the operational Eta forecasts initialized at 23/18 (purple; 30-h forecast) and 24/18 (brown; 6-h forecast) at a) GSO and b) CHS. Also plotted are the 300-, 325- and 350-K moist adiabats. 3.15: 132 Accumulated liquid water equivalent precipitation (contours at 5 mm and every 10 mm from 10 mm, with the 20-mm contour dashed, the 40-mm contour heavy, and light (dark) shading from 50 (80) mm) for a) 24/12-25/12 and b) 25/12-26/12 from the Unified Precipitation Dataset. 3.16: 153 Accumulated liquid water equivalent precipitation for 24-26 January 2000 (contours at 5 mm and every 10 mm from 10 mm, with the 20-mm contour dashed, the 40-mm contour heavy, and light (dark) shading from 50 (80) mm; adapted from Brennan and Lackmann 2005). 3.17: 154 Precipitation (contours at 5-mm and every 10 mm from 10 mm, with the 20-mm contour dashed, the 40-mm contour heavy, and light (dark) shading from 50 (80) mm) accumulated during the indicated experiments from the start of the simulation at 24/18 to 25/12 is shown. 3.18: 156 Calculated for the indicated experiments and thresholds are the: a) threat scores and b) bias for the precipitation accumulated from the start of the simulation at 24/18 to 25/12. The Brennan and Lackmann (2005) analysis constitutes the truth field. 3.19: 158 An analysis of liquid water equivalent precipitation accumulated on 24-26 January 2000 (contours at 5-mm and every 10 mm from 10 mm, with the 20-mm contour dashed, the 40-mm contour heavy, and light (dark) shading from 50 (80) XV Preliminaries mm) adapted from Brennan and Lackmann (2005) is presented in panel a). The same plotting convention is used in panel b) for precipitation accumulated during the ozone/GEM experiment from the start of the simulation at 24/18 to 25/12. Panel c) presents the ozone-influenced 4D-Var assimilation forecast of precipitation (contours every 10 mm from 10 mm) accumulated from the initializing time of 24/12 to 25/12 from Jang et al. (2003; their Fig. 16.d). 3.20: 160 An analysis of liquid water equivalent precipitation accumulated on 24-26 January 2000 (contours at 5-mm and every 10 mm from 10 mm, with the 20-mm contour dashed, the 40-mm contour heavy, and light (dark) shading from 50 (80) mm) adapted from Brennan and Lackmann (2005) is presented in panel a). The same plotting convention is used for precipitation accumulated during the GEM (panel b)) and ozone/GEM (panel c)) experiments from the start of the simulations at 24/18 to 25/12. Panels d) and e) present, respectively, the control and ozone-influenced 4D-Var assimilation forecasts of precipitation (contours every 10 mm from 10 mm) accumulated from the initializing time of 24/12 to 25/12 from Jang et al. (2003; their Figs. 16.b, 16.d). 3.21: 165-166 Sea level pressure (purple, 4-hPa contour interval, 1000-hPa contour heavy) and 1000-500 hPa thickness fields (brown, 6-dam contour interval with a heavy, solid line for the 540-dam contour) are shown for experiments initialized at 24/18. The reanalysis ERA-40 sea level pressure cyclone is plotted in violet. Also shown, when available, are rawinsonde-derived thickness contours, plotted as per the simulation field but in orange. Titles indicate the experiment name, forecast hour, and actual date/time. Note that the date/time varies by column and the experiment by row. 3.22: 168-169 Lightly smoothed EPV-derived dynamic tropopause potential temperatures (4-K contour interval, with the 316-K contour dashed and values less than 304 K shaded) are shown for experiments initialized at 24/18. At 25/00, the rawinsonde- derived 316-K contour (dark, solid) is added. Titles indicate the experiment name, forecast hour, and actual date/time. Note that the date/time varies by column and the experiment by row. Note also that the region plotted changes with time. 3.23: 171-172 The 250-hPa height (purple, 6-dam interval, with the 1026 (1032)-dam contour heavy solid (dash)), wind (brown, (half) barb equals (2.5) 5 m s-l, pennant equals 25 m s-1) and isotach (shading every 5 m s"1 from 55 m s"1) fields are shown for experiments initialized at 24/18. Also shown, when available, are rawinsonde- derived heights (violet) and winds (orange), plotted as per the simulation fields, and isotachs (contours in shades of orange every 5 m s"1 from 55 m s"1). Titles XVI Preliminaries indicate the experiment name, forecast hour, and actual date/time. Note that the date/time varies by column and the experiment by row. 3.24: 173 Shown are analyses at 24/12 of 250-hPa heights (purple, 6-dam interval, with the 1026 (1032)-dam contour heavy solid (dash)), winds (brown (half) barb equals (2.5) 5 m s~l, pennant equals 25 m s-1) and isotachs (every 5 m s-1 from the 15-m s-1 black contour, with shading from 55 m s-1) from the indicated sources. Rawinsonde wind speeds (m s-1) are also provided in panel b). 3.25: 175-176 The 500-hPa height (purple, 3-dam contour interval, with the 546 (549)-dam contour heavy solid (dot-dash)) and ascent (contours every 5 (10) xlO-3 hPa sA from -5 (-20) to -20 (-70) x 103 hPa s1 in orange, brown and black) fields, as well as the advection of cyclonic absolute vorticity by the geostrophic winds (positive- valued contours every 2 x 10"9 s"2 in shades of green), are shown for experiments initialized at 24/18. Note that 0-h forecast fields of omega are not available. Also shown, when available, are rawinsonde contoured 500-hPa heights (violet), plotted as per the simulation fields. Titles indicate the experiment name, forecast hour, and actual date/time. Note that the date/time varies by column and the experiment by row. 3.26: 178-179 The 850-hPa temperature (dark green contours every 3 °C with the 0-°C contour heavy and values increasing from northwest to southeast), mixing ratio (light blue contours at 4, 5, 6 g kg"1 with values increasing from northwest to southeast), ascent (contours at -4, -12xl0"3 hPa s-1 in brown and orange) and sea level pressure (purple, 4-hPa contour interval with values increasing from southeast to northwest) fields are shown for experiments initialized at 24/18. Note that 0-h forecast fields of omega are not available. Also shown, when available, are rawinsonde contoured 850-hPa temperatures (plotted as per the simulation temperatures but in light green) and mixing ratios (black dotted contours at 4, 5, 6 g kg-1). Titles indicate the experiment name, forecast hour, and actual date/time. Note that the date/time varies by column and the experiment by row. 3.27: 181-182 The 925-hPa equivalent potential temperature (brown, 280-, 285-, 290- and 300-K contours, values increasing from northwest to southeast) and sea level pressure (violet, 4-hPa contour interval with a heavy 1000-hPa contour and values increasing from southeast to northwest) fields are shown for experiments initialized at 24/18. Also shown, when available, are rawinsonde-derived contours of 925-hPa equivalent potential temperature (K), plotted as per simulation temperatures but in orange. Note that the enclosed contour over South Carolina and Georgia represents a cold pool. Titles indicate the experiment name, forecast hour, and actual date/time. Note that the date/time varies by column and the experiment by row. XVll Preliminaries 3.28: 184 Shown for CHS (Charleston, SC) at 0000 UTC 25 January 2000 from the 6-h forecast of the ERA (red), ozone/ERA (pink), Eta (purple), ozone/Eta (violet), GEM (brown) and ozone/GEM (peach) simulations initialized at 24/18, and as observed (black) are a) a skew-T log-p plot of temperature (°C, solid) and dew point temperature (°C, dashed) with the 300-, 325- and 350-K moist adiabats, along with horizontal winds ((half) barb equals (2.5) 5 m s-1, pennant equals 25 m s-1), and b) a log-p versus temperature plot of equivalent potential temperatures (K), along with moisture transport vectors (cm s-1), where the length of the 1000- hPa ERA (red) moisture transport vector represents 11.5 cm s-1. 3.29: 188 Precipitation (contours at 5 mm and every 10 mm from 10 mm, with the 20-mm contour dashed, the 40-mm contour heavy, and light (dark) shading from 50 (80) mm) accumulated from 24/12 to 25/12 during the indicated experiments, initialized at 23/18, is shown. 3.30: 189 Calculated for the indicated experiments, initialized at 23/18, and thresholds are the: a) threat score and b) bias for the precipitation accumulated from 24/12 to 25/12. The Brennan and Lackmann (2005) analysis constitutes the truth field. 3.31: 191-194 Sea level pressure (purple, 4-hPa contour interval, 1000-hPa contour heavy) and 1000-500 hPa thickness fields (brown, 6-dam contour interval with a heavy, solid line for the 540-dam contour) are shown for experiments initialized at 23/18. The reanalysis ERA-40 sea level pressure cyclone is plotted in violet. Also shown, at 24/12 and 25/00, are rawinsonde-derived thickness contours, plotted as per the simulation field but in orange. Titles indicate the experiment name, forecast hour, and actual date/time. Note that the date/time varies by column and the experiment by row. 3.32: 196-199 Lightly smoothed EPV-derived dynamic tropopause potential temperatures (4-K contour interval, with the 316-K contour dashed and values less than 304 K shaded) are shown for experiments initialized at 23/18. At 24/12 and 25/00, the rawinsonde-derived 316-K contour (dark, solid) is added. Titles indicate the experiment name, forecast hour, and actual date/time. Note that the date/time varies by column and the experiment by row. Note also that the region plotted changes with time. 3.33: 201-202 The 500-hPa height (purple, 3-dam contour interval, with the 546 (549)-dam contour heavy solid (dot-dash)) and ascent (contours every 5 (10) xlO-3 hPa s-1 XVlll Preliminaries from -5 (-20) to -20 (-70) x 10"3 hPa s-1 in orange, brown and black) fields, as well as the advection of cyclonic absolute vorticity by the geostrophic winds (positive- valued contours every 2 x 10"9 s"2 in shades of green), are shown for experiments initialized at 23/18. Also shown, when available, are rawinsonde contoured 500- hPa heights (violet), plotted as per the simulation fields. Titles indicate the experiment name, forecast hour, and actual date/time. Note that the date/time varies by column and the experiment by row. 3.34: 204-205 The 850-hPa temperature (dark green contours every 3 °C with the 0-°C contour heavy and values increasing from northwest to southeast), mixing ratio (light blue contours at 4, 5, 6 g kg"1 with values increasing from northwest to southeast), ascent (contours at -4, -12xl0-3 hPa s-1 in brown and orange) and sea level pressure (purple, 4-hPa contour interval with values increasing from southeast to northwest) fields are shown for experiments initialized at 23/18. Also shown, when available, are rawinsonde contoured 850-hPa temperatures (plotted as per the simulation temperatures but in light green) and mixing ratios (black dotted contours at 4, 5, 6 g kg-1). Titles indicate the experiment name, forecast hour, and actual date/time. Note that the date/time varies by column and the experiment by row. XIX Preliminaries List of Tables 2.1: 111 Factork values 2.2: 121 Inversion subdomain boundaries 2.3: 122 Sponge zone grid point coefficients 3.1: 149 Numerical experiments 3.2: 150 Principal MC2 settings 3.3: 157 Onshore accumulated precipitation forecast rankings for simulations initialized at 24/18 3.4: 189 Onshore accumulated precipitation forecast rankings for simulations initialized at 23/18 xx Chapter 1: Introduction Chapter 1: Introduction 1.1 Motivation 1.1.1 Quantitative precipitation forecasting According to the 8th United States (U.S.) Weather Research Program, what people want to know most about the weather is whether it is going to "rain or snow, and if so, how much" (Fritsch et al. 1998). Accurate Quantitative Precipitation Forecasts (QPF) are not only the top priority for the average person, they are also of intrinsic importance, being a prerequisite for the accurate forecasting of high impact weather events such as ice storms, snowstorms, floods and flash floods. On average, flash floods cause greater yearly property damage than all other weather-related natural phenomena (Fritsch et al. 1998). Furthermore, governments and industry base decisions on the QPF: should hydroelectric power be generated, crops irrigated, golf courses watered, snowmaking conducted or highways salted? Better maintenance decisions, aided by improved forecasts, can mitigate the impact of both winter storms (Ralph et al. 2005) and routine weather events, which can, as a group, be of economical significance (Pielke et al. 2007). For these reasons, the QPF was declared to be "the most important and significant challenge of weather forecasting" (Fritsch et al. 1998). Historically, numerical 24-3 6-h probability of measurable precipitation forecasts have been less reliable and have improved more slowly than model 3 6-h 500-hPa geopotential height field predictions, as demonstrated by Fig. 1.1. 1 Chapter 1: Introduction Annual average threat scores for manual National Oceanic and Atmospheric Administration (NOAA) Hydrometeorological Prediction Center forecasts of at least 1.00 in. (25.4 mm) of precipitation are also low, as seen in Fig. 1.2. The threat score, which measures how well the location of the precipitation is forecast, ranges from a perfect one to zero. Threat scores of 0.2 and 0.1 typically translate, respectively, to slightly more than a third and to approximately 20% of the observed area being correctly forecast (Fritsch et al. 1998). Although manual QPFs earn higher threat scores than numerical QPFs, the two are strongly related (see Fig. 1.3); if we can improve the numerical QPFs, we can expect the manual QPFs to improve also. i» • • ! y «1 i .PvV~ 1 8 « -I / \f vi in A***^^**4 W 39 - jr*^** 10 1 I h5 «i 7* !«» S5 '»} Year Fig. 1.1 Numerical model skill scores for 36-h 500-hPa geopotential height forecasts for North America and adjacent waters (open circles), and for 24-36-h probability of measurable precipitation forecast skill with respect to climatology at approximately 100 stations in the U.S. (solid circles; taken from Roebber and Bosart 1998). 2 Chapter 1: Introduction Annual HPC Threat Scores; 1.00 Inch Day 1 / Update / Day 2 / Day 3 1961196S19891973 197?19611885 198919931987 2001 Year Day 1 Update Day 2 • Day 3 Fig. 1.2 Annual threat scores for the NOAA Hydrometeorological Prediction Center for 24-h forecasts of 1.00 in. (25.4 mm) or more of precipitation (taken from Fritsch and Carbone 2004). 24-Hour 1.00" QPF Verification Day 1 Forecast — HPC vs. NGM 0.5 — — — • 0.4 ID 10-3 \ A M A iA i\ i\ V f IV Ar»9! &K9I fte*9S OaW ScpW fag 9$ JuiSfl JLAST fctepSS *,»» Month Nested Grid Model — HPC Forecasters Fig. 1.3 Monthly threat scores for the NOAA Hydrometeorological Prediction Center for 24-h forecasts of 1.00 in. (25.4 mm) or more of precipitation for 1991- 1999 (taken from Fritsch and Carbone 2004). 3 Chapter 1: Introduction It is important to keep in mind that, despite increasing numerical model skill and spatio-temporal resolution, the QPF is "still a very challenging and difficult task" (Richard et al. 2003). Although predictability is significantly lower for convection-dominated summers than for cool seasons, when precipitation is mainly stratiform (see Fig. 1.3), winter precipitation is still difficult to forecast, even with a very short lead time (Benjamin et al. 2004). The worst winter precipitation forecast difficulties may be associated with convection. 1.1.2 Initial conditions and numerical weather prediction model forecast error The largest Numerical Weather Prediction (NWP) model forecast errors are more often a result of initial condition errors than errors internal to the model (Rabier et al. 1996, Richard et al. 2003). According to Langland et al. (2002), very large forecast errors (e.g. cyclone positions wrong by hundreds of kilometers) can be caused by initializing temperature and wind velocity errors of only a few degrees and a few meters per second, respectively. The rapid nonlinear growth of these initial condition errors limits mesoscale predictability (Zhang et al. 2002). Rabier et al. (1996), Boer (2003) and Walser et al. (2004) all found that the fastest growing errors were typically small-scale/high wavenumber structures. However, Colle et al. (2000), Miguez-Macho and Paegle (2000), Grimit and Mass (2002) and Roebber and Gyakum (2003) all noted a high degree of forecast sensitivity to larger-scale initial conditions. In fact, Colle et al. (2000) and Roebber and Gyakum (2003) found that accurate mesoscale forecasts, particularly 4 Chapter 1: Introduction for greater rainfall rates (Colle et al. 2000), simply could not be produced from insufficiently accurate synoptic-scale fields; moisture and vertical motion fields are both influenced by the synoptic-scale flow (Brennan and Konrad 2004). Initial conditions are generated by assimilating observations into a model (Miguez-Macho and Paegle 2001). In data assimilation, according to Uppala et al. (2005), "The observations and background forecast are combined using statistically based estimates of their errors; in variational assimilation this is achieved by minimizing the sum of error-weighted measures of the deviations of analysed values from the observed and background values." If the model first guess field is too far from the observations, the data assimilation and quality control systems may reject the observations (Hello and Arbogast 2004). Where there are no observations to assimilate, the first guess field becomes the analysis and the model is left to drift (Hello and Arbogast 2004). Pendelbury et al. (2003) found that, while operational analyses differed only slightly in data rich regions, they differed far more in data sparse regions, with the greatest differences over the Antarctic continent. Recovery from inaccurate initial conditions may take time, as the data assimilation system only nudges the model slowly towards a correct initial state (Bua 2003). As numerical weather prediction models improve and shift to higher resolutions, forecast improvements will be limited mainly by the frequency and quality of the observations (Emanuel et al. 2007, Pendelbury et al. 2003, Benjamin et al. 2004, Dabberdt et al. 2005). Numerical forecasts in extratropical regions are particularly sensitive to initial condition errors generated in data sparse areas (Demirtas and Thorpe 1999). Forecasts that are inconsistent over initializing times and models often indicate 5 Chapter 1: Introduction the presence of initial condition errors (Buizza and Chessa 2002, Hello and Arbogast 2004.) This forecast sensitivity has been confirmed by a plethora of studies, including: Fritsch and Carbone (2004), who stated that data assimilation is critical to the improvement of convective precipitation forecasting; Bua (2003) who noted that convectively active data poor areas are particularly harmful to numerical forecasting, given that models tend to simulate convection poorly, as indicated by Fig. 1.3's seasonal variation in forecast skill. For instance, Dickinson et al. (1997) determined that the inability of the Medium Range Forecast (MRF) model to simulate the incipient stages of the March 1993 superstorm was due to the failure of its cumulus parameterization scheme; Grimit and Mass (2002), who complained that the considerable degree of uncertainty in the upstream initial conditions, due to the data sparsity of the Eastern Pacific Ocean, can produce large forecast errors over Western North America; McMurdie and Mass (2004), who found that large upper-level initial condition uncertainties in the Pacific Ocean adversely affected the short-term forecasting of a cyclone striking Oregon; Ralph et al. (2004) who studied Eastern Pacific atmospheric rivers, or "narrow regions of strong horizontal water vapor flux", which are poorly observed despite their ability to generate heavy rainfall due to orographic lifting; Schultz et al. (2002), who reported that the data void region upstream of the Intermountain West in the U.S. "is a concern even for short-range forecasts"; Faccani et al, (2003), who blamed difficulties of high-resolution forecasting in the complex terrain of the Alps partly on the Mediterranean's data sparsity; Hello and Arbogast (2004), who concluded that the failure of short-term forecasts of a major December 1999 storm in France was due to the data sparsity of the Atlantic 6 Chapter 1: Introduction Ocean: an earlier, 90-h forecast was able to predict the intense storm, as the critical upper-level feature, being situated over Newfoundland at that time, was well-resolved in the initializing fields. Fig. 1.4 North American rawinsonde stations (taken from University of Wyoming 2007). WW 120"ff 5C=W ffi"W aDW Fig. 1.5 The North American distribution of aircraft meteorological observations for 0000 UTC 17 March 2006 (taken from Thepaut and Lalaurette 2007). Manually-transmitted aircraft (AIREP; red), Aircraft Meteorological Data Reporting (AMDAR; blue), Aircraft Communications Addressing and Reporting System (ACARS; green) reports are included. 7 Chapter 1: Introduction The relative data sparsity of both Canada and the oceanic regions surrounding the U.S. is evident from Fig. 1.4's map locating rawinsonde stations, which are a traditionally important source of data, and Fig. 1.5 's display of routes on which aircraft data, which constitute a newer source of data, are collected. Aircraft are often the primary supplier of nonsynoptic upper-air (typically from 25,000-45,000 ft or -7,500-14,000 m) data over the U.S. and a critical supplier of data over oceans, even at synoptic times (Moninger et al. 2003). Thus, the many data void regions evident in Fig. 1.5 are of great concern, particularly considering that "one of the most significant impediments to progress in forecasting weather over North America is the relative paucity of routine observations over data-sparse regions adjacent to the U.S." (Emanuel et al. 2007); the lack of observations over the U.S. South East coast is a concern, since surface ridging in this area promotes moisture transport northwards from the Gulf of Mexico (Carrera et al. 2004). It should be noted that the number of radiosonde observations has declined since the late 1980s (Uppala et al. 2005) and that the relative superiority of the United States' network of rawinsonde data should not be taken for granted; Bosart (1990) warned that the North American radiosonde network had degraded over the five years prior to his report. Furthermore, Moninger et al. (2003) reported that the number of U.S. carriers' Aircraft Communication Addressing and Reporting System (ACARS) aircraft data reports per hour vary by more than a factor of four, peaking in the evening and early morning, with weekends providing only 60% of the number of mid-week reports. Observations decrease 8 Chapter 1: Introduction during "extended periods of poor weather" both in the region experiencing poor weather and at the cancelled flights' destinations. ACARS and Aircraft Meteorological DAta Relay (AMDAR) data compete with radiosonde data as the most important data source for the Eta model. Unfortunately, aircraft data provide few moisture reports. Humidity information has been provided by satellite radiances only in cloud-free regions until recently, despite the fact that cloudy areas are often the most sensitive regions in terms of initial condition errors (Andersson et al. 2005), and despite the fact that poor measurements of water vapour severely hinder the improvement of numerical forecasts, especially QPFs (Dabberdt et al. 2007). The impact that additional observations can have on numerical forecasts is demonstrated by the assimilation of Global Aircraft Data Set (GADS) data in Goddard Earth Observing System analyses: this assimilation altered wind speeds by up to 90%, with the influence of the 250-200-hPa GADS data extending throughout the 500-50 hPa layer and persisting for several days (Rukhovets et al. 1998). The extent of this impact is not surprising, given that Thorpe (1986) stated that upper-level Potential Vorticity (PV; based on the product of absolute vorticity and the potential temperature gradient, as discussed in Section 2.1.2) and surface potential temperature are often the most crucial fields when determining the balanced flow structure, while Hakim (2005) found that short-term forecasts are more sensitive to initial condition errors in the middle and upper troposphere than in the lower troposphere, Liniger and Davies (2003) determined that accurately specifying tropopause-level PV anomalies was quite possibly "a necessary 9 Chapter 1: Introduction prerequisite for the successful prediction" of the sustained precipitation events they studied, and Laroche et al. (2002) established that the maximum amplitude of their fastest growing initial condition error was in the upper troposphere. Indeed, although Demirtas and Thorpe (1999) found that modifying an upper-level PV anomaly sometimes had only a small impact on surface development, Browning et al. (2000) found that shifting initializing tropopause depressions by a mere few hundred kilometers was able to improve the strength, location and shape of a forecast surface cyclone. Targeted weather observations (made in North Pacific Ocean data sparse and/or sensitive regions in an effort to improve downstream continental forecasts; McMurdie and Mass 2004) were used by Szunyogh et al. (2002) in an attempt to improve severe winter storm forecasts. In approximately two thirds of this study's cases, surface pressure and 300-hPa wind forecasts were improved by the targeted observations, with the average surface pressure forecast error reduced by 19%. The drawback of targeted observations is that sufficient data must be collected for them to be accepted by the assimilation system, which may then render the collection time too long to be practical (Dabberdt et al. 2005). The data sparsity of Canada is a concern given that the genesis of mobile 500-hPa troughs, which are associated with strong downstream forcing for ascent, occurs preferentially in northwesterly flow during upper-level frontogenesis (Schultz and Sanders 2002); downstream for these mobile troughs is, thus, quite possibly the U.S., as it was during the east coast snowstorm of 24-25 January 2000, which is the event that is used to validate this research's methodology (see Chapter 3). Indeed, Smith (2003) reported that cold core upper-level cutoff 10 Chapter 1: Introduction cyclones, which produce approximately 30% of the annual precipitation in the North East United States, have a genesis maximum in the (data sparse) Hudson , Bay region. Unfortunately, Hudson Bay is one of the most sensitive regions for initial condition errors (Rabier et al. 1996). 1.1.3 Initial conditions and satellite data Satellites are the primary source of observations in data sparse regions (Zapotocny et al. 2005), providing "relatively unaliased measurements with high temporal and horizontal resolution" (Emanuel et al. 2007). Thus, a "key area of research involves improving the ability to assimilate satellite observations" (Ralph et al. 2005). This assimilation should improve significantly the initialization of dynamically important mesoscale features in data sparse regions (Fritsch et al. 1998). Indeed, Mo et al. (1995) found that the inclusion of satellite data in the late 1970s, including Operational TIROS-N Vertical Sounder (TOVS) retrievals and cloud-tracked winds from geostationary satellites, had a significant impact on the quality of southern hemispheric reanalyses. Buehner (2002) also found a significant positive impact on Southern Hemispheric mass and wind fields with the assimilation of six-hourly marine surface winds derived from a satellite-based scatterometer. Pendelbury et al. (2003) reported that numerical forecast improvements over the Australian region since 1998-1999 were likely due, apart from enhanced horizontal and vertical resolutions, to the assimilation of satellite data. Tropical and extratropical cyclone surface winds and typhoon tracks were improved by Leidner et al. (2003) and Zhao et al. (2005), respectively, with the 11 Chapter 1: Introduction assimilation of scatterometer data in the former study and satellite temperatures and winds in the latter study. Furthermore, Zapotocny et al. (2005) found that, while assimilating rawinsonde mass and wind data had the greatest overall positive impact on 24-h Eta forecasts, Geostationary Operational Environmental Satellite (GOES) precipitable water, wind and radiance data had the greatest impact on moisture fields. Satellite observations are also of interest for the dynamics they imply; a "remarkable resemblance" between water vapour satellite images and tropopause- level isentropic PV fields was noted by Liniger and Davies (2003) and is demonstrated in Fig. 1.6. In this Figure, dry dark (moist light) areas in the satellite imagery are collocated with locally higher (lower) PV values. Demirtas and Thorpe (1999) found that any mismatches between the two fields were generally due to model error. These authors believe that extracting the dynamical information contained in the water vapour field probably has a greater impact on numerical forecasts than the assimilation of the water vapour field itself, since this assimilation might not adjust winds and temperatures. However, Swarbrick (2001) warns that "the relationship between PV and water vapour images is very complex and subject to numerous caveats": it is valid only near the polar front and, to some extent, poleward; it is not a one-to-one relationship as it is valid for developing but not decaying cyclones, and not, in general, for anticyclones; tropopause folds can be hidden by a layer of cirrus. Nonetheless, this relationship is sufficiently close that the water vapour imagery can act as quality control for numerical analyses and forecasts. 12 Chapter 1: Introduction 30*W 20*W 10*W Fig. 1.6 Meteosat water vapour imagery (grey shades) and 315-K isentropic surface PV (contour interval of 0.5 Potential Vorticity Units) at 0000 UTC 24 January 1996 (taken from Demirtas and Thorpe 1999). The Demirtas and Thorpe (1999) method of extracting the dynamical information implied by the satellite water vapour imagery consists of modifying the 3-dimensional (3D) PV field manually to align the PV field with the water vapour image. The modified 3D PV field is inverted, producing dynamically consistent initializing height, temperature and wind fields, which are then assimilated into the model as bogus observations. Unfortunately, the data assimilation system sometimes weakens the added data. Swarbrick (2001) avoided this smoothing by inserting wind and temperature increments directly into the model initializing fields over a series of time steps, the increments being the differences of the fields derived from inverting the original and modified PV fields. Demirtas and Thorpe (1999) significantly improved the short-range forecast skill in cases of upper tropospheric analysis errors. Hello and Arbogast (2004) 13 Chapter 1: Introduction used the Demirtas and Thorpe (1999) methodology to adjust the Quasi Geostrophic PV (QGPV) field, which is accurate for wavenumbers smaller than 8, in an attempt to improve the forecasting of the 27 December 1999 storm. This was a fatal storm that caused much material damage in France. Although the maximum adjustment to the analysis geopotential height field was near 380 hPa, the forecast of the surface cyclone was improved significantly, particularly with respect to its location. However, Swarbrick (2001), who used a method similar to that of Demirtas and Thorpe (1999), did not obtain significant positive results in any of the five cases studied; the PV/water vapour mismatches were sometimes too complicated to be corrected properly by this manual method that lacks any precise rules and that provides guidance on the PV location adjustment but not on the PV magnitude adjustment, which is determined heuristically. This is a typical problem, as satellite data tend to provide information on field gradients rather than absolute values (Pendelbury et al. 2003). Swarbrick concluded that extracting the dynamical information contained in the water vapour imagery in this qualitative and subjective manner is very useful diagnostically, but is "unlikely to improve operational forecasting of cyclonic systems"; a quantitative methodology is required operationally. Satellite total column ozone fields, particularly the high-gradient regions, also contain dynamical information (Riishojgaard 1996). The high correlation between total column ozone and various dynamical fields is discussed in Section 2.1.4. In Fig. 1.7, which presents fields associated with the 24-25 January 2000 east coast snowstorm, an event that is discussed at length in Section 3.1, 200-hPa 14 Chapter 1: Introduction height field troughs (ridges) are collocated with locally higher (lower) total column ozone values. Reader and Moore (1995), Davis et al. (1999) and Olsen et al. (2000) all suggested that the ozone data contain information on the structure of tropopause-level features. Peuch et al. (2000) observed that successive observations of total column ozone, which is considered a tracer, yield winds. Since the total column ozone dynamical information can be extracted in an objective manner (see Sections 2.1.5 and 2.3), satellite total column ozone data are potentially useful operationally. Fig. 1.7 Total column ozone (solid, 15-DU contour interval, dashed 290-DU contour and shading for values greater than 350 DU), valid at local noon on the indicated date, and ERA-40 200-hPa heights (grey, 24-dam contour interval), valid at 1800 UTC. 15 Chapter 1: Introduction Unfortunately, satellite data lack vertical resolution. As Buehner (2002) said, "the effectiveness of introducing scatterometer wind data largely depends on how the information at the surface is spread vertically and to the other variables". Riish0jgaard (1996), Peuch et al. (2000), Zou and Wu (2005) and Jang et al. (2003; see Section 2.1.5) attempted to sidestep this issue by using a 4- Dimensional Variational (4D-Var) data assimilation system. Davis et al. (1999) described a less computationally expensive methodology that converts the satellite 2-dimensional (2D) field of total column ozone to a 2D dynamical Mean Potential Vorticity (MPV) field, which is then converted to a 3D PV field. Finally, this last field is inverted, yielding model initializing heights, winds and temperatures. The methodology presented in Section 2.3 is based on this Davis et al. (1999) process, which is reviewed in detail in Section 2.1.5. 1.2 Objectives Section 1.1 revealed that NWP model precipitation forecasts are both less accurate and improving more slowly than height field forecasts. This lag in precipitation forecasting skill is extremely unfortunate, given that the QPF is a top priority for both the average person and for governments and industry. Initial condition errors, not the NWP models themselves or their lack of resolution, are primarily responsible for the current inaccuracy of the QPF. Initial conditions are generated by assimilating observations into a model. If no observations are available, the model first guess field becomes the analysis, and the model is free to drift. Recovering from model drift can take time, as assimilated observations 16 Chapter 1: Introduction merely nudge a model towards the correct initial state. Given that satellites are the primary source of observations in data sparse regions, increasing the assimilation of satellite data is a key area of research. Since the dynamical information inherent in satellite total column ozone data can be extracted using an automated procedure, this information is of great interest. Given the known QPF problem, given the fact that initial condition errors are the principal cause of this problem, and given the existence of a proven satellite data source, the general purpose of this research is to improve the QPF by developing an automated procedure that converts satellite total column ozone data to NWP model initializing fields, thereby extracting the dynamical information inherent in these data. If this technique is deemed successful, it would be of great interest to operational forecasting centres, particularly in association with weather systems originating in data void regions. Thus, a second general goal for this research is that some or all of the developed procedure be useable by operational forecast centres. In association with these two general goals, the research must meet four specific objectives. The first two objectives define skills that must be demonstrated for the methodology to be considered successful, while the last two objectives define criteria of operational usefulness. Thus, the four specific objectives of this research are: 1. Starting from satellite total column ozone data, to analyse a realistically deep height field trough in association with the unforecasted U.S. east coast snowstorm of 24-25 January 2000; 17 Chapter 1: Introduction The 24-25 January 2000 east coast snowstorm caused record-breaking snowfall along the U.S. east coast, as will be discussed in Section 3.1.1. This unforecasted precipitation occurred in the presence of an extremely deep and narrow upper-level trough that extended from northern Canada into the Gulf of Mexico (Fig. 2.2). Thus, a successful forecast of this event's extreme precipitation requires the analysis of a realistically deep trough, hence the first objective. Furthermore, having to produce a realistically deep trough is an important test of the proposed methodology's ability to create a realistic 3D field from the original 2D satellite field. The technique proposed in this research for the vertical distribution of the 2D field's values may also be of use in the assimilation of other satellite fields or of single-level aircraft observations. 2. Starting from satellite total column ozone data, to forecast significant onshore precipitation during the 24-25 January 2000 east coast snowstorm; Operational NWP models did, indeed, predict heavy precipitation in association with the 24-25 January 2000 east coast snowstorm. Unfortunately, the precipitation was forecast to remain offshore (see Section 3.1.1). Thus, the second objective of this research is not simply to forecast significant precipitation in association with this event, but to generate significant precipitation onshore. A successful forecast would validate the presented methodology. It would also indicate the potential of total column ozone data to improve QPFs in general. Consequently, it would also indicate the advisability of assimilating satellite total column ozone data routinely in an operational setting. 18 Chapter 1: Introduction 3. To develop a methodology that, starting from total column ozone data, generates an ensemble member that is as independent as possible of an operational centre's assimilation system in order to bypass errors present in the operational first guess field; The methodology developed should generate NWP model initializing fields with as little recourse as possible to analysed fields. This would create an ensemble member that is as independent as possible of the data assimilation system and, consequently, of other ensemble members; an independent ensemble member might be capable of forecasting an event that a group of related members might all miss. With systems originating in data void areas, the weighting of the ozone-influenced ensemble member could be augmented, in recognition of the local paucity of assimilated observations. 4. To develop a methodology to convert a 2D total column ozone field to a 3D dynamical field that can be adapted to 3D- and 4D-Var data assimilation. Since many operational forecast centres use 3D- or 4D-Var data assimilation systems, as much of the procedure as possible presented should be adaptable to these systems in order for this research to be as useable as possible by these centres, which constitutes the second general goal of this research. For instance, the correct vertical distribution of the total column ozone increment has been problematic for both 3D- and 4D-Var data assimilation (see Section 2.1.5); the technique developed to fulfill this thesis' first objective of analysing a realistically deep trough will also be of interest to these data assimilation systems. Other components of the presented methodology that are of interest to variational data 19 Chapter 1: Introduction assimilation systems are the in depth study of the correlation of total column ozone and MPV, and the utilization of only the more reliable, dynamically- selected portions of the regressed MPV field. Furthermore, the technique developed to interpolate the total column ozone field temporally will be of interest for a 3D-Var data assimilation system. Thus, the four specific objectives of this research 1) test the validity of the presented methodology that attempts to improve the QPF by converting satellite total column ozone data to NWP model initializing fields, and 2) require that the methodology be of practical use to operational forecast centres. In the process of meeting these objectives we have developed novel methodologies to interpolate the total column ozone field temporally, avoid contamination by overly-conserved total column ozone ridges, map a 2D MPV field vertically, and avoid inverted height field dipoles. We have also refined the total column ozone/MPV regression. 3.1 Thesis overview In this first chapter we have broadly discussed the refereed literature on the forecasting problem and data assimilation in general. In Chapter 2 we will provide a complete literature review on ozone along with our procedure to convert total column ozone data to NWP model initial conditions. Chapter 3 provides an overview of the literature on the 24-25 January 2000 snowstorm and our simulations of this event. Finally, our procedure and simulation results are summarized in Chapter 4, which also presents our conclusions. 20 Chapter 2: The Conversion of Total Column Ozone data to model initializing fields Chapter 2: The Conversion of Total Column Ozone Data to Numerical Weather Prediction Model Initializing Fields, and its application to the 24-25 January 2000 East Coast Snowstorm This Chapter commences with an introduction, in Section 2.1, to total column ozone and its links to various dynamical fields, including PV and MPV, which are also described. In addition, this introduction includes a review of the assimilation of total column ozone in NWP models. Section 2.2 describes the data sets used during this research. Finally, Section 2.3 presents the methodology to convert total column ozone data to NWP model initializing fields. The mechanics and rationale of each step of the proposed procedure are discussed in detail, while the effect of each step is illustrated using the 24-25 January 2000 east coast snowstorm. 21 Chapter 2: The Conversion of Total Column Ozone data to model initializing fields This page is left intentionally blank. 2.1: Total column ozone and its relationship to meteorological fields 2.1: Total column ozone and its relationship to meteorological fields 2.1.1 The generation and behaviour of total column ozone The concentration of ozone in a volume is determined by the rates of photochemical destruction and generation, and by the net transport into or out of the volume (the National Aeronautics and Space Administration, or NASA, 2002). Latitudinally, generation occurs at the Equator and destruction at high latitudes (Hou et al. 1991). Vertically, photochemistry occurs from 30 to 50 km (Salby and Callaghan 1993), at sufficiently low altitudes that oxygen is plentiful, and at sufficiently high altitudes that high energy ultraviolet radiation is plentiful (NASA 2002). Below 30 km, transport processes dominate the ozone distribution increasingly with decreasing altitude (Dutsch 1978), resulting in low-stratospheric ozone molecule lifetimes ranging from weeks (Salby and Callaghan 1993) to months (Riish0jgaard 1996). Ozone may consequently be considered a passive tracer at this level (Schoeberl and Krueger 1983, Bowman and Krueger 1985, Riishojgaard 1996). Although ozone mixing ratios maximize in the mid stratosphere near 30 km, with winter hemispheric altitudes higher (Vaughan and Price 1991, Orsolini et al. 1998), most of the ozone molecules are located at lower levels (Olsen et al. 2000) just above the tropopause (Salby and Callaghan 1993), owing to the greater air density found at lower elevations. Tropospheric ozone mixing ratios are lower than stratospheric ratios by two orders of magnitude, with the largest vertical gradients located just above the tropopause (Riishajgaard and Kallen 1997.) 23 2.1: Total column ozone and its relationship to meteorological fields Therefore, the concentration of ozone molecules found just above the tropopause dominates the total column ozone field (Peuch et al. 2000), which is based on the vertical integral of a column's ozone molecules (Olsen et al. 2000). Total column ozone is easier to measure, both from the surface and by satellite, than the 3D field of ozone mixing ratio (Riishojgaard and Kallen 1997). The generation of ozone at the Equator and its destruction at high latitudes results in a basic total column ozone distribution that decreases with latitude (Dutsch 1978, Hou et al. 1991). The observed latitudinal distribution, where polar air is ozone-rich and tropical air ozone-poor (Dobson et al. 1929, Reed 1950), with the strongest latitudinal gradient observed in late winter and spring (Dutsch 1978) is established by the Brewer-Dobson circulation, as first proposed in general terms by Dobson et al. (1930). This circulation, which is induced by the stratospheric breaking of planetary and gravity waves (Haynes et al. 1991), ascends in Equatorial regions into the stratosphere, collects newly photochemically-generated ozone molecules, transports the molecules poleward, and, poleward of ± 30°, downwards into the lower stratosphere (NASA 2002). The high-latitude descent, which is accompanied by radiative cooling (Danielsen 1968), can take months (Salby and Callaghan 1993). The circulation's loop is closed by the equatorward transport of ozone molecules by baroclinic waves (Danielsen 1983). The meridional profile of the ozone column is tempered by the intensity of the wave breaking: weak planetary wave driving results in a total column ozone latitudinal maximum in the region of the edge of the polar vortex, at approximately 60°N, while stronger wave driving strengthens the residual 24 2.1: Total column ozone and its relationship to meteorological fields circulation and pushes the total column ozone maximum poleward (Hou et al. 1991). Embedded in the climatologically smoothly increasing (up to the polar vortex) latitudinal gradient of total column ozone, are four meteorological regimes: tropical, midlatitude, polar and arctic (Hudson et al. 2003). Along with characteristic tropopause height ranges, the regimes have distinct total column ozone ranges of 250-300, 325-360, 410-450 and 340-390 DU, respectively. A Dobson Unit describes the thickness, measured in 10"5 m, of the layer that would be formed if all the ozone molecules in the vertical column were brought to the surface at standard pressure and temperature, or 1013.25 hPa and 0°C (NASA 2002). Thus, a total column ozone value of 300 DU represents a 3-mm layer. On an annual basis, total column ozone values increase by up to 1% with increased solar activity and decrease by 1-4% 1-2 years after a major volcanic eruption, such as El-Chichon (1982) or Mt. Pinatubo (1992; Geller and Smyshlyaev 2002). At the hemispheric scale, the Northern Hemisphere not only has larger mean total column ozone values than the Southern Hemisphere (Bowman and Krueger 1985), but it also has a greater seasonal variation of values as a result of more intense transport processes (Dutsch 1978). In the Northern Hemisphere, a given location's total column ozone maximum occurs in late winter to spring, while the minimum occurs in late autumn (Dobson and Harrison 1926, Dobson et al. 1929, Dobson et all930, Reed 1950, Bowman and Krueger 1985), with a greater range of values at higher-latitude locations due to similar fall minima but far larger spring maxima (Dobson and Harrison 1926, Reed 1950). The maximum/minimum difference is on the order of 150 DU 25 2.1: Total column ozone and its relationship to meteorological fields (Dobson and Harrison 1926), with yearly maximum values varying four times as much as yearly minimum values, due to the stronger transport processes of late winter and spring (Dutsch 1978, Allen and Reck 1997). Although the total column ozone field is found to react to disturbances from meso- to planetary-scale (Schoeberl and Krueger 1983), the strongest response occurs in reaction to atmospheric flow perturbations just above the tropopause (Dutsch 1978, Dethof and Holm 2004), owing to the domination of the total column ozone field by this level's molecules, as mentioned above (Riishojgaard and Kallen 1997), which are caused by medium-scale (wavenumbers 4-7) synoptic, largely baroclinic weather disturbances (Mote et al. 1991, Allen and Reck 1997). Dobson and his colleagues (Dobson and Harrison 1926, Dobson et al. 1929, 1930, 1946) were the first to note the strong relationship between total column ozone and both surface weather conditions and upper atmospheric conditions, with high and low values of total column ozone associated with cyclonic and anticyclonic conditions, respectively. Baroclinic waves perturb the total column ozone field by advecting ozone molecules meridionally and vertically in the tropopause/lower stratosphere in the presence of strong horizontal and vertical ozone gradients (Schoeberl and Krueger 1983, Mote et al. 1991, Riishojgaard 1996, Riishojgaard and Kallen 1997, Orsolini et al. 1998, Petzoldt 1999). The meridional advection consists of winds associated with cyclonic (anticyclonic) systems transporting ozone-rich (ozone- poor) air equatorwards (polewards), resulting in locally large (small) total column ozone values. Vertically, the depression (elevation) of the tropopause in an upper-level trough (ridge) creates a greater (lesser) vertical extension for the 26 2.1: Total column ozone and its relationship to meteorological fields ozone-rich stratosphere (and a lesser (greater) vertical extension for the ozone- poor troposphere), leading to stratospheric convergence (divergence) aloft, resulting in greater (lesser) total column ozone values locally (Ohring and Muench 1960, James et al. 2000, James and Peters 2002). Thus, the meridional and vertical advections reinforce each other (Reed 1950): both advections increase (decrease) the total column ozone value with the passage of a trough (ridge). Vertical transports are responsible for at most one third of the synoptic- scale total column ozone perturbation (Reed 1950). As one might expect, larger tropopause disturbances accompanied by stronger horizontal and vertical motions result in greater total column ozone perturbations (Reed 1950, Vaughan and Price 1991). While the total column ozone response to a passing baroclinic system often reaches 20% (~ 70 DU) of the zonal mean (Schoeberl and Krueger 1983), an increase of 100 DU was measured by Olsen et al. (2000) in association with an intense Midwestern cyclone. Also observed during midlatitude winters are total column ozone "mini- holes", which are "synoptic-scale ozone minima at least 70 DU below climate mean levels for the respective location and season" (James and Peters 2002). They last for a few days (Petzoldt 1999) and are three quarters due to the vertical and meridional advections of ozone-poor air in the presence of a tropopause-level ridge (wavenumber 6), and one quarter due to a mid-stratospheric equatorwards extrusion of ozone-poor polar vortex air (Allen and Nakamura 2002), caused by variations in planetary-scale waves (wavenumbers 1-2; Petzoldt 1999, James and Peters 2002). Although these mini-holes represent the superposition of two 27 2.1: Total column ozone and its relationship to meteorological fields basically independent dynamical features, they are fairly common in both hemispheres during mid- and high-latitude winters: over 500 mini-holes were recorded during 10 midlatitude winters by James and Peters (2002). Fig. 2.1 Total column ozone (15-DU contour interval, with the 290-DU contour dashed and values greater than 350 DU shaded), valid at local noon on the day indicated, and ERA-40 200-hPa heights (grey contours, with the 1152-dam contour wide and a 24-dam contour interval), valid at 1800 UTC. The red circles track the feature that evolves into the upper-level trough associated with the 24-25 January 2000 east coast snowstorm. The total column ozone fields for 22-25 January 2000 are presented in Fig. 2.1. The circled region of high ozone values, which, given its tendency to be collocated with an upper-level height field trough (see Fig. 1.7), will be referred to hereafter as a "trough" to avoid confusion, moves from west of Hudson Bay on the 22nd to the southeast, stretching from Hudson Bay to Lake Superior and into the Great Plains on the 23rd and extending all along the eastern seaboard on the 24th, where it was responsible for record-breaking snowfall, as will be discussed 28 2.1: Total column ozone and its relationship to meteorological fields in Section 3.1.1. By the 25th, the trough has evolved into a cutoff Low. Note that "ridges", or regions collocated with upper-level height field ridges, are defined as regions having total column ozone values less than 290 DU (dashed contour), while troughs (shaded) are defined as regions having values greater than 350 DU. This air mass delineation agrees well with Hudson et al. (2003), who defined tropical total column ozone values as less than 300 DU, midlatitude values as less than 360 DU and arctic values as more than 340 DU, as discussed earlier in this Section. 2.1.2 The generation and behaviour of potential vorticity Ertel Potential Vorticity (EPV) is based on the product of the inertial and static stabilities. It is conserved following adiabatic, frictionless motion in a baroclinic, compressible flow (Hoskins et al. 1985, Davis and Emanuel 1991). Thus, it is a "quasi-conservative scalar" (Danielsen 1968). EPV is calculated using equation {2.1}: EPV = — (y + Vxv).V0 {2 1} p where p is the density, f the planetary vorticity vector, v the velocity vector, and 0 potential temperature. The equation is fully three dimensional. The vorticities describe the inertial stability, and the gradient of potential temperature the static stability (Danielsen 1983). Note that, while PV is positive in the Northern Hemisphere, it is negative in the Southern Hemisphere as a result of that hemisphere's negative Coriolis parameter. Discussions in this chapter concerning 29 2.1: Total column ozone and its relationship to meteorological fields latitudinal profiles of PV assume that the absolute value has been taken of the negative Southern Hemispheric values. Thus, PV is maximized at high latitudes (Danielsen 1983) and in the middle stratosphere (Danielsen 1968), where inertial and static stabilities are maximized, respectively. According to Danielsen (1968), PV acts as a stratospheric tracer when mixing processes are more important than diabatic heating gradients. Locally large values of PV are associated with increased static stability, depressed tropopause levels, troughs, cyclones and warm low-level potential temperature anomalies, while locally small values are associated with decreased static stability, elevated tropopause levels, ridges, anticyclones and cold low-level potential temperature anomalies (Hoskins et al. 1985). The strength of these PV anomalies decays with vertical distance from their centers (James and Peters 2002). Strengthening an upper-level PV anomaly by 2-3 PVU, where 1 PVU, or Potential Vorticity Unit, equals 1 x 10~6 K m2 kg"1 s_1, which is a typical tropospheric PV value for midlatitude, synoptic-scale flow (Bluestein 1993), deepens a linked surface cyclone by approximately 5 hPa; the cyclone track is determined by a combination of the strength and shape of the upper-level PV anomaly (Swarbrick 2001). Given a balance condition and boundary conditions, a 3D PV distribution is invertible: a boundary value problem is specified and solved (Hoskins et al. 1985; see Section 2.3.3.1 for details). The inversion is as accurate as the degree to which the balance condition represents the state of the atmosphere. Since the inversion yields balanced wind, temperature and height fields, the PV field contains knowledge of most aspects of the structure of a synoptic-scale system. 30 2.1: Total column ozone and its relationship to meteorological fields The dynamic tropopause, which is a boundary but not substantial surface (Danielsen 1968) that separates the stratosphere from the troposphere (Danielsen 1983), is defined for this thesis as the 2.0-PVU surface. The large-scale transport of tropospheric air polewards and stratospheric air equatorwards produces undulations in the dynamic tropopause, which are ridges and troughs, respectively. The dynamic tropopause potential temperature fields for 22-25 January 2000 are presented in Fig. 2.2. As will be discussed in Section 2.2.1, the total column ozone field values are measured near local noon, which corresponds to approximately 1800 UTC over North America. A comparison of Fig. 2.1 and the 1800-UTC panels of Fig. 2.2 demonstrates the similarities between the total column ozone and dynamic tropopause potential temperature fields; despite differences in the two fields, including the stronger gradients of the temperature field, which are to be expected, given that the temperature and ozone fields describe shallow and deep atmospheric layers, respectively, troughs (shaded regions) and ridges (dashed and paler contours) are basically collocated. 31 2.1: Total column ozone and its relationship to meteorological fields """^TSTTV \ f \ Xl/fr / /^_~^N^i \ If (K( /s^^S\\ ' \^/ ^t\\\ (I Ilk A UOi l -so " i a) 00 UTC 22 January 2000 b) OS UTC 22 January 2000 :.-..J..l..lJ N/\riV ilfl l 1 JF s^ii / > nil v\ / 1 /\i \ C /'X llfvlo^ 'Z^f^y §r \ |t||« ^s^L^ ^2iftft= = i ^^IH^=: 3^ - ~g-^ -j — — *"ey lit i \ \ T -120%: 7^7 '"-"so" c) 12 UTC 22 January 2000 d) 18 UTC 22 January 2000 • ^^^^r III 30 f -120\\> r-«tfT\^ e) 00 UTC 23 January 2000 f) 06 UTC 23 January 2000 9) 12 UTC 23 January 2000 h) 18 UTC 23 January 2000 Fig. 2.2 ERA-40 dynamic tropopause potential temperatures (4-K contour interval, with the 316-K contour dashed and values less than 304 K shaded), valid at 1800 UTC. The red circles track the feature that evolves into the upper-level trough associated with the 24-25 January 2000 east coast snowstorm. 32 2.1: Total column ozone and its relationship to meteorological fields msmswxmmm 1 \ \vOr I IllV A—O MPVI ) ///J' v /dry V ' ^m^zfwQ , ;V6o f^ i) 00 UTC 2^ January 2000 j ) 0G UTC 2*\ January 2000 k) 12 UTC 2H January 2000 1 ) 18 UTC 2^1 January 2000 t Co/ A r ••'( n\\l ' !Ssl«K a —. «. _ x^_ / 1 ra ^s^rf^^c-^*x^ ^~~T^-=^. ,;• ^gyf5^•^^r^y 1 F^—~x\ ^ 1 V \IS§L ' fw5 f.p | IX. m) 00 UTC 25 January 2000 n) 06 UTC 25 January 2000 \jij-ij- W ; ^j\Y* 'JCrii isii^ TJF-120%- P*? -6tk i. o) 12 UTC 25 January 2000 P) 18 UTC 25 January 2000 Fig. 2.2 continued. 33 2.1: Total column ozone and its relationship to meteorological fields 2.1.3 A description of mean potential vorticity Mean potential vorticity (MPV; PVU) provides a summarizing view of deep- layer atmospheric dynamics. It is defined by equation {2.2}: . Ptop MPV = — jPV(p)dp {2.2} Ptop Pbottom "bottom where p is pressure. Although, according to Allaart et al. (1993), the value of the lower bounding pressure level (pbottom) is insignificant, given that PV values below 400 hPa are close to zero, hence contribute little to the integral, the value of the upper bounding pressure level (ptop) is important, since the PV/ozone mixing ratio correlation becomes anticorrelation above 50 hPa (Allaart et al. 1993). Salby and Callaghan (1993), who correlated vertically-averaged ozone mixing ratio and equivalent barotropic PV, found little sensitivity to their upper boundary near 22 km, or =50 hPa. Various bounding pressure values are discussed in the literature: Davis et al. (1999) used PV from 500-50 hPa, Zou and Wu (2005) used PV from 400-50 hPa, and Jang et al. (2003) used PV from 500-100 hPa when calculating MPV (see Section 2.1.5). Northern Hemispheric midlatitude values of MPV range from 2-8 PVU. The MPV fields for 22-25 January 2000, which are based on PV from 400- 50 hPa, are presented in Fig. 2.3. As per the total column ozone field of Fig. 2.1, high-MPV regions will be referred to as "troughs" to avoid confusion. While a general resemblance is evident between the temperature fields of Fig. 2.2 and the MPV fields of Fig. 2.3, a closer resemblance is found between the 1800-UTC MPV fields and Fig. 2.1 's ozone fields; troughs, or the shaded regions, 34 2.1: Total column ozone and its relationship to meteorological fields Fig. 2.3 ERA-40 Mean Potential Vorticity (MPV; calculated from the geopotential and streamfunction fields as per equation {2.23} in Section 2.3.3.1; 0.5-PVU contour interval, with the 5.5-PVU contour dashed and values greater than 7 PVU shaded). The red circles track the feature that evolves into the upper- level trough associated with the 24-25 January 2000 east coast snowstorm. translating to MPV values of 7 PVU or more, and ridges, or the regions of paler contours enclosed by the dashed contour, translating to MPV values of 5.5 PVU or less, are more tightly collocated, with both fields exhibiting the weaker 35 2.1: Total column ozone and its relationship to meteorological fields Fig. 2.3 continued. gradients typical of deep-layer atmospheric fields. The biggest difference between the ozone and MPV fields is arguably the strength of the Atlantic Ocean ridge; all 1800-UTC MPV panels contain a far stronger ridge in this region than that shown in the ozone fields. Concerning troughs, note that, on the 23r , the tip 36 2.1: Total column ozone and its relationship to meteorological fields of the circled short-wave trough of interest points more to the west in the ozone field than in the 1800-UTC MPV field, and that, to the south of Newfoundland, the ozone field trough is far deeper than the MPV field trough, while, on the 24 , the wings at the southern end of the circled trough of interest extend laterally far more in the ozone than in the 1800-UTC MPV field. 2.1.4 The correlation of ozone and dynamical variables Dobson and his coauthors (Dobson et al. 1929, 1930) were the first to discover ozone's dynamical characteristics, noting a strong correlation between upper tropospheric to lower stratospheric pressure and total column ozone. Using pressure at 375 K, or approximately 14 km, Salby and Callaghan (1993) measured this correlation at greater than 0.70 poleward of 30°N. Note that correlation coefficients are not directly comparable between studies, as time periods, horizontal resolutions and methodologies vary. This high value reflects the fact that the total column ozone field is most strongly correlated with changes in evanescent disturbances near the tropopause, such as wavenumbef 5 disturbances and synoptic scale baroclinic waves decaying with height above the tropopause (Schoeberl and Krueger 1983). This is true in part because these disturbances' vertical and horizontal advections act in the same sense (as discussed in Section 2.1.1) and in part because these disturbances' constant phase with height causes the advection at different levels to be mutually reinforcing; the vertical and horizontal advections of winter propagating planetary scale waves (wavenumbers 1 and 2) do not necessarily reinforce each other, as the sense of upper 37 2.1: Total column ozone and its relationship to meteorological fields stratospheric horizontal advection depends on latitude, and one level's advection may oppose another's, as a result of the wave's phase varying with height (Schoeberl and Krueger 1983). Maximum correlations were found to occur at midlatitudes by both Ohring and Muench (1960), who correlated total column ozone with 100-Pa heights and Barsby and Diab (1995), who correlated total column ozone with 500-, 300- and 100-hPa heights. The latter study also noted that at lower latitudes, the 100-hPa heights were best correlated, while at higher latitudes, 300-hPa heights exhibited the strongest values, possibly reflecting the latitudinal slope of the dynamic tropopause. Although correlations varied with longitude and year, spring and summer were generally more highly correlated than autumn and winter, while higher (>0.89) and lower (<0.45) correlations were always associated with cyclonic and anticyclonic circulations, respectively. Petzoldt (1999), introducing a mid-stratospheric element, found that, at 60°N, while total column ozone is more highly correlated in summer with 300-hPa heights than with 30-hPa temperatures, the reverse is true in winter. However, correlating both fields with ozone simultaneously yielded the highest correlation of all: 0.93 for October. The correlation between ozone mixing ratio and PV, both of which increase with height from the troposphere up to the mid stratosphere, was measured by Danielsen (1983), with respect to latitudinally, longitudinally and temporally averaged fields, at close to unity in the layer from approximately 8 to 22 km (= 50 hPa; Allaart et al. 1993) where transport processes dominate. At higher altitudes, where photochemical processes dominate, anticorrelation is observed; the PV 38 2.1: Total column ozone and its relationship to meteorological fields source is at higher altitudes than that of ozone. In addition, both ozone and PV values increase polewards from the Equator up to the edge of the polar vortex. Within the polar vortex, the lower-latitude correlation between ozone and PV transitions to anticorrelation; the PV source is at higher latitudes than that of ozone (Danielsen 1983). Reflecting the similar ozone mixing ratio and PV vertical profiles below 22 km, these two fields were reported by both Beekman et al. (1994) and Langford et al. (1996) to be strongly correlated within stratospheric intrusions into the troposphere. The former study evaluated this correlation at 0.83. When these two fields do not agree on the exact position of a front, as sometimes happens, Hudson et al. (2003) believe the ozone field to be more accurate, especially in regions with no rawinsonde observations. However, one must remember that the ozone/PV correlation is constant only in the absence of photochemical and diabatic processes, the former being a source/sink for ozone alone and the latter for PV alone (Danielsen 1983). The decorrelations due to photochemistry and latent heating are greatest during spring/summer and winter, respectively (Beekman et al. 1994). Shapiro et al. (1982), noting similar displacements of PV and ozone by tropopause-level advections, demonstrated a total column ozone/tropopause elevation correlation by showing that the total column ozone high-gradient area was collocated with the tropopause-level jet stream axis, with the jet stream wind speed apparently proportional to the gradient's intensity. The authors proposed that this correlation was sufficiently strong for total column ozone data to be used to nowcast "the location and intensity of atmospheric flows in the vicinity of the tropopause". Schubert and Munteanu (1988), investigating the total column 39 2.1: Total column ozone and its relationship to meteorological fields ozone/tropopause pressure correlation further, found that the highest (>0.6) values were located at midlatitudes for synoptic-scale disturbances, with rapid and more gradual declines equatorward and poleward, respectively. Summer correlation values were higher than winter values, with the summertime high values extending over a wider band of latitudes, possibly due to reduced horizontal advection during this season. Longitudinally, the Atlantic and European sectors were more highly correlated than the Pacific and North American sectors, while storm track regions had the strongest correlation of all. The correlation between total column ozone and MPV (defined in Section 2.1.3), which reintroduces the combination of tropospheric and stratospheric correlation components found by Petzoldt (1999) to produce the strongest correlation coefficient, as discussed above, was measured by Allaart et al. (1993) at approximately 0.87. The strongest correlations were found during winter and spring, when high-latitude total column ozone values are large and the atmosphere is synoptically active. Less well correlated days occurred with either a "sudden loss of a large amount of ozone or a local diabatic change in PV". Davis et al. (1999) calculated an average midlatitude (25°N-70°N) correlation of 0.83 for 5- day anomalies of total column ozone and MPV over the Atlantic Ocean and Europe during February. The average tropical (0°N-25°N) value was a mere 0.2. Davis et al. (1999) daily correlation coefficients varied significantly, with higher amplitude disturbances more highly correlated, and troughs more strongly correlated than ridges. 40 2.1: Total column ozone and its relationship to meteorological fields 2.1.5 Ozone and numerical weather prediction models Riish0jgaard is a pioneer in the area of ozone assimilation. He managed, to a large extent, to reconstruct the flow field from a purely zonal flow by assimilating perfect simulated ozone mixing ratios into a barotropic vorticity-equation model using 4D-Var (Riishojgaard 1996). However, when assimilating less perfect data generated by a more realistic 3D model, the process was less successful; while the assimilation improved the first guess field's meridional flow, the zonal flow was sometimes degraded. Taking heed of the dangers of dynamically linking ozone during assimilation, both Derber and Wu (1998), using the operational National Centers for Environmental Prediction (NCEP) 3D-Var ozone assimilation scheme, and Dethof and Holm (2004), using the European Centre for Medium-Range Weather Forecasts (ECMWF; Uppala et al. 2005) operational forecasts' 4D-Var ozone assimilation scheme, assimilated ozone profiles and/or total column ozone without dynamical linkage; the ozone data contributed to an ozone analysis required by the model's radiative transfer calculations. Struthers et al. (2002), who assimilated ozone profiles and/or total column ozone values into a global general circulation model at the University of Reading's Data Assimilation Research Centre, also assimilated ozone without any dynamical linkage. In both ECMWF Re-Analysis (ERA-40; Dethof and Holm 2004) 3D-Var ozone assimilation and Goddard Earth Observing System version 4 general circulation model 4D-Var ozone assimilation (Stajner et al. 2006), ozone is not only not linked dynamically, but does not even feed back into radiative calculations. 41 2.1: Total column ozone and its relationship to meteorological fields Although Dethof and Holm (2004) did not link assimilated ozone data dynamically, both they and Peuch and his coauthors (Peuch et al. 2000), extracted tropopause-level wind information from differences between successive sets of ozone data, with expectations that the temperature field would adjust to wind field alterations. Indeed, the former study found that the assimilation of highly accurate model-generated total column ozone observations did yield significant improvements in both wind and temperature fields in an idealized experiment. However, the assimilation of actual observations was found to be extremely sensitive to observational error; the less accurate the assimilated data, the less positive, or more negative, was their impact. Riish0jgaard (1996) also warned of the possibility of deriving model ozone fields with a correct vertical integral, but an incorrect vertical distribution. This problem was encountered in the ERA-40 (Dethof and Holm 2004), where the 3D- Var assimilation scheme was left unguided by the insufficient observational vertical resolution and so assigned analysis corrections according to the ozone background error covariance matrix's estimation of the most likely vertical distribution. Thus, it is not surprising that Struthers et al. (2002) found that their analyzed ozone fields were closest to the verifying observations when both ozone profile and total column ozone data were assimilated. Randall et al. (2005) encountered the opposite problem while constructing a 3D distribution of ozone from vertical profiles of ozone: the data were well resolved vertically but were geographically limited. To overcome this limitation, PV fields were combined with the ozone profiles, using PV/ozone correlations, to 42 2.1: Total column ozone and its relationship to meteorological fields construct a 3D ozone field. In regions where ozone behaves as a passive tracer, the constructed field was in close agreement with simulated fields. With a view to improving hurricane track forecasts, Zou and Wu (2005) used a 4D-Var scheme to assimilate dynamically-linked Total Ozone Mapping Spectrometer (TOMS) non-gridded level-2 total column ozone data in a hurricane prediction model. In the hurricane environment, within a domain encompassing the North Atlantic Ocean and coastal North America from 14°-59°N, the authors made use of the close relationship between total column ozone and MPV. MPV was calculated using NCEP reanalysis PV from 400 to 50 hPa, where "NCEP reanalysis" is formally known as the National Centers for Environmental Prediction - National Center for Atmospheric Research reanalysis (Kalnay et al. 1996, Mo and Higgins 1996). In the hurricane eye, the authors made use of the close total column ozone/340-K geopotential height relationship. Within the hurricane environment, two linear regression models were developed by Zou and Wu (2005) using a 14-day period: for the regime pertaining to points weakly influenced by the hurricane, characterized by a strong total column ozone/MPV correlation, and for the regime containing hurricane- generated deep convection, which is characterized by lower total column ozone values. The first regime's regression model initially considered points having a total column ozone value of at least 293 DU, which, according to Hudson et al. (2003; see Section 2.1.1), precludes these points from belonging to a tropical air mass. A linear regression was performed. All points with a fitting error greater than the product of 1.4 and the standard error were then removed from the set of points considered. The regression/point elimination procedure was conducted 43 2.1: Total column ozone and its relationship to meteorological fields twice more. The set of data points, Si, then consisted of all data points from the entire domain that fell within a specified distance of the third regression's line. The regression performed on the points in Si constituted the regression model applicable to the first regime, of weak hurricane influence. A regression was then performed on all points from the domain not in Si. Points not in Si that fell within a specified distance of the new regression's line constituted the set S2. The regression performed on the points in S2 provided the regression model applicable to the second regime, of strong hurricane influence. Points belonging to neither Si nor S2, amounting to less than 3% of the total number of points, were not used. While the daily total column ozone/MPV correlation varied between 0.55 and 0.92 with all points in the domain considered, where low correlations accompanied hurricane intensification, the correlation for Si ranged between 0.88 and 0.97 and for S2 between 0.78 and 0.97. It is interesting to note that approximately one third of the points in Si, or the weak hurricane influence regime, have values lower than 293 DU (their Fig. 4), despite the fact that only points having total column ozone values greater than 293 DU, corresponding to non-tropical air mass points, were initially considered, while approximately one fifth of the points in S2, or the strong hurricane influence regime, have values greater than 293 DU; the mathematical regression system has produced two regression models that have little memory of their underlying physical basis; two virtually parallel lines have simply been drawn though the domain's data points. Given that there is a smaller distance from each point to the nearest line when two lines are available versus one, it is not surprising that correlations increased and standard error decreased with the new two-regime 44 2.1: Total column ozone and its relationship to meteorological fields system. That the new system yields a more accurate ozone-derived MPV field remains to be demonstrated. Concerning the hurricane itself, Zou and Wu (2005) equated the local maximum of TOMS total column ozone that is embedded in a low total column ozone-valued region on the order of a few hundred kilometers in width, to subsidence in the hurricane eye region. They found that this ozone-derived hurricane position deviated on average about 30 km from the Tropical Prediction Center's best track for mature hurricanes. This is well within the best track error range. Furthermore, in the presence of vertical tilt, the total column ozone maximum and best track could both be correct. The correlation between total column ozone and 340-K geopotential height within a radius of 500 km from the hurricane centre was strong, varying from 0.82 to 0.96. The vertical distribution of the ozone-derived MPV or height increments was not discussed in Zou and Wu (2005). TOMS non-gridded level-2 total column ozone data were also assimilated with full dynamical linkage by Jang et al. (2003). Their 4D-Var assimilation scheme transformed model MPV, which was based on PV from 500 to 100 hPa, to total column ozone using a standard linear regression, then minimized the difference between the model-derived and observed total column ozone values. The Jang et al. (2003) MPV to total column ozone regression system used a 12-day period and a domain extending from the Equator to 60°N over North and Central America and adjacent waters. Separate regression models were developed for Equatorial (0°-20°N), middle (20°N-40°N) and higher latitudes (40°N-60°N). The middle latitude band was most highly correlated (0.81-0.82), followed by the 45 2.1: Total column ozone and its relationship to meteorological fields higher latitude band (0.67-0.69) and Equatorial regions (0.18-0.34). The considerable jump in correlation values between bands suggests that there may also be jumps in calculated slope and intercept values, which would result in regressed field value discontinuities at the two latitudinal borders. The model-derived total column ozone error covariance matrix in Jang et al. (2003) consists of diagonal entries, following the assumption that no data measurement's error is correlated to any other data measurement's error. These entries were set to 9.42 DU, representing the product of the 3% absolute observational error (McPeters et al. 1998) and an averaged total column ozone value of 314 DU. This system provides lower effective percent error values for troughs than ridges, as the former are associated with larger total column ozone values in reality than the latter; for a typical trough (ridge) value of 350 (275) DU, 9.42 DU represents an error of 2.69% (3.43%). This makes sense, given that TOMS data seem to be more reliable in trough than ridge regions. Jang et al. (2003) found that assimilating both ozone and rawinsonde data together versus rawinsonde data alone strengthened the PV distribution above 350 hPa across the base of the upper-level short wave trough, but weakened the distribution from 400-460 hPa (their Fig. 9). Furthermore, when both types of data were assimilated, a very strong PV gradient was exhibited from 250-350 hPa, and a very weak gradient from the 3-PVU contour at 350 hPa to the 2-PVU contour at 520 hPa. This evidence suggests that the vertical distribution of the total column ozone increment in the Jang et al. (2003) 4D-Var assimilation system needs to be adjusted, in order to promote an increased downward penetration, in terms of PV, of the ozone increment. 46 2.1: Total column ozone and its relationship to meteorological fields Davis et al. (1999) developed a method to derive model initializing height, temperature and wind fields from total column ozone data without using an assimilation scheme. The main steps of their methodology, on which this thesis' method (see Section 2.3) is based, consist of: 1) Constructing 5-day anomaly fields of total column ozone (interpolated onto the 2.5° x 2.5° NCEP reanalysis grid) and MPV (calculated using NCEP PV from 500-50 hPa). Only one quarter of the globe is processed at a time, where local noon at the centre of each global quarter matches an NCEP grid time. This results in temporal mismatches of no more than three hours. 2) Performing a standard linear regression on the two anomaly fields as a function of latitude using a one month period. 3) Converting the regressed MPV field to a 3D PV field by mapping the former onto one of two available composite NCEP latitudinally-dependent PV vertical profiles. The profile representing an upper-level trough (ridge) was generated using all points at a given latitude having an MPV anomaly greater (less) than the mean plus (minus) one standard deviation. 4) Temporally interpolating each level of the PV field from local noon to the given global quarter's universal time using advection by non-divergent NCEP winds. Unfortunately, vertical profiles constructed during the previous step's vertical mapping may be distorted at this stage by advection that varies in strength and direction with level. 5) Constructing a full 3D PV field by combining the temporally-interpolated anomalous PV field with the NCEP 5-day mean PV field. 47 2.1: Total column ozone and its relationship to meteorological fields 6) Inverting the full ozone-derived PV field from 500 to 50 hPa along with NCEP fields from 1000 to 500 hPa using Charney's nonlinear balance and NCEP- derived boundary condition fields. The inversion yields balanced heights, temperatures and non-divergent winds. Davis et al. (1999) found that ozone-derived and analysis winds differed sometimes in the vicinity of sharp ridges. Since strong ridges are often accompanied by deep clouds, this difference could either indicate faulty total column ozone values, despite the TOMS algorithm's accommodation of clouds (McPeters et al. 1998), or the non-conservation of PV in the presence of diabatic ridge-building; since diabatic heating constitutes a sink for MPV but not for total column ozone (see Section 2.1.4), such heating would cause the MPV field to exhibit a stronger ridge than the ozone field. 48 2.2: Data sets 2.2: Data sets 2.2.1 Technical details concerning the total column ozone data The ozone data used in this project are measured by the Total Ozone Mapping Spectrometer (TOMS) aboard the polar-orbiting Earth Probe satellite. Earth Probe is currently at a 750-km orbit (McPeters et al. 1998), yielding 84% and 100% coverage at the Equator and poleward of 30°N, respectively; oceanic and continental regions are equally well sampled. The instantaneous field of view ranges from 38 x 38 km at nadir, when the sensor is pointing directly at the ground, to 70 x 140 km at the extreme off-nadir, when the sensor is pointing its farthest to the side. The local equator crossing time during the ascending portion of the orbit is 11:16 am, resulting in Northern Hemispheric ozone measurements valid near local noon. For North America, local noon is close to 1800 UTC. Note that, as the satellite moves from east to west with the sun, eastern values are valid at an earlier time than western values. The TOMS instrument measures the solar irradiance and the radiance backscattered by the Earth's atmosphere; data void regions exist at high winter latitudes due to a lack of solar irradiance. A radiative transfer model calculates the backscattered radiance as a function of several known parameters and the unknown total column ozone. The ozone value is obtained by comparing the measured and calculated radiances. Derived total column ozone values are estimated to have an absolute error of ±3%, and a random error, which can be higher at high latitudes, of ±2%. Fields of version 8 daily average total column 49 2.2: Data sets ozone, which are output on a 1° latitude x 1.25° longitude grid by NASA, are used for this project. Only top quality data contribute to this level 3 gridded product. Unlike the MODIS instruments on the satellites Terra and Aqua, which provide high (1-km) resolution total column ozone data, but which require cloud- free skies to operate (Seemann et al. 2003), the TOMS algorithm accommodates the presence of clouds by referring to climatological cloud height charts and (below-cloud) climatological ozone profiles (McPeters et al. 1998). Although the presence of clouds can affect the accuracy of the total column ozone value (if the clouds are significantly higher than the climatological height, the tropospheric ozone increment and, consequently, the total column ozone values are underestimated; Olsen et al. 2000), this effect tends to produce an error on the order of only a few DU (Vaughan and Price 1991). 2.2.2 Model analyses and forecasts This thesis uses dynamical and moisture fields from the European Centre for Medium-Range Weather Forecasts (ECMWF; Uppala et al. 2005) Re-Analysis (ERA-40; Dethof and Holm 2004). The ERA-40 reanalysis is generated with a spectral resolution of T159 and 60 vertical levels. The top level is 0.1 hPa. High resolution (T106, or approximately 1.125° latitude (125 km) by 1.125° longitude (96 km at 40° latitude) pressure level fields were obtained from the University Corporation for Atmospheric Research (UCAR). This project also uses dynamical and moisture fields from the National Centers for Environmental Prediction - National Center for Atmospheric Research 50 2.2: Data sets (NCEP-NCAR; Kalnay et al. 1996, Mo and Higgins 1996) reanalysis (hereafter the NCEP reanalysis). This reanalysis is generated with a spectral resolution of T62 (=210 km) and 28 vertical levels, where the top level is 3 hPa. The pressure level fields used in this thesis have a horizontal resolution of 2.5° latitude (277.5 km) by 2.5° longitude (212.6 km at 40° latitude) and are available from the National Oceanic and Atmospheric Administration's (NOAA) Climate Diagnostics Center. The ERA-40 and NCEP reanalyses should be considerably more accurate than any operational analysis, given that more data are assimilated during their generation. Considering the higher resolution of the former reanalysis along with the fact that it is a newer product, this reanalysis should be the more accurate of the two. Analyses of dynamical and moisture fields produced operationally by the Global Environmental Multiscale model (GEM; Cote et al. 1998a, 1998b, Chouinard et al. 1994) were provided by Recherche en Prevision Numerique (RPN), a division of Environment Canada. The GEM model has a horizontal resolution of 400 x 200 grid points, or approximately 0.9° latitude (100 km) by 0.9° longitude (77 km at 40° latitude), and 28 vertical levels up to 10 hPa. Operational Eta (Black 1994) analyses of dynamical and moisture fields and forecasts of dynamical, moisture and accumulated precipitation fields were provided by the National Centers for Environmental Prediction (NCEP). The operational resolution of the Eta in January 2000 was 32 km (~ 0.3°) horizontally and 45 levels vertically (EMC 2007b, where "EMC" represents NCEP's 51 2.2: Data sets Environmental Modeling Center), with a rigid lid at 25 hPa (Rogers et al. 2007). Unlike the global (re)analyses described above, the operational Eta domain is regional. The Eta model domain is presented in Fig. 2.4. Fig. 2.4 The topography (m) of the operational Eta domain (taken from NARR 2007, where "NARR" represents the North American Regional Reanalysis). 2.2.3 Precipitation analyses The reader is referred to Section 3.1.2 for a detailed description of the two precipitation analyses used in this thesis: the Brennan and Lackmann (2005) and U.S. Unified Precipitation Dataset analyses. The former is reproduced by permission of the American Meteorological Society, while the latter is provided by the NOAA. 2.2.4 Water vapour satellite imagery Geostationary Operational Environmental Satellite (GOES) water vapour imagery was provided by the National Climatic Data Center (NCDC). 52 2.3: An illustrated description of the procedure 2.3: The conversion of total column ozone data to model initializing fields The generation of model initial conditions from satellite total column ozone fields consists of the following steps: 1) Spatial interpolation of the ozone and analysis fields to a lat-lon grid; 2) Temporal interpolation of the ozone fields from local noon to a universal time; 3) Performance of a least squares method linear regression on a set of ozone and Mean Potential Vorticity (MPV; see Section 2.1.3) fields; 4) Regression of the chemical ozone field to a dynamical MPV field; 5) Synthesis of the regressed and analysed MPV fields; 6) Vertical mapping of the 2D synthesized MPV field onto average Potential Vorticity (PV) profiles to create a 3D PV field; 7) Inversion of the 3D PV field to obtain model initializing wind, height and temperature fields. Steps 1-5, which together convert a total column ozone field to an MPV field, are discussed in Section 2.3.1, while steps 6 (vertical mapping) and 7 (PV inversion) are discussed in Sections 2.3.2 and 2.3.3, respectively. An example of each step will be provided by the processing of the 24 January 2000 total column ozone field. 53 2.3: An illustrated description of the procedure 2.3.1 The conversion of total column ozone to mean potential vorticity 2.3.1.1 Spatial interpolation of total column ozone To conduct our calculations on a uniform grid, we first interpolate all fields used in this research to a global 1.125° latitude by 1.125° longitude grid (versus the 2.5° x 2.5° grid used in Davis et al. 1999; see Section 2.1.5). This represents a minor change in resolution for the total column ozone, ERA-40 and GEM fields (see Section 2.2), but a greater change for the 32-km (~ 0.3°) resolution Eta fields. Deo L-^^CJ YJ nam* a) The Eta and computation domains Fig. 2.5 The topography (m, shaded) of the operational Eta domain has been interpolated from its native Lambert conic conformal grid to a Mercator grid. White regions are outside the native Eta grid. The computation region for the ozone to model initial conditions conversion is indicated by the black box. Also plotted are Eta subdomain 200-hPa temperatures (2-°C contour interval) embedded within the ERA-40 domain. 54 2.3: An illustrated description of the procedure Since the native Eta grid is a regional grid (see Fig. 2.4), Eta fields are interpolated to a subdomain of the ERA-40 global latitude-longitude domain. Subdomain boundaries are assigned the average of the ERA-40 and Eta values. This embedding of the Eta fields should not affect calculations within the computation region, as this region, except for the extreme southeast corner (see Fig. 2.5), is well within the native Eta domain. That the embedding creates no field discontinuities is demonstrated by the realistic temperature contours of Fig. 2.5. 33 32; 5 30 a) Hi 9h-1 atitude region b) Lou-latitude region Fig. 2.6 Problematic spatially-interpolated total column ozone values (5-DU contour interval) bordering a) high-latitude and b) low-latitude data void regions (shaded) appear as bull's eyes. Unfortunately, the spatial interpolation assigns unreliable values to grid points neighbouring total column ozone data void regions, where the ozone is zero-valued (see Fig. 2.6). Data void regions exist at high winter latitudes where there is no sunlight, such that the TOMS instrument is unable to function, as well as at low latitudes, owing to the satellite's altitude being insufficient to provide 55 2.3: An illustrated description of the procedure complete coverage at these latitudes (see Section 2.2.1). Points in and neighbouring data void regions are included in neither the regression calculations (see Section 2.3.1.3) nor the ozone to MPV field conversion (see Section 2.3.1.4). 2.3.1.2 Temporal interpolation of total column ozone Given that our test case occurs in North America and that local noon is 1800 UTC at 90°W, which runs through the U.S., we interpolate the total column ozone values, within an area slightly larger than Section 3.2's modeling domain, from local noon to 1800 UTC; an interpolation that involves the smallest possible temporal mismatches should produce the smallest errors possible. The temporal interpolation scheme, which is based closely on, but is not identical to, the Davis et al. (1999) scheme, does not consider wave propagation. Pure advection is performed. This is deemed appropriate, given that a synoptic- scale, wave 5 disturbance in total column ozone "simply results from advection by the wind field associated with the wave" (Schoeberl and Krueger 1983); the temporal interpolation scheme simply undoes or continues the process by which the total column ozone disturbance was created. The temporal mismatch needing to be corrected by the interpolation is defined by Equation 2.3: St = (X - Xc)lCO {2.3} where Xc (radians) is the central longitude, or the longitude (90°W) at which local noon represents the specified universal time (1800 UTC), A, (radians) the longitude of a given grid point and oo the planetary angular velocity, which is valued at 56 2.3: An illustrated description of the procedure 27r/(24*3600) s"1. Thus, 8t is negative (positive) for grid points west (east) of the central longitude, so that local noon ozone values are brought backwards (forwards) in time to the universal time. For grid points west (east) of the central longitude, ozone values valid at the universal time are found downstream (upstream) of the given grid point. In westerly (easterly) winds, the ozone field at the universal time is stretched outwards from (condensed towards) the central longitude with respect to the local noon field. If we define the destination grid point as the grid point in the universal time field for which we are finding the appropriate ozone value, and the departure point as the (not necessarily grid) point in the local noon field having the ozone value valid at the destination grid point, then, once 5t has been calculated using equation {2.3}, the location of the departure point relative to the destination grid point is calculated using equations {2.4} and {2.5}: Sx = uSt {2.4} Sy = vSt {2.5} where u and v, the advecting winds (m s"1), are ERA-40 dynamic tropopause winds, halved. Although not explicitly stated by Davis et al. (1999), the halving of the wind strength is suggested by their equation for 8t on p. 3383, which produces a numerical value half that produced by equation {2.3}. Given that wind strengths are maximized at the tropopause, and that the majority of the ozone molecules reside just above the tropopause (see Section 2.1.1) where the winds are weaker, it is understandable that diminishing the advecting winds produces a higher correlation coefficient. This relationship is portrayed by Fig. 57 2.3: An illustrated description of the procedure 2.7, which demonstrates that switching from unaltered winds to winds divided by 1.5 yields a noticeable increase in the total column ozone/MPV correlation value, with a smaller increase produced by switching from dividing the winds by 1.5 to 2.0. Since dividing the winds by more than 2.0 brings no noticeable increase in the correlation coefficient, we halve the advecting winds. w jj> 0.9 c o v> c g 0.87 O 1.0 1.5 2.0 2.5 Wind-dividing factor (dimensionless) Fig. 2.7 Correlation coefficients (dimensionless) calculated using various factors (dimensionless) to divide the ozone-advecting winds. The distances (m) calculated by equations {2.4} and {2.5} are converted to differences of latitude and longitude (radians) using equations {2.6} and {2.7}: Slatitude = Sy I R {2.6} Slongitude - Sx I R cos( lat) {2.7} for R the radius of the earth (m) and lat the latitude of the destination grid point (radians). 58 2.3: An illustrated description of the procedure In contrast to Davis et al. (1999), who simply used the nearest grid point's ozone value, in this research, the local noon ozone value at the precise location determined by equations {2.3}-{2.7} is calculated using the inverse Cressman method (Cressman 1959), as per equation {2.8}, where a grid point's weighting, wn, is calculated by equation {2.9}: YjWn0zonen n=l,4_ ^Cressman ^~i {2-8} n=l,4 R2 -Dl W n = ,2 , „2 {2-9} R + Dn where the summation is over the four grid points surrounding the departure point, R (m) is the maximum radius of influence and Dn (m) the distance from the departure point to a given grid point. The value of R varies, being equal to the longest side of the grid cell containing the departure point. This results in three to four grid points having a non-zero weighting, which provides the scheme with sufficient knowledge of the surrounding field while avoiding undesirable smoothing. Destination grid points are assigned the missing data value of 200 DU, which was determined by a subjective examination to be below valid total column ozone values in our region of interest during the period considered, whenever the departure point falls within one grid point of a data void region, in order to avoid contamination of the regression by spurious values produced during the spatial interpolation (see Section 2.3.1.1). This system increases slightly the spatial extent of the original data void regions. 59 2.3: An illustrated description of the procedure The interpolation scheme described by equations {2.3}-{2.9} is divided into in three-hourly segments. The first segment is performed for temporal mismatches of up to three hours. It uses advecting winds valid at the specified universal time, which, for North America is 1800 UTC. If the total temporal mismatch calculated by equation {2.3} is greater than three hours, representing a longitude difference greater than 45°, a second segment of up to three hours is employed. In this case, the temporal mismatch equals the difference of the total temporal mismatch and three hours, and the departure point determined by the first segment becomes the destination point of the second. The winds used are a linear interpolation of those valid at the universal time and 6 hours earlier (later) for points east (west) of the central longitude, interpolated spatially to the new destination point by the inverse Cressman scheme described by equations {2.8} and {2.9}. If required by the modeling domain, a third interpolation segment would be introduced for original temporal mismatches of up to nine hours, or longitude differences of up to 135°. Using multiple interpolation segments introduces curvature into the temporal interpolation trajectory, which should contribute to a more accurate universal time ozone field. Davis et al. (1999) permitted only one interpolation segment. However, their maximum temporal mismatch was confined to three hours, or the equivalent of one segment of our interpolation scheme, since exactly one quarter of the globe was interpolated to a given universal time, versus our unrestricted global portion; this severely reduces the flexibility when establishing a model domain. Figure 2.8 presents the original local noon and temporally interpolated total column ozone fields from 24 January 2000. The region plotted constitutes 60 2.3: An illustrated description of the procedure Fig. 2.8 Plotted for 24 January 2000 are a) the original total column ozone field valid at local noon with ERA-40 dynamic tropopause winds valid at 1800 UTC ((half) barb equals (2.5) 5 m s"1, pennant equals 25 m s"1), and b) the temporally- mapped total column ozone field valid at 1800 UTC. The ozone fields are plotted with a contour interval of 25 DU, where smaller values are shown in lighter shades of grey, and shading from 350 DU. Section 3.2's modeling domain. As described above, in regions with westerly (easterly) winds, the local noon field has been stretched outwards from (towards) 90°W, the interpolation scheme's central longitude. The effect is strongest where the winds are strong and/or the longitudinal distance from the central longitude is 61 2.3: An illustrated description of the procedure large. For instance, at the location marked "A", the region marked by a small circular contour has moved to the southwest during the interpolation and has joined a larger region of similar values, while at the location marked "B", the shaded area has clearly moved eastwards. Apart from differences already mentioned between our temporal interpolation and that of Davis et al. (1999), the former and latter interpolations are performed, respectively, before and after the conversion of total column ozone to 3D PV. It is the choice of dynamic tropopause winds as the advecting agent that permits our early temporal interpolation. This choice is made viable by the fact that the large majority of the ozone molecules resides just above the dynamic tropopause (see Section 2.1.1); the advecting winds operate on the bulk of the ozone molecules accurately with respect to direction and strength. Davis et al. (1999), on the other hand, advect each level's ozone-derived PV with that level's nondivergent winds, which were obtained by inverting analysed PV. Unfortunately, differential advection may distort their constructed ozone-derived PV vertical profiles: PV values at 50, 250 and 500 hPa may be advected at different speeds and in different directions. Such a distortion is not an issue for our procedure as the PV vertical profiles are constructed after the temporal interpolation. Furthermore, our early temporal interpolation should act to align total column ozone and MPV features before the regression is performed, thereby increasing the accuracy of the regression. Details of our temporal interpolation are of interest for the 3D-Var, but not 4D-Var, assimilation of total column ozone. 62 2.3: An illustrated description of the procedure 2.3.1.3 Total column ozone / mean potential vorticity regression scheme The total column ozone/Mean Potential Vorticity (MPV; see Section 2.1.3) regression uses MPV calculated from PV^O) (defined by equation {2.23}), so that the form of PV on which ozone-derived PV is based is identical to the form of PV inverted in Section 2.3.3. This consistency reduces the degree of smoothing produced by the inversion. The least squares method linear regression is performed using equations {2.10} and {2.11} (Hastings 1997): 1 _n. 1 _n {2.10} 1=1 1 = 1 nYuxiyt- Yxi 11 yi i=l V/=l Ai=l J m = {2.11} n 2 f n \ nH(xi) - Hxi i=\ \i=\ J where b is the intercept and m the slope of the best fit line describing the relationship between fields X and Y, which consist of n x and y points, respectively. The correlation coefficient between X and Y, pXY, is calculated using equation {2.12} (Hastings 1997): Cov(X,Y) PXY = {2.12} GX (Hastings 1997): 63 2.3: An illustrated description of the procedure 1 " (1 x " ~\( 1 " ^ cov(xj)=-Y x y —Y. i -T,y. {2.13} J i i H n n ,i=l= \ i=l J \ .-=1 J {2.14} where x , the mean value of all x points is calculated by equation {2.15} 1 " {2.15} In order to avoid contamination of the regression statistics by unreliable points near data void regions generated during the initial spatial interpolation (see Section 2.3.1.1), grid points with ozone values smaller than or equal to 245 DU do not contribute to the calculations if any neighbouring grid point is valued at 200 DU or less. The regression domain extends from 17.35°N to 65.94°N and 150.95°W to 39.08°W. Unless explicitly stated otherwise, all figures in this a) All latitudes 500 N=49737 p=0.89 0 o 400 N O c E 8 300 "55 o CTAY=141 MeanAY=17.7 200 0 3 6 9 12 Mean Potential Vorticity (PVU) Fig. 2.9 Total column ozone (DU)/MPV (PVU) data points from the indicated latitude bands are shown with the respective regressed lines. Available (filtered) points are plotted in black (green). The heavy line along the abscissa is created by points from data void regions. 64 2.3: An illustrated description of the procedure b) <30N c) 30-40N 500 • - N=11557 N=12210 p=0.74 p=0.86 Q, £ 400 c 400 o o N N O O £ O O 300 ••-o• »•• cAY=8.3 aAY=12.8 Mean AY=10.5 Mean AY= 16.4 0 3 6 9 12 Mean Potential Vorticity (PVU) Mean Potential Vorticity (PVU) d) 40-50N e) >=50N 500 500 N=11200 N=11970 Q, £ 400 £ 400 O o N N O O £ £ o O o 300 O 300 15 -§-o• aAY=15.4 aAY=14.2 Mean AY=20.4 Mean AY=20.9 200 200 Mean Potential Vorticity (PVU) Mean Potential Vorticity (PVU) Fig. 2.9 continued. subsection are based on data points from all latitudes of the domain combined and 10-23 January 2000, with MPV calculated using ERA-40 PV from 400-50 hPa. 65 2.3: An illustrated description of the procedure Since the total column ozone/MPV correlation coefficient unquestionably varies with latitude (see Section 2.1.4), some studies have assumed that the ozone/MPV regression scheme should also vary either with latitude (Davis et al. 1999, Jang et al. 2003) or air mass (Zou and Wu 2005; see Section 2.1.5). However, despite the fact that the regression line for the green filtered low- latitude points (Fig. 2.9.b) is rotated with respect to the line for the filtered points from all latitudes (Fig. 2.9.a), reflecting the low-latitude line's smaller slope and 25 f All <30 30-40 40-50 >=50 Latitude band (°N) 190 All <30 30-40 40-50 >=50 Latitude band (°N) Fig. 2.10 Regression slopes (a) and intercepts (b) for the indicated latitude bands. 66 2.3: An illustrated description of the procedure higher intercept (Fig. 2.10), these low-latitude points are, nonetheless, following the same general direction as the points from the other latitude bands; the lower correlation may be more a result of the less elongated region covered by the filtered low-latitude data points and less an indication that this air mass behaves fundamentally differently. Furthermore, the fact that the highest correlation (p; panels' upper left) of all is obtained by points from all latitude bands, for which the slope and intercept are, following the low-latitude behaviour, smaller and larger, respectively, than those of the three higher latitude bands, and the fact that all latitude bands have similar numbers of filtered points (N; panels' upper left), indicating that the low-latitude filtered points are not dominating the set of filtered points from all latitudes, together suggest that the low-latitude points do not belong to a separate regime. Likewise, the fact that the 30°-40°N latitude band is the most highly correlated latitude band suggests that the intercepts from the two most northerly latitude bands are unrealistically low. Therefore, our regression uses the filtered points from all latitude bands, as this set of points is the most highly correlated and as there is no evidence that the regression scheme should vary with latitude. It is important to note that the standard deviation of the distribution of vertical distances from the regression line to each filtered data point (GAY; panels' lower right) is not significantly smaller than the mean such vertical distance (Mean AY; panels' lower right). This indicates that there are not two separate regimes hidden unseen amongst the multitude of data points present (N). 67 2.3: An illustrated description of the procedure A comparison of our slope and intercept values to those given by Jang et al. (2003) is meaningless, given that their MPV is calculated using different bounding pressure levels (see Section 2.1.3). Davis et al. (1999) do not provide the values of their best fit line parameters. Zou and Wu (2005), on the other hand, define MPV as we do and they also provide parameter values. However, their regression scheme (described in Section 2.1.5) is quite different to ours, rendering a comparison of regression parameter values meaningless. H 30 hPa ED 50 hPa M 70 hPa iS 5 0.87 O 250 300 400 500 Lower bounding level (hPa) Fig. 2.11 Correlation coefficients (dimensionless) calculated using the indicated MPV upper and lower bounding pressure levels (hPa). The upper and lower bounding pressure levels used to calculate the MPV employed in the total column ozone/MPV regression were determined with the help of Fig. 2.11. This figure demonstrates quite clearly that the upper bounding pressure level should be at least 50 hPa. Given that the ozone mixing ratio/PV correlation becomes anticorrelation above approximately 50 hPa (see Section 68 2.3: An illustrated description of the procedure 2.1.3), 30 hPa seems an unwise choice as the upper bounding level, despite the fact that using 30 hPa can yield the highest correlation coefficient for a given lower level value. Thus, 50 hPa is selected as the upper boundary level for the MPV calculation, which agrees with the value chosen by Davis et al. (1999) and Zou and Wu (2005), but which is higher than the 100 hPa value used by Jang et al. (2003; see Section 2.1.3). Although, with a 50-hPa upper level, a lower level of 300 hPa produces a slightly higher correlation value than 400 hPa, the latter level was chosen as the lower bounding pressure level for this research, partly because no published study has used such a high lower level value and partly because the difference in correlation value is minimal; a 400-hPa lower level might produce the higher correlation value with a different set of dates. Zou and Wu (2005) also used 400 hPa as the lower level, while Davis et al. (1999) and Jang et al. (2003) used 500 hPa (see Section 2.1.3). w o 0.9 c o "w c o & a 0.88 o c o J2 g 0.87 O ERA-40 NCEP GEM Regression (re)ana!ysis Fig. 2.12 Correlation coefficients (dimensionless) calculated using the indicated (re)analyses. 69 2.3: An illustrated description of the procedure Two interesting points are illustrated by Fig. 2.12: 1) the quality of the (re)analysis used to calculate MPV has a greater impact than its resolution, since using the 2.5° x 2.5° NCEP reanalyses (see Section 2.2.2) produces a higher correlation coefficient than the approximately 0.9° x 0.9° GEM operational analyses; lower quality analyses might incorrectly position a feature, or include the effects of spurious latent heating; 2) extrapolating the trend of increasing correlation coefficient with increasing (re)analysis quality suggests that using an even more accurate set of fields than that provided by the ERA-40 would increase the coefficient further. This implies that the total column ozone fields are, on the whole, more accurate than even the ERA-40 fields. Given that the ERA-40 fields are the most accurate available, producing the highest correlation coefficient calculated, we use ERA-40 fields for this research's total column ozone/MPV regression. Although it would be desirable to perform the total column ozone/MPV regression using a time period centered on the target date, it is not possible to do so in an operational setting; fields from after the target date are still unknown. It is extremely unwise to use the time period centered on the target date from any previous year, or from any combination of years, given that the base level of total column ozone varies from year to year (see Section 2.1.1). Thus, since we wish to simulate an operational setting in this research, the regression time period is taken from the days leading up to the target date. The length of the regression time period was determined with the help of Fig. 2.13. This figure states clearly that using too short a time period, such as 10 d, significantly decreases the correlation coefficient calculated. Using a long time 70 2.3: An illustrated description of the procedure period is also disadvantageous. The fact that the 22-d period produces a higher coefficient than the 18-d period is surprising, although this relative order might change with a different set of calculation dates. This research's regression scheme uses a 14-day period, which yields the highest correlation coefficient of this figure. This is equal or comparable to the 14- and 12-day periods used by Zou and Wu (2005) and Jang et al. (2003), respectively, and far shorter than the one month used by Davis et al. (1999; see Section 2.1.5). 0 o 8 0.88 ^^^^"» o C IO 0.87 O 10 14 18 22 o Regression time period (d) Fig. 2.13 Correlation coefficients (dimensionless) calculated using the indicated regression time periods (d). Details of our regression scheme are of interest for both the 3D-Var and 4D- Var assimilation of total column ozone. 71 2.3: An illustrated description of the procedure 2.3.1.4 Total column ozone regression The 2D chemical field of total column ozone is converted to a 2D dynamical field of MPV by equation {2.16} using the intercept (y) and slope (m) calculated in Section 2.3.1.3. TCozone: ,• — y MPVUj= -M {2.16} m Since our area of interest is entirely in the Northern Hemisphere, MPV values are constrained to remain between 0 and 20 PVU, as values lower than 0 are unphysical and higher than 20 PVU are unrealistic. The corresponding range for the Southern Hemisphere would be -20 to 0 PVU. In order to avoid contamination of the ozone-derived MPV field by unreliable points generated during the initial spatial interpolation near data void regions (see Section 2.3.1.1), a grid point's MPV value is set to a missing data value if the ozone value is smaller than or equal to 200 DU or is smaller than or equal to 245 DU with a neighbouring grid point valued at 200 DU or less. The calculated MPV field is smoothed using equation {2.17} with the weightings calculated by equation {2.18}. I+n J+n *sr>Tr i=I-nj=J-n MPViJ= T^r^n {2-17} i=I-nj=J-n for i=I and j=J: wij=a {2.18a} ^ = (^fc <2-18b} 72 2.3: An illustrated description of the procedure where a is the smoothing coefficient and n determines the number of points involved in the summations. The denominator of equation {2.18b} represents the number of non-central points involved in a summation. Since very light smoothing yields the best results, we set a to 0.995. The initial smoothing pass is conducted with n set at unity. If, at a given grid point, no valid data points are encountered during this pass, the grid point is assigned a missing data value. A second smoothing pass is then conducted to replace missing data values. During this pass, where each grid point is processed until its MPV value is determined, and where n is initially set to unity, the value of n increments by one until at least one valid point is encountered that can contribute to the calculation of an MPV value. The regressed MPV field is an almost identical reproduction (in terms of the shape of the fields' features) of the temporally-mapped total column ozone field (see Fig. 2.14). Note that the low-latitude data void areas have been filled in during the field conversion. However, although the regressed and analysed MPV fields are very similar in general terms, these two fields are not identical (see Fig. 2.15); in comparison to the analysed field, the regressed eastern seaboard trough is deeper, with a greater width across its base and a more important extension into the Atlantic Ocean, the western trough has a weaker southwards extension, the Atlantic ridge is weaker, and the western ridge is stronger. 73 2.3: An illustrated description of the procedure Fig. 2.14 Plotted for 1800 UTC 24 January 2000 are: a) temporally-mapped total column ozone (contour interval of 25 DU with shading from 350 DU), and b) regressed MPV (contour interval of 1.2 PVU from 1.8 PVU with shading from 6.6 PVU). In both panels, paler shades of grey represent smaller values. The water vapour imagery of Fig. 2.16.b, 2.16.d, where white (dark) regions suggest ridges (troughs), confirms the presence of a strong eastern seaboard trough that widens at the base, but not the presence of the regressed Atlantic Ocean extension. The strength of the water vapour western trough is difficult to 74 2.3: An illustrated description of the procedure h) ERfl-^0 MPV Fig. 2.15 Regressed and ERA-40 MPV valid at 1800 UTC 24 January 2000 are shown in panels a) and b), respectively. These fields are plotted using a contour interval of 1 PVU for solid lines (where smaller values are represented by paler shades of grey), a dashed line at 5.5 PVU and shading from 7 PVU. Note that the contour intervals of Figs. 2.14.b and 2.15.a are different. determine. Figure 2.16 confirms the analysed strong Atlantic ridge and indicates the presence of a strong western ridge over the U.S., but perhaps a weaker ridge to the north than that seen in the regressed field. Panels a and c of this figure imply that the ERA-40 western ridge does not penetrate sufficiently 75 2.3: An illustrated description of the procedure c) GOES 10 WV25/00:00 d) GOES 8 WV25/00:15 Fig. 2.16 Shown for the indicated January 2000 day/UTC time are a), c) GEOS 10, and b), d) GOES 8 water vapour images. northwards in the western part of the continent, resulting in coastal depressions that appear to be both too deep and too big; the strength and extent of the ozone- derived coastal depressions are seemingly more reasonable. The overly weak regressed Atlantic ridge is most likely due to a diabatic process, which constitutes a source/sink for PV but not for total column ozone (see Section 2.1.4): latent heating due to heavy precipitation off the eastern seaboard has previously warmed the upper troposphere (not shown), which warmth is then advected eastwards, according to the winds of Fig. 2.8, thereby increasing the spatial scale of the discrepancy between the regressed and analysed fields. This ridge building would also have acted to reduce the magnitude of the 76 2.3: An illustrated description of the procedure eastern seaboard trough's Atlantic extension. Thus, the fact that the regressed field exhibits an overly weak Atlantic ridge and an overly deep and elongated trough extension is due to the inability of the total column ozone field to "see" the diabatically-produced ridge building. 2.3.1.5 Synthesis of ozone-derived and analysis mean potential vorticity As mentioned in the previous section, total column ozone fields do not immediately exhibit ridges built by latent heat release. Total column ozone values may also be less reliable in the vicinity of ridges than of troughs given that, in cloudy regions, which are often associated with ridging, the TOMS algorithm uses tropospheric ozone values deduced from climatological tropospheric ozone profiles and climatological cloud heights. Furthermore, total column ozone mini- holes (see Section 2.1.1) are embedded in ridges. Considering the approximately 50,000 points that contribute to the regression scheme, it seems unlikely that the presence of a mini-hole would adversely affect the accuracy of the regression. However, the mini-hole itself will still be reproduced in the regressed field as a region within a ridge with overly low MPV values. Since it thus appears that the regressed MPV field is not 100% reliable, owing to inaccuracies in the total column ozone field, we strengthen the accuracy of the ozone-derived MPV field by synthesizing the regressed and analysed MPV fields (see Fig. 2.15). The synthesis is conducted, at latitudes no more than 61°N, in recognition of the decorrelation between MPV and total column ozone that occurs within the polar vortex (see Section 2.1.4) by: 1) copying the analysis MPV field to the synthesized field, 2) overlaying all synthesized values of at least 77 2.3: An illustrated description of the procedure 7 PVU (shaded regions in Fig. 2.15.b) with regressed values, as long as the regressed value is no less than 3 PVU, 3) overlaying all synthesized values with regressed values of at least 7 PVU (shaded regions in Fig. 2.15.a), 4) overlaying all synthesized values with analyzed values of 5.5 PVU or less (the region of pale solid contours in Fig. 2.15.b enclosed by the dashed contour). Note that model accumulated precipitation forecasts remain virtually unchanged when the definition of a ridge in step 4 is redefined as values of 6.0 PVU or less, despite the fact that this redefinition does alter initializing height fields slightly. In other words, recognizing the greater accuracy of the ozone troughs and the relative weakness of the ozone ridges, the analysed trough is erased, so as not to produce an overly large synthesized trough, the regressed trough inserted and the analysis ridge laid on top. There has been no reference in the literature to the utilisation of only selected regions of a total column ozone field, whether dynamically-selected or not. The synthesized MPV field, along with the regressed and ERA-40 MPV fields, is presented in Fig. 2.17. Also plotted in this figure are lines indicating the location of the vertical cross sections of Fig. 2.21-2.24. The synthesized MPV field clearly exhibits analysed Atlantic and western ridges and regressed troughs, although the spatial extent of the regressed trough's southern portion has been reduced. On the other hand, the southern extension of the analysed western trough, as well as the small analysed Pacific Ocean depression, has been erased. Fig. 2.17 The a) regressed, b) synthesized, and c) ERA-40 MPV fields for 1800 UTC 24 January 2000 are shown, with a contour interval of 1 PVU for solid lines (where smaller values are represented by paler shades of grey), a dashed line at 5.5 PVU and shading from 7 PVU. The straight lines indicate the location of the cross sections of Figs. 2.21-2.24. 78 2.3: An illustrated description of the procedure a) Regressed MPV b) Synthesized MPV c) ERfl-^0 MPV Fig. 2.17 See caption on previous page. 79 2.3: An illustrated description of the procedure c) Rawinsonde: 25/00 d) ERR-^IO: 25/00 Fig. 2.18 Shown for the indicated dates, where "24/12" denotes 1200 UTC 24 January 2000 are a), c) MPV calculated from analysed rawinsonde data and b), d) ERA-40 MPV. The contour interval is 1 PVU for solid lines (where smaller values are represented by paler shades of grey), with a dashed line at 5.5 PVU and shading from 7 PVU. Triangles (squares) mark sounding stations contributing data at all (some of the) ten pressure levels contributing to the MPV calculation. MPV calculated from rawinsonde data, analysed onto this research's 1.125° by 1.125° latitude longitude grid using Gempak's Barnes objective analysis (Koch et al. 1983) with ERA-40 first guess fields, is presented in Fig. 2.18, along with ERA-40 MPV fields valid at the same times. Note that MPV fields presented in previous figures are all valid at 1800 UTC 24 January 2000 (hereafter 24/18), while Fig. 2.18's fields are valid at 24/12 and 25/00. Although the time discrepancy precludes a direct comparison between the rawinsonde-derived (Fig. 80 2.3: An illustrated description of the procedure 2.18.a, 2.18.c) and synthesized (Fig. 2.17.b) MPV fields, the strong rawinsonde- derived MPV ridge over Georgia at 24/12, presumably generated diabatically by the precipitation described in Brennan and Lackmann (2005; see Section 3.1.2), has likely weakened the east coast MPV trough. Rawinsonde-derived diabatic heating over the Carolinas and Virginia, evident at 25/00, has likely continued to weaken the trough further. Interestingly, the ERA-40 MPV field exhibits insufficient ridging both over Georgia at the earlier time and over South Carolina at the later time. This results in an ERA-40 trough that extends too far south at the earlier time, while, at the later time, the cut-off Low and the bend in the dashed contour over South Carolina are both too far north. This research's synthesizing process, which improves the regressed MPV field's trough by reducing its southerly extent, is unable to produce perfect results; the southern region of the synthesized trough remains, according to the rawinsonde-derived truth fields of Fig. 2.18, both too strong, owing to the inability of the total column ozone field to "see" the MPV-destroying diabatic processes (see Section 2.1.4), and too extensive, owing to the ERA-40's underestimation of the local ridging. Thus, at 1800 UTC, while the ERA-40 trough is probably fairly accurate, the synthesized trough is definitely too strong. Since all fields derived after this point will no longer have been produced via the manipulation of a total column ozone field alone, given this section's synthesizing process, the derived fields will be called "ozone-influenced", and not the stronger "ozone-derived". Details of this field synthesis are of interest for both the 3D-Var and 4D-Var assimilation of total column ozone. 81 2.3: An illustrated description of the procedure 2.3.2 Mean potential vorticity to potential vorticity conversion 2.3.2.1 Construction of average potential vorticity profiles The conversion of the 2D MPV field to a 3D PV field is conducted by mapping the synthesized MPV field onto average PV profiles, following Davis et al. (1999). In this research, each grid point is provided with a set of 12 average P V profiles, ranging from that of an extreme ridge to that of an extreme trough. As indicated by Fig. 2.19's flow chart, for each grid point, the mean MPV value and standard deviation (a) are calculated for the grid point's set of ERA-40 space/time points, following equations {2.14} and {2.15}, which assume a normal distribution of MPV values. The manner in which the set of points is established is discussed below. The algorithm next determines to which of the 12 available MPV categories the grid point's ozone-influenced MPV value belongs, the categories having the 11 boundaries consisting of the mean MPV value ±2.5a, representing an extreme ridge or trough, ±2a, ±1.5a, ±la, ±0.5a, +0a. The first and last categories consist of MPV values less than or equal to the mean -2.5a and greater than the mean +2.5a, respectively. The average PV value for each level is then calculated using all points from the full set of space/time points that have an MPV value within the determined MPV category. The average PV profile is constructed by stacking the individual levels' average PV values vertically. The MPV value of this constructed profile is labeled the "average" MPV value. Given the fact that the vertical mapping focuses heavily on the ratio of the synthesized and average MPV values (see Section 2.3.2.2), it is important to provide a sufficient number of MPV categories; as this ratio moves away from 82 2.3: An illustrated description of the procedure The generation of the average PV profile for a hypothetical case Using the MPV values of all elements in a given grid point's set of space/time points calculate: • The mean MPV value, e.g. 8.3 PVU • The standard deviation, a, of the MPV values, e.g. 1.4 PVU I Determine to which of the 12 MPV categories the point's ozone-influenced MPV value (e.g. 10.1 PVU) belongs. The numbers for this hypothetical case are in PVU. Mean MPV -2.5 a -2.0 a -1.5 a -1.0 a -0.5 a +0.0 a +0,5 a +1.0 a +1.5 a +2.0 a +2.5 a 4.8 5.5 6.2 6.9 7.6 8.3 9.0 9.7 10.4 11.1 11.8 A • A A A A A A t A A A I Calculate each level's average PV value using all points from the set of space/time points having an MPV value: • >= Mean MPV + 1.0 a (9.7 PVU) • <= Mean MPV + 1.5 a (10.4 PVU) I Create the grid point's average PV profile by vertically stacking the individual levels' average PV values. Fig. 2.19 A Flow chart outlining the steps for the generation of a given grid point's average PV profile, using a hypothetical case as an example. 83 2.3: An illustrated description of the procedure unity, the mapped profile moves increasingly away from the average profile, which can produce unrealistic results. On the other hand, if too many MPV categories are provided, the mapping ratio is too close to unity, resulting in an overly smooth ozone-influenced PV profile, which also produces inferior results. Thus, for this research, 12 MPV categories are used. Davis et al. (1999) provide only two categories of MPV anomaly: either greater than the mean +la or less than the mean -1 a (see Section 2.1.5). If a grid point's synthesized MPV value represents either an extreme ridge or an extreme trough, it is possible that that grid point's set of space/time points will contain no elements characterized by an MPV value lying within the appropriate MPV category. In such a situation, the boundary of the MPV category on the side towards the mean is shifted by one. For instance, if the category is from the MPV mean -2.5o to the mean -2c, the new category becomes the MPV mean -2.5a to the mean -1.5a. The search is again conducted for at least one space/time point having the appropriate MPV value. Only one point is required for the construction of the average PV profile, as it was found to be more important to provide a profile of a similar MPV value than to provide a smoother profile derived from more points but with a less similar MPV value. If no such point is found, boundaries are successively shifted until at least one point is found. If it is an extreme synthesized trough or ridge that is being processed, such that the MPV category is defined as containing MPV values less than or equal to the mean -2.5a or greater than the mean +2.5a, it is always the boundary towards the mean that is shifted. If it is a synthesized MPV value that is closer to the mean that is being 84 2.3: An illustrated description of the procedure processed, the algorithm alternates between shifting the boundary towards the mean (done first) and towards the extreme. It is interesting to note that none of the four grid points of Fig. 2.20 is able to provide six separate ridge profiles, while three out of four are able to provide six trough profiles. Davis et al. (1999) did not alter category boundaries, as only two MPV categories were considered. Given the seasonal variation of climatological mass fields (Bluestein 1993), average PV profiles will also vary with season. Therefore, the set of space/time points from which the average PV profiles are constructed must include only points from the same season as the target date. On the other hand, as many space/time points as possible are desired, in order to be able to provide at least one point representing each available MPV category. Thus, optimally, a long, e.g. 30-40-y, dataset would be used, from which dates within the same month as the target date would be selected. Such a long-term set of dates would undoubtedly include the unusually high low-latitude PV values observed during this event (see, e.g., the superstorm of 1993; Huo et al. 1999a, 1999b). However, for our demonstration of the vertical mapping process, the space/time points from the two weeks prior to the target date plus the target date itself are used, which cannot be done operationally, but which provides points with anomalously high low-latitude PV values. It is likely, though not explicitly stated, that Davis et al. (1999) used all dates from their one month of data. Considering the primarily latitudinal but also longitudinal variation between the four sets of average PV profiles presented in Fig. 2.20, it is necessary to restrict the extent of the region providing space/time points. However, if too small a region is used, no points will be available to contribute to extreme 85 2.3: An illustrated description of the procedure a)54.64°N, 143.04°W b) 54.64°N, 82.02°W 50 I 1 70 . I 1 J> - 100 1 f'jyjr Q_ ! .c f;/A >"-' 150 LU_) 3 V) 200 y Mr v> MB g> 250 - Q_ 300 400 mean MPV = 6.7PVU - mean MPV = 8.3PVU = 1.4PVU 500 ^MPV = 1.4 PVU 600 02 10 20 30 02 10 20 30 Potential vorticity (PVU) Potential vorticity (PVU) c) 30.91 °N, 143.04°W d) 30.91 oN,82.02°W 50 W • *r <-2.5 70 -2.5:-2.0 _ -2.0:-1.5 _ -1.5:-1.0 ~100 -1.0:-0.5 Q_ -0.5:-0.0 f 150 0.0:0.5 — 0.5:1.0 w 200 1.0:1.5 1.5:2.0 S> 250 2.0:2.5 °- 300 >2.5 mean MPV=5.0PVU 400 mean MPV=3.5PVU -MPV=15PVU 500 .= 1.2 PVU 600 02 10 20 30 0 2 10 20 30 Potential vorticity (PVU) Potential vorticity (PVU) Fig. 2.20 Average PV vertical profiles (PVU) available at two latitudes and two longitudes. The legend indicates the range of MPV values (in terms of the number of standard deviations, o, from the mean MPV value) characterizing the subset of points - of the grid point's set of space/time points - that contributes to the corresponding average PV profile. 86 2.3: An illustrated description of the procedure ridge/trough profiles. Therefore, a 9 by 9 grid point box, representing a 10° latitude by 10° longitude region, centred on the grid point being processed was used in this research. For grid points near the edge of the domain, the region is shifted until it lies entirely within the domain. Davis et al. (1999) calculated statistical profiles as a function of latitude. Although neither 3D-Var nor 4D-Var data assimilation use average profiles, this method of constructing average vertical profiles could be of interest for the processing of other 2D fields. 2.3.2.2 Vertical mapping The 2D synthesized MPV field is converted to a 3D PV field by mapping each grid point's MPV value onto the appropriate average PV profile, constructed as discussed in Section 2.3.2.1. The mapped PV value at a given grid point (i,j) and level k, is calculated using equation {2.19}: 'MPV • • (MPV • • ^ 1VX1 r *PV r map;i,j,k• • i syn;i,j . (factork) syn;i,j Pym;iJtk {2.19} y 1V11MPV y av;i,j• • J \ MPVavi i where MPVsyn;ij is the synthesized MPV value at. grid point (i,j), MPVav;io the MPV value of the grid point's constructed average PV profile (see Section 2.3.2.1), PVaV;ij,k the value of the grid point's average PV profile at level k, and factork the level-dependent multiplicative factor. The firstoccurrenc e of the ratio of the synthesized and average MPV values in equation {2.19} constitutes a constant mapping coefficient. Since 12 average profiles are available, this ratio is close to unity, rendering the term multiplied by factork a small adjustment to the 87 2.3: An illustrated description of the procedure constant mapping coefficient. The presence of the factor term transforms the constant mapping coefficient into a level-varying mapping coefficient. Values used for factor in this research are presented in Table 2.1. Table 2.1 Factor values Level (hPa) 600 500 400 300 250 200 150 100 70 50 Factork (dimen 0.3 0.6 0.9 0.6 0.2 -0.75 -0.85 -0.95 -0.98 0 sion! ess) The effect of the constant mapping coefficient is to assign the MPV increment predominantly to upper levels: if an average PV profile has a 70-hPa value of 15 PVU and a 250-hPa value of 5 PVU, and if the MPV ratio is 1.1, then the mapped values become 77 and 5.5 PVU, representing a difference of 7 and 0.5 PVU, respectively; the positive MPV increment has been converted into a significant stratospheric trough, while the troposphere has remained virtually unchanged. This result is not physical. Our level-varying coefficient, on the other hand, assigns the MPV increment predominantly to levels below 200 hPa, producing a far more realistic result. The stronger 50-200-hPa (panel a) and 200- 500-hPa (panel b) PV troughs produced, respectively, by constant and level- varying mapping coefficients, are clearly visible above Fig. 2.21 's eastern seaboard trough. It seems reasonable to assume that Davis et al. (1999) used a constant mapping coefficient, given that details of their vertical mapping scheme are not discussed. 88 2.3: An illustrated description of the procedure Fig. 2.21 For 1800 UTC 24 January 2000, cross sections of PV are shown along the line indicated in panel b) of Fig. 2.17, where the PV fields have been vertically mapped using a) a constant mapping coefficient, and b) a level-varying mapping coefficient. The PV fields are plotted every 1 PVU to 13 PVU and every 2 PVU from 13 PVU, with shading from 2-3 PVU. The vertical mapping is conducted automatically for the eight levels from 50 to 400 hPa (50, 70, 100, 150, 200, 250, 300, 400 hPa), since these are the levels involved in calculating the total column ozone-correlating MPV field. The mapping is then permitted to continue down to 600 hPa, as the dynamic tropopause does, on occasion, sink so low, and as the total column ozone field contains information about the dynamic tropopause, given that most of the ozone molecules reside just above this level (see Section 2.1.1). Mapping onto the average profile at 500 and 600 hPa is conducted only if either the profile's or mapped PV value on the level above is at least 1.5 PVU. As soon as both PV values fall below 1.5 PVU no mapping occurs at any lower level (i.e. at 500 and/or 600 hPa) and the ERA-40 PV value is transferred unmapped to the ozone- influenced profile. Thus, the vertical mapping procedure produces a 3D PV field with 10 levels from 600 to 50 hPa. 89 2.3: An illustrated description of the procedure In order to conserve the synthesized field's MPV values during the vertical mapping, which the constant mapping coefficient does perfectly, our mapping, employing the level-varying coefficient, is conducted iteratively at each grid point until the MPV value calculated from the mapped PV profile is within 1.0 x 10" PVU of the synthesized MPV value. Unfortunately, this condition can be too demanding under strong ridges: the reduction of values by the mapping procedure and the constriction that PV values remain positive, in order to preserve physical Northern Hemispheric values, can together result in the impossibility of reducing the mapped MPV value sufficiently. Therefore, no more than 250 iterations are conducted, after which the synthesized and mapped MPV values tend to agree to two decimal places. Fig. 2.22 Cross sections of PV along the lines indicated in Fig. 2.17 are shown for 1800 UTC 24 January 2000 using: a) PV fields obtained by vertically mapping synthesized MPV using a level-varying mapping coefficient, and b) ERA-40 PV(^, A comparison of the ozone-influenced, mapped using the level-varying coefficient, and ERA-40 PV vertical cross sections of Fig. 2.22 reveals that the two sections are very similar to first order, in that they both have collocated 90 2.3: An illustrated description of the procedure primary troughs with flanking ridges. Thus, the dynamical forcing represented by these fields should also be similar. There are differences, however. The analysis cross section exhibits a PV minimum at 150 hPa, which the ozone-influenced section does not; our vertical mapping procedure is incapable of producing a minimum above a maximum as, on average, PV increases with altitude, a fact that is reflected in our average PV profiles. Furthermore, the ozone-influenced trough is deeper and wider than that of the analysis. This is mainly a reflection of the deeper, wider trough in the synthesized MPV field versus the analysis field (see Fig. 2.17), but also partly due to the exaggeration of the 200-500-hPa wave during the mapping in order to counteract the PV inversion's smoothing (see Section 2.3.3). Demirtas and Thorpe (1999) exaggerated their satellite water vapour imagery-guided PV adjustment in an almost completely successful attempt to circumvent smoothing induced by the data assimilation system. Because the ozone-influenced principal trough is so wide, its secondary upstream trough is less well defined than that of the analysis. Note, however, that the flanking ridges are of a comparable strength due to the overlaying of ERA-40 MPV ridges during the synthesizing process (see Section 2.3.1.5). It is important to note that, although the vertical mapping of each grid point in isolation could theoretically introduce imbalances in the mapped 3D PV field, Section 2.3.3's PV inversion is guaranteed to yield a set of balanced fields. As discussed in Section 2.1.5, 3D-Var and 4D-Var data assimilation schemes have both encountered difficulties in correctly distributing the total column ozone increment in the vertical (Dethof and Holm 2004 with respect to 3D-Var, Jang et 91 2.3: An illustrated description of the procedure al. 2003 with respect to 4D-Var). Adapting our level-varying mapping coefficient to these data assimilation schemes could benefit these schemes substantially. 2.3.3 Potential vorticity inversion 2.3.3.1 Davis and Emanuel (1991) methodology The ozone-influenced 3D PV field is inverted following the method described in Davis and Emanuel (1991), with two minor modifications described in Section 2.3.3.2. The process inverts PV^O), which is a form of PV derived from Ertel Potential Vorticity (EPV). As discussed in Section 2.1.2, EPV is conserved following adiabatic, frictionless motion in a baroclinic, compressible flow. For convenience, equation {2.1}, defining EPV, is reproduced as equation {2.20}: EPV = —(f + Vxv)*V0 {2.20} P where p is the density, f the planetary vorticity vector, v the velocity vector, and 0 potential temperature. The equation is fully three dimensional. The vorticities describe the inertial stability, and the gradient of potential temperature the static stability (Danielsen 1983). When deriving PV(T,0), Davis and Emanuel (1991) replace the full winds in equation {2.20} with nondivergent winds, which can be expressed in terms of a streamfunction following equation {2.21 } (Davis et al. 1999): x Vx¥=kxV ¥ {2.21} 92 2.3: An illustrated description of the procedure where *F is the stream function and k the unit vertical vector. Assuming hydrostacy, potential temperature can be expressed in terms of the geopotential using equation {2.22} (Davis and Emanuel 1991, Zhang et al. 2000): * = -3%r <2-22> where O is the geopotential and n the Exner function (Haltiner and Williams 1980). PV0F,3>), which can be derived from equations {2.20}-{2.22} by assuming hydrostacy once again and using the Exner function as the vertical coordinate, is calculated using equation {2.23} (Davis and Emanuel 1991): 32vp 2 PvCv, The Charney balance equation is used as the PV inversion's required balance condition (equation {2.24}; Charney 1955, Zhang et al. 2000, Lynch 2003). This balance condition relates the wind and geopotential fields, while preventing the occurrences of large-amplitude inertio-gravitational oscillations. It applies to flows where the Rossby number exceeds unity, but assumes a quasi-hydrostatic equilibrium. It is derived by taking the horizontal divergence of the horizontal equations of motion, while neglecting terms involving vertical motion. Nondivergence is assumed, and horizontal winds are expressed in terms of a streamfunction. 93 2.3: An illustrated description of the procedure 2 x fd2x¥] d2x¥d2*¥ v o = v.(yv F)-2 {2.24} dxdy dx2 dy' where f is the Coriolis parameter, and the divergence operator is two-dimensional. Geostrophy is obtained with constant f and negligible non-linear terms. For axisymmetric flow, gradient wind balance results (Morgan and Nielsen-Gammon 1998), making the Charney balance equation very accurate for highly-curved flows (Zhang et al. 2000). Equations {2.23} and {2.24} constitute a set of two equations for two unknowns: ¥ and O. The vertical derivatives of *F and O are specified on horizontal boundaries using equation {2.22} with analysis temperatures. Replacing The analysis value of O constitutes that variable's lateral boundary condition. Analysis winds provide the lateral boundary condition for *F. Before solving equations {2.23} and {2.24}, these equations are non-dimensionalized. The sum of the two non-dimensionalized equations is solved by successive over-relaxation for *¥. The difference of the two non-dimensionalized equations is then solved by successive over-relaxation for O. It is considered that a solution has been obtained when the maximum difference between successive solutions is less than 9 9 9 1 0.1 m s" and 0.1 m s" for O and *¥, respectively. Under-relaxation is applied each time either ¥ or O is solved, to force the solution of the set of equations. As long as the 3D PV field is positive everywhere, an "apparently unique" convergent solution is obtainable (Davis and Emanuel 1991). 94 2.3: An illustrated description of the procedure The streamfunction field is calculated from pressure-level horizontal winds using spectral transforms at a T106 resolution, which is the resolution of the native ERA-40 grid (see Section 2.2.2). Software to perform this calculation was provided by NCEP's Climate Prediction Center and is available at ftp://ftp.cpc.ncep.noaa.gov/wd51we/reanl_software. First guess and boundary condition fields are provided by ERA-40 reanalysis, GEM analysis or operational Eta analysis fields (see Section 2.2.2); multiple experiments are performed in this research (see Section 3.2) with each field source in turn providing both the inversion boundary conditions, including horizontal boundary condition fields at 700-hPa, and the low-level model- initializing fields up to and including at 700 hPa. Since the inversion guarantees output fields that are stable internally, and a single source provides 700-hPa fields and 700-hPa boundary conditions, stability between the upper- and lower-level sets of fields across 700 hPa is ensured. Although stability would also be guaranteed by inverting a combination of analysis fields from 1000-700 hPa and ozone-influenced fields from 600-50 hPa, it was considered undesirable to introduce PV inversion-induced smoothing unnecessarily at low levels. Unfortunately, GEM analyses provide no 600-hPa fields. In order to promote consistency between PV inversions, 600-hPa GEM fields are created: temperature and wind fields are calculated as the average of the 500- and 700-hPa fields with respect to the natural logarithm of pressure, while the height field is calculated hypsometrically (Bluestein 1992) using 600-hPa virtual temperatures. Similarly, operational Eta analyses provide fields at 75 and 50 but not at 70 or 30 hPa. Since, as mentioned in Section 2.3.1.1, the regional Eta fields are 95 2.3: An illustrated description of the procedure embedded in the global ERA-40 fields after interpolation to the latitude/longitude grid, and since the ERA-40 does not provide 75-hPa fields for this embedding, the Eta 75-hPa fields cannot be used either at 75 hPa or to create 70-hPa fields. Thus, when inverting PV with Eta-derived boundary conditions and first guess fields, ERA-40 70-hPa fields are used. ERA-40 30-hPa fields are also used in this situation, as the highest-level fields provided by the Eta are at 50 hPa. Since Eta fields are provided no higher than 50 hPa, making it impossible to calculate the 50-hPa boundary condition PV^O) field, and since combining ERA-40 PV and Eta height, temperature and wind fields at 50 hPa, while using ERA-40 fields at both 70 and 30 hPa might promote instability, ERA-40 fields are also used at 50 hPa when inverting PV using Eta boundary conditions. It is unlikely that this borrowing of ERA-40 first guess and boundary condition fields at these high levels will significantly affect this research's short-term forecasting results. Fig. 2.23 Cross sections of PV along the line indicated in panel c) of Fig. 2.17 are shown for 1800 UTC 24 January 2000 using: a) EPV calculated from the original ERA-40 fields, and b) EPV calculated from fields produced by inverting ERA-40 PVOF,®). Full PV fields are plotted every 1 PVU to 13 PVU and every 2 PVU from 13 PVU. Panel a) also shows the difference of the two ERA-40 EPV fields (inverted-original; shading intervals of 0.5 PVU with a solid (dashed) contour at + (-) 0.5 PVU). 96 2.3: An illustrated description of the procedure The PV inversion outputs model-initializing height, temperature and nondivergent wind fields on the original 10 vertical mapping levels from 600 to 50 hPa, as well as on the bounding levels of 700 and 30 hPa. Unfortunately, the output fields are somewhat smoothed, as demonstrated by Fig. 2.23's comparison of ERA-40 EPV as calculated from original and inverted fields. In this figure, the central trough, secondary upstream trough and both flanking ridges have all been smoothed by the inversion. Browning et al. (2000) low-level PV anomalies were also considerably smoothed by PV inversion. Although Davis and Emanuel (1991) found little difference between full winds and output nondivergent winds, the smoothing of Fig. 2.23 is likely a result of the nondivergence of the inverted winds: this research's finer horizontal grid resolution of 1.125° by 1.125° versus the 2.5° by 2.5° resolution of Davis and Emanuel (1991) is better able to resolve smaller-scale features, which are associated with greater divergence. The principal trough of Fig. 2.23 has weakened by 2 PVU at 250 hPa during the inversion, while the 2- and 3-PVU contours have each been raised by approximately 100 hPa. This is a significant lifting of the dynamic tropopause, which can be expected to have serious dynamical repercussions. 2.3.3.2 Modifications to the Davis and Emanuel (1991) methodology We modify the Davis and Emanuel (1991) PV inversion scheme described in Section 2.3.3.1 in two ways. Firstly, convergence is unobtainable with our calculation grid and input fields and the prescribed constant over-relaxation parameters for *F and 97 2.3: An illustrated description of the procedure relative fineness of our 1.125° by 1.125° horizontal resolution, as opposed to the 2.5° by 2.5° resolution of Davis and Emanuel (1991), and/or by the large number (3626) of grid points within our inversion domain. Table 2.2 Inversion subdomain boundaries Subdomain # West (°W) East (°W) South (°N) North (°N) 1 -149.625 -103.500 33.750 60.750 2 -117.000 -72.000 33.750 60.750 3 -85.500 -40.500 33.750 60.750 4 -149.625 -103.500 24.500 47.250 5 -117.000 -72.000 24.500 47.250 6 -85.500 -40.500 24.500 47.250 The second modification was introduced in response to the generation of a spurious dipole by the inversion, which raised western heights and lowered eastern heights. As the dipole was possibly a consequence of our large inversion domain, and the subsequent inability of the boundary conditions to guide the inversion sufficiently, the domain was divided into six subdomains. Since these subdomains overlap considerably (see Table 2.2), each subdomain's outer three rows of grid points, where the boundary conditions have the strongest influence on output field values, can be discarded, leaving a seven grid point sponge zone to ensure a smooth field transition between adjacent subdomains. Sponge zone grid point values are determined by equation {2.25}: 98 2.3: An illustrated description of the procedure fieldsponge,i = C\,ifield\,i + Cl,ifleld2,i > i=1>7 I2-25} where the coefficients Q and C2 are given in Table 2.3 for the situation where i=l and i=7 are closer to the centre of fields 1 and 2, respectively. Table 2.3 Sponge zone grid point coefficients Grid point # 1 2 3 4 5 6 7 Coefficient Ci 0.85 0.75 0.65 0.50 0.35 0.25 0.15 Coefficient C2 0.15 0.25 0.35 0.50 0.65 0.75 0.85 As a result of the smoothing produced by the PV inversion (demonstrated by Fig. 2.23), and the fact that EPV fields are somewhat smoother than PV^O) fields (compare Fig. 2.24.b, 2.24.d), and the fact that ozone-influenced EPV is calculated from inverted fields, which include non-divergent winds, ozone- influenced EPV (panel c) is a far smoother field than the ozone-influenced inversion input PV field based on PV(xF,0) (panel a). Furthermore, although the ozone-influenced EPV cross section still exhibits a deep, wide trough flanked by ridges, this trough is now slightly weaker than that oftheERA-40, despite the fact that the synthesized MPV trough is deeper than that of the ERA-40 (see Fig. 2.17). The greater width of the ozone-influenced MPV trough has been maintained. Although the ozone-influenced inverted EPV trough is slightly weaker than the ERA-40 EPV trough (see Fig. 2.24), the ozone-influenced 500-hPa eastern seaboard inverted height field trough is deeper than that of the ERA-40 (see 99 2.3: An illustrated description of the procedure Fig. 2.24 Cross sections of PV for 1800 UTC 24 January 2000 along the lines indicated in Fig. 2.17 are presented from the following sources: a) vertical mapping of ozone-influenced MPV using a level-varying mapping coefficient, b) ERA-40 PV^F,®), c) EPV calculated from ozone-influenced inverted fields, and d) ERA-40 EPV. The PV fields are plotted every 1 PVU to 13 PVU and every 2 PVU from 13 PVU, with shading from 2-3 PVU. Fig. 2.25), more accurately reflecting the relative strengths of the two MPV troughs (see Fig. 2.17). Also reflecting the MPV fields, the ozone-influenced 500-hPa western height field trough is weaker than that of the ERA-40. ERA-40 500-hPa winds tend to be 5-10 m s"1 stronger than inverted ozone-influenced winds. The weakness of the latter winds may reflect the fact that the former are full and the latter nondivergent winds, which weakness was surely enhanced by 100 2.3: An illustrated description of the procedure b) ERn-^O Fig. 2.25 Shown for 1800 UTC 24 January 2000 are a) inverted and b) ERA-40 500-hPa heights (12-dam contour interval, with a wider 540-dam contour) and winds ((half) barb equals (2.5) 5 m s"1, pennant equals 25 m s"1). the inversion's smoothing of the ozone-influenced flanking ridges, which were borrowed from the ERA-40 during the synthesis of Section 2.3.1.5. Although the leading edges of the 546- and 552-dam contours at 24/12 and 25/00, respectively, display insufficient curvature, while the cut-off low at 25/00 is too round and shallow, according to the height and wind observations, the 101 2.3: An illustrated description of the procedure c) Riuinsonde: 25/00 d) ERfl-^0: 25/00 Fig. 2.26 Shown at 500 hPa for the indicated dates, where "24/12" denotes 1200 UTC 24 January 2000, are a), c) analysed rawinsonde heights (6-dam contour interval, with a wider 540-dam contour) with observed heights (dam) and winds ((half) barb equals (2.5) 5 m s"1, pennant equals 25 m s"1), and b), d) ERA-40 heights and winds, plotted using the same conventions. ERA-40 500-hPa height field trough is fairly accurate at both 24/12 and 25/00 (see Fig. 2.26). Thus, while the depth of the ERA-40 trough at 24/18 (see Fig. 2.25) is likely approximately correct, the ozone-influenced trough is definitely too strong. This agrees with the assessment of Fig. 2.17's ERA-40 and ozone-influenced MPV troughs. However, the significant curvature in the leading edge of the ozone-influenced trough is likely more accurate than the lesser curvature of the ERA-40 trough. 102 2.3: An illustrated description of the procedure b) ERR-HO Fig. 2.27 Shown for 1800 UTC 24 January 2000 are a) inverted and b) ERA-40 200-hPa heights (18-dam contour interval, with a wider 1170-dam contour) and winds ((half) barb equals (2.5) 5 m s"1, pennant equals 25 m s"1). The stronger ERA-40 500-hPa winds at 24/18 (see Fig. 2.25) reflect the observed magnitudes of Fig. 2.26 better than the weaker ozone-influenced winds of Fig. 2.25. Note that the ERA-40 winds, which are frequently too weak at 24/12 (see Fig. 2.26), cannot be considered absolutely accurate. At 200 hPa, the 24/18 ozone-influenced eastern seaboard trough and winds (see Fig. 2.27) are also stronger and weaker, except at the base of the trough, 103 2.3: An illustrated description of the procedure c) Rawlnsonde: 25/00 d) ERfi-40: 25/00 Fig. 2.28 Shown at 200 hPa for the indicated dates, where "24/12" denotes 1200 UTC 24 January 2000, are a) c) analysed rawinsonde heights (12-dam contour interval, with a wider 1170-dam contour) with observed heights (dam) and winds ((half) barb equals (2.5) 5 m s"1, pennant equals 25 m s"1), and b), d) ERA-40 heights and winds, plotted using the same conventions. respectively, than those of the ERA-40. The strength of the ERA-40 trough at 24/12 and 25/00 is accurate according to the rawinsonde-derived trough (see Fig. 2.28), although the orientation is slightly faulty: the ERA-40 trough transitions from having a more positive tilt to having a more negative tilt than that exhibited by the rawinsonde-derived trough. Thus, the ERA-40 trough at 24/18 (Fig. 2.27) is likely of the correct strength, while the ozone-influenced trough is too strong. Furthermore, since the ERA-40 200-hPa winds resemble the observed winds 104 2.3: An illustrated description of the procedure closely at both 24/12 and 25/00 (see Fig. 2.28), the stronger ERA-40 winds at 24/18 can be considered more accurate than the weaker ozone-influenced winds of Fig. 2.27. Since 3D-Var and 4D-Var data assimilation do not use PV inversion, these assimilation schemes will not encounter the inversion-induced smoothing. This is a distinct advantage for these assimilation systems. 2.3.4 Summary The procedure presented in this thesis for converting a total column ozone field to model initializing fields can be summarized as follows: I. Convert the total column ozone field to an MPV field: 1. Spatially interpolate the total column ozone field and all analyses to a global 1.125° latitude by 1.125° longitude grid using linear interpolation, 2. Temporally interpolate the local noon total column ozone field to the uniform time chosen according to the region of interest (1800 UTC for eastern North America) using our novel method of pure advection by ERA- 40 dynamic tropopause winds divided by 2.0, 3. Calculate total column ozone/MPV regression parameters using, as determined by our in depth study, valid points from all latitudes together, MPV based on ERA-40 PV from 400 to 50 hPa, and a regression period of two weeks prior to the target date in the target date's year, 4. Perform the regression, smoothing the derived MPV field with a coefficient of 0.995, 105 2.3: An illustrated description of the procedure 5. Synthesize the regressed and ERA-40 MPV fields by erasing the analysis trough, inserting the regressed trough and overlaying the analysis ridge. Such a synthesizing procedure is novel; II. Convert the 2D MPV field to a 3D PV field: 1. Generate average PV profiles using an unprecedented 12 MPV categories, a minimum of only one space/time point, a 10° latitude by 10° longitude grid box centred on the given grid point, and a period of two weeks plus the target date itself, 2. Map the synthesized MPV field vertically onto each grid point's appropriate average PV profile using our innovative level-varying mapping coefficient with automatic mapping from 50-400 hPa and optional mapping at 500 and 600 hPa; III. Invert the 3D PV field to produce model-initializing fields using Davis and Emanuel (1991)'s method plus the following modifications: 1. Decrease the over-relaxation parameters for *F and O as convergence approaches. Such a decrease has not been discussed previously, 2. Divide the inversion domain into six subdomains to prevent the generation of height field dipoles. The use of inversion subdomains has not been documented. The described procedure is completely automated: once parameter values are set, a shell script calls a series of programs that together read in the input total column ozone and analysis fields and output numerical weather prediction model initializing fields. This degree of automation renders the procedure useful for operational forecast centres. 106 Chapter 3: Simulations using ozone-influenced initial conditions Chapter 3: The simulation of the 24-25 January 2000 East Coast Snowstorm using ozone-influenced initial conditions This chapter commences with an introduction to the 24-25 January 2000 east coast snowstorm (see Section 3.1). This introduction consists of a synoptic overview of the event and its forecasting as well as a review of previous research on the event, of which there is a considerable amount, owing to the non-existent operational forecast lead time for the event coupled with its significant societal impact. Section 3.2 presents simulations of the event by the Mesoscale Community Compressible model (MC2), where initializing fields are provided by (re)analyses alone and by a combination of (re)analyses and ozone-influenced fields. These simulations comprise the validation of Section 2.3's methodology that converts total column ozone data to model initializing fields. 107 Chapter 3: Simulations using ozone-influenced initial conditions This page is left intentionally blank. 3.1: A synoptic overview and previous research on the 24-25 January 2000 east coast snowstorm 3.1: A synoptic overview of and previous research on the 24-25 January 2000 east coast snowstorm 3.1.1 A synoptic overview of the snowstorm and its forecasting The 24-25 January 2000 east coast snowstorm generated a significant amount of precipitation along the U.S. eastern seaboard, as demonstrated with respect to the Carolinas and Virginia by Fig. 3.1. Even though some of the precipitation fell as rain, freezing rain and sleet, the storm total snowfall record was broken at the Raleigh-Durham, North Carolina airport with 20.3 in (~ 51.6 cm), and daily snowfall records were broken in the District of Columbia region at the Washington Reagan National, Baltimore/Washington International and Dulles International airports with 9.3, 10.3 and 10.3 in (=23.6, 26.0 and 26.0 cm), a) Analyzed precipitation: 2^/12-26/12 Fig. 3.1 Accumulated liquid water equivalent precipitation for 24-26 January 2000 (contours at 5 mm and every 10 mm from 10 mm, with the 20-mm contour dashed, the 40-mm contour heavy, and light (dark) shading from 50 (80) mm; adapted from Brennan and Lackmann 2005). 109 3.1: A synoptic overview and previous research on the 24-25 January 2000 east coast snowstorm respectively (NCDC 2000, where "NCDC" represents National Climatic Data Center). Locations in 15 states along the eastern seaboard received more than 10 in (~ 25.0 cm) of snow. Snowfall rates of 2 in (~ 5.0 cm) h"1 were reported by five states and 4 in (= 10.0 cm) h"1 by North Carolina. Snowdrifts of 4 feet (~ 1.2 m) were common, with Maryland reporting drifts up to 8 feet (= 2.4 m). These heavy snowfalls had a major societal impact: government and other offices, schools, stores, and bus, train and air transportation systems shut down, coastal flooding occurred, roofs and buildings collapsed, and power outages affected hundreds of thousands of utility customers. The total cost of the storm for the state of North Carolina alone was estimated at 800 million U.S. dollars. Two to three hundred trees were downed just in the city of Clinton, South Carolina. Many people died from car accidents, hypothermia and snow-shoveling-induced heart attacks. Unfortunately, the prediction of this storm was "one of the major failures of the operational forecast system" (Zupanski et al. 2002); all National Weather Service (NWS) operational models failed. Forecasts initialized as late as 1200 UTC 24 January were still predicting that the heavy precipitation would remain offshore. Figure 3.2's operational Eta (see Section 2.2.2) forecasts of precipitation accumulated in the Carolinas and Virginia from 1200 or 1800 UTC 24 to 1200 UTC 25 January, initialized at 1800 UTC 23 or 24 January, clearly demonstrate the shift inland of the entire precipitation region, and the development of a self-contained onshore maximum, with increasing initialization time. Unfortunately, the later forecast's values are still substantially lower, by 40 110 3.1: A synoptic overview and previous research on the 24-25 January 2000 east coast snowstorm mm, than those of Fig. 3.1 's analysis. Heavy onshore precipitation was finally predicted by the 0000 25 January forecasts, by which time significant precipitation had already fallen in the Carolinas (Zupanski et al. 2002). This almost non-existent lead time earned the event the media label of the "surprise snowstorm" (NCDC 2000). b) 2^/18 Eta: 2^/18-25/12 Fig. 3.2 Accumulated liquid water equivalent precipitation (contours at 5 mm and every 10 mm from 10 mm, with the 20-mm contour dashed, the 40-mm contour heavy, and light (dark) shading from 50 (80) mm) for a) 24/12-25/12 and b) 24/18-25/12 from the operational Eta runs initialized at 23/18 and 24/18, respectively. Ill 3.1: A synoptic overview and previous research on the 24-25 January 2000 east coast snowstorm The 24-25 January 2000 east coast snowstorm was triggered by the upper- level trough circled in Figs. 2.1-2.3, which is also apparent in the water vapour satellite imagery and 200-hPa height fields of Fig. 3.3. The trough moves south and east from its development site to the west of Hudson Bay at 0000 UTC on the 22nd (hereafter date/times will be abbreviated, such that 0000 UTC 22 January 2000 will be referred to as 22/00 in the interests of brevity) until, at 24/12, it is approaching the U.S. eastern seaboard. The southern portion of the trough subsequently starts to decay as a result of latent heating, and an upper-level cut off low is formed. 112 3.1: A synoptic overview and previous research on the 24-25 January 2000 east coast snowstorm al) GOES 8 WV 22/0015 i2) ERR-^0 22/0000 bl) GOES 8 WV 22/1215 i>2) ERR-^0 22/1200 cl) GOES 8 WV 23/0015 c2) ERFI-'HO 23/0000 dl) GOES 8 WV 23/1215 d2) ERfl-40 23/1200 Fig. 3.3 Shown for the indicated January 2000 day/UTC time are GOES 8 water vapour images (left columns) and ERA-40 200-hPa height fields ( right columns, 12-dam contour interval, with the 1176-dam contour heavy). The red circles track the water vapour feature that evolves into the upper-level trough associated with the 24-25 January 2000 east coast snowstorm. 113 •3.1: A synoptic overview and previous research on the 24-25 January 2000 east coast snowstorm el) GOES 8 WV 24/0015 e2) ERfl-^0 2^/0000 fl) GOES 8 WV 24/1215 f2) ERR-^IO 2^/1200 gl) GOES 8 WV 25/0015 92) ERR-^0 25/0000 hi) GOES 8 WV 25/1215 h2) ERR-^0 25/1200 Fig. 3.3 continued. 114 3.1: A synoptic overview and previous research on the 24-25 January 2000 east coast snowstorm Fig. 3.4 ERA-40 sea level pressure (solid, 4-hPa contour interval) and 1000-500- hPa thickness fields (dot-dash, 6-dam contour interval with a wide, solid line for the 540-dam contour). At the surface, the cyclone responsible for this event is apparent at 22/00 over the U.S. Great Plains (see Fig. 3.4). Being situated under a decaying 1000-500- hPa thickness ridge, the central pressure gradually increases from 1001 hPa at 22/00 to 1013 hPa at 23/18 as the cyclone meanders towards the Gulf of Mexico. 115 3.1: A synoptic overview and previous research on the 24-25 January 2000 east coast snowstorm o) 12 UTC 25 January 2000 p) 18 UTC 25 January 2000 Fig. 3.4 continued. From 23/18, under the influence of the approaching thickness trough, the central pressure begins to deepen again as the cyclone tracks eastwards across the Gulf of Mexico to Florida then northeastwards along the eastern seaboard. The central pressure plunges from 1003 hPa at 24/18 to 993 hPa at 25/00, reaching 979 hPa by 25/18, as the tip of the thickness trough curls around the cyclone. 116 3.1: A synoptic overview and previous research on the 24-25 January 2000 east coast snowstorm c) 00 UTC 25 January 2000 d) 0G UTC 25 January 2000 Fig. 3.5 ERA-40 sea level pressure (solid, 4-hPa contour interval), 850-hPa temperature (dash, 4-°C contour interval, 0-°C contour heavy) and 850-hPa mixing ratio fields (increasingly dark shading from 4-7 g kg-1). Low-level warm air advection occurring to the east and northeast of the surface cyclone (see Fig. 3.5) triggered heavy offshore precipitation during the event. Onshore, precipitation was generated by a combination of low-level warm air advection and cyclonic vorticity advection aloft in the presence of 850-hPa mixing ratios on the order of 4-7 g kg"1. Presented in Fig. 3.6 are Eta forecasts initialized at 23/18, which will hereafter be referred to as forecasts from the 23/18 Eta run. The 1800 UTC initialization time of this run permits a direct comparison between this run's 117 3.1: A synoptic overview and previous research on the 24-25 January 2000 east coast snowstorm forecasts and forecasts initialized by ozone-influenced fields; over North America, ozone-influenced initializing fields are available most easily near 1800 UTC each day (see Section 2.2.1). A comparison of Fig. 3.4's ERA-40 fields and Fig. 3.6's forecasts reveals that, although the Eta sea level pressure cyclone is initialized only slightly too far to the north, by 24/06 the cyclone is a considerable distance to the northeast of the ERA-40 cyclone, with the result that it is too far ahead of the thickness trough to profit from the forcing for ascent associated with that feature. This results in a central pressure deepening of merely 15 hPa by 25/18 by the Eta cyclone, versus the dramatic 34-hPa central pressure drop of the ERA-40 cyclone. Furthermore, the base of the Eta thickness trough is slightly too far to the west at 24/06, and even more so at 24/12. Its continued slight displacement to the west at 24/18 may also have prevented cyclone-deepening phase locking between the trough and surface cyclone. The initialized surface cyclone from the 24/18 Eta run (Fig. 3.7), in contrast, is only very slightly to the northeast of the ERA-40 cyclone at 24/18. Furthermore, the 24/18 Eta run's thickness trough at 24/18 also resembles that of the ERA-40 closely, with the result that the Eta's cyclone and trough are in phase. This combination produces a respectable cyclone central pressure of 983 hPa at 25/18. 118 3.1: A synoptic overview and previous research on the 24-25 January 2000 east coast snowstorm a) 18 UTC 23 January 2000: F00 \J^^^MpS^mt^ J /Y^/^A '-XT' .ta \\^\^^y^\ Y^fM^^^vM1 r /^^K^ij-i-< ' ^~^y/fs^?/MAr~\\/'' ^!^-//y^Hj -*C§1?! \t \ T£te^*"^7/X /^^"jTTVa; A \ t\y&>i3rf ir^\f^-%>') S^jHW—_1// ^/Sml"^l/^T^^^^^^f^ M mi--t -'. :f^m$^^M__;-3^p/-- - b) 00 UTC 2^ January 2000: FOG c) OG UTC 2^ January 2000: F12 Wt^^^^mU ^ft-» \ K. 7/T^M^tvlJiSrifl tr\ ><^ i /(_A%5)Jv^% S£S-^X />*£32z^ ^^//^S^^^J^H^ >^^l^^ v. ^igS y^.^.L ^ ///^WW^>?C ^^^S ^2- ^ f- 0 f'Mir* y~~ J y/^&w\ **^. ^fe/M:(^ % d) 12 UTC 2^ January 2000: F18 e) 18 UTC 2^ January 2000: F2^ XfK/c-2£^?^4' \ V1V/V:. >[ /' ¥ / 111 M^k ?AVV^ \^ qkJ\ t) 00 UTC 25 January 2000: F30 9) OG UTC 25 January 2000: F36 h) 12 UTC 25 January 2000: F^2 1) 18 UTC 25 January 2000: F^I8 Fig. 3.6 Eta operational forecasts initialized at 23/18 of sea level pressure (solid, 4-hPa contour interval) and 1000-500 hPa thickness (dot-dash, 6-dam contour interval with a wide, solid line for the 540-dam contour). 119 3.1: A synoptic overview and previous research on the 24-25 January 2000 east coast snowstorm d) 12 UTC 25 January 2000: F18 e) 18 UTC 25 January 2000: F2^ Fig. 3.7 Eta operational forecasts initialized at 24/18 of sea level pressure (solid, 4-hPa contour interval) and 1000-500 hPa thickness (dot-dash, 6-dam contour interval with a wide, solid line for the 540-dam contour). Whereas onshore low-level warm air advection was exhibited by the ERA-40 fields from 24/12 through 25/00 (Fig. 3.5), no such advection is forecast by the 23/18 Eta run (Fig. 3.8), although it is forecast from its initialization at 24/18 through 25/00 by the later Eta run (Fig. 3.9). Thus, while the earlier Eta run had no onshore forcing for ascent associated with either the thickness trough or low- level thermal advection, the later Eta run forecasts the presence of both types of forcing for ascent. This indicates the probable presence of positive feedback mechanisms in the 24/18 Eta run, which were absent in the earlier run, such that 120 3.1: A synoptic overview and previous research on the 24-25 January 2000 east coast snowstorm Fig. 3.8 Eta operational forecasts initialized at 23/18 of sea level pressure (solid, 4-hPa contour interval), 850-hPa temperature (dash, 4-°C contour interval, 0-°C contour heavy) and 850-hPa mixing ratio (increasingly dark shading from 4-7 g kg1). warm advection increases the thermal ridge, thereby shortening the thermal wavelength and increasing the associated forcing for ascent. Also, the advection of warm air destabilizes the atmosphere above, such that a given forcing for ascent produces stronger vertical motions. Mixing ratio values at 850 hPa in the later Eta run are comparable to the ERA-40 values. 121 3.1: A synoptic overview and previous research on the 24-25 January 2000 east coast snowstorm Fig. 3.9 Eta operational forecasts initialized at 24/18 of sea level pressure (solid, 4-hPa contour interval), 850-hPa temperature (dash, 4-°C contour interval, 0-°C contour heavy) and 850-hPa mixing ratio (increasingly dark shading from 4-7 g kg1). Fig. 3.10 Eta operational forecasts initialized at 23/18 of dynamic tropopause potential temperature (lightly smoothed; 4-K contour interval with a dot-dash (dashed) contour for 304 (316) K). Also shown is the Eta and ERA-40 dynamic tropopause potential temperature difference field (Eta - ERA-40; 5-K shading interval from 5 to 20 K, with positive (negative) values surrounded by a solid (dotted) contour). 122 3.1: A synoptic overview and previous research on the 24-25 January 2000 east coast snowstorm a) 18 UTC 23 January 2000: F00 1 1 1 1 \ ! X /WfjwV/> \/sir~sj/: xyy^^ w b) 00 UTC 24 January 2000: FOG c) 06 UTC 2H January 2000: F12 d) 12 UTC 2<\ January 2000: F18 e) 18 UTC 2H January 2000: F24 f) 00 UTC 25 January 2000: F30 g) 06 UTC 25 January 2000: F36 r/\ w. /i; / V /' 1 i c'r Jj h) 12 UTC 25 January 2000: F42 i) 18 UTC 25 January 2000: F48 Fig. 3.10 See caption on previous page. 123 3.1: A synoptic overview and previous research on the 24-25 January 2000 east coast snowstorm Fig. 3.11 Eta operational forecasts initialized at 24/18 of dynamic tropopause potential temperature (lightly smoothed; 4-K contour interval with a dot-dash (dashed) contour for 304 (316) K). Also shown is the Eta and ERA-40 dynamic tropopause potential temperature difference field (Eta - ERA-40; 5-K shading interval from 5 to 20 K, with positive (negative) values surrounded by a solid (dotted) contour). The dynamic tropopause potential temperature fields forecast by the 23/18 and 24/18 Eta runs are presented in Figs. 3.10 and 3.11, respectively. The shaded difference field of Fig. 3.10 first indicates at 24/12 that the troughs of the 23/18 Eta run and the ERA-40 are diverging: the Eta trough extends insufficiently into the Gulf of Mexico and exhibits too great a positive tilt. Between 24/12 and 24/18 this divergence increases radically with the failure of the 23/18 Eta run to 124 3.1: A synoptic overview and previous research on the 24-25 January 2000 east coast snowstorm reproduce the ERA-40's cut-off low. Major differences between the two troughs persist through the remainder of the event. These sudden major trough errors stem from both a series of small differences along the upstream edge of the initializing trough, which seem to propagate along the edge of the trough, reaching the base at 24/06, and also from overly warm regions within the upstream ridge that propagate eastwards, also reaching the base of the trough at 24/06. These warm ridge regions block the southward extension of the Eta trough, particularly at 24/12. Also evident in this figure is the comparative lack of ridge-building by the 23/18 Eta run over the Atlantic Ocean and in coastal regions during the event. The 24/18 Eta run's initializing dynamic tropopause potential temperature field of Fig. 3.11 exhibits a slightly weak cut-off low, which has virtually vanished twelve hours later. However, the strength of the Eta Atlantic Ocean ridge-building is now at least as vigorous as that of the ERA-40, although the Eta ridge-building over coastal regions still tends to be somewhat weak. Dynamic tropopause potential temperature fields from the ERA-40 and the 23/18 and 24/18 Eta runs featuring the southeast of the U.S. at 25/00 are presented in Fig. 3.12. Also plotted in each panel of this figure is a line indicating the location of Fig. 3.13's corresponding vertical cross section as well as markers indicating the locations of Fig. 3.14's vertical profiles. The position of the cross section line varies, since it is constructed so as to traverse both the surface cyclone and the base of the trough. The presence of a cut-off Low in the later Eta run, albeit an overly weak one, as well as the later run's more vigorous Atlantic Ocean ridging, compared to the earlier Eta run, is readily apparent. The trough of the 125 3.1: A synoptic overview and previous research on the 24-25 January 2000 east coast snowstorm Fig. 3.12 Dynamic tropopause potential temperatures (4-K contour interval, with the 316-K contour dashed and values less than 304 K shaded), and winds ((half) barb equals (2.5) 5 ms-1, pennant equals 25 m s"l) at 25/00 for a) the ERA-40, and for the Eta runs initialized at b) 23/18 and c) 24/18. The triangle (square) marks the location of CHS (GSO), while the straight lines indicate the locations of the cross sections of Fig. 3.13. 126 3.1: A synoptic overview and previous research on the 24-25 January 2000 east coast snowstorm earlier Eta run is not only too far north and too weak, but it also lacks the negative tilt that characterizes those of the ERA-40 and the later Eta run, resulting in more westerly winds over the Carolinas. Note the presence of ascent-producing diffluence in the ERA-40 and 24/18 Eta run, as well as the complete lack of diffluence in the 23/18 Eta run, over the Carolinas. This translates to weaker winds over the Carolinas in the earlier Eta run. Vertical cross sections from the ERA-40 and both Eta runs along the lines indicated in Fig. 3.12 are presented in Fig. 3.13. The 23/18 Eta run's trough resembles that of the ERA-40 the least, being narrow and shallow with the flattest 3-PVU contour. Nonetheless, the 24/18 Eta run's trough is still shallower and narrower than that of the ERA-40. Upstream of the trough, the earlier Eta run's secondary trough is the least pronounced and the farthest from the primary trough, while its upstream ridge, at the western edge of the section, is the weakest. The shape of the later Eta run's dynamic tropopause resembles that of the ERA-40 much more closely. Ascent downstream of the trough is far stronger in the ERA- 40 and 24/18 Eta run than in the earlier Eta run. This is due to a stronger upper- level trough and/or weaker static stability, represented by a less horizontally- stratified equivalent potential temperature field. Soundings at 25/00 for Greensboro, North Carolina (GSO) and Charleston, South Carolina (CHS) as well as vertical profiles from the ERA-40 and 23/18 and 24/18 Eta runs at these locations, which are indicated in Fig. 3.12, are presented in Fig. 3.14. Not surprisingly, the 23/18 Eta run's tropospheric temperatures are the least accurate, being too cold at low and mid levels at GSO and too warm at low levels and too cold at mid levels at CHS. While the ERA-40 dew point 127 3.1: A synoptic overview and previous research on the 24-25 January 2000 east coast snowstorm c) 2^/18 Eta: FOG Fig. 3.13 Vertical cross sections of PV (solid, 1-PVU contour interval, shaded from 2-3 PVU), equivalent potential temperature (dashed, 5-K contour interval), omega (grey solid (dashed) for positive (negative) values, 2xlO~3-hPa s~l contour interval, zero contour omitted). 128 3.1: A synoptic overview and previous research on the 24-25 January 2000 east coast snowstorm 0 30 GO a) GSO: Greensboro, NC ou 1 ' ' ^r ^ <*•"' ' * sr ' ' s \ ' ' ' '' is^*r \ '• f s 50- ^i_ Vii \ \ * * 7 sJ' \ \ " / Jw | \ \ '/ / 4r 70- \ • \ \ '' / X^ \ \ \ y'' / ^^ \\ \\ \\ ' ' ' / / ^^r ^ 100- \ \ \ yi' / ^,-T \ \ \/" / f^ff \ \ '\ i f/r \ \ ' ' \ / MM 150- \ V ' \/ ' >4^ \ ' \ x\ /w 200- \ ''' V'' .^X 250- y A ijp\ 300- -s^.v$r ^( \ *' ^ < H \ \ ^00- •*"~^" V\-s M \ \ V v \ s]\ \ \ 500- ^ - X\\ lY\ \ \ 700- *A §gg =. JOLS 1— 1 1 -30 0 30 GO b) CHS: Charleston, SC Fig. 3.14 Skew-T log-p plots of temperature (°C, solid), dew point temperature (°C, dashed) and horizontal winds ((half) barb equals (2.5) 5 m s"l, pennant equals 25 m s"1) at 0000 UTC 25 January 2000 as observed (black), from the ERA-40 (red), and from the operational Eta forecasts initialized at 23/18 (purple; 30-h forecast) and 24/18 (brown; 6-h forecast) at a) GSO and b) CHS. Also plotted are the 300-, 325- and 350-K moist adiabats. 129 3.1: A synoptic overview and previous research on the 24-25 January 2000 east coast snowstorm temperatures tend to be excellent, except for excessive mid-level moisture at CHS, and the 24/18 Eta run's moisture content is excellent upto450hPa, the 23/18 Eta run is extremely dry at both locations, which happens, most likely by pure luck, to translate to a very accurate upper-level moisture content at CHS. Active precipitation is strongly suggested at both locations by the existence of a tropospheric layer where temperatures and moist adiabats are aligned in the presence of high relative humidities. All profiles exhibit such a layer except those of the 23/18 Eta run. Given the lack of onshore precipitation generated by the 23/18 Eta run (see Fig. 3.2), it makes sense that this run's profiles do not suggest active precipitation. Although the ERA-40 and 24/18 Eta run's winds are overly weak at GSO, particularly those of the ERA-40, their winds are overall fairly accurate. The 23/18 Eta run's winds at GSO, on the other hand, are variations of westerlies from 700 to 250 hPa, when they should be from the south or south-southeast. This lack of onshore flow produces the run's cool temperatures and dewpoint temperatures from 700 to 400 hPa, and also its lack of onshore precipitation. At CHS, on the other hand, while the ERA-40 winds are accurate, the 24/18 Eta run's winds are too westerly from 600-250 hPa and the 23/18 Eta run's winds are far too westerly from 600-100 hPa, too weak from 400-200 hPa and too strong above 200 hPa. Given.the inaccuracies present in the discussed 23/18 Eta run's fields, and the greater accuracy of the 24/18 Eta run's fields, the improvement in the Eta precipitation forecasts with increasing initializing time, as seen in Fig. 3.2, is to be expected. 130 3.1: A synoptic overview and previous research on the 24-25 January 2000 east coast snowstorm The 24-25 January 2000 U.S. east coast snowstorm was chosen as the test case for this thesis' methodology since: 1) the widespread operational forecast bust indicates that this case is a challenge to forecast, and 2) accurate verifying fields are available, given that the upper-level trough did spend time over the data rich U.S. Thus, if the methodology proves successful, by analyzing a realistically deep upper-level trough and producing significant onshore precipitation, under these toughest of conditions, it should also be successful when forecasting other events, whether challenging or not, and whether the upstream region is data rich or data poor, which would render the methodology of interest to operational forecast centres. 3.1.2 Previous research Several articles on this unexpected storm have been published. The focus of the studies is primarily the first half of the event, or the period up to 1200 UTC 25 January 2000 (25/12); it was this initial part of the event that caught the forecasters by surprise. A review of the discussions pertaining to this portion of the storm is presented chronologically. Each article, unfortunately, presents a different precipitation analysis as the truth field. Many are based on a gridded NCEP product, which, in turn, is based on rain gauge data. Automated Surface Observation System (ASOS) gauges officially underestimate rainfall values by less than 4% and liquid equivalent snowfall values by 40-50% (NWS 2007). However, Colle et al. (1999) report that these underestimations can rise to 5-15% and over 60%, respectively, due to wind 131 3.1: A synoptic overview and previous research on the 24-25 January 2000 east coast snowstorm effects and evaporation. For this event, the Raleigh-Durham, North Carolina ASOS reported 20.1 mm of liquid-equivalent precipitation, while the real value was closer to 60.2 mm, representing an underestimation of 66.6% (Brennan and Lackmann 2005). Furthermore, the density of automated measurement sites is fairly low, further reducing the credibility of the gridded NCEP product. Fig. 3.15 Accumulated liquid water equivalent precipitation (contours at 5-mm and every 10 mm from 10 mm, with the 20-mm contour dashed, the 40-mm contour heavy, and light (dark) shading from 50 (80) mm) for a) 24/12-25/12 and b) 25/12-26/12 from the Unified Precipitation Dataset. 132 3.1: A synoptic overview and previous research on the 24-25 January 2000 east coast snowstorm The U.S. Unified Precipitation Dataset (UPD) analyses of Fig. 3.15, which include both automated and NWS cooperative observer network data, are based on a much greater density of measurements. However, in addition to the inclusion of the problematic gauge values, the generation of the analyses employs a radius of influence on the order of 200 km in order to accommodate western U.S. data sparsity (Wei Shi, personal communication).. With such a large radius, not only are local maxima damped, but, in a case where the precipitation region is narrow, as is the situation with this event, all values are likely diminished. The Brennan and Lackmann (2005; hereafter BL) precipitation analysis for 24-26 January 2000 (Fig. 3.1; adapted from their Fig. 1) is based purely on cooperative observer network liquid water equivalent precipitation observations from Virginia, North Carolina, South Carolina and Georgia. The 474 quality- controlled observations, translating to approximately 240 observations per day, are principally 7-am (1200 UTC) 24-h totals (Mike Brennan, personal communication). Daily totals are more accurate than the sum of 24 hourly values. The quality and number of the observations suggest that the BL analysis closely approximates the truth field, and will be used as such in this thesis. Since the UPD fields of Fig. 3.15 for 24/12-25/12 and 25/12-26/12 indicate that relatively little precipitation was produced in the Carolinas/Virginia area from 25/12-26/12, the BL analysis, which is valid from 24/12 to 26/12 can be considered a good approximation for 24/12 to 25/12. The BL analysis of Fig. 3.1 indicates that the 24-25 January 2000 east coast snowstorm produced, principally between 24/12 and 25/12, 40 mm over approximately half of the Carolinas, with two maxima of 80-90 mm along the 133 3.1: A synoptic overview and previous research on the 24-25 January 2000 east coast snowstorm border between the two Carolinas and a third similarly-valued maximum in South Carolina near the border with Georgia. In the earliest article published on this event, Langland et al. (2002) used the Navy Operational Global Atmospheric Prediction System (NOGAPS) to investigate dry-dynamics adjoint model sensitivities, in terms of initializing temperature, wind and pressure fields, with respect to the energy-weighted forecast error norm over the eastern U.S. and western North Atlantic Ocean. The sensitivities were calculated for forecasts ending at 25/12, or the mid point of the event. The NOGAPS forecasts were produced at a T79 (=150 km or 1.35°) horizontal resolution, with 18 vertical levels up to 10 hPa. Relatively small (within operational analysis uncertainty) but rapidly growing critical errors in the upstream initializing wind and temperature fields were identified in Langland et al. (2002) as the source of the 72-h forecast's cyclone position and central pressure errors. Maximum vertically integrated sensitivities for this forecast are located over western and central North America, with lesser values over the eastern Pacific and the region west of Hudson Bay (their Fig. 7). Langland et al. (2002) compared the 72-h forecast initialized by the operational analysis to the forecast initialized with adjoint model sensitivities- perturbed initial conditions; initializing moisture and surface temperature fields were common to both simulations. The 72-h forecast error norm was reduced by nearly 75% in the perturbed initial condition forecast, while this forecast's cyclone position and central pressure errors decreased from the unperturbed forecast's 1860 km and 7 hPa to 105 km and 6 hPa, respectively. Furthermore, 134 3.1: A synoptic overview and previous research on the 24-25 January 2000 east coast snowstorm the perturbed forecast was able to capture the short wave trough, while the control forecast was not. Buizza and Chessa (2002) discussed the forecasting of the January 2000 east coast storm by the ECMWF operational deterministic forecast and the 51-member ensemble prediction system. The resolutions of these two systems were T319 (= 60 km or 0.54°) with 60 vertical levels, and T159 (« 120 km or 1.08°) with 40 vertical levels, respectively. The Buizza and Chessa (2002) ensemble system forecasts initialized at 23/12 and 24/12 assigned a 30% probability of 20 mm of precipitation accumulating between 24/12 and 25/12 over coastal North Carolina and, much more realistically, over the eastern half of the Carolinas, respectively (their Fig. 12). Their deterministic forecasts initialized at 23/12 and 24/12 respectively predicted a small 20-mm region in North Carolina and a larger 20-mm region principally over North Carolina with a small 40-mm region in coastal South Carolina (their Fig. 9). Thus, while magnitudes are low in all forecasts, they increased with the later initializing time; the ensemble system's forecast outperformed the deterministic forecast. The first Buizza and Chessa (2002) deterministic forecast to predict the cyclone with any accuracy was also the 24-h forecast initialized at 24/12, which had cyclone position and intensity errors of 200 km and 2 hPa, respectively. Five ensemble prediction system members, or approximately 10% of the members, in the 48-h forecast initialized at 23/12 had comparable cyclone intensity and position errors. 135 3.1: A synoptic overview and previous research on the 24-25 January 2000 east coast snowstorm Buizza and Chessa (2002) concluded that the operational deterministic forecast was able to predict a major storm only 24 h prior to the validation time, while the ensemble prediction system provided a serious warning of a major event 48 h prior to the validation time. It is interesting to note that the ensemble mean 48-h forecast exhibited slowly-varying sea level pressure fields incapable of predicting a major event (their Figs. 5, 6). Further Buizza and Chessa (2002) sensitivity studies determined that errors in the forecasting of this event were highly sensitive to moist processes. Zupanski et al. (2002) investigated the impact of using a 3D-Var versus 4D- Var data assimilation system on the 24-h forecast (24/12-25/12) of accumulated precipitation. The 3D-Var system was the NCEP operational mesoscale 3D-Var system. The 4D-Var system assimilated the observations used operationally in the 3D-Var system, plus the NCEP Stage IV National Mosaic 4-km database of hourly accumulated precipitation values for the continental U.S. These values are based on rain gauge and radar data. The model used for this study was the regional Eta model with the 32-km, 45-layer resolution operational at the time of the event. The 3D-Var simulation's precipitation forecast is comparable to the operational forecast of Fig. 3.2, as it exhibits a small area of 40 mm over the North Carolina coast (their Fig. 4). The 4D-Var simulation's forecast is a great improvement over the 3D-Var forecast, as it produces a 60-mm area in South Carolina, versus three maxima of 80-90 mm in Fig. 3.1's BL analysis, with an extensive, though smaller than in Fig 3.1, 40-mm region in the Carolinas (their Fig. 4). 136 3.1: A synoptic overview and previous research on the 24-25 January 2000 east coast snowstorm The undeniable superiority of the Zupanski et al. (2002) 4D-Var precipitation forecast over their 3D-Var forecast indicates the magnitude of the assimilation system's impact on the prediction of this event. Since the two simulations have almost identical initializing and 24-h forecast sea level pressure fields, only a slight eastwards shift of the 850-hPa PV trough by the 4D-Var simulation, and virtually identical upper-level PV fields, the authors attribute the superiority of the 4D-Var precipitation forecast to increased initializing surface convergence and precipitable water content over the eastern half of Georgia. Zhang et al. (2002) investigated how model resolution and initial condition variations affect the forecast of the 24-25 January 2000 east coast storm. They initialized the fifth-generation Pennsylvania State University-National Center for Atmospheric Research nonhydrostatic Mesoscale Model (MM5) at 24/00, and verified the 24/12-25/12 accumulated precipitation forecasts. Initializing fields were generated by reanalyzing the operational Eta analysis with existing surface and upper-air observations, while lateral boundary conditions, which were updated every six hours, were provided by real-time operational Eta forecasts. The Zhang et al. (2002) model resolution experiments involved three two- way nested domains with horizontal resolutions of 30, 10 and 3.3 km. The 30-km forecast exhibits a 70-mm maximum in coastal South Carolina that is well located, according to the BL analysis of Fig. 3.1 but that is not self-contained (their Fig. 7). This forecast misses the remaining two BL analysis maxima. In general, forecast values are too low by at least 30 mm. Although values from the 3.3-km forecast reach 90 mm along the most easterly portion of North Carolina's coast (their Fig. 1), which is too high by 40 mm according to the BL analysis, 137 3.1: A synoptic overview and previous research on the 24-25 January 2000 east coast snowstorm owing to the close proximity of a heavy offshore precipitation region, precipitation values are also far too low on the whole in this simulation. However, this forecast was able to produce an inland 40-mm maximum across the border of the two Carolinas, which is too low by 40-50 mm according to the BL analysis. The authors attributed the 3.3-km simulation's improved positioning, including the existence of a self-contained onshore maximum, to increased ridging over the eastern portion of the Carolinas, which pushed the precipitation inland. The upper-level positive PV anomaly was also more inland in this simulation. In order to investigate the impact of initial condition variations on the accumulated precipitation forecast, Zhang et al. (2002) initialized the MM5 at a 30-km resolution with operational Eta analyses that had not been reanalyzed with surface and upper-level observations, and also with 2.5° x 2.5° horizontal resolution ECMWF fields. Omitting the observations' reanalysation resulted in a maximum initializing 300-hPa wind magnitude difference (with respect to the initializing winds from the analysis with reanalyzed observations) of over 12 ms"1 at Little Rock, Arkansas in the base of the upper-level trough (their Fig. 10), a 6-h forecast placing the surface cyclone slightly to the northwest of the reanalyzed simulation's cyclone (their Fig. 11), and a precipitation region with comparable onshore values, but shifted to the east and north of the reanalyzed 30-km forecast (their Fig. 12). Initializing the MM5 with the ECMWF fields resulted in greater initializing 300-hPa wind magnitude differences in general, with a Little Rock difference of over 16 m s"1 (their Fig. 10), a 6-h forecast placing the surface cyclone to the south-southeast of the reanalyzed simulation's cyclone (their Fig. 138 3.1: A synoptic overview and previous research on the 24-25 January 2000 east coast snowstorm 11), and virtually no onshore precipitation (their Fig. 12). Thus, variations in the initializing fields affected the precipitation forecast more than the surface cyclone forecast. Further experimentation by Zhang et al. (2002) involved removing individual soundings when reanalyzing the Eta analysis during the generation of the initial conditions. These relatively minor adjustments to the initializing fields were found to produce large differences in the small-scale structure of the precipitation forecast, although sea level pressure forecasts, once again, remained virtually unchanged. Jang et al. (2003) assessed how assimilating various types of data affected the forecast of the 24-25 January 2000 U.S. east coast storm. Simulations were initialized at 24/12 and performed by the MM5 at a 30-km 27-layer resolution. Accumulated precipitation forecasts for 24/12-25/12 were verified. Initializing fields were provided by NCEP analyses either as is or with additional assimilated radiosonde and/or TOMS non-gridded level-2 total column ozone data. The 4D- Var assimilation of radiosonde data involved interpolating model winds and temperatures to radiosonde locations, while the 4D-Var assimilation of total column ozone involved transforming model MPV to total column ozone, as discussed in Section 2.1.5. Jang et al. (2003) found that assimilated total column ozone data dominated upper-level initializing fields, while radiosonde data dominated at lower levels. This may be due in part to problems with the vertical distribution of the total column ozone increment, as discussed in Section 2.1.5. While increasing 360-K PV at the base of the short wave trough by 2.5 PVU through the assimilation of 139 3.1: A synoptic overview and previous research on the 24-25 January 2000 east coast snowstorm ozone data (their Fig. 7) may be considered beneficial, increasing PV off the North Carolina/Virginia coast by the same amount is most likely a degradation of the field, despite the presence of a total column ozone trough in this area (Fig. 2.1), given that ERA-40 dynamic tropopause potential temperatures show ridging in the vicinity at this time (Fig. 2.2) and that Zhang et al. (2002) noted that the precipitation was driven onshore by strong ridging in this area due to diabatic heating. Although the overall values in the Jang et al. (2003) "as is" NCEP control precipitation forecast are low by 20 mm, according to the BL analysis of Fig. 3.1, the forecast does exhibit two maxima, of 50 and 70 mm, which are onshore, but only barely (their Fig. 16.b). The main problem with this forecast is that the precipitation region has not penetrated sufficiently inland. Assimilating radiosonde data shifts the precipitation region too far to the north (their Fig. 16.c), resulting in an unwanted 60-mm maximum in coastal North Carolina. In general, precipitation values in this forecast are comparable to those of the control simulation. Unfortunately, assimilating both radiosonde and total column ozone data shifts the coastal 60-mm maximum even farther north (their Fig. 16.d). However, a second, self-contained, 40-mm maximum has appeared on the border between the two Carolinas. Furthermore, the entire precipitation field has been pushed significantly inland. Thus, although values remain too low overall, assimilating both radiosonde and total column ozone produced the most accurate forecast of the three experiments. Although the Jang et al. (2003) assimilation of total column ozone data alone had almost no effect on the development of the surface cyclone, assimilating both 140 3.1: A synoptic overview and previous research on the 24-25 January 2000 east coast snowstorm ozone and radiosonde data, versus either assimilating the latter alone or no data assimilation, deepens the cyclone more rapidly, reduces track errors and improves the cyclone's shape. Kleist and Morgan (2005), following in the footsteps of Langland et al. (2002), adjusted model initializing fields with perturbations based on dry- dynamics adjoint-derived sensitivities in order to improve the forecast of the 24- 25 January 2000 U.S. east coast snowstorm. MM5 36- and 48-h model simulations ending at 25/12 were performed at a 60-km, 16-level resolution, with a lid at 100 hPa. Initializing and boundary condition fields were provided by the 1° x 1° (1° latitude « 111 km) NCEP final analysis. The unperturbed Kleist and Morgan (2005) 36- and 48-h forecasts place the overly weak surface cyclone, characterized by central pressure errors of 6 and 11 hPa, respectively, too far east, with positional errors of 100 and 530 km, respectively (their Figs. 3, 5, 6). Ascent at 700 hPa in these unperturbed forecasts is primarily offshore and tilts insufficiently with height. The unperturbed 48-h forecast of 24-h accumulated precipitation ending at 25/12 exhibits a self- contained onshore maximum of 20 mm in South Carolina, and values up to 70 mm in coastal North Carolina due to the close proximity of an offshore maximum (their Fig. 19). This forecast does not resemble the BL analysis of Fig. 3.1. The combined sensitivities of Kleist and Morgan's (2005) four response functions to the 36-h forecast's initializing 700-hPa temperatures indicate the need for additional ridging downstream of the mid-level thermal trough, along with a deepening of the trough itself (their Fig. 10). In the vertical plane, 141 3.1: A synoptic overview and previous research on the 24-25 January 2000 east coast snowstorm maximum sensitivities occur from 850 to 500 hPa and tilt upstream with height (their Fig. 11). With respect to initializing 500-hPa relative vorticities, Kleist and Morgan (2005) calculations indicate, not unexpectedly, that lower tropospheric circulation is sensitive to the 500-hPa trough throughout the 36-h forecast; initially both the trough and, to a lesser extent, the small-scale ridge immediately upstream of the trough, need to be strengthened; subsequently, the trough must be destroyed through diabatic processes (their Fig. 12). The authors noted that diffluence associated with the height trough during the development of the cutoff low is a primary cause of the onshore precipitation-producing ascent. The importance of the upstream 500-hPa trough is reinforced by the response functions' sensitivities to the 48-h forecast's initializing 500-hPa relative vorticities (their Fig. 13). Kleist and Morgan (2005) initializing energy-weighted forecast error sensitivities-derived perturbations for the 48-h forecast are originally small- scaled, small-valued (within the limits of analysis uncertainty), mid-tropospheric, and characterized by an upshear tilt (their Fig. 15). The perturbations grow significantly with time while shifting to the upper and lower troposphere and losing their tilt (their Fig. 16). After 12 h, the largest perturbations are in the upper troposphere. Despite the fact that these perturbations lead to a mere 46% reduction in the 48-h forecast error over the eastern portion of the U.S. and adjacent waters, the surface cyclone, frontogenesis and vertical motion field forecasts all improve considerably (their Figs. 3, 6, 17) . Although the 24-h accumulated precipitation forecast ending at 25/12 (their Fig. 19) does not greatly resemble the BL analysis of Fig. 3.1, the overall values of this perturbed forecast 142 3.1: A synoptic overview and previous research on the 24-25 January 2000 east coast snowstorm have increased substantially over those of the unperturbed forecast; there is now an extensive region in the Carolinas and Virginia receiving over 40 mm of precipitation and a self-contained onshore 80-mm maximum in North Carolina. Brennan and Lackmann (2005) described the importance of a low-level positive PV anomaly over Georgia during the 24-25 January 2000 U.S. east coast snowstorm; the circulation associated with this anomaly, which was diabatically produced during precipitation over Alabama, Georgia and South Carolina from 24/06-24/12, helped to transport the event's heavy precipitation inland. The study performed experiments with the MM5, using a 36-km, 37-level resolution. Simulations were initialized at 24/09, with initializing fields and boundary conditions, updated every three hours, provided by analyses from the 40-km, 40- level resolution Rapid Update Cycle (RUC; Benjamin et al. 2004) model. The Brennan and Lackmann (2005) piecewise PV inversion of the MM5 low- level positive PV anomaly, that by 25/00 is located over the coasts of Georgia and South Carolina, reveals that the balanced circulation associated with this anomaly is the principal agent of low- and mid-tropospheric onshore moisture flux during the east coast event (their Figs. 17, 18) and a significant contributor to the ascent- producing convergence in the Carolinas (their Fig. 19). Thus, this circulation is a crucial component of the mechanism responsible for generating the event's heavy onshore precipitation. This PV anomaly also deepens the surface cyclone and pulls it westwards. The authors asserted that the operational NWP models' difficulties in predicting the precursor precipitation and its associated PV anomaly, with lead times as short as six hours, contributed significantly to their failure to predict the inland penetration of the east coast event's precipitation. 143 3.1: A synoptic overview and previous research on the 24-25 January 2000 east coast snowstorm The Brennan and Lackman (2005) 39-h accumulated precipitation forecast ending at 26/00 contains a well-placed 90-mm maximum across the border of the Carolinas near the coast (their Fig. 13). Furthermore, the observed tongue of higher values extending across South Carolina towards Georgia is also forecast. Unfortunately, the forecasted tongue's 40-mm values are too low by 30 mm. The authors noted that MM5 12- and 4-km horizontal resolution simulations showed similar precipitation forecasts for both the precursor event and subsequent east coast event, indicating that horizontal resolution is not an important parameter in the forecasting of this major event, if the simulation includes the formation of the precursor precipitation that is responsible for generating the low-level PV anomaly. The consensus of this group of studies is that the forecasting of this event is extremely sensitive to the initial conditions, whether associated with height, wind and/or temperature fields (Langland et al. 2002, Zhang et al. 2002, Kleist and Morgan 2005), precipitable water content and convergence fields (Zupanski et al. 2002), or a combination of the above (Brennan and Lackmann 2005). While Zhang et al. (2002) found sensitivity to model horizontal resolution, Brennan and Lackmann (2005) did not. The 24-25 January 2000 east coast snowstorm was selected as the object of the next section's simulations as a challenging test for the ozone-influenced initializing fields; they must produce an accurate precipitation forecast in association with a case that is exceedingly sensitive to initial condition errors. Furthermore, because this event occurs over the data rich continental U.S. where the (re)analyses are expected to be at their most accurate, it will be extremely 144 3.1: A synoptic overview and previous research on the 24-25 January 2000 east coast snowstorm difficult for the ozone-influenced fields to improve on the traditionally-initialized forecasts. Thus, if the ozone-influenced fields are able to perform comparatively well under these challenging conditions, they can be expected to perform reliably in data sparse regions, where traditionally-initialized models are at their least reliable. 145 3.1: A synoptic overview and previous research on the 24-25 January 2000 east coast snowstorm This page is left intentionally blank. 3.2: Simulations of the 24-25 January 2000 east coast snowstorm 3.2: Simulations of the 24-25 January 2000 East Coast Snowstorm by the Mesoscale Compressible Community Model (MC2) The 24-25 January 2000 east coast snowstorm was selected as the test case partly because forecasts of this event are exceedingly sensitive to initial condition errors (see Section 3.1.2), so that simulating this event truly challenges the ozone- influenced initializing fields, and partly because the event is located over the data rich U.S., so that the (re)analyses' fields should be at their most accurate. A comparison of the ozone- and traditionally-initialized forecasts will then serve to characterize the behaviour, including the strengths and weaknesses, of ozone- initialized forecasts. Once this behaviour is understood, ozone-influenced initializing fields can be used in data sparse regions, where (re)analyses are less accurate (see Section 1.1.2) and ozone-influenced initial conditions can make their greatest contribution. Note that since this test case is located over a data rich region, the only expectation from the ozone-influenced initial conditions is that they produce a forecast on the same order of accuracy as the (re)analyses. 3.2.1 The numerical model and experimental setup 3.2.1.1 The Mesoscale Compressible Community Model (MC2) The Mesoscale Compressible Community model (MC2; Benoit et al. 1997) is a Canadian atmospheric prediction research model. It was developed by The Atmospheric Environment Service, a division of Environment Canada (Jasper and 147 3.2: Simulations of the 24-25 January 2000 east coast snowstorm Kaufmann 2003). The MC2 is a limited area, fully compressible, nonhydrostatic model. It uses a semi-implicit, semi-Lagrangian scheme. The implicit methods reconcile the higher accuracy of the fully compressible Navier-Stokes model equations with the long time steps appropriate for mesoscale model integrations. Semi-Lagrangian schemes reduce noise levels, which both permits longer time steps and affords a greater accuracy in coarser resolution simulations. The model's Gal-Chen height coordinate is similar to a terrain-following sigma surface at low levels, but by the model's top this coordinate produces horizontal surfaces. Physical processes are parameterized using the fully united Recherche en Prevision Numerique (RPN) physics package (Mailhot et al. 1998). For these simulations, version 4.9.8 of the MC2 dynamics and version 4.1 of the physics package were used. 3.2.1.2 Experimental setup Our objective is to: 1) evaluate the ability of ozone-influenced upper-level fields to produce an accurate precipitation forecast, 2) characterize the strengths and weaknesses of the ozone-influenced initializing fields, 3) determine the relative importance of low- and upper-level fields in the production of this event's onshore precipitation, and 4) consider why the operational Eta forecasts initialized up to and including 24/12, or the start of the event, failed. To this end, six modeling experiments are performed (see Table 3.1), where each experiment uses a different set of initializing fields. The six experiments consist of three pairs, with each pair defined by the source of the low-level fields. The upper-level fields of each pair are provided either by the source of that pair's low-level fields 148 3.2: Simulations of the 24-25 January 2000 east coast snowstorm or by ozone-influenced fields. A comparison of the three forecasts initialized by ozone-influenced upper-level fields both to each other, so that the effect of the lower-level fields is considered, and to their respective pairs, so that the effect of the upper-level fields is considered, will serve to address the objectives listed above. In experiments involving upper-level ozone-influenced initializing fields, stability across the 700-hPa boundary level is ensured by having the experiment's source of low-level fields also provide the PV inversion boundary conditions, including those at 700 hPa (see Section 2.3.3.1). An experiment's source of low- level fields also provides moisture fields at all levels. The simulations were conducted on the RPN IBM supercomputer azur, which has an AIX operating system. Table 3.1 Numerical experiments Experiment name 600-30-hPa fields 1000-700-hPa fields ERA ERA ERA Ozone-influenced Ozone/ERA ERA (inverted) Eta Eta Eta Ozone-influenced Ozone/Eta Eta (inverted) GEM GEM GEM Ozone-influenced Ozone/GEM GEM (inverted) To permit a direct comparison of their forecasts, lateral boundary conditions for all experiments are provided by the ERA-40 reanalysis, and model settings are constant. The principal settings are listed in Table 3.2. Initial experimentation 149 3.2: Simulations of the 24-25 January 2000 east coast snowstorm determined that the simulation of this event was virtually insensitive to the precipitation schemes used. This is not surprising, given that "simulations of deep precipitating storm systems are 'forgiving' of subtle sensitivities within a Table 3.2 Principal MC2 settings Parameter Setting Horizontal resolution (km) 32 Number of grid points (x,y) (290,148) Number of vertical levels 35 Height of top level (km) 30 Convective precipitation scheme Kain and Fritsch Stratiform precipitation scheme Kong and Yau Time step (minutes) 2 Radiation calculation interval (minutes) 14 Order of explicit horizontal diffusion 6 microphysics scheme since there is abundant lift and abundant precipitation" (Thompson et al. 2004). The precipitation schemes are described by Kain and Fritsch (1990) and Kong and Yau (1997) and, as used in the MC2, by Mailhot et al. (1998). The modeling domain encompasses the region shown in most of Section 2.3's plots (see, e.g., Fig. 2.8). It is sufficiently large, with extensive upstream areas to the west and north, that the initial conditions can be expected to capture all features of importance to the modeling of this event. Since this research is concerned principally with whether precipitation is forecast onshore or not, and if so, whether the amounts forecast are both significant and accurately located in general terms, the 32-km resolution should be sufficiently fine. According to Mass et al. (2002), little is gained in numerical weather prediction over the eastern 150 3.2: Simulations of the 24-25 January 2000 east coast snowstorm half of the U.S. beyond a 20-40-km resolution, owing to the relatively quiet topography. Moreover, although Zhang et al. (2002) found sensitivity to model horizontal resolution in the modeling of the 24-25 January 2000 east coast snowstorm, Brennan and Lackmann (2005) did not (see Section 3.1.2). The 32- km horizontal resolution of the current simulations is similar or identical to resolutions used by Zupanski et al. (2002), Zhang et al. (2002), Jang et al. (2003) and Brennan and Lackmann (2005) (see Section 3.1.2), which permits a direct comparison of simulation results. The simulations end at 1200 UTC 25 January 2000, after which time little precipitation fell in the Carolinas (see Section 3.1.2). The experiments are initialized at 1800 UTC on both the 23rd and 24th: the hour is determined by the fact that total column ozone is measured at approximately 1800 UTC over North America (see Section 2.2.1); the later day evaluates the ability of the ozone- influenced fields to initialize a successful forecast, while the earlier day explores the length of lead time available. Unfortunately, since the precipitation started near 1200 UTC on the 24th, the simulations initialized on the 24th cannot hope to produce accurate storm total precipitation fields, particularly in South Carolina where the event started. Furthermore, in these simulations the model is permitted no spinup time whatsoever. The accuracy of the precipitation forecasts will be evaluated with the help of the threat score (Murphy 1996) and bias (Colle et al. 1999), which are defined by equations {3.1} and {3.2}, respectively. 151 3.2: Simulations of the 24-25 January 2000 east coast snowstorm TS = {3.1} F+Q-C t ' Bias^F/o <3-2} where, for a given threshold, C is the number of correctly forecast points, F the number of forecast points, and O the number of observed points. The threat score measures how well the location of precipitation at or above a given threshold is forecast. It ranges in value from a perfect unity to zero. The average day-1 threat score earned by the NOAA Hydrometeorological Prediction Center in 2000 for 24-h forecasts of 1.00 in (25.4 mm) or more of precipitation was approximately 0.24 (see Fig. 1.2). The bias indicates how well the model predicts the frequency of the event for a given threshold. Bias values range from zero to infinity, with an overly wet (dry) forecast being characterized by a bias that is greater (less) than unity. The typical 12-36-h forecast bias for manual NWS QPFs is 1.25 for the 1-in (25.4- mm) threshold (Olson et al. 1995). Note that a higher bias makes it easier to earn a higher threat score: as the number of points forecast increases, the number of points correctly forecast most likely increases also. Note also that if no points are incorrectly forecast - forecast but not observed - the threat score and bias are mathematically equivalent. 152 3.2: Simulations of the 24-25 January 2000 east coast snowstorm 3.2.2 Modeling results 3.2.2.1 Simulations initialized at 1800 UTC 24 January 2000 For the reader's convenience, Fig. 3.1, the Brennan and Lackmann (2005; BL) analysis of precipitation accumulated from 24/12 to 26/12 is reproduced as Fig. 3.16. Fig. 3.17 presents our six experiments' forecasts of precipitation accumulated from 24/18 to 25/12. Threat scores and biases earned by these forecasts are presented in Fig. 3.18. Fig. 3.16 Accumulated liquid water equivalent precipitation for 24-26 January 2000 (contours at 5 mm and every 10 mm from 10 mm, with the 20-mm contour dashed, the 40-mm contour heavy, and light (dark) shading from 50 (80) mm; adapted from Brennan and Lackmann 2005). 153 3.2: Simulations of the 24-25 January 2000 east coast snowstorm : / ''•• / \ f J f 1 jCj^^^ | I 1 \ \ 4 a ) ERR h) Ozone/ERR c ) Et a d) Ozo n e/Et a e ) GEM f) Ozo n e/GEM Fig. 3.17 Precipitation (contours at 5 mm and every 10 mm from 10 mm, with the 20-mm contour dashed, the 40-mm contour heavy, and light (dark) shading from 50 (80) mm) accumulated during the indicated experiments from the start of the simulation at 24/18 to 25/12 is shown. 154 3.2: Simulations of the 24-25 January 2000 east coast snowstorm The Eta forecast is the worst of the (re)analysis-initialized forecasts: it is characterized by the lowest onshore precipitation values, which never exceed 50 mm, and, therefore, earns the lowest threat scores and biases of the three (re)analyses for thresholds above 10 mm (see Fig. 3.18). Moreover, the onshore precipitation contours are meridional, whereas the lower-valued contours of the BL analysis are parallel to the coastline. The GEM onshore forecast is the best of the (re)analysis-initialized forecasts: it exhibits the highest values, well-located 70-mm maximum values near the border of the Carolinas, good inland penetration, and the correct contour orientation for contours under 40 mm. Not surprisingly, this excellent forecast earns the highest threat scores and biases of the three (re)analyses at and above 20 mm. The ozone/ERA onshore precipitation forecast is less accurate than that of ERA, according to both subjective and objective evaluations, owing to the fact that the precipitation region penetrates inland less. Objectively, the ozone/Eta forecast is worse than that of Eta. However, although the ozone/Eta forecast exhibits lower precipitation values than that of Eta in North Carolina, which is unfortunate and which is responsible for the lower objective scores, it also exhibits higher values in South Carolina. This shift of the precipitation in the ozone/Eta forecast towards South Carolina results in a field shape that better matches that of the BL analysis. It, therefore, seems warranted to override the objective evaluation and consider the ozone/Eta forecast superior to that of Eta. 155 3.2: Simulations of the 24-25 January 2000 east coast snowstorm _ a) Threat scores V) ' ERA c Oz/ERA "3 0.75 ot'' Eta £ l£\"'""" " Oz/Eta E *^Nv """"' GEM B 0.5 ^sj^^v ''''"''// Oz/GEM O "'"Vs w 0.25 ''''>„ ^^tii,, £ 0 : «c 0 10 20 30 40 50 60 Threshold (mm) b) Bias 1 Fig. 3.18 Calculated for the indicated experiments and thresholds are the: a) threat scores and b) bias for the precipitation accumulated from the start of the simulation at 24/18 to 25/12. The Brennan and Lackmann (2005) analysis constitutes the truth field. The best forecast overall is produced by ozone/GEM: this forecast shows the deepest inland penetration of the 40-mm contour, and is the only forecast to exhibit a self-contained onshore maximum, of 60 mm, which is located almost perfectly across the border of the Carolinas. Furthermore, this forecast earns the top threat scores and biases at almost all thresholds. Unfortunately, the precipitation values of even this forecast are underforecast by approximately 20 156 3.2: Simulations of the 24-25 January 2000 east coast snowstorm mm in North Carolina and even more in South Carolina, hence the dry biases. The late initializing time (see Section 3.2.1.2) may be partly to blame for the latter problem. Table 3.3 ranks the simulations' onshore accumulated precipitation forecasts. The subjective evaluation of the forecasts overrules the objective rankings, determined by threat scores earned, only by placing the ozone/Eta forecast above that of Eta, for the reasons cited above. Table 3.3 Onshore accumulated precipitation forecast rankings for simulations initialized at 24/18 Simulation Ranking ozone/GEM 1 GEM 2 ERA 3 ozone/ERA 4 ozone/Eta 5 Eta 6 Compared to published 24-h forecasts of onshore accumulated precipitation ending at 25/12 (see Section 3.1.2), the ozone/GEM, GEM and ERA forecasts far surpass the Buizza and Chessa (2002) deterministic forecast and surpass or are comparable to their ensemble 30% probability of 20 mm of precipitation forecast. Zupanski et al.'s (2002) 3D-Var forecast is surpassed by those of the ozone/GEM, GEM, ERA and ozone/ERA simulations, while their 4D-Var forecast is surpassed only by those of the two GEM experiments. The Jang et al. (2003) simulation that assimilated both radiosonde and total column ozone data produced their most inland-penetrating precipitation region. This degree of penetration is surpassed by the.ozone/GEM forecast (see Fig. 3.19). Furthermore, the ozone/GEM forecast does not exhibit the unwanted North Carolina coastal maximum seen in the Jang 157 3.2: Simulations of the 24-25 January 2000 east coast snowstorm a) Analysis b) Ozone/GEM c) Jang et al. (2003) Fig. 3.19 An analysis of liquid water equivalent precipitation accumulated on 24- 26 January 2000 (contours at 5-mm and every 10 mm from 10 mm, with the 20- mm contour dashed, the 40-mm contour heavy, and light (dark) shading from 50 (80) mm) adapted from Brennan and Lackmann (2005) is presented in panel a). The same plotting convention is used in panel b for precipitation accumulated during the ozone/GEM experiment from the start of the simulation at 24/18 to 25/12. Panel c) presents the ozone-influenced 4D-Var assimilation forecast of precipitation (contours every 10 mm) accumulated from the initializing time of 24/12 to 25/12 from Jang et al. (2003; their Fig. 16.d). et al. (2003) forecast. Thus, our novel procedure produces an onshore accumulated precipitation forecast that is superior to the ozone-influenced 4D-Var assimilation forecasting of the case, despite the technological superiority of 4D- Var assimilation. Furthermore, the ozone/GEM onshore accumulated precipitation forecast is unambiguously superior to that of GEM, while the Jang et 158 3.2: Simulations of the 24-25 January 2000 east coast snowstorm al. (2003) ozone-influenced forecast is only partially better than their control forecast (see Fig. 3.20). Unfortunately, none of Fig. 3.17's precipitation fields display the heavy South Carolina precipitation region produced by the Jang et al. (2003) control forecast. The Zhang et al. (2002) 30- and 3.3-km forecasts, which are initialized at 24/00, are inferior to the ozone/GEM and GEM forecasts and comparable to that of ERA. However, the Brennan and Lackmann (2005) forecast of precipitation accumulated from 24/09 to 26/00 surpasses all forecasts of Fig. 3.17: this forecast contains an onshore, correctly-valued and located 90- mm maximum on the border of the Carolinas, while the collocated ozone/GEM maximum reaches only 60 mm. Note, however, that much of this particular discrepancy may be a result of the later ending time of the Brennan and Lackmann (2005) accumulation period, given that over 20 mm of precipitation accumulated in the region of the maximum from 25/12-26/12 (see Fig. 3.15). More importantly, the Brennan and Lackmann (2005) field exhibits a 40-mm tongue extending from their maximum across South Carolina towards Georgia. Although this represents a 30-mm underprediction, it is missing entirely from the ozone/GEM forecast. Fig. 3.20 An analysis of liquid water equivalent precipitation accumulated on 24- 26 January 2000 (contours at 5-mm and every 10 mm from 10 mm, with the 20- mm contour dashed, the 40-mm contour heavy, and light (dark) shading from 50 (80) mm) adapted from Brennan and Lackmann (2005) is presented in panel a). The same plotting convention is used for precipitation accumulated during the GEM (panel b)) and ozone/GEM (panel c)) experiments from the start of the simulations at 24/18 to 25/12. Panels d) and e) present, respectively, the control and ozone-influenced 4D-Var assimilation forecasts of precipitation (contours every 10 mm from 10 mm) accumulated from the initializing time of 24/12 to 25/12 from Jang et al. (2003; their Figs. 16.b, 16.d). 159 3.2: Simulations of the 24-25 January 2000 east coast snowstorm a) Analysis b)GEM c) Ozone/GEM ao w re * d) Jang et al. (2003) control e) Jang et al. (2003) ozone Fig. 3.20 See caption on previous page. 160 3.2: Simulations of the 24-25 January 2000 east coast snowstorm Thus, although far from perfect, the two GEM forecasts, particularly the ozone/GEM forecast, are superior to almost all of the published precipitation forecasts. When even the ozone/GEM forecast is surpassed by a published forecast, the most significant difference lies in South Carolina. The ozone/GEM underprediction in this area is likely due to this simulation's late initialization time of 24/18, at which point precipitation had already been falling for six hours in South Carolina. Considering the first objective given in Section 3.2.1.2, concerning whether ozone-influenced upper-level initializing fields are capable of producing accurate precipitation forecasts, the forecast produced by ozone/GEM earned threat scores ranging from 0.31 to 0.79 for thresholds of 40 mm or less, including 0.59 (0.46) at 20 (30) mm. These excellent threat scores were earned despite the forecast's being characterized by biases less than unity (see Fig. 3.18), which increases the difficulty of earning high threat scores, as discussed in Section 3.2.1.2. This forecast's 20- and 30-mm threat scores far surpass the average day-1 threat score of approximately 0.24 earned by the NOAA Hydrometeorological Prediction Center in 2000 for 24-h forecasts of 1.00 in (25.4 mm) or more of precipitation (see Fig. 1.2). The exceptional threat scores of the ozone/GEM forecast, together with the above comparison of Fig. 3.17's forecasts to published forecasts, demonstrate that ozone-influenced upper-level initializing fields are indeed capable of producing excellent precipitation forecasts. The most significant finding is the superiority of the QPF produced by our novel procedure over the 161 3.2: Simulations of the 24-25 January 2000 east coast snowstorm technologically more sophisticated ozone-influenced 4D-Var assimilation forecast of Jangetal. (2003). Considering the second objective of characterizing the strengths and weaknesses of the ozone-influenced upper-level initializing fields, a weakness of these upper-level initializing fields is the fact that they are strongly dependent on the quality of the low-level initializing fields: a single source (GEM) provides low-level initializing fields for both the best precipitation forecast involving ozone and the best forecast not involving ozone, while a single source (Eta) is associated with both the worst ozone and non-ozone forecasts. The strength of this dependence on the low-level initializing fields' quality most likely varies by case; the development of some events is linked heavily to either low- or upper- level features alone, while the development of others is linked to features at both levels. In contrast, a strength of the ozone-influenced initializing fields is that they are able, even over the data rich eastern U.S., to improve the precipitation forecast for a given source of low-level fields, e.g. in the ozone/Eta and ozone/GEM experiments. Considering the third objective, which is to determine the relative importance of the low- and upper-level initializing fields for the simulation of the east coast snowstorm of 24-25 January 2000, the fact that the precipitation forecasts vary more with the source of low-level fields than with the source of upper-level fields suggests that, to first order, details in the low-level fields are more important than details in the upper-level fields for the forecasting of this event. This is not to say 162 3.2: Simulations of the 24-25 January 2000 east coast snowstorm that the quality of the upper-level fields is irrelevant, given the feedback that occurs between the various atmospheric levels. The examination of a variety of fields at different levels will now be conducted in order to clarify why the two GEM experiments performed so well, why ozone/GEM outperformed GEM, why Eta performed poorly, and which fields at which levels were crucial in determining the quality of precipitation forecast produced. Figure 3.21 demonstrates that forecasting the sea level pressure cyclone accurately is not a prerequisite for an accurate onshore precipitation forecast for this event: although the ozone/GEM (best precipitation forecast) cyclone is both well located and of a perfect strength at 25/00, by 25/06 overly weak, double cyclones have developed. The GEM simulation (2nd best precipitation forecast) also develops the double cyclone by 25/06 after exhibiting the worst cyclone location of the six simulations at 25/00. On the other hand, the Eta simulation (worst precipitation forecast) cyclone at 25/00 has an excellent central pressure and is the most accurately-located, followed by excellent positioning and strength at 25/06. Following the same pattern, the two GEM 1000-500-dam thickness field troughs of Fig. 3.21, while exhibiting the desired negative tilt, are the weakest of all the simulations' troughs, being noticeably shallower than the rawinsonde- derived trough at 25/00. The Eta trough, on the other hand, which is one of the deepest exhibited throughout this period, matches the rawinsonde-derived contours well at 25/00. Although one might expect that the deeper Eta trough 163 3.2: Simulations of the 24-25 January 2000 east coast snowstorm would produce greater forcing for ascent accompanied by more precipitation, the GEM and ozone/GEM 540-dam contours do tend to extend to the south of South Carolina; even these weaker troughs are sufficiently deep to provide strong ascent forcing in our area of interest. Furthermore, the southerly extent of the two GEM simulations' 534-dam contours is comparable to those of the other simulations. Fig. 3.21 Sea level pressure (purple, 4-hPa contour interval, 1000-hPa contour heavy) and 1000-500 hPa thickness fields (brown, 6-dam contour interval with a heavy, solid line for the 540-dam contour) are shown for experiments initialized at 24/18. The reanalysis ERA-40 sea level pressure cyclone is plotted in violet. Also shown, when available, are rawinsonde-derived thickness contours, plotted as per the simulation field but in orange. Titles indicate the experiment name, forecast hour, and actual date/time. Note that the date/time varies by column and the experiment by row. 164 3.2: Simulations of the 24-25 January 2000 east coast snowstorm a 1) ERR F00: 21/18 bl ) ERR FOG: 25/00 \^ _, -!L' ~^p *'/ /fj t^T " **•• >v *" \ ^^%1 ? / - ^s?^ ~ \ •f/r / / / X N y jr»* /\i/i i y***A \ v / / 135SP-r<^ (flpi -*• __ /? ^ --<9oJ 7 \ •" -^\7 12) Oz/ERR FOO:21/18 b2) Oz/ERR FOG: 25/00 \ \ ' / ' ^>^^r*'^~~- Xt ' 1 \^ /f _- a5) GEM FOO:21/18 b5) GEM F06: 25/00 a6) Oz/GEM FOO: 21/18 b6) Oz/GEM F06: 25/00 Fig. 3.21 See caption on previous page. 165 3.2: Simulations of the 24-25 January 2000 east coast snowstorm g-S^j -~^^ w^ y%£ \ 3s> j % 81 / / f"* ^ S' J ,N jT "*' ^^ " - \ // c \ —'\/ 7 / c1) ERA F12:25/OG c2) Oz/ERn F12:25/06 c3) Eta F12:25/0G cl) Oz/Eta F12:25/OG c5) OEM F12:25/06 c6) Oz/GEM F12:25/06 Fig. 3.21 continued. 166 3.2: Simulations of the 24-25 January 2000 east coast snowstorm The Eta dynamic tropopause potential temperature trough resembles that of ERA closely at all times (see Fig. 3.22). However, it is the GEM cut-off Low that best matches the shape and tilt of the rawinsonde-derived cut-off Low at 25/00, despite the weakness of its initializing trough. Note that these observations may not be of great significance, given that the three ozone troughs resemble each other closely at all times; the similarity suggests that it is not features in the dynamic tropopause potential temperature field that are crucial in determining the accuracy of the onshore precipitation forecast. As with the dynamic tropopause potential temperature troughs, the ozone 250-hPa height field troughs most resemble each other (see Fig. 3.23), reinforcing the notion of the upper-level features' lesser relevance during this period for the successful forecasting of this event's onshore precipitation. Compared to the rawinsonde-derived trough of 25/00, the ozone troughs are too shallow and, like those of the (re)analyses, too far east. While the GEM trough is also weak at this time, the depth of the Eta trough is the most accurate. Interestingly, the inaccurate direction of the ozone initializing winds, a probable consequence of their nondivergence, has been corrected by 25/00, although they remain weak. Unfortunately, not even ERA or Eta, despite the accuracy of their winds at 25/00, Fig. 3.22 Lightly smoothed EPV-derived dynamic tropopause potential temperatures (4-K contour interval, with the 316-K contour dashed and values less than 304 K shaded) are shown for experiments initialized at 24/18. At 25/00, the rawinsonde-derived 316-K contour (dark, solid) is added. Titles indicate the experiment name, forecast hour, and actual date/time. Note that the date/time varies by column and the experiment by row. Note also that the region plotted changes with time. 167 3.2: Simulations of the 24-25 January 2000 east coast snowstorm a5) 6EM F00:21/18 a6) Oz/GEM TOO: 21/18 Fig. 3.22 See caption on previous page. 168 3.2: Simulations of the 24-25 January 2000 east coast snowstorm c1) ERA F12:25/06 c2) Oz/ERR F12:25/06 mi c3) Et a F12: 25/06 c4) Oz/Eta F12:25/06 c5] GEM F12: 25/06 c6) Oz/GEM F12:25/06 Fig. 3.22 continued. 169 3.2: Simulations of the 24-25 January 2000 east coast snowstorm reproduces the observed easterly wind component at GSO (Greensboro) in central North Carolina at 25/06, which would have driven the precipitation inland. Such a wind direction could be produced by shifting the northern part of the downstream portion of the 1026-dam (heavy) contour westwards, as in the generation of a cut-off Low. Although the simulations' 250-hPa field features from 24/18 onwards do not seem to be of critical importance in the production of this event's onshore precipitation, differences in the 250-hPa fields at 24/12 are intriguing: although all three (re)analyses underestimate wind speeds at 24/12 over most of the area shown in Fig. 3.24, the Eta speeds are by far the least accurate. In fact, the first guess field's winds were so inaccurate at this time that the operational Eta rejected the 250-hPa 62 m s"1 wind speed observation at FFC (Peach tree, Georgia; EMC 2007a). Perhaps contributing to this rejection, 250-hPa wind data at Tampa, Florida (TBW), Birmingham, Alabama (BMX) and Slidell, Louisiana (LIX) were unavailable for this operational run. It is quite possible that feedback within the atmosphere from the considerable 250-hPa wind speed inaccuracies at 24/12 contributed to the poor Eta and ozone/Eta precipitation forecasts. Fig. 3.23 The 250-hPa height (purple, 6-dam interval, with the 1026 (1032)-dam contour heavy solid (dash)), wind (brown, (half) barb equals (2.5) 5 m s~l, pennant equals 25 m s-1) and isotach (shading every 5 m s"1 from 55 m s") fields are shown for experiments initialized at 24/18. Also shown, when available, are rawinsonde-derived heights (violet) and winds (orange), plotted as per the simulation fields, and isotachs (contours in shades of orange every 5 m s"1 from 55 m s"1). Titles indicate the experiment name, forecast hour, and actual date/time. Note that the date/time varies by column and the experiment by row. 170 3.2: Simulations of the 24-25 January 2000 east coast snowstorm ?/-w \t\ / / ,2 7 7' a 1) ERn F00: 21/18 bl) ERA F06: 25/00 *" — "•" v*e- fy^ / ' V ' \ / 3 3 W-" / * ^ , / •/~j~]' ' i2) Oz/ERfl F00: 21/18 b2) Oz/ERfl FOG: 25/00 a3) Et a FOO: 21/18 b3) Eta FOG: 25/00 ^•/Tf-J al) Oz/Eta FOO:21/18 bl) Oz/Eta FOG:25/00 a5) GEM FOO: 21/18 J>5) GEM FOG: 25/00 : S3*R- ' 'r-V W<\ K J __3 3 V^ 'V./'-<^-;--> ~~~8T ;v' /-7V7 / / / 'f i. n i i a6) Oz/GEM FOO:21/18 bG) Oz/GEM FOG: 25/00 Fig. 3.23 See caption on previous page. 171 3.2: Simulations of the 24-25 January 2000 east coast snowstorm / ' ' i i i > ' ' ' .!/ / /' ' / / / , / / c 1) ERR F12: 25/OG c2) Oz/ERfl F12: 25/06 c3) Et a F12: 25/06 ^ » _ _ / r - •gj*- \ *A i/ V 33^ •'/ \ \8*N \ % \ *«...-••• / cH) Oz/Eta F12:25/06 ...... , ...,, j i i v 3"^" '' J / ' ' iii •a i |-^ / 2: j i i -77/ • / / / c5) GEM F12:25/06 —. — It 1 / J 1' 1' / ' J1 ^\ : (i. i / \33N — -111 j c6) Oz/GEM F12:25/06 Fig. 3.23 continued. 172 3.2: Simulations of the 24-25 January 2000 east coast snowstorm Fig. 3.24 Shown are analyses at 24/12 of 250-hPa heights (purple, 6-dam interval, with the 1026 (1032)-dam contour heavy solid (dash)), winds (brown (half) barb equals (2.5) 5 m s~l, pennant equals 25 m s-1) and isotachs (every 5 m s-> from the 15-m s_1 black contour, with shading from 55 m s-1) from the indicated sources. Rawinsonde wind speeds (m s-1) are also provided in panel b). The importance of 500-hPa ascent is indicated by the fact that the onshore accumulated precipitation fields of Fig. 3.17 correspond closely in shape to the sum of the 500-hPa ascent regions of Fig. 3.25. Given this correspondence, it is not surprising that ozone/GEM, which produced the best forecast, consistently exhibits the strongest onshore ascent, followed by GEM, which produced the 2nd best forecast. Compared to the two GEM simulations' ascent regions, the Eta ascent region penetrates inland far less and exhibits values of half the magnitude. 173 3.2: Simulations of the 24-25 January 2000 east coast snowstorm Since Fig. 3.25 demonstrates clearly that geostrophic cyclonic vorticity advection forces the 500-hPa ascent, we can conclude that ozone/GEM and GEM have the most accurate 500-hPa height fields: despite the apparent lack of a distinct negative tilt at 25/00 in the former simulation's trough and the lack of depth in that of the latter simulation, both these troughs are able to generate geostrophic cyclonic vorticity advection in the desired location. Since the former simulation's advection is stronger than the latter's, we conclude that the ozone/GEM height field is more accurate than that of GEM. Although, at 25/00, Eta does produce the desired vorticity advection onshore accompanied by ascent, confirming the fairly high accuracy of the height field, at 25/06 the Eta ascent region appears to be pushed to the east and north by the overly large cut-off low. Thus, the configuration of the 500-hPa height field, which generates the geostrophic cyclonic vorticity advection and associated ascent fields, seemingly determines the accuracy of the accumulated precipitation forecast for this event. Fig. 3.25 The 500-hPa height (purple, 3-dam contour interval, with the 546 (549)- dam contour heavy solid (dot-dash)) and ascent (contours every 5 (10) xlO-3 hPa s-1 from -5 (-20) to -20 (-70) x 10-3 hPa s-1 in orange, brown and black) fields, as well as the advection of cyclonic absolute vorticity by the geostrophic winds (positive-valued contours every 2x10" s" in shades of green), are shown for experiments initialized at 24/18. Note that 0-h forecast fields of omega are not available. Also shown, when available, are rawinsonde contoured 500-hPa heights (violet), plotted as per the simulation fields. Titles indicate the experiment name, forecast hour, and actual date/time. Note that the date/time varies by column and the experiment by row. 174 3.2: Simulations of the 24-25 January 2000 east coast snowstorm a 1) ERR F00: 2*1/18 hi) ERA F06:25/00 v V /n// / //?. !(r / '/ ' 'A ' 'V ^I v^($vL>v A CX-l^djSit J I V /M&K Yi^fe 1 ^ 11. •/ \u33(/' - S\{n^(0^H^&k' v\\\Wi J^^^t^rnit M\ \\V^f\ «M'i /I i2) Oz/ERfl F00: 2*1/18 b2) Oz/ERR FOG: 25/00 —i f—p' » fv H s a3) Et a F00: 2*1/18 Jb3) Et a FOG: 25/00 V "vA/ // tJKJH VA//' / '/ 'f\' ^--! ' a5) GEM F00: 2*1/18 b5) GEM F06: 25/00 a6) Oz/GEM F00: 2*1/18 b6) Oz/GEM F06: 25/00 Fig. 3.25 See caption on previous page. 175 3.2: Simulations of the 24-25 January 2000 east coast snowstorm c 1) ERR F12: 25/06 \ \&<\ ' _i * i c2) Oz/ERR F12:25/OG j/$/^3)i( 'V36^P/' -> c3) Eta F12: 25/OG x \ /A \ 3 6* • • 7 Mx)}fi~PH \ ' V //-\ i \ A, 1/ 1 uySjll i i \ \ : ^/7 1 \ O OJ 1 V//V "JmWfM ''"'' \ \8n^; ( cl) Oz/Eta F12:25/06 c5J GEM F12:25/06 \ -^8A "'. cG) Oz/GEM F12:25/06 Fig. 3.25 continued. 176 3.2: Simulations of the 24-25 January 2000 east coast snowstorm The GEM and ozone/GEM simulations, which produced the two best precipitation forecasts, are initialized with the highest 850-hPa mixing ratios over Georgia and both Carolinas (see Fig. 3.26). This correlation of forecast quality and initializing moisture content in Georgia confirms Zupanski et al.'s (2002) results (see Section 3.1.2). At 25/00, the mixing ratios of these two simulations are greater than those observed for the most part. However, GEM and ozone/GEM are best at capturing the warming described by the westward push of the 0-°C contour in the Carolinas at 25/00 and 25/06. The combination of this warmth and the excessive moisture content suggests a decrease in stability for the two GEM simulations over the Carolinas, facilitating ascent. In contrast, the Eta 850-hPa atmosphere is cooler and, therefore, likely more stable. Perhaps surprisingly in view of the increased Eta stability, the Eta and ERA simulations exhibit the largest onshore regions of 850-hPa ascent at 25/00. However, these ascent regions, which coincide with areas of geostrophic warm air advection, are not collocated with the onshore regions of 850-hPa ascent-indicating Q-vector convergence inBrennan and Lackmann (2005; their Fig. 19), valid three hours Fig. 3.26 The 850-hPa temperature (dark green contours every 3 °C with the 0-°C contour heavy and values increasing from northwest to southeast), mixing ratio (light blue contours at 4, 5, 6 g kg"1 with values increasing from northwest to southeast), ascent (contours at -4, -12xl0"3 hPa s-1 in brown and orange) and sea level pressure (purple, 4-hPa contour interval with values increasing from southeast to northwest) fields are shown for experiments initialized at 24/18. Note that 0-h forecast fields of omega are not available. Also shown, when available, are rawinsonde contoured 850-hPa temperatures (plotted as per the simulation temperatures but in light green) and mixing ratios (black dotted contours at 4, 5, 6 g kg-1). Titles indicate the experiment name, forecast hour, and actual date/time. Note that the date/time varies by column and the experiment by row. 177 3.2: Simulations of the 24-25 January 2000 east coast snowstorm a 1 ) ERR FOO: 24/18 bl) ERR F06:25/00 12) Oz/ERfl FOO: 24/18 b2) Oz/ERR F06: 25/00 /T /6 yf ••/Writ's'—rx /:7Q4 i3) Eta F00:24/18 b3) Et a FOG: 25/00 a4) Oz'/Et a FOO: 24/18 b4) Oz/Eta FOG: 25/00 15) GEM FOO:24/18 b5J GEM FOG: 25/00 a6) Oz/GEM FOO: 24/18 bS). Oz/GEM F06: 25/00 Fig. 3.26 See caption on previous page. 178 3.2: Simulations of the 24-25 January 2000 east coast snowstorm c 1 ) ERR F12: 25/06 c2) Oz/ERfl F12f25/0S c3) Eta F12: 25/OG c*l) Oz/Et a F12: 25/06 c5) 6EM F12: 25/06 c6) 0z/6EM F12:25/06 Fig. 3.26 continued. 179 3.2: Simulations of the 24-25 January 2000 east coast snowstorm earlier. It is the GEM and ozone/GEM simulations' regions of ascent that are closest to being collocated with these regions of Q-vector convergence. Note that the onshore accumulated precipitation fields, including the significant inland penetration of the ERA 5- and 10-mm contours, is associated strongly with ascent at 500 not 850 hPa (see Figs. 3.17, 3.25, 3.26). This finding agrees with Kleist and Morgan's (2005) determination that the onshore precipitation was associated with ascent at upper levels. At 925 hPa, the two GEM simulations are initialized with the highest equivalent potential temperatures in Georgia and South Carolina (see Fig. 3.27). However, at 25/00, the two GEM simulations are the only simulations to fail to suggest the observed warm region in North Carolina, while all simulations fail to reproduce the observed cold pool in South Carolina. At 25/06, all simulations' temperatures are comparable. Thus, it seems unlikely that surface instability was a major factor in the increased GEM and ozone/GEM precipitation values. Moreover, geostrophic warm air advection is indicated primarily in coastal areas, confirming that surface-level fields do not represent an important distinguishing factor among the varying simulations. Fig. 3.27 The 925-hPa equivalent potential temperature (brown, 280-, 285-, 290- and 300-K contours, values increasing from northwest to southeast) and sea level pressure (violet, 4-hPa contour interval with a heavy 1000-hPa contour and values increasing from southeast to northwest) fields are shown for experiments initialized at 24/18. Also shown, when available, are rawinsonde-derived contours of 925-hPa equivalent potential temperature (K), plotted as per simulation temperatures but in orange. Note that the enclosed contour over South Carolina and Georgia represents a cold pool. Titles indicate the experiment name, forecast hour, and actual date/time. Note that the date/time varies by column and the experiment by row. 180 3.2: Simulations of the 24-25 January 2000 east coast snowstorm -y4i [•;•'••[••//'? •^•Sm -§§4 6 J a 1) ERR F00: 21/18 bl ) ERR FOG: 25/00 12) Oz/ERR F00:21/18 b2) Oz/ERR F06: 25/00 13) Et a FOO: 21/18 b3) Et a F06: 25/00 il) Oz/Eta FOO:21/18 bl) Oz/Eta FOG:25/00 • _>4 >y- //'/^' rj^: / v1 *" / ^^ .' V lr' / -^3'/' i$f'••• l /•^ 7'^^& ' i5) GEM FOO:21/18 b5) GEM FOG: 25/00 / >r , I \ s . a6) Oz/GEM FOO:21/18 b6) Oz/GEM FOG: 25/00 Fig. 3.27 See caption on previous page. 181 3.2: Simulations of the 24-25 January 2000 east coast snowstorm c 1 ) ERR F12: 25/06 c2) Oz/ERR F12: 25/06 c3) Eta F12:25/06 cH) Oz/Eta F12: 25/06 c5) GEM F12: 25/06 c6) 0z/6EM F12: 25/06 Fig. 3.27 continued. 182 3.2: Simulations of the 24-25 January 2000 east coast snowstorm While all six simulations duplicate the observed temperature profile at CHS (Charleston, South Carolina) at 25/00 admirably, apart from the surface-level cool layer (see Fig. 3.28), no simulation captures the extent of the observed potential instability, indicated by panel a's dry layer above 700 hPa over a moist layer, and confirmed by panel b's equivalent potential temperature profiles. Although the two GEM simulations exhibit no potential instability in panel b, they exhibit a deep layer (700 to 400 hPa) of basically neutral potential stability. Furthermore, these simulations duplicate panel a's observed cold advection from 700 to 400 hPa overlying warm advection, indicating the ongoing static destabilization of the atmosphere. Cold (warm) advection is signified by the counter-clockwise (clockwise) rotation of the winds with increasing height. Perhaps most importantly, the two GEM simulations exhibit the strongest onshore moisture transport from 1000 to 775 hPa (see panel b), which is, in fact, slightly too strong. The Eta simulation is characterized by potential instability from 600 to 500 hPa, but it lacks cold advection from 700 to 400 hPa, and its moisture transport is insufficiently onshore. Note that the ozone/GEM static destabilization and onshore moisture transport are both stronger than those of GEM. Thus, having examined a variety of fields at a several levels, the most important differences between the GEM and ozone/GEM simulations that produced good precipitation forecasts and the Eta simulation that produced a poor precipitation forecast are contained in the 500-hPa height, geostrophic cyclonic vorticity advection and ascent fields, as well as in the 850-hPa moisture and temperature, and, consequently, stability fields. Furthermore, at CHS at 25/00, the two GEM simulations, compared to that of Eta, were characterized by a 183 3.2: Simulations of the 24-25 January 2000 east coast snowstorm -30 0 30 60 a) CHS temperatures, dewpoint temperatures and winds 850H 925 1000 280 290 300 310 b) CHS equivalent potential temperatures and moisture transport vectors Fig. 3.28 Shown for CHS (Charleston, SC) at 0000 UTC 25 January 2000 from the 6-h forecast of the ERA (red), ozone/ERA (pink), Eta (purple), ozone/Eta (violet), GEM (brown) and ozone/GEM (peach) simulations initialized at 24/18, and as observed (black) are a) a skew-T log-p plot of temperature (°C, solid) and dew point temperature (°C, dashed) with the 300-, 325- and 350-K moist adiabats, along with horizontal winds ((half) barb equals (2.5) 5 m s-1, pennant equals 25 m s-1), and b) a log-p versus temperature plot of equivalent potential temperatures (K), along with moisture transport vectors (cm s-1), where the length of the 1000- hPa ERA (red) moisture transport vector represents 11.5 cm s-1. stronger cold advection from 700 to 400 hPa, suggesting a greater ongoing static destabilization of the atmosphere, and a stronger onshore moisture transport up to 775 hPa. 184 3.2: Simulations of the 24-25 January 2000 east coast snowstorm Similarly, the superiority of the ozone/GEM precipitation forecast to that of GEM can be attributed to the former simulation's more accurate 500-hPa fields, as well as to a greater ongoing static destabilization of the atmosphere and a greater onshore moisture flow at CHS at 25/00. It seems likely that the GEM boundary condition fields, particularly at 700 hPa, influenced the ozone/GEM upper-level initializing fields positively, given that the ozone/GEM precipitation forecast is far superior to the other two ozone forecasts. Thus, for horizontal fields, features in the 850-, 700- and 500-hPa fields are crucial to the production of this event's heavy onshore precipitation, while features in the sea level pressure, 1000-500-hPa thickness, dynamic tropopause potential temperature, 250- and 925-hPa fields are deemed not to have been critical during this period. Concerning this research's 2nd objective of characterizing the strengths and weaknesses of the ozone-influenced initializing fields, the fact that these fields respond strongly to the 700-hPa boundary conditions can be considered both a weakness, in that they are affected significantly by the boundary conditions, as demonstrated by the variation in the initializing 500-hPa height fields of Fig. 3.25, and a strength, in that they are capable of responding to these boundary conditions, thereby demonstrating flexibility. The ability of the ozone-influenced 250-hPa winds to switch from initializing southwesterlies to the (re)analyses' southerlies within six hours in the eastern half of Fig. 3.23, presumably by adding a divergent component, demonstrates that the nondivergence of the ozone- influenced initializing winds need not be considered a weakness. 185 3.2: Simulations of the 24-25 January 2000 east coast snowstorm Concerning our 3r objective of determining the relative importance of the low- and upper-level fields in the production of this event's onshore precipitation, this section's discussion indicates that low- (850-hPa moisture and temperature) and mid-level (700-hPa boundary condition and 500-hPa ascent) fields are considerably more important than upper-level, e.g. 250-hPa height, fields during the simulations' period. Concerning this research's 4 objective of considering why the operational Eta forecast failed, our Eta simulation exhibited a 500-hPa ascent field (see Fig. 3.25) that was weak at 25/00, despite the fairly accurate height field of that time, and that penetrated insufficiently inland and into South Carolina at 25/06, due to the presence of the overly large cut-off Low. The Eta initializing 500-hPa trough, which was the deepest of the three (re)analyses, likely spawned the problematic cut-off Low at 25/06. At 850 hPa, the initializing Eta atmosphere was colder and drier in South Carolina than the initializing GEM atmosphere, rendering the atmosphere more stable. The fact that the Eta simulation produced an extensive 850-hPa onshore ascent region at 25/00 is not important, given that the shape of the onshore accumulated precipitation forecast agrees best with the 500-hPa ascent field. Thus, an overly deep Eta initializing mid-level trough combined with an overly dry and cool low-level initializing atmosphere is responsible for the poor Eta accumulated precipitation forecast. 186 3.2: Simulations of the 24-25 January 2000 east coast snowstorm 3.2.2.2 Simulations initialized at 1800 UTC 23 January 2000 Figure 3.29 presents the forecasts of precipitation accumulated from 24/12 to 25/12 during the six experiments initialized at 1800 UTC 23 January 2000. This period covers the entire precipitation period for the Carolinas, in contrast to the accumulation period of Fig. 3.17, which started six hours later. It is clearly evident from this figure that all six forecasts are extremely poor, in that onshore precipitation values are either very low or non-existent. The low threat scores and biases of Fig. 3.30 confirm this subjective assessment. The three ozone forecasts' scores are the worst of all, owing to the almost uniform non-existence of onshore precipitation; ozone/Eta earns zero-valued threat scores and biases. The ERA forecast, by virtue of its inland penetration, earns the best scores overall, followed by that of GEM. Forecast rankings, which are identical whether determined objectively or subjectively, are provided in Table 3.4. The fact that the ozone and (re)analysis experiments' forecasts are ordered identically indicates that the source of the low-level and PV inversion boundary condition fields strongly influences the precipitation forecasts. 187 3.2: Simulations of the 24-25 January 2000 east coast snowstorm a ) ERR b) Ozone/ERR c ) Et a Ozone/Et a e ) GEM f) Ozone/GEM Fig. 3.29 Precipitation (contours at 5 mm and every 10 mm from 10 mm, with the 20-mm contour dashed, the 40-mm contour heavy, and light (dark) shading from 50 (80) mm) accumulated from 24/12 to 25/12 during the indicated experiments, initialized at 23/18, is shown. 188 3.2: Simulations of the 24-25 January 2000 east coast snowstorm a) Threat scores CO 10 JO) ERA c o Oz/ERA to 0.75 - Eta c Oz/Eta d) k_ j= ^ 10 20 30 40 50 60 Threshold (mm) b) Bias 20 30 40 60 Threshold (mm) Fig. 3.30 Calculated for the indicated experiments, initialized at 23/18, and thresholds are the: a) threat score and b) bias for the precipitation accumulated from 24/12 to 25/12. The Brennan and Lackmann (2005) analysis constitutes the truth field. Table 3.4 Onshore accumulated precipitation forecast rankings for simulations initialized at 23/18 Simulation Ranking ERA 1 GEM 2 Eta 3 ozone/ERA 4 ozone/GEM 5 ozone/Eta 6 189 3.2: Simulations of the 24-25 January 2000 east coast snowstorm Concerning these simulations' sea level pressure fields, the three ozone experiments exhibit some of the most accurately-located, albeit slightly weak, cyclones from 24/12 to 25/00, despite having dropped their initialized sea level pressure cyclones by the 6-h forecast (see Fig. 3.31). However, it was determined in the previous section that a good cyclone forecast is not a prerequisite for an accurate onshore precipitation forecast for this event. More importantly, therefore, the three ozone troughs fail to deepen by 24/06, remaining overly shallow and wide through 25/00, as compared to the rawinsonde-derived trough and those of the (re)analyses. Interestingly, by 25/06 the ozone troughs resemble those of the three analyses once again. Fig. 3.31 Sea level pressure (purple, 4-hPa contour interval, 1000-hPa contour heavy) and 1000-500 hPa thickness fields (brown, 6-dam contour interval with a heavy, solid line for the 540-dam contour) are shown for experiments initialized at 23/18. The reanalysis ERA-40 sea level pressure cyclone is plotted in violet. Also shown, at 24/12 and 25/00, are rawinsonde-derived thickness contours, plotted as per the simulation field but in orange. Titles indicate the experiment name, forecast hour, and actual date/time. Note that the date/time varies by column and the experiment by row. 190 3.2: Simulations of the 24-25 January 2000 east coast snowstorm il ) ERR F00: 23/18 b\) ERR FOG:21/00 12) Oz/ERR FOO:23/18 b2) Oz/ERR F06:21/00 a3) Et a F00: 23/18 b3) Et a F06: 21/00 al) Oz/Eta FOO:23/18 bl) Oz/Eta FOG:21/00 i5) GEM FOO:23/18 b5) GEM FOG: 21/00 16) Oz/GEM FOO: 23/18 b6) Oz/GEM F06: 21/00 Fig. 3.31 See caption on previous page. 191 3.2: Simulations of the 24-25 January 2000 east coast snowstorm c 1 ) ERR F12: 2^/06 dl) ERR F18:2*1/12 V •v V^. -j Is s\_y 3^' k—^-^' /^ s- G.S^ ~y* - —-•'^Zz^^ '^S^A j^-~ —— - ^ / ./... .!"> — LL / -L '- —• -sWM-2- - -{15 ~\ ~~ c2) Oz/ERR F12:2*1/06 d2) Oz/ERR F18:21/12 c3) Et a F12: 21/06 d3) Et a F18: 21/12 cl) Oz/Et a F12: 21/06 dl) Oz/Eta F18:21/12 c5) GEM F12:21/06 d5) GEM F18: 21/12 c6) Oz/GEM F12: 21/06 d6) Oz/GEM F18:21/12 Fig. 3.31 continued. 192 3.2: Simulations of the 24-25 January 2000 east coast snowstorm e 1) ERR F21: 2*1/18 f 1 ) ERR F30: 25/00 e2) Oz/ERR F21: 21/18 *2) Oz/ERR F30: 25/00 e3) Eta F21:21/18 f 3) Et a F30: 25/00 el) Oz/Et a F21: 21/18 fl) Oz/Et a F30: 25/00 e5) OEM F21:21/18 f5) GEM F30: 25/00 eG) Oz/GEM F21: 21/18 f6) Oz/GEM F30: 25/00 Fig. 3.31 continued. 193 3.2: Simulations of the 24-25 January 2000 east coast snowstorm 91) ERR F36:25/06 92) Oz/ERR F36:25/06 /I /uS^/^X/^C li 93) Et a F36: 25/06 91) Oz/Et a. F36: 25/06 95) GEM F36 :25/06 C v -/' MSTZZ** N^ v~-/"7 VV'/'Aril/ N ^ j <3& -- -/ "* ""^y **• / """*"/'*- /// //V/ /S-ryl / v,_ i *•*"•( ' J// J ^•^ w. \ -—fity />^ / / 96) Oz/GEM F36: 25/06 Fig. 3.31 continued. 3.2: Simulations of the 24-25 January 2000 east coast snowstorm The dynamic tropopause potential temperature troughs of the three (re)analyses' experiments compare extremely well to the rawinsonde-derived trough at 24/12, although they are all too deep at 25/00 (see Fig. 3.32). In contrast, the ozone experiments' troughs are considerably weaker than those of the (re)analyses' experiments at the initializing time, and they remain weak throughout the simulation. As demonstrated in Section 2.3, the methodology presented in that section preserves features in the total column ozone field during the conversion of the ozone field to model initializing fields. Investigating the weakness of the original ozone feature is beyond the scope of the current project. Fig. 3.32 Lightly smoothed EPV-derived dynamic tropopause potential temperatures (4-K contour interval, with the 316-K contour dashed and values less than 304 K shaded) are shown for experiments initialized at 23/18. At 24/12 and 25/00, the rawinsonde-derived 316-K contour (dark, solid) is added. Titles indicate the experiment name, forecast hour, and actual date/time. Note that the date/time varies by column and the experiment by row. Note also that the region plotted changes with time. 195 3.2: Simulations of the 24-25 January 2000 east coast snowstorm a 1) ERR FOO: 23/18 bl) ERR F06: 2^/00 a2) Oz/ERR FOO: 23/18 b2) Oz/ERR F06: 2-H/00 a3) Et a FOO: 23/18 b3) Eta F06:2^/00 s.H) Oz/Et a FOO: 23/18 b<\) Oz/Eta FOG: 2^/00 a5) GEM FOO:23/18 b5) GEM FOG:2^/00 a6) Oz/GEM FOO: 23/18 b6) Oz/GEM F06: 2^/00 Fig. 3.32 See caption on previous page. 196 3.2: Simulations of the 24-25 January 2000 east coast snowstorm cl) ERR F12:2*1/06 dl ) ERR F18: 2*1/12 I ' 4 - - '\ c2) Oz/ERfl F12:2*1/06 6.2) Oz/ERR F18: 2*1/12 c3) Eta F12:2*l/06 d3) Et a F18: 2*1/12 c*l) Oz/Eta F12:2*l/06 d*U Oz/Et a F18: 2*1/12 c5) GEM F12: 2*1/06 d5) GEM F18: 2*1/12 cG) Oz/GEM F12: 2*1/06 dG) Oz/GEM F18: 2*1/12 Fig. 3.32 continued. 197 3.2: Simulations of the 24-25 January 2000 east coast snowstorm f6) Oz/GEM F30:25/00 Fig. 3.32 continued. 3.2: Simulations of the 24-25 January 2000 east coast snowstorm g 1 ) ERR F3B: 25/06 92) Oz/ERR F3G: 25/06 93) Et a F36: 25/06 9-H) Oz/Et a F36: 25/06 95) GEM F36:25/06 96) Oz/GEM F36: 25/06 Fig. 3.32 continued. 199 3.2: Simulations of the 24-25 January 2000 east coast snowstorm It was noted in the previous section concerning the simulations initialized at 24/18 (later simulations),, that the onshore 500-hPa ascent and precipitation fields were strongly associated. Therefore, given the lack of onshore 500-hPa ascent produced by the simulations initialized at 23/18 (earlier simulations; see Fig. 3.33), it is perhaps not surprising that the earlier simulations produced minimal, if any, onshore precipitation. What is perhaps more interesting is that 500-hPa ascent is strongly associated with geostrophic cyclonic vorticity advection in the later simulations (see Fig. 3.25) but not in the earlier simulations (see Fig. 3.33), possibly owing to an increased static stability in the earlier simulations; the three ozone simulations, despite being characterized by overly shallow troughs, manage to generate onshore geostrophic cyclonic vorticity advection but no onshore ascent or precipitation. Fig. 3.33 The 500-hPa height (purple, 3-dam contour interval, with the 546 (549)- dam contour heavy solid (dot-dash)) and ascent (contours every 5 (10) xlO"3 hPa s-1 from -5 (-20) to -20 (-70) x 10-3 hPa s-1 in orange, brown and black) fields, as well as the advection of cyclonic absolute vorticity by the geostrophic winds (positive-valued contours every 2 x 10"9 s"2 in shades of green), are shown for experiments initialized at 23/18. Also shown, when available, are rawinsonde contoured 500-hPa heights (violet), plotted as per the simulation fields. Titles indicate the experiment name, forecast hour, and actual date/time. Note that the date/time varies by column and the experiment by row. 200 3.2: Simulations of the 24-25 January 2000 east coast snowstorm a 1 ) ERR F18: 2*1/12 bl ) ERR F2*l: 2*1/18 i2) Oz/ERR F18: 2*1/12 b2) Oz/ERR F2*): 2*1/18 ' •' 4 3.3) Et a F18: 2*1/12 b3) Et a F2*|: 2*1/18 a*n Oz/Et a F18: 2*1/12 b*l) Oz/Et a F2*l: 2*1/18 l 1 / ^ // i, r s * ,3 s /"N ' II'- I !' ' ' \ ; 'vfe^v'•/•'•••'•':•) a5) GEM F18: 2*1/12 b5) GEM F2*|: 2*1/18 a6) Oz/GEM F18: 2*1/12 b6) Oz/GEM F2*l: 2*1/18 Fig. 3.33 See caption on previous page. 201 3.2: Simulations of the 24-25 January 2000 east coast snowstorm •^^6N \ \JB •.s \ N \ l \ i / \ x \ \ \\ f^k u • \ ** 3v3 N ^"ru^a & c 1) ERA F30: 25/00 dl ) ERR F3G: 25/06 c2) Oz/ERfl F30:25/00 d2) Oz/ERfl F36:25/OG K > / / // ,t \Y ' / / " 1 if f IrH Mil y// c3) Et a. F30: 25/00 d3) Et a F3G: 25/06 CH) Oz/Et a F30: 25/00 dl) Oz/Eta F36:25/06 c5) GEM F30:25/00 d5) GEM F36: 25/06 cG) Oz/GEM F30: 25/00 dG) Oz/GEM F36: 25/06 Fig. 3.33 continued. 202 3.2: Simulations of the 24-25 January 2000 east coast snowstorm The 850-hPa fields of Fig. 3.34 confirm the higher static stability of the simulations initialized at 23/18, suggested by the 500-hPa fields of Fig. 3.33: compared to rawinsonde-derived fields, all simulations are too dry at both 24/12 and 25/00, while being only slightly too warm at 24/12 and definitely too cold at 25/00. Furthermore, the fact that the onshore 850-hPa ascent of these simulations, which is collocated with geostrophic warm air advection, is virtually insignificant and is seen only at 24/12 and 24/18 also suggests a statically stable atmosphere. Therefore, given that the stronger (re)analysis 500-hPa troughs were unable to generate significant onshore precipitation, the inability of the three ozone simulations to generate onshore precipitation is probably due less to the underdevelopment of the ozone troughs and more to the overly strong static stability generated in all six experiments. Investigating the cause of this excessive static stability is beyond the scope of the current research. Fig. 3.34 The 850-hPa temperature (dark green contours every 3 °C with the 0-°C contour heavy and values increasing from northwest to southeast), mixing ratio (light blue contours at 4, 5, 6 g kg"1 with values increasing from northwest to southeast), ascent (contours at -4, -12xl0-3 hPa s-1 in brown and orange) and sea level pressure (purple, 4-hPa contour interval with values increasing from southeast to northwest) fields are shown for experiments initialized at 23/18. Also shown, when available, are rawinsonde contoured 850-hPa temperatures (plotted as per the simulation temperatures but in light green) and mixing ratios (black dotted contours at 4, 5, 6 g kg-1). Titles indicate the experiment name, forecast hour, and actual date/time. Note that the date/time varies by column and the experiment by row. 203 3.2: Simulations of the 24-25 January 2000 east coast snowstorm a 1 ) ERA F18: 21/12 b\ ) ERR F21:21/18 a2) Oz/ERfl F18: 21/12 J>2) Oz/ERfl F21: 21/18 a3) Eta F18:21/12 b3) Et a F21: 21/18 al) Oz/Eta F18:21/12 bl) Oz/Eta F21: 21/18 i5) GEM F18:21/12 b5) GEM F21: 21/18 16) Oz/GEM F18: 21/12 bB) Oz/GEM F21: 21/18 Fig. 3.34 See caption on previous page. 204 3.2: Simulations of the 24-25 January 2000 east coast snowstorm c 1) ERR F30: 25/00 dl) ERR F36:25/OG c2) Oz/ERR F30: 25/00 d2) Oz/ERR F3G: 25/OG c3) Eta F30: 25/00 d3) Et a F36: 25/06 cM) Oz/Eta F30:25/00 d*\) Oz/Eta F36: 25/06 c5) GEM F30: 25/00 d5) GEM F36: 25/06 cB) Oz/GEM F30: 25/00 d6) Oz/GEM F36: 25/06 Fig. 3.34 continued. 205 3.2: Simulations of the 24-25 January 2000 east coast snowstorm Thus, no experiment initialized at 23/18 was able to develop accurately the crucial 500-hPa ascent and 850-hPa temperature and moisture, and, consequently stability, fields. Since even the three (re)analyses, with their deeper initializing upper-level troughs, were unable to simulate the event's 500-hPa ascent field, the weakness of the ozone-influenced upper-level initializing troughs cannot be blamed entirely for the failed ozone precipitation forecasts: the overly stable atmospheres produced by all six experiments prevented the conversion of 500-hPa forcing for ascent into actual ascent. The fact that the ozone and (re)analysis experiments' forecasts are ordered identically indicates that the low-level and PV inversion boundary condition fields strongly influence these simulations. The fact that all precipitation forecasts are poor indicates that these fields most likely contain non-negligible faults. These faults are most likely responsible for the simulations' overly strong static stability. Thus, concerning the 2n objective of this research, a weakness of the ozone- influenced initializing fields is that even perfect ozone-influenced upper-level initializing fields cannot guarantee an accurate forecast; if the low-level temperature and moisture fields are inaccurate to the point of significantly corrupting the static stability profile, then even perfect upper-level fields will be unable to generate precipitation. Unfortunately, given the poor performance of all six experiments, the simulations initialized at 23/18 are unable to indicate with any precision the length of lead time that the ozone-influenced initializing fields are capable of providing; the poor performance of the ozone experiments is not linked solely to errors in the upper-level initializing fields. The fact that the ozone precipitation 206 3.2: Simulations of the 24-25 January 2000 east coast snowstorm forecasts were not significantly worse than those of the (re)analyses suggests that the ozone fields should be capable of providing some lead time for other events. 3.2.3 Summary of modeling results 1. Findings from the simulations initialized at 24/18: • Although the ozone-influenced upper-level initializing fields degraded the ERA accumulated precipitation forecast, they improved both the Eta and GEM forecasts. Ozone/GEM produced the best forecast of all. This indicates that ozone-influenced initializing fields have the ability to improve precipitation forecasts, even in the simulation of an event in a data rich area. The fact that ozone-influenced upper-level initializing fields were able to improve the GEM precipitation forecast unambiguously is an unprecedented result; the Jang et al. (2003) ozone-influenced forecast improved their control precipitation forecast only partially. • Our novel procedure was able to produce a precipitation forecast that is superior to the Jang et al. (2003) ozone-influenced 4D-Var assimilation forecast, despite the greater technological superiority of 4D-Var. • The fact that the three ozone precipitation forecasts differed substantially indicates that the ozone-influenced upper-level initializing fields require good quality low-level and PV inversion boundary condition fields in order to produce accurate precipitation forecasts. • Crucial to the production of onshore precipitation during this event were 500-hPa height, geostrophic cyclonic vorticity advection and ascent fields, 207 3.2: Simulations of the 24-25 January 2000 east coast snowstorm and 850-hPa moisture and temperature fields. At CHS at 25/00, the ongoing static destabilization from the surface to 400 hPa and the onshore moisture transport from the surface to 775 hPa were important. • Features of the simulations' sea level pressure, 1000-500-hPa thickness, dynamic tropopause potential temperature, 250- and 925-hPa fields had a less obvious impact on the generation of this event's onshore precipitation. • The Eta experiment performed poorly because, compared to the two GEM simulations, its: — 500-hPa ascent region was weak and penetrated insufficiently inland, owing to the presence of an overly large cut-off low at 25/06. The depth of the Eta initializing trough, which was the deepest of the three (re)analyses, likely spawned the problematic cut-off low; — initializing 850-hPa atmosphere was too dry and cool, and, consequently, stable, over South Carolina; — ongoing atmospheric destabilization and onshore moisture transport were both weak at CHS at 25/00; — 250-hPa winds were far too weak at 24/12, before the start of the simulations. • Ozone/GEM produced a better precipitation forecast than GEM because: — its 500-hPa height field was more accurate, leading to stronger onshore geostrophic cyclonic vorticity advection and ascent; — its ongoing static destabilization of the atmosphere and onshore moisture flow were both stronger at CHS at 25/00. 208 3.2: Simulations of the 24-25 January 2000 east coast snowstorm • Ozone-influenced 250-hPa initializing winds gained a divergent component within six hours. 2. Additional findings from the simulations initialized at 23/18: • The presence of errors in the low-level initializing fields was indicated by the inaccuracy of all onshore accumulated precipitation forecasts. • Additional errors in the ozone-influenced upper-level initializing fields, for instance, the weakness of the upper-level troughs, were responsible for the further degradation of the precipitation forecasts. • The poor quality of the ozone precipitation forecasts cannot be blamed entirely on the trough weakness; the excessive static stability in all six experiments hindered the conversion of 500-hPa forcing for ascent to actual ascent. • Given the poor precipitation forecasts of all six experiments, this set of simulations was unable to evaluate the length of lead time that the ozone- influenced upper-level fields are capable of providing. 209 3.2: Simulations of the 24-25 January 2000 east coast snowstorm This page is left intentionally blank. Chapter 4: Summary and Conclusions Chapter 4: Summary and Conclusions 4.1 Summary We have presented a methodology for generating model initializing fields from satellite total column ozone data. We then test the validity of the presented methodology by using the MC2 to simulate the 24-25 January 2000 east coast snowstorm. 4.1.1 Generation of model initializing fields from satellite total column ozone data The principal features of the methodology to convert a total column ozone field to model initializing fields are: I. The conversion of the total column ozone field to an MPV field by: 1. Temporally interpolating the local noon total column ozone field to 1800 UTC using pure advection by ERA-40 dynamic tropopause winds divided by 2.0, 2. Converting the total column ozone field to an MPV field with regression parameters calculated using valid points from all latitudes together, MPV based on ERA-40 PV from 400 to 50 hPa, and a regression period of two weeks prior to the target date in the target date's year, 211 Chapter 4: Summary and Conclusions 3. Synthesizing the regressed and ERA-40 MPV fields by erasing the analysis trough, inserting the regressed trough and overlaying the analysis ridge; II. The conversion of the 2D MPV field to a 3D PV field by: 2. Generating average PV profiles using 12 MPV categories, a minimum of only one space/time point, a 10° latitude by 10° longitude grid box centred on the given grid point, and a period of two weeks plus the target date itself, 3. Mapping the synthesized MPV field vertically onto each grid point's appropriate average PV profile using a level-varying mapping coefficient with automatic mapping from 50-400 hPa and optional mapping at 500 and 600 hPa; III. The inversion of the derived 3D PV field to generate model initializing fields. The Davis and Emanuel (1991) PV inversion method is used with the following principal modification: 1. The inversion domain is divided into six subdomains to prevent the generation of height field dipoles. The most important aspects of this methodology that are not documented in the literature are: • The use of analyzed dynamic tropopause advecting winds in the temporal interpolation of the total column ozone field. This permits the alignment of the ozone and MPV fields prior to the regression parameter calculations, which should increase the accuracy of those parameters. 212 Chapter 4: Summary and Conclusions This technique is of interest to the 3D-Var assimilation of total column ozone; • The detailed study of how best to correlate total column ozone and MPV fields. This study should be of great use to anyone working with these two fields, including those who assimilate total column ozone using 3D- or 4D-Var techniques; • The idea of dynamically-selecting the most reliable features (troughs) of the total column ozone field, instead of rejecting all total column ozone data as a result of undeniable problems in the vicinity of ridges, owing to the inability of the ozone field to "see" diabatic ridge-building. Even if total column ozone data are used operationally only to correct initializing troughs over data sparse regions, that gain in data should improve model performance. This feature selection is of interest to the 3D- and 4D-Var assimilation of total column ozone; • The generation of average PV vertical profiles. Once these profiles have been created for a given grid point and time period, they can be used repeatedly over many years, as per a climatology. They are, thus, computationally inexpensive. Although average profiles are probably not of interest in the variational assimilation of total column ozone, they might be of interest in the processing of other 2D fields; • The use of level-varying coefficients for the vertical mapping of synthesized MPV onto the average profiles. This technique is of definite interest for all variational assimilation of total column ozone. As discussed in Section 2.1.5, the correct vertical distribution of the MPV or 213 Chapter 4: Summary and Conclusions total column ozone increment is known to be problematic, with acknowledged inaccuracies in the ERA-40 (Dethof and Holm 2004). In the same section, evidence was also provided of an incorrect vertical distribution of the increment by Jang et al. (2003). This technique may also be relevant to the assimilation of other satellite fields, and of single- level aircraft data. • The demonstration of a successful PV inversion, despite the use of a subdivided domain. As horizontal resolutions increase, augmenting the number of inversion domain grid points, the inversion-induced height field dipole that we encountered will occur more frequently. Our subdivision technique eliminates this dipole. It is, therefore, important. Problems associated with this methodology that could not be eliminated include: • The smoothing induced by the PV inversion. Although the use of subdomain divisions reduced the degree of smoothing somewhat, the smoothing was not eliminated. 4.1.2 Validation of the ozone-influenced model initializing fields The validation of the presented methodology involves six MC2 simulations of the 24-25 January 2000 east coast snowstorm. Three sets of low-level fields (ERA-40, Eta and GEM) are used, where "low-level" consists of levels up to 700 hPa. An experiment's source of low-level fields also provides moisture fields at 214 Chapter 4: Summary and Conclusions all levels. Upper-level fields are either from the same source as the low-level fields, or are derived using input from a total column ozone field. PV inversion boundary condition fields are provided by the same source as the low-level fields. These six simulations were initialized at 1800 UTC on both the 23rd and 24th. The principal ozone-related findings from the simulations initialized at 1800 UTC 24 January 2000, or six hours after the onset of precipitation in South Carolina, are: • The best onshore accumulated precipitation forecast was initialized with ozone-influenced upper-level fields. This forecast compares extremely well against published forecasts; it is even superior to an ozone-influenced 4D-Var assimilation forecast, despite this assimilation system's greater technological superiority. The single published forecast that surpasses it does so principally on account of its higher values in South Carolina. The lower values in South Carolina of our best forecast are possibly unavoidable, given the experiment's late initialization time six hours after the onset of precipitation in that state; • Ozone-influenced upper-level initializing fields improved the onshore accumulated precipitation forecast for two out of the three sources of low- level fields, even in this data rich eastern U.S region. The unambiguous improvement of the GEM onshore accumulated precipitation forecast by the inclusion of ozone data is unparalleled, as the single published ozone- influenced precipitation forecast, that of Jang et al. (2003), only partially improved the control forecast. 215 Chapter 4: Summary and Conclusions • Ozone-influenced upper-level initializing fields require good quality low- level fields in order to produce accurate precipitation forecasts; • Ozone-influenced 250-hPa initializing winds gained a divergent component within six hours. Concerning the six simulations initialized at 1800 UTC 23 January 2000: • Ozone-influenced upper-level initializing fields degraded the onshore accumulated precipitation forecast for all three sources of low-level fields; • The lead time afforded by ozone-influenced upper-level fields could not be evaluated, given that all six experiments performed poorly. The most important aspects of the validation of the presented methodology are that: • Ozone-influenced upper-level initializing fields can produce excellent precipitation forecasts, improving, even in a data rich area, on forecasts initialized entirely by analyses. This demonstrates that assimilating total column ozone data is of operational interest, particularly for data sparse regions; • Our methodology, owing to its novel procedures, was able to produce an ozone-influenced precipitation forecast that surpasses an ozone-influenced 4D-Var forecast, despite the technological superiority of 4D-Var assimilation; • The quality of the precipitation forecast produced using ozone-influenced upper-level initializing fields is affected by the (in)accuracy of the low- level fields provided. The extent of the impact of this (in)accuracy, or, 216 Chapter 4: Summary and Conclusions conversely, of the ozone-influenced initializing fields, on the forecast will be determined in part by whether the surface cyclone's development is more strongly associated with upper- or low-level dynamics. 4.2 Conclusions Concerning the four objectives of this thesis, which were originally stated in Section 1.2: Objective 1: Starting from satellite total column ozone data, to analyse a realistically deep height field trough in association with the unforecasted U.S. east coast snowstorm of 24-25 January 2000. Comment 1: Although the ozone-influenced initializing trough was slightly too deep at 500 hPa and slightly too weak at 250 hPa for the simulations initialized at 24/18, it is fair to say that it was "realistically deep". Thus, starting from a total column ozone field, "a realistically deep trough" was, indeed, analysed in association with the unforecasted U.S. east coast snowstorm of 24-25 January 2000. Objective 2: Starting from satellite total column ozone data, to forecast significant onshore precipitation during the 24-25 January 2000 east coast snowstorm. Comment 2: It is possible to produce an excellent accumulated precipitation forecast of the east coast snowstorm with significant onshore values using upper- 217 Chapter 4: Summary and Conclusions level dynamical initializing fields influenced by a satellite total column ozone field. Our best ozone-influenced onshore accumulated precipitation forecast of the event, that of ozone/GEM, is superior or equal to all but one published forecast, which may remain unsurpassed due to the fact that our simulation was initialized six hours after the onset of precipitation in South Carolina; the overly low values in that state are possibly unavoidable with our late initialization time. Of great significance is the fact that the ozone/GEM onshore accumulated precipitation forecast is superior to an ozone-influenced 4D-Var assimilation forecast, despite the technological superiority of 4D-Var assimilation. Furthermore, our inclusion of ozone-influenced upper-level initializing fields unambiguously improved the GEM precipitation forecast, while the Jang et al. (2003) 4D-Var ozone-influenced forecast is only partially superior to their control forecast. Thus, the ozone/GEM onshore accumulated precipitation forecast represents an important achievement and a validation of the presented methodology. The fact that the ozone-influenced upper-level initializing fields improved the forecast for two of the three sets of low-level fields is particularly significant, given that the event was located over the data rich eastern U.S. where the models can be expected to be at their most accurate. The fact that the ozone- influenced initializing fields are generated from a single 2D field makes this achievement no less than astounding. Objective 3: To develop a methodology that, starting from total column ozone data, generates an ensemble member that is as independent as possible of an operational centre's assimilation system. 218 Chapter 4: Summary and Conclusions Comment 3: The methodology converting a total column ozone field to model initializing fields above 700 hPa is completely automated. Moreover, the initializing fields produced by this methodology have been validated by the MC2 simulations. The methodology is, therefore, of interest operationally and could easily be used to generate an ensemble member. A benefit of this ensemble member is that its upper-level fields would be almost completely independent of the operational assimilation system. Where the forecast involves a data poor area or where forecasts from traditionally-initialized simulations lack coherence, either over initializing times or between ensemble members, denoting a problem in the initializing fields, the forecast initialized with ozone-influenced fields could be given a greater weighting. An entire group of ozone-influenced ensemble members could also be created operationally very easily by varying Table 2.1's factork values, which would concentrate the MPV increment at different levels. Objective 4: To develop a methodology that converts a 2D total column ozone field to a 3D dynamical field, of which components can be adapted for 3D- and 4D-Var data assimilation. Comment 4: Many components of the presented methodology could be adapted to the 3D- and 4D-Var assimilation of total column ozone. Both assimilation systems would be interested in our in depth study of total column ozone/MPV regression, the dynamical selection of portions of the total column ozone field for assimilation, and the use of level-varying vertical mapping coefficients. A 3D- Var system would further be interested in the presented temporal interpolation scheme. Since variational assimilation bypasses this research's PV inversion, the 219 Chapter 4: Summary and Conclusions smoothing introduced by the inversion does not affect the ozone assimilation. Thus, combining the appropriate components of the presented methodology with variational assimilation could produce the best results of all. In conclusion, this thesis has both presented a methodology to generate numerical weather prediction model upper-level initializing fields from satellite total column ozone fields, and has demonstrated that these ozone-influenced upper-level initializing fields are capable of improving the precipitation forecast for a record-breaking event. This methodology could greatly benefit operational weather forecasting centres, particularly in regards to data sparse regions. Thus, this research contributes to remedying the current situation where "a large fraction of current observations are not being assimilated into today's model" (Fritsch and Carbone 2004). It has also answered the call by the 8th United States Weather Research Program (Fritsch et al. 1998) to use satellite data more. Finally, this research also fulfills the first recommendation of the 7l United States Weather Research Program (Emanuel et al. 2007), which promotes "the use of suitably designed data sensitivity experiments for assessing the effectiveness of present and proposed data sources and observation strategies". 4.3 Future work The presented methodology has been validated by the simulation of a single event. More cases need to be simulated in order to evaluate more precisely the potential of the ozone-influenced upper-level initializing fields. It would be 220 Chapter 4: Summary and Conclusions useful to select the additional test cases from a variety of seasons, in recognition of both the seasonal variation of total column ozone, where Northern Hemispheric maximum values are recorded in winter/spring and minimum values in late autumn, and its seasonal variability, with Northern Hemispheric yearly maximum values varying four times as much as yearly minimum values (see Section 2.1.1). Optimally, some cases would be selected from the largely data sparse Southern Hemisphere, where both smaller mean total column ozone values and a smaller seasonal variation of values are observed, owing to less intense transport processes (see Section 2.1.1). Since not all precipitation events are equally predictable "even for days with comparatively similar synoptic conditions" (Walser et al. 2004), simulating multiple events serves to reduce the impact of an individual case's predictability. Note, however, that ozone-influenced initializing fields may be of interest principally in association with the less predictable events, where traditionally- initialized forecasts vary considerably between models and initializing times, indicating initial condition uncertainties. Simulating multiple events would also help to clarify the lead time that ozone-influenced fields are capable of providing. Furthermore, the factork values for the level-varying vertical mapping coefficient of Section 2.3.2.2 could be determined more precisely if multiple events were simulated. Following the discussion in Section 2.3.1.4 concerning the inability of the total column ozone field to "see" and, consequently, advect diabatically-built ridges, an investigation needs to be conducted into the length of time required for the total column ozone field to reflect diabatically-produced changes in the MPV 221 Chapter 4: Summary and Conclusions field. It can then be determined whether diabatic changes in the MPV field, and the advection of those changes, should be tracked with a view to adjusting the total column ozone field before the temporal interpolation of Section 2.3.1.2. Performing such an adjustment should render the synthesizing process of Section 2.3.1.5 unnecessary. Finally, since our best ozone-influenced QPF surpassed the Jang et al. 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