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Investigation of Warm Season Convective Cloud and Precipitation Properties through the Integrative Analysis of Aircraft In-situ Measurements, Ground-based Observations, and WRF Simulations

Item Type text; Electronic Dissertation

Authors Wang, Jingyu

Publisher The University of Arizona.

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INVESTIGATION OF WARM SEASON CONVECTIVE CLOUD AND PRECIPITATION

PROPERTIES THROUGH THE INTEGRATIVE ANALYSIS OF AIRCRAFT IN-SITU

MEASUREMENTS, GROUND-BASED OBSERVATIONS, AND WRF SIMULATIONS

Jingyu Wang

A Dissertation Submitted to the Faculty of the

DEPARTMENT OF HYDROLOGY AND ATMOSPHERIC SCIENCES

In Partial Fulfillment of the Requirements

For the Degree of

DOCTOR OF PHILOSOPHY

In the Graduate College

THE UNIVERSITY OF ARIZONA

2018

STATEMENT BY AUTHOR

This dissertation has been submitted in partial fulfillment of the requirements for an advanced degree at the University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library.

Brief quotations from this dissertation are allowable without special permission, provided that an accurate acknowledgement of the source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his or her judgment the proposed use of the material is in the interests of scholarship. In all other instances, however, permission must be obtained from the author.

SIGNED: Jingyu Wang

ACKNOWLEDGEMENTS

I gratefully acknowledge the sponsor of U.S. Department of Energy (DOE) Atmospheric

Radiation Measurement (ARM) Program, as well as the National Oceanic and Atmospheric

Administration (NOAA) Research to Operation (R2O) Program, whose sponsorship allowed me to pursue my education and research at the Department of Hydrology and Atmospheric Sciences,

University of Arizona.

I am grateful to my advisors: Drs. Xiquan Dong and Baike Xi, and committee members: Drs.

Xubin Zeng, C. L. Larry Winter, Greg M. McFarquhar, and Pieter Hanzenberg. I would also express my sincere appreciation to Drs. Aaron D. Kennedy, Christopher L. Castro and Thomas J.

Galarneau for the insightful discussions, which kept me motivated throughout my entire study period.

I would also thank my previous committee members and all the faculties from the

Department of Atmospheric Sciences, University of North Dakota. Thanks to Dr. Leon Osborne

Jr., Michael R. Poellot, Cedric A. Grainger, Mark A. Askelson, Gretchen Mullendore, Jianglong

Zhang and David J. Delene. Special thanks to Dr, Andrew J. Heymsfield from National Center for Atmospheric Research (NCAR), who introduced me to the community of aircraft in-situ instrumentation.

I would say thank you to all my fellow students and to administrative and supporting staff in

Department of Hydrology and Atmospheric Sciences, especially, to Sandy Holford, Lupe

Romero, Sarah Warren, Mike Eklund and Thomas Phelan for caring attitude and continuous support.

Finally, I am grateful to my wife who whole-heartedly supported me through my entire study period, and I would say thank you to my daughter Joyce for being an important part of my life.

TABLE OF CONTENTS LIST OF TABLES ...... 8 LIST OF FIGURES ...... 9 ABSTRACT ...... 15 CHAPTER 1: INTRODUCTION ...... 17 1.1 IMPORTANCE OF CONVECTIVE SYSTEMS ...... 17 1.2 OBSERVATION SYSTEMS FOR CLOUD AND PRECIPITATION ...... 18 1.2.1 Aircraft In-situ Measurements ...... 18 1.2.2 Radar Measurements ...... 20 1.2.3 Surface In-situ Measurements ...... 21 1.2.4 Areal Precipitation Datasets ...... 22 1.3 SYNOPTIC PATTERNS RELATED TO CONVECTIVE SYSTEMS ...... 27 1.4 OBJECTIVES ...... 36 CHAPTER 2: PRESENT STUDY...... 37 2.1 INVESTIGATE ICE CLOUD PROPERTIES OF MCSs FROM AIRCRAFT IN-SITU MEASUREMENTS ...... 37 2.2 INVESTIGATE LIQUID CLOUD AND PRECIPITATION PROPERTIES of MCSs FROM AIRCRAFT AND SURFACE MEASUREMENTS ...... 38 2.3 EVALUATE WRF SIMULATED PRECIPITATION ...... 40 2.4 FUTURE RESEARCH DIRECTIONS ...... 48 REFERENCES ...... 50 APPENDIX A: INVESTIGATION OF ICE CLOUD MICROPHYSICAL PROPERTIES OF DCSS USING AIRCRAFT IN-SITU MEASUREMENTS DURING MC3E OVER THE ARM SGP SITE ...... 59 ABSTRACT ...... 60 1. INTRODUCTION ...... 61 2. DATA ...... 66 2.1 PSD MEASUREMENTS ...... 66 2.2 IWC/LWC MEASUREMENTS ...... 68 2.3 PHASE DETERMINATION ...... 70 3. RESULTS AND DISCUSSION ...... 73 3.1 RECALIBRATION OF MASS-DIMENSIONAL RELATIONSHIPS ...... 74 3.2 FITTING THE OBSERVED PSDS ...... 82 3.3 MULTIMOMENT ASSESSMENTS OF FITTED PSD PARAMETERS ...... 83

* 3.4 EMPIRICAL RELATIONSHIPS BETWEEN FITTED PARAMETERS AND Ze ...... 89 4. SUMMARY AND CONCLUSIONS...... 94 ACKNOWL.EDGEMENTS ...... 97 APPENDIX A: CALIBRATION AND TREATMENT OF BASELINE DRIFT FOR NEVZOROV TWC PROBE ...... 98 REFERENCES ...... 99 APPENDIX B: INVESTIGATION OF LIQUID CLOUD MICROPHYSICAL PROPERTIES OF DEEP CONVECTIVE SYSTEMS: 1. PARAMETERIZATION OF RAINDROP SIZE DISTRIBUTION AND ITS APPLICATION FOR STRATIFORM RAIN ESTIMATION ..... 107 ABSTRACT ...... 108 1. INTRODUCTION ...... 108 2. DATA ...... 113 2.1 AIRCRAFT IN-SITU MEASUREMENTS ...... 114 2.2 GROUND-BASED RADAR OBSERVATIONS ...... 118 2.3 SURFACE RAIN RATE MEASUREMENTS ...... 121 3. NEW DSD PARAMETERIZATION SCHEME AND ITS APPLICATION FOR PRECIPITATION ESTIMATION ...... 123 3.1 FITTING TO THE IN-SITU MEASURED DSDS ...... 125 3.2 SEMIEMPIRICAL RELATIONSHIPS BETWEEN FITTED DSD PARAMETERS AND Ze ...... 129 3.3 APPLICATION OF NEWLY PARAMETERIZED DSDS FOR PRECIPITATION ESTIMATES AND ASSESSMENT ...... 131 3.4 EVALUATION OF MARSHALL-PALMER Z-R RELATIONSHIPS USED IN Q2 PRECIPITATION ESTIMATES ...... 140 4. SUMMARY AND CONCLUSIONS...... 144 ACKNOWLEDGEMENTS ...... 147 APPENDIX A ...... 148 APPENDIX B ...... 149 REFERENCES ...... 150 APPENDIX C: INVESTIGATION OF LIQUID CLOUD MICROPHYSICAL PROPERTIES OF DEEP CONVECTIVE SYSTEMS: 2. PARAMETERIZATION OF RAINDROP SIZE DISTRIBUTION AND ITS APPLICATION FOR CONVECTIVE RAIN ESTIMATION ..... 162 ABSTRACT ...... 163 1. INTRODUCTION ...... 163 2. DATA ...... 166

3. RESULTS...... 174 3.1 SENSITIVITY OF FITTING SPECTRUM SUBSET TO THE PRECIPITATION ESTIMATION ...... 174 3.2 COMPARISON BETWEEN DIFFERENT PARAMETERIZATION SCHEMES ..... 180 3.3 EVALUATION OF THE NEW CR PRECIPITATION ESTIMATION ...... 182 4. SUMMARY AND CONCLUSIONS...... 185 ACKNOWLEDGEMENTS ...... 186 REFERENCES ...... 187 APPENDIX D: EVALUATION OF NORTHERN AND SOUTHERN GREAT PLAINS WARM SEASON PRECIPITATION EVENTS IN WRF. PART II: ANALYSIS OF OBSERVED AND SIMULATED PRECIPITATION ...... 196 ABSTRACT ...... 197 1. INTRODUCTION ...... 198 2. DATA AND METHODOLOGY ...... 200 3. RESULTS...... 201 3.1 THE SOUTHERN GREAT PLAINS ...... 201 3.2 THE NORTHERN GREAT PLAINS ...... 212 3.3 EVALUATION OF NSSL-WRF SIMULATION USING STANDARD PERFORMANCE INDICES ...... 219 4. SUMMARY AND DISCUSSIONS ...... 222 ACKNOWLEDGEMENTS ...... 225 REFERENCES ...... 226

LIST OF TABLES

Table 1. The statistical comparisons between NSSL-WRF simulations and Stage IV observations based on grid-points at the precipitation accumulation intervals of 1-hour, 3-hour, 6-hour, and 24- hour over the SGP and NGP regions...... 41

Table A. 1. The University of North Dakota Citation II aircraft probes used in this study...... 66

Table A. 2. The criteria of using multiple sensors to detect supercool liquid water content ...... 73

Table A. 3. The summary of aircraft flight date, time, altitude, temperature and NEXRAD radar reflectivity along the aircraft track for the six selected DCS cases during MC3E...... 74

Table A. 4. The mass contribution from particles with D > 4,000 μm to the calculated total IWC ...... 79

Table A. 5. Means and standard deviations of the PSD parameters from fitted gamma-type-size- distributions, measured equivalent NEXRAD radar reflectivity (Ze), and calculated one (Ze*) using the observed PSDs ...... 87

Table A. 6. Means and standard deviation of total number concentration (Nt), maximum diameter (Dmax), median mass diameter (Dm) using the observed PSDs and empirical fitted relationships (Dm* and IWC*) ...... 87

Table B. 1. Summary of surface rain rate measurements ...... 123

Table B. A1. Aircraft probes’ diameter and width for each bin used in SR rain rate calculation ...... 148

Table B. B1. Summary of 17 NASA GPM GV Automatic Parsivel Unit (APU) measurements ...... 149

Table C. 1. The shape corrected raindrop volume-equivalent diameter classification for the APU...... 173 Table D. 1. Daytime and nighttime 12-hour accumulated precipitation from Stage IV observations, NSSL-WRF simulations, and their differences for each class of the SGP and the NGP SOMs...... 208

Table D. 2. Precipitation intensity and coverage from Stage IV and NSSL-WRF for each class of the SGP SOM. Precipitation is separated into total, convective rain (CR), and stratiform rain (SR) components...... 211

Table D. 3. As in Table D. 2 but for the NGP SOM ...... 217

Table D. 4. The performance indices of NSSL WRF simulation for each class over both the SGP and the NGP...... 222

LIST OF FIGURES

Figure 1. UND Citation II aircraft configuration...... 19

Figure 2. The distribution of NEXRAD radars (black dot) and the observed radar echoes at 2 km above ground level (colored contour) ...... 20

Figure 3. Comparisons of accumulated precipitation amount (a) OK Mesonet gauge-based observation (127 stations), (b) radar-based estimation (Q2 hourly gauge-adjusted QPE), and (c) the Stage IV data during Mid-latitude Continental Convective Clouds Experiment (MC3E, April 22 – June 6, 2011). The extrapolated spatial distribution at the locations of 127 Mesonet stations using the data from (d) tipping bucket measurements, (e) Q2 QPE (e), and (f) Stage IV data. ..24

Figure 4. (a) The accumulated precipitation amount as a function of accumulated precipitation hours at 127 Mesonet stations (black dots), as well as the classified convective rain (CR, red dots) and stratiform rain (SR, green dots) during the entire MC3E (46 days) using the 5-minute Mesonet observations. (b) Same as (a) but the 5-minute Mesonet observations are accumulated into hourly data and the criterion for separating CR and SR is set to be 10 mm hr-1. (c) Changing the input data to Q2_ajusted QPE at Mesonet stations with the same criterion (10 mm hr-1) for separating CR and SR. (d) Same as (c) but changing the input data to Stage IV at Mesonet stations with a criterion of 5 mm hr-1 for separating CR and SR...... 26

Figure 5. The domains of Southern Great Plains (SGP) and Northern Great Plains (NGP). Blue boxes for the synoptic pattern analysis, and red boxes for the NSSL WRF precipitation evaluation...... 30

Figure 6. SOM result for synoptic pattern based on the input variable from NARR. For (a), (b), (c), (d), (e), and (f), the left panel represents the 500 mb geopotential height anomaly, right panel represents the 900 mb relative humidity (color filled) and mean surface level pressure (dash lines). (g) and (h) are for the composite results from (a), (b), and (c), named Type 1 synoptic pattern, (i) and (j) are for the composite results from (d), (e), and (f), named Type 2 synoptic pattern...... 32

Figure 7. Similar to Figure 6 but over the NGP region...... 33

Figure 8. The seasonal variation of the occurrence frequency of Type 1 storms (blue bars) and Type 2 storms (red bars) over the SGP (a) and NGP (b) regions...... 34

Figure 9. The comparison of the SGP annual precipitation between Stage IV observations (a, d) and NSSL WRF simulations (b, e) between the Type 1 (upper panel) and the Type 2 (lower panel), as well as their corresponding direction variation (c, f), where red lines represents the zonal variation and blue represents the meridional variation, and solid (dash) line for Stage IV (NSSL WRF) data...... 43

Figure 10. Same as Figure 9 but over the NGP...... 44

Figure 11. The diurnal cycle comparison between Stage IV observations (solid lines) and NSSL

WRF simulations (dash lines) for Type 1 (a, b) and Type 2 (c, d) synoptic patterns over the SGP (a, c) and the NGP (b, d). The local night is shaded gray from 0600 to 2000 LST, and the total bias between the two datasets are also calculated for each time period as shown below the diurnal curves...... 45

Figure A. 1. A schematic diagram of flight trajectories (black lines) superimposed on Convective- Stratiform-Anvil (CSA) classified Deep Convective Systems (DCSs). For six selected cases: (a) 27 April 2011, (b) 1 May 2011, (c) 11 May 2011, (d) 18 May 2011, (e) 20 May 2011, and (f) 24 May 2011 during the Midlatitude Continental Convective Clouds Experiment (MC3E). The classification of DCS components (CC-Convective Core; SR-Stratiform; AC-Anvil Cloud) follows the methodology of Feng et al. 2011...... 65

Figure A. 2. (a) NEXRAD radar reflectivity cross-section along the aircraft track (contour), aircraft altitude (black) and temperature (red). (b) Super-cooled liquid water content (SLWC) was identified by one of the following measurements: the Rosemount Icing Detector (RID, blue line, a sudden drop in frequency due to SLWC occurrence), by King Probe (high LWC, cyan line), and CDP probe (high LWC, red line; and high CDP concentration, red circle), accounting for particles with D < 50 μm. (c) Samples of 2DC and CIP image during the SLWC detection recorded by other instruments, accounting for particles with D > 50 μm...... 71

Figure A. 3. A schematic sketch of determining the coefficient a and exponent b of mass- dimensional relationship (IWC~ aDb). Calculated IWCs from PSDs at different time (left column) should be the same as measured IWCs (right column)...... 76

Figure A. 4. (a) Frequency distributions of the ratios of the IWCs calculated from PSDs using the BF95 method (a=0.00294, b=1.9, black line) and the newly derived mass-dimensional relationship from aircraft in situ measurements (IWCprobes, red line) during MC3E (a=0.00365, b=2.1) to the Nevzorov measured IWCs (IWCNEV) for the samples with Dmax < 4,000 μm, following the suggestion of Korolev (2013). (b) The ratios of IWCprobes to IWCNEV increase but their 2 corresponding correlations (R ) decrease with increased Dmax values. (c) The averaged IWCprobes (red line) and IWCNEV (black line) at different Dmax values, and the underestimation precentages of the IWCNEV (blue line) relative to the IWCprobes at different Dmax values...... 77

Figure A. 5. (a) NEXRAD radar reflectivity cross-section along the aircraft track (contour), aircraft altitude (black) and temperature (red) on 20 May 2011 during MC3E. (b) IWC measured from Nevzorov probe (blue) and IWC calculated using recalibrated mass-dimensional relationship (~aDb, red). (c) The maximum diameter measured (green) and median mass diameter (black) and (d) The total number concentration (cyan) derived from a combination of 2DC and HVPS measurements...... 80

Figure A. 6. The observed PSDs at different aircraft legs (blue bars) and their corresponding fitted gamma-type-size-distributions (red lines) during the case of 20 May 2011. (a) ~ 7.3 km, 14:15 UTC (left and right); (b) ~ 6.6 km, 14:02 (left) and 14:35 UTC (right); (c) ~5.8 km, 13:54 (left) and 14:52 UTC (right); (d) ~ 5.0 km, 13:41 (left) and 14:55 UTC (right); (e) ~4.0 km, 13:34 (left) and 15:08 UTC (right)...... 82

Figure A. 7. The multi-moment assessments in (a) first moment (Dm), (b) third moment (IWC), and (c) sixth moment (equivalent NEXRAD radar reflectivity Ze) between calculated values using the PSDs constructed from fitted gamma-type-size-distributions and observed PSDs on 20 May case. Scattering comparisons are shown in right column...... 84

Figure A. 8. Similar to Figure A. 7 but using Taylor diagram to display the comparisons in Dm, IWC, and Ze calculated using the PSDs constructed from fitted gamma-type-size-distributions and the observed PSDs for the six selected cases. In the polar coordinate system, the distance from origin to a certain point represent the normalize standard deviation (standard deviation of fitted results divided by standard deviation of observational results), and the angle from the x direction represent the correlation between fitted results and observational results...... 88

Figure A. 9. Parameterization of originally fitted λ values as a function of calculated equivalent NEXRAD radar reflectivity Ze* using observed PSDs (5,589 5-s samples) for the six selected cases during MC3E...... 90

Figure A. 10. Intercept N0 and slope µ as functions of originally fitted λ values. (a) all N0 and λ values and (b) all µ and λ values. (c, d) Same as (a, b) but for Ze* > 12 and (e, f) for Ze* ≤ 12. .91

Figure B. 1. (a) 2D view of the flight trajectory (white dash line), ARM SGP site (red diamond), GPM GV stations (purple triangles), and Mesonet sites (black triangles) superimposed on Convective-Stratiform-Anvil (CSA) classified components (CC: Convective Core, SR: Stratiform Region, and AC: Anvil Clouds) of a Deep Convective System (DCS) on 20 May 2011. A snapshot of the entire system at one instance is shown in the left corner. (b) Similar to (a) but 3D view (the transition of aircraft trajectory from blue to red corresponds to flight time), and the XY-plane represents NEXRAD radar reflectivity factors to show the horizontal variability of the DCS at an altitude of 2500 m...... 113

Figure B. 2. (a) Equivalent raindrop diameters melted from ice crystal aggregates calculated by a mass dimensional relationship, mass=aDb where a = 0.00365 and b = 2.1 (Wang et al., 2015). (b) Probability and cumulative probability of surface disdrometer measured raindrop diameter at the ARM SGP site...... 116

* Figure B. 3. Comparisons between the calculated equivalent radar reflectivity factors Ze using in situ measured full spectrum of raindrop size distributions (DSDs) (red circles) and the DSDs < 4 mm (black circles) with the collocated NEXRAD measured radar reflectivity factors (Ze) along the aircraft flight tracks (a total of 1126 5-s averaged samples in this study)...... 119

Figure B. 4. Variation of the fitted parameters of Gamma function (N0Γ, μΓ, λΓ, in red solid lines) and Exponential function (N0E and λE, in red dash lines) compared to the observed original DSDs (blue bars) with respect to time T (UTC) and NEXRAD radar reflectivity Ze. (a) T1 = 47250 s (~13.125 UTC), Ze = 30 dBZ. (b) T2 = 47310s, Ze = 28 dBZ. (c) T3 = 47790s, Ze = 27 dBZ. (d) T4 = 47910s, Ze = 26 dBZ, a few instances during the 20 May 2011 case...... 124

Figure B. 5. (a) Gamma fitted DSD shape parameter μΓ as a function of slope parameter λΓ. (b) Gamma fitted DSD intercept parameter N0Γ as a function of slope parameter λΓ. (c) Exponentially

fitted DSD intercept parameter N0E as a function of slope parameter λE...... 125

Figure B. 6. Probability density function of Gamma fitted shape parameter (μΓ) from aircraft data (blue bars), and Gaussian distribution with mean value of 0.58 and standard deviation of 1.15 (red line)...... 128

Figure B. 7. (a) Time series comparison among disdrometer reconstructed, NEXRAD measured, and NOAA S-band radar reflectivity factors at cloud base during 20 May 2011. (b) Comparison between disdrometer reconstructed exponential slope parameter λE and retrieved one from this study. (c) Taylor diagram of radar reflectivity factors at cloud base for all selected six cases. (d) The same as (c) but in term of slope parameter λE...... 131

Figure B. 8. Time series of (a) NEXRAD cross-sectional radar reflectivity factors and CSA classification (at bottom), (b) NOAA S-band radar reflectivity factors, and rain rates for SR regions from: (c) the RD-80 surface disdrometer measurement, (d) Q2 product, and (e) retrieval generated by this study over the ARM SGP site...... 134

Figure B. 9. Left column (a, c, e, g, and i), same as Figure B. 7a but only the SR samples identified by UND CSA algorithm were extracted from the eight selected cases in this study. Right column (b, d, f, h, and j), comparisons among measured surface rain rates (black lines), Q2 products (blue lines), and retrievals from this study (red lines) at 2DVD-SN25, BREC, CARL, MARE, and STIL stations...... 136

Figure B. 10. Statistical comparisons of 5-min rain rates among disdrometer and Mesonet measurements, Q2 product, and retrieval from this study at (a) the ARM SGP site, (b) 2DVD stations, and (c) Mesonet stations for SR regions...... 137

Figure B. 11. Spatial distributions of daily accumulated SR precipitation amount from original Q2 precipitation estimation (first column, a, f, k, and p) and retrievals from this study (fifth column, e, j, o, and t), as well as the extrapolated results at the locations of 14 available disdrometer and Mesonet stations using the data extracted from: direct measurements (third column, c, h, m, and r), Q2 estimation (second column, b, g, l, and q), and this study’s retrievals (fourth column, d, i, n, and s), over a domain of 1o × 1o centered on the ARM SGP site on 1 May, 11 May, 20 May, and 24 May...... 138

Figure B. 12. (a) Comparison in Z-R curves between Marshall-Palmer (blue line) and this study (red line). (b) Similar to (a) but in logarithmic scale and five operational schemes were included to have Q2 precipitation estimate: convective (green), tropical (yellow), stratiform-east (black), stratiform-west (dash black). (c) Comparisons among Marshall-Palmer (blue line), this study (red line), Tokay and Short (1996) SR scheme, and Iguchi (2000) SR scheme. (d) All the valid Ze and corresponding rain rate records for SR regions from 17 Automatic Parsivel Unit (APU) sites during the entire MC3E campaign (22 April 2011 to 6 June 2011, black dots), as well as the Z-R relationships from Marshall-Palmer (blue line), this study (red solid line), and the direct regression line of APU observations (red dash line)...... 141

Figure C. 1. (a) The accumulated convective rain duration during MC3E, and the distributions of

(b) Mesonet rain gauges and (c) disdrometers...... 168

Figure C. 2. Exponentially fitted intercept parameter (N0E) as a function of slope parameter (λE) for the convective rain samples (red dots, 2011-2015) and the stratiform samples (green dots, 2011) collected by the RD-80 disdrometer at the SGP central facility...... 169

Figure C. 3. Probability and cumulative probability of maximum raindrop diameter measured by the APUs during MC3E for (a) stratiform rain (SR) and (b) convective rain (CR)...... 170

Figure C. 4. Rain rate comparison between Mesonet measurements and collocated Q2 estimates for all collocated convective rain (CR) samples...... 171

Figure C. 5. Comparison of radar reflectivity (Ze) between NEXRAD observations and collocated APU calculations...... 172

Figure C. 6. (a) Gamma fitted DSDs using three different subsets of the DSD spectrum. (b) Comparison of mean normalized errors between rain rates calculated from the APU observed DSDs and Gamma fitted DSDs with respect to different subsets of DSD spectrum...... 176

Figure C. 7. (a) The comparison of the μΓ-λΓ relationships between three different subsets of spectrum from this study and from Cao et al. (2008). (b) The probability distributions of μΓ from the subsetting scheme of channel 14 and Gaussian...... 178

Figure C. 8. (a) Similar to the Figure C. 6 but using Exponential fitting...... 179

Figure C. 9. The comparison between (a) fitted N0E-λE relationship and constant λE assumption, and their applications in (b) N0E distribution, (c) Ze- λE relationship, as well as (d) Ze- N0E relationship...... 181

Figure C. 10. The scatter plot of measured rain rates (Mesonet and APUs) vs. their collocated Ze (NEXRAD observed and APU calculated) at cloud base during MC3E, overlain by the newly developed Z-R relationship (red solid line) and the traditional Z-R relationship (red dash line)...... 182

Figure C. 11. The example of (a) CSA classification based on 3D radar reflectivity and (b) the observed near-surface differential reflectivity (ZDR) from single radar observation sampled on 09:05 UTC May 20th, 2011, as well as (c) the conceptual relationships between environmental variables and rain rate retrieval...... 184

Figure D. 1. Examples of precipitation cases for each class within the SGP SOM: (a) Class 1: April 14 2007, (b) Class 2: April 26 2011, (c) Class 3: May 25 2011, (d) Class 4: July 11 2008, (e) Class 5: August 11 2011, and (f) Class 6: May 13 2009...... 204

Figure D. 2. Diurnal cycles of precipitation rate from Stage IV observations (solid lines) and NSSL-WRF simulations (dashed lines) for (a) Class 1, (b) Class 2, (c) Class 3, (d) Class 4, (e) Class 5, and (f) Class 6 of the SGP SOM. The local night is shaded gray from 1800 to 0600 LT.

...... 205

Figure D. 3. Daily averaged, 12-hour accumulated precipitation amount for Stage IV (a, d), NSSL- WRF (b, e), and bias (c, f, NSSL WRF - Stage IV) during the day (a, b, c) and night (d, e, f) for each class in the SGP SOM...... 207

Figure D. 4. Box plots of precipitation intensity (a, b) and coverage (c, d) for Stage IV (a, c) and NSSL-WRF (b, d) for each class in the SGP SOM. Total precipitation is given by white boxes while convective rain (CR) is red, and stratiform rain (SR) is blue...... 209

Figure D. 5. Examples of precipitation cases for each class within the NGP SOM (a) Class 1: storm on June 11 2008, (b) Class 2: May 23 2007, (c) Class 3: April 15 2011, (d) Class 4: July 19 2011, (e) Class 5: July 15 2011, (f) Class 6: April 1 2014...... 212

Figure D. 6. Same as Figure D. 2, but for the NGP...... 213

Figure D. 7. Same as Figure D. 3, but for the NGP...... 214

Figure D. 8. Same as Figure D. 4, but for the NGP...... 215

Figure D. 9. Taylor diagrams for normalized standard deviation vs. correlation (a, c) and ratio vs. agreement index (b, d) for each class in the SGP (a, c) and the NGP (b, d)...... 221

ABSTRACT

Mesoscale convective systems (MCSs) can be separated into a precipitation portion which includes convective rain (CR) and stratiform rain (SR) and a non-precipitation canopy portion, the former dominates much of warm season (April - September) intense rainfall over the mid-latitudes, while the latter plays a significant role in the atmospheric radiation budget due to the its extensive spatial coverage. The convective rain (≥5 mm hr-1) portion features the most intense rainfall rate compared to the long-lasting stratiform rain (<5 mm hr-1) portion with large area coverage, which strongly corresponds to the high flood risk level. In order to improve the understanding of cloud- precipitation microphysical properties and their interactions for the cloud-resolving model, the

Department of Energy (DOE) Atmospheric Radiation Measurement (ARM) conducted a field campaign in a collaborative effort with NASA’s Global Precipitation Measurement (GPM) mission Ground Validation (GV) program, the Midlatitude Continental Convective Clouds

Experiment (MC3E), at the ARM Southern Great Plains (SGP, 36° 36' 18" N, 97° 29' 6" W) site from April to June 2011. During the MC3E field campaign, the University of North Dakota (UND)

Citation II research aircraft carried out the major in situ measurements of cloud microphysical properties.

By separating the MCSs into ice-phase layer and liquid-phase layer, this study investigates microphysical properties at each layer using the measurements collected by UND Citation II aircraft. For ice-phase layer, the focus is on the correction of cloud ice water content (IWC) and the reconstruction of particle size distribution (PSD) based on multiple sensors measurements. For liquid-phase layer, this study concentrates on the better parameterization of raindrop size distribution (DSD) and its application in radar-based rain rate retrieval.

In addition to the investigation of MCSs’ microphysical properties, another major part of

16 this dissertation regards the long-term statistical analysis of the warm season (April-September) precipitation over the Great Plains (GP). Specifically, two subdomains, namely the Southern Great

Plains (SGP, 99.985o W to 94.985o W, 34.66o N to 38.66o N) and Northern Great Plains (NGP,

100.75o W to 95.75o W, 45o N to 49o N) are selected. By using Self-Organizing-Map (SOM) method, a total of 300 convective systems during the period 2007-2014 are objectively classified into 6 classes according to the integrative analysis of synoptic characteristics over each sub-domain respectively. Despite the difference in regional climatology, both regions demonstrate prominent seasonal contrast in dominant synoptic patterns. The early summer convective systems are more impacted by the extratropical cyclone, while the late summer/early fall events are strongly associated with subtropical ridge. Based on the SOM results, the real-time weather forecast product generated by the National Oceanic and Atmospheric Administration (NOAA) National

Severe Storms Laboratory (NSSL) is evaluated using National Centers for Environmental

Prediction (NCEP) Stage IV data for each individual SOM class over each region.

CHAPTER 1: INTRODUCTION

1.1 IMPORTANCE OF CONVECTIVE SYSTEMS

In the 20th century, flooding has been the greatest natural disaster in the United States, caused

$6 billion in economic loss and 140 deaths annually (USGS, 2006). In order to better characterize the flooding hazard for the purpose of the quantitative risk assessment, the estimations of recurrence interval, duration, and peak discharge of flood flows have been thoroughly studied using a variety of regression methods with inputs of catchment area, elevation, precipitation, local orographic factors, etc. (e.g., Ahearn, 2004; Roland and Stuckey, 2008; Flynn 2003). Among those modeling parameters, the input of precipitation plays an important role for its significance in the hydrologic cycle as well as its largest variability in precipitation types, seasonal variations, and spatial distribution. Of all precipitating weather events, the Mesoscale Convective Systems (MCSs) contribute up to 60% of the total precipitation in central US (Fritsch et al., 1986; Ashley et al.,

2003), and the occurrence of MCSs is more frequent in warm season than in cold season. Thus, the investigation of warm season MCSs is critical for the hydrological cycle, as well as the flooding risk assessment.

Through the combination of the NEXRAD radar and GOES satellite observations, Feng et al. (2011) developed a hybrid cloud Convective-Stratiform-Anvil classification algorithm (CSA) which objectively separates the convective systems into the components of convective core (CC), stratiform rain (SR), and anvil clouds (AC). They found that the SR regions have the largest coverage of warm season rainfall over the mid-latitudes, while the CC regions account for the most intense precipitation, and the AC regions mainly feature in their influence on the atmosphere’s radiation budget. Feng et al. (2012) also found that the rain rate of CC is almost one order of magnitude higher than that over SR, causing a surge in accumulated precipitation amount within

18 a short time period, which corresponds to higher probability of flooding events. Differences in cloud and precipitation characteristics between CC and SR have been investigated through a variety of platforms, including space-borne satellite observations (e.g., Tropical Rainfall

Measuring Mission, Yang and Smith, 2008; GOES, Behrangi et al., 2009), ground-based radar observations (e.g., National Mosaic and Multi-Sensor Quantitative Precipitation Estimation, Feng et al. 2011 and 2012; Stenz et al., 2014, 2016), ground-based remote sensing and surface measurements (Giangrande et al., 2014; Wu et al., 2013; Tao et al., 2013; Tian et al., 2016), and aircraft in-situ measurements (Beard et al., 1986; Wang et al., 2015 and 2016). Moreover, for the investigation of cloud microphysical properties and processes, a series of field campaigns (e.g.,

MC3E, IPHEX, GCPEX, etc.) were conducted by the joint effort of multiple agencies with emphasize on aircraft in situ measurements, and the UND Citation II research aircraft was the major vehicle for the measurements of cloud microphysical properties.

1.2 OBSERVATION SYSTEMS FOR CLOUD AND PRECIPITATION

1.2.1 Aircraft In-situ Measurements

The University of North Dakota (UND) Citation II research aircraft was one of the primary research aircraft deployed during multiple field campaigns and was fully equipped for cloud physics research. The UND aircraft probes used in this study are shown in Figure 1. The particle size distributions (PSDs) and raindrop size distributions (DSDs) are constructed based on the combination of two optical array probes (OAPs), namely 2-dimensional cloud (2DC, measuring hydrometeors from 30 to 3000 µm in diameter) probe and High-Volume Precipitation

Spectrometer (HVPS-3, measuring hydrometeors from 150 µm to 1.9 cm). The Nevzorov total water content (TWC) probe measures the total cloud water content including both liquid and ice

19 water contents for each layer of MCSs, and the Nevzorov liquid water content (LWC) sensor and the king hot wire LWC probe specifically measures the LWC in liquid-phase layer, and is also applied for the estimation of supercooled liquid water content (SLWC) in the mixed-phase layer.

Rosemount Icing Detector (RID) utilizes the vibrating change caused by the icing process for the directly detection of supercooled liquid droplets. The Droplet Measurement Technologies (DMT)

Cloud Droplet Probe (CDP, measuring hydrometeors from 3 to 50 µm) is also used for the detection of supercooled liquid droplets and the estimation of SLWC. Lastly, a large number of the DMT Cloud Imaging Probe (CIP) images, as well as 2DC images, are analyzed for the morphology study of hydrometeors.

Figure 1. UND Citation II aircraft configuration. (Photo courtesy of Dr. David J. Delene)

Data were collected and preprocessed using a Model 300 Data Acquisition and Playback system (manufactured by Science Engineering Associates), and the PSDs were calculated using software developed by Aaron Bansemer at the National Center for Atmosphere Research (Field et al., 2006). Cloud particle sizes measured by OAPs were sorted into bins accordingly based on the diameter D of smallest circle that encloses the particle (Heymsfield and Parrish, 1978; Field et al.,

2006; Korolev, 2007). Cloud particles were not used in this study with the following conditions:

(1) the area ratio (the ratio of the projected area of the particle to the area of a circumscribed circle

(McFarquhar and Heymsfield, 1996)) is less than 0.1, and (2) the area ratio is less than 0.2 and the particle size is 20 times greater than the resolution of the probe (Field et al., 2006).

Figure 2. The distribution of NEXRAD radars (black dot) and the observed radar echoes at 2 km above ground level (colored contour)

1.2.2 Radar Measurements

Densely distributed across the entire continental US, the Next-Generation Radar (NEXRAD)

21 consists of 159 high resolution S-band Doppler radars (WSR-88D) operated by the National

Weather Service (NWS). As shown in Figure 2, NEXRAD network can generate the 3D radar reflectivity mosaic field, providing detailed information of the pattern and movement of weather systems. Moreover, the near-surface radar echoes are directly related to the precipitation intensity, based on which the quantitative precipitation estimation (QPE) products are calculated using appropriate Z(radar reflectivity factor)-R(rain rate) relationships. Completed in 2013, the dual- polarization upgrade of ENXRAD network added vertical polarization to the horizontal radar waves, which facilitate the hydrometeor classification practice as rain, hail, snow, etc. have different dual-polarization signatures.

In addition to national NEXRAD network, the Department of Energy (DOE) Atmospheric

Radiation Measurement Program (ARM) deployed a dense radar network over the SGP with working frequencies different from the weather surveillance NEXRAD radar (S-band), including the C-band scanning ARM precipitation radar (CSAPR), Ka-band scanning ARM cloud radar

(KASACR), Ka-band ARM zenith radar (KAZR), millimeter wavelength cloud radar (MMCR),

W-band ARM cloud radar (WACR), W-band scanning ARM cloud radar (WSACR), and X-band scanning ARM precipitation radar (XSAPR). Those ground-based radars add more radiometric details to the NEXRAD 3D radar product from the perspectives of both cloud and precipitation.

1.2.3 Surface In-situ Measurements

Different from the radiometric remote sensing technology which utilizes radar echo to retrieve near-surface precipitation, surface in-situ rain gauges directly measure the precipitation amount at the surface. The Mesonet tipping-bucket network is a point-based precipitation measurement system, which consists of 127 stations scattered over the state of Oklahoma, providing the dense rain rate observations with the high accuracy (Bin et al., 2008). However, the

22 traditional tipping-bucket can only provide the measurement of bulk precipitation properties like precipitation rate and amount, leaving the detailed raindrop size distribution (DSD) undetected.

To fill that gap, the RD-80 disdrometer is deployed at the SGP central facility for the DSD measurement. Moreover, to compensate to the intrinsic issues associated with traditional disdrometers based on pressure transducer including big uncertainty and limited DSD size range

(Joss and Waldvogel, 1967, 1969; Kinnel, 1976), more advanced OTT automatic parsivel units

(APUs) using laser optical technology were densely distributed at 17 stations around the SGP central facility during MC3E (Brawn and Upton, 2008; Kathiravelu et al., 2016). Instead of bulk precipitation properties, APUs detect each individual raindrop in size, fall velocity, and deformation, providing more accurate rain rate estimation and DSD reconstruction.

1.2.4 Areal Precipitation Datasets

There are several reliable precipitation datasets with different temporal and spatial resolutions. Compared to sparse distribution of rain gauge measurements and the uncertainties associated with remote sensing retrieval (Stenz et al., 2014 and 2016), precipitation radar can provide Quantitative Precipitation Estimation (QPE) with higher spatial, temporal resolution, and large spatial coverage. Based on the Next Generation Weather Radar (NEXRAD, S-band) network of Weather Surveillance Radar-1988 Doppler (WSR-88D) radars, the NOAA National Severe

Storms Laboratory (NSSL) produces a national (CONUS) 3D gridded radar mosaic coverage with

1 km horizontal resolution, 31 vertical levels (resolution varies from 200 m to 2000 m), and 5 min temporal resolution (https://www.nssl.noaa.gov/projects/q2/nmq.php), which is referred to as

National Mosaic and Multi-Sensor Quantitative (NMQ) Precipitation Estimation (QPE, Q2) system. The Q2 3D radar mosaic can provide the cloud horizontal morphology information for

23 cloud classification, and the vertical cloud structure information that is not available by observations from other platforms.

As another key component in NMQ Q2 system, the Q2 QPE can provide the quantitative rain rate estimation over the domain of CONUS with the update cycle of 5-minute and spatial resolution of 1 km, which is generated by applying appropriate Z-R relationships (Zhang et al.

2011) to cloud base radar reflectivity. However, the Q2 precipitation data tend to overestimate the rain rate (Ann et al. 2016) due to the constant exponential intercept (N0) assumption in raindrop size distribution (DSD) reconstruction as discussed in Wang et al. (2016). Moreover, the QPEs from radar observations also suffer from occasional ground clutter problems associated with radar beam ducting caused by temperature inversions (Turton et al. 1988), which can generate erroneous precipitation amounts.

To overcome the overestimation issue of the radar-based QPE, direct gauge observations are included to correct the positive bias in hourly basis, which is referred to as Q2_adjusted hereafter.

Because of the scarcity of surface rain gauge observations, Q2_adjusted still leaves large ungauged areas vulnerable to the potential ground clutter contamination. This issue has been greatly reduced in the National Centers for Environmental Prediction (NCEP) Stage IV precipitation data (4 × 4 km spatial resolution and hourly update cycle) using multi-sensor observations with manual quality control (Lin and Mitchell 2005; Baldwin and Mitchell 1998).

In order to assess the performance of different spatial precipitation datasets, the spatial distribution of total precipitation amount during the MC3E was generated by extrapolation at the location of 127 Mesonet stations (Figure 3a) using the data from Mesonet tipping bucket measurements (Figure 3d) and compared to the result using the data from Q2_adjusted QPE

(Figure 3e) as well as from NCEP Stage IV data (Figure 3f). The overall distributions are quite

24 similar among those three datasets, but Q2 has notable difference in the magnitude of severe precipitation regions over the center and east boundary of Oklahoma, which again verifies the overestimation issue in adjusted Q2 QPE for the severe precipitation events. Meanwhile, the

NCEP Stage IV data match better with Mesonet observations. As a result, the NCEP Stage IV data are utilized in this study as the “ground truth” of precipitation field for the evaluation of WRF simulation.

The partitioning for convective rain (CR) and stratiform rian (SR) can be easily achieved by using the 5-minute 3D radar reflectivity mosaic and the Convective-Stratiform-Anvil (CSA) algorithm. However, on the temporal scale of 1 hour (the minimum time step of both Q2_adjusted and Stage IV), the CSA method merely relied on the radar reflectivity is greatly limited because of the drastic cloud development on sub-hourly scale. As a result, the separation of CR and SR

25 was commonly conducted using the rainfall-rate criterion (RRC) method, for which the 10 mm hr-

1 was widely used for hourly data (Tokay and Short, 1996; Nzeukou et al., 2004; Giangrande et al., 2014).

In order to test the performance of RRC method for CR portion, the sensitivity study of CR intensity was conducted as shown in Figure 4, where the 5-minute Mesonet observations and corresponding CSA cloud type information were used as the ground truth. In Figure 4a, each black dot represents a Mesonet station, for whose position corresponds to the accumulated precipitation amount (y-axis, accumulated at the time step of 5-minute) and accumulated precipitation duration

(x-axis, also from 5-minute observation) during MC3E. Meanwhile, the red dots represent CR portion and green dots for SR portion which are separated using the CSA algorithm. Two distinct trends are shown for different types of precipitation where the CR averaged intensity is 19.73 mm hr-1. In Figure 4b, by temporal upscaling the Mesonet observations from 5-mintue to hourly through averaging, the RRC method with 10 mm hr-1 threshold is applied to the hourly Mesonet data. The newly generated hourly CR intensity information (19.14 mm hr-1) is well maintained compared to its original higher temporal resolution data in Figure 4a, while the SR portion became more scattered with less intensity which can be attributed to the dilution of SR samples from non- precipitating events, which cannot be removed with threshold of rain rate less than 10 mm hr-1.

Then, the RRC method was applied to the Q2_adjusted QPE at the Meosnet locations in Figure 4c, in which very similar pattern was found in comparison with Figure 4b. However, overestimation issue remains with higher CR intensity (21.85 mm hr-1). From the perspective of retaining the intensity information of CR precipitation, the RRC method with 10 mm hr-1 threshold can bridge the gap in temporal resolution between 5-minute data and hourly data. However, the 10 mm hr-1

RRC threshold suitable for hourly data with spatial resolution of 1 × 1 km cannot be directly

26 applied to Stage IV data with 4 × 4 km resolution, for which the upscaling of the 10 mm hr-1 threshold is required for CR precipitation extraction.

Suggested by Rosenfeld et al. (1990), the optimal convective rain rate cutoff falls between

4-6 mm hr-1 at the spatial resolution of 4 × 4 km, as lower value would include stratiform rains which makes the areal averaged rain rates more scattered. In this study, pixels in Stage IV data greater than 5 mm hr-1 are identified as CR, and the separation of CR and SR with the input of

Stage IV data is shown in Figure 4d. In Figure 4d, even there exists considerable decrease in both averaged CR intensity (21.85 mm hr-1 to 13.17 mm hr-1) and SR intensity (2.28 mm hr-1 to 1.65 mm hr-1) from 1 × 1 km grid to 4 × 4 km grid due to the scale effect, the coherence of scattered data points is not impacted (CR: R2 from 0.97 to 0.96; SR: R2 from 0.96 to 0.98).

1.3 SYNOPTIC PATTERNS RELATED TO CONVECTIVE SYSTEMS

One of the early efforts that synthesize heavy precipitation events with synoptic conditions was Maddox et al. (1978), who categorized the weather patterns related to extreme rainfall and flash flooding over the CONUS into the types of “synoptic” (a strong upper-level trough, coupled with a slowing moving surface front, can produce persistent precipitation in the warm sector of a cold front with sufficient southerly moisture transport), “frontal” (corresponding to precipitation on the cool side of a boundary), “meso-high” (similar to frontal but more cold pool driven, so precipitation commonly occur ahead of the front with faster southeastward propagation), and

“western” (not explicit defined but is more related to topographic lifting as well as North American monsoon). For the GP climatology, as it's located at the lee side of Rocky Mountains, the westerly dry maritime Pacific air meets the northward transport of tropical moist air from the Gulf of

Mexico, forming a mesoscale gradient in dewpoint temperature (i.e. dryline), which is strongly related to initiation of severe weather (e.g., McCarthy and Koch, 1982; Bluestein and Parker 1993).

Observed by atmospheric sounding and winder profilers (e.g., Bonner, 1968; Zhong et al., 1996),

28 a significant increase in southerly wind at levels of 300 – 800 m above the ground often takes place from midnight to early morning hours (Parish and Oolman, 2010, Song et al., 2016). Termed as

Low-Level Jet (LLJ), it accounts for the majority of northward moisture transport, and is believed to be an important factor in the development and maintenance of mesoscale convective systems over the GP (Higgins et al., 1997; Pu and Dickinson, 2014).

To investigate the relation of LLJ to synoptic environment, Mitchell et al. (1995) applied a synoptic classification scheme over the GP specifically. Depending on the different dominant synoptic features and weather systems' positions relative to them, five weather patterns are identified as follows: 1. warm sector of an extratropical cyclone; 2. Ahead of the warm front of an extratropical cyclone; 3. Behind the cold front of an extratropical cyclone; 4. Polar high; and 5.

Vicinity and west of a subtropical ridge. This classification demonstrates a great similarity to its predecessor in Maddox (1978), except for the category 4, under which is commonly associated with clear sky. Based on previous studies, extratropical cyclone and subtropical ridge are identified as severe weather related synoptic patterns, which correspond to the upper and lower

SOM classes respectively.

The mechanism of precipitation generation is straightforward for extratropical cyclone, with upper level trough building up, a surface frontal boundary forms accordingly with the aid of the

LLJ moisture transport (Fan et al., 2017). As the LLJ becomes stronger towards the midnight, heavy regional precipitation occurs as a result. Different for the extratropical cyclone, the subtropical ridge promotes sinking motion over the GP, leaving vast area under the cold and dry condition. However, commonly observed over the central states ranging from the Gulf Coast to the Great Lakes during the warm season, the heavy precipitation is still generated at the periphery of the high pressure center, thus this kind of precipitation pattern is termed as “ring-of-fire” or

“ridge rollers” (Galarneau and Bosart, 2006).

Dominated by the subtropical high pressure system, the air is most stable towards the center of the high pressure, where a subsidence inversion layer (capping inversion) is formed as the result of widespread descending air. The near-surface layer is heated and compressed by the high pressure but also trapped by the subsidence inversion, so the formation of thunderstorm is prohibited even with aloft cold air. However, this inversion becomes weaker towards the edge of the high pressure, which allows convection to occur with sufficient moisture supply, thus a ring precipitation band can form at the periphery of the high pressure with clockwise rotation.

Compared to the storms associated with extratropical cyclone, which is mainly driven by large scale frontal forcing, the initiation of “ring-of-fire” convection relies heavily on the disturbance aloft (e.g., the advection of maximum vorticity by a short-wave trough or weather systems at finer scope) which may have less organized precipitation band, thus cannot be explicitly resolved by

Convective Allowing Model (CAM).

Introduced by Kohonen et al. (1996), Self-Organizing Map (SOM) is an unsupervised learning process which allows users to rearrange the data in an array of nodes that are self- organized and represent an entire continuum of synoptic categorizations. At first, the nodes are initialized based on random values, then each vector is added to the SOM and traversed by all nodes. The node with the minimum Euclidian distance for that specific vector is the winner. By the modification of the winner and its surrounding nodes, they are pulled closer to the input vector.

After that, another vector from the input dataset is traversed by all nodes until all input vectors are considered. Through an iterative process, all nodes are self-organized into a pattern where nodes with greater similarity cluster together and less similar nodes are separated apart, such that the corners of SOM tend to represent the extreme cases with a smooth continuum in between (Sheridan

30 and Lee 2011).

For the synoptic analysis, near-surface level and 500 mb level are commonly considered in the operational setting because they are useful for the pattern recognition purpose. As a result, a series of NARR variables at these two levels are chosen as input vectors for the training of SOM, including mean sea level pressure (MSLP), relative humidity (RH), geopotential height, and winds (u and v components) at both 900 mb and 500 mb. In order to mitigate the bias aroused by seasonal variation in 500 mb geopotential height filed, the height anomaly is calculated instead of direct use of geopotential height (Kennedy et al. 2016). In addition, the 900 mb level is chosen to represent near-surface because surface level contains more uncertainties with less confidence in accuracy (Mesinger et al. 2006).

Figure 5. The domains of Southern Great Plains (SGP) and Northern Great Plains (NGP). Blue boxes for the synoptic pattern analysis, and red boxes for the precipitation evaluation.

The SOM method is applied over the two subdomains of the GP, namely the Southern GP

(SGP) and the Northern GP (NGP) as shown in Figure 5 (blue boxes). With the focus of warm season (April-September) heavy precipitation, cases (1200 to 1200 UTC) that account for the upper 90% regional total precipitation are considered for the SOM training.

With the initially determined 28 nodes suggested by Kennedy et al. (2016), SOM results are generated with detailed description. Through an objective grouping process based on mean

Euclidian distance between nodes (detailed process available in Hagenhoff et al. 2018), the number of synoptic patterns is reduced to six as shown in Figure 6a to 6f over the SGP. By comparing the

500 mb geopotential height anomaly, Classes 1, 2, and 3 share a common feature of southwesterly wind while Classes 4, 5, and 6 are dominated by northwesterly wind. For the comparisons of

MSLP and 900 mb RH, the less moist but deeper low pressure signature is found from the left to right (ad → be→ cf), but the upper panel is more saturated than the lower panel with more complicated near-surface features in general. By combination of the upper 3 classes as well as the lower 3 classes, simplified composite patterns are generated and named as Type1 and Type 2, respectively. For the upper air condition (Figure 6g vs. Figure 6i), the two patterns have distinct prevailing wind directions. Type 1 is mainly dominated by the trough located in the center of the domain which is potentially aroused by extratropical cyclones, while Type 2 is strongly affected by the ridge close to the west boundary of the domain which could result from the poleward invasion of subtropical high pressure systems. The 500 mb analysis can also be supported by the near-surface condition (Figures 6h and 6g). Compared to Type 2, Type 1 pattern demonstrates a deeper low pressure center (1006 vs. 1008 mb) with more sufficient moisture (56 vs. 51 %) and larger moisture contrast (59 vs. 53 %), forming a frontal boundary, which is often associated with extratropical cyclones. For Type 2, controlled by subtropical high pressure, saturation is more

32 difficult to reach and MSLP has less variability. However, as mentioned above, heavy precipitation can also occur under this synoptic pattern around the periphery of the “meso-high”, termed as “ring of fire” pattern.

Figure 7. Similar to Figure 6 but over the NGP region.

Similar to Figure 6, the SOM results over the NGP region are shown in Figure 7, where distinct features are found between upper panel and lower panel in 500 mb geopotential height anomaly. By regrouping the six classes into two, a similar contrast pattern (to the SGP) is also found, where Type 1 is also dominated by the southwesterly flow and strongly affected by the

34 upper level trough, while the signature of ridge for Type 2 is not as prominent as the SGP, but appears more like zonal flow. For the near-surface conditions, Type 1 corresponds to a surface low pressure system centered at the southeast of the domain with lower MSLP (1005 vs. 1010 mb) but higher RH (59 vs. 57 %) than Type 2, while the latter is mainly dominated by a broad surface high pressure without spatial variation as shown in Figure 7j.

Figure 8. The seasonal variation of the occurrence frequency of Type 1 storms (blue bars) and Type 2 storms (red bars) over the SGP (a) and NGP (b) regions.

The SOM results over both regions indicate that the heavy precipitating events during warm season can be either impacted by extratropical cyclones (Type 1) or subtropical ridges (Type 2), which roughly follows previous studies of GP climatology regimes (e.g., Mitchell et al. 1995).

Those two distinct weather patterns both have notable seasonable variations in response to global scale circulation, which are further examined in Figure 8. For each region, the two weather patterns are sorted into early (April to May), middle (June to July), and late (August to September) phases of the warm season, and their frequencies of occurrence are calculated and compared accordingly. For the SGP region (Figure 8a), a clear decreasing trend is found for the Type 1

(extratropical cyclone related) while Type 2 becomes dominant towards the late warm season.

Located immediately under the tropopause, polar jet stream plays a significant role for the cyclogenesis over the mid-latitude. As the jet stream intensities, a jet streak forms with upper level divergence, which efficiently pumps air out of the vertical air column. In response to the aloft divergence, a low pressure system is generated at the surface level in order to draw in air. The configuration of low-level convergence with upper-level divergence favors the upward motion in the whole air column, thus an extratropical cyclone is generated (Wash et al. 1990). Different from the genesis of the Type 1 weather pattern, the occurrence of subtropical ridge mainly relies on the poleward invasion of the subtropical high pressure system. As a direct result of solar heating, warm air rises near the equator and cold air sinks at mid-latitude. The subsidence of air forms a subtropical ridge close to the 30o N in the northern hemisphere (Chang et al. 1990). Following the intensification of Hadley circulation's north branch from early warm season to late summer, the subtropical ridge reaches its most northern latitude in early fall. This seasonal variation is well matched by the increasing frequency of occurrence of the Type 2 storms, which further proves those heavy precipitating cases are strongly affected by the strength and extension of the subtropical ridge.

The strength of polar jet stream greatly relies on the south-north temperature difference. As the poleward invasion of subtropical ridge, the meridional temperature gradient between cold arctic air and warm tropical air becomes small, which weakens the jet stream. This trend is also well captured by the decreasing trend in Type 1 storms, which explicitely explains the dependence of Type 1 precipitation on extratropical cyclones. Similar to the SGP region, statistics of two weather patterns is shown in Figure 8b for the NGP. Instead of monotonic variation, the portion of Type 1 events bounces up at the end of warm season (August to September), and

36 correspondingly subtropical ridge related cases decrease. This anomaly probably suggests that the

Canada cold front starts to play a role in early fall precipitation, as the NGP region has further north location than the SGP.

It is necessary to note that the weather patterns affected by extratropical cyclones and subtropical ridges are not mutually exclusive, and some cases cannot be clearly classified through manual analysis of weather charts. Additionally, only the NARR data at 0000 UTC (the middle time of defined case duration) are used as the input for the training of the SOM, so the transitions from Type 1 to Type 2 or vice versa are not fully considered. The purpose of the objective weather pattern classification is to set a frame in which the performance of NSSL-WRF precipitation simulation can be systematically evaluated againist long-term Stage IV ovservations. This study will shed light on the forcing mechanisms responsible for heavy precipitation and will improve understanding of the biases in model simulations.

1.4 OBJECTIVES

With the knowledge of the importance of MCSs, as well as the distinctions between CR and

SR, this dissertation seeks to investigate MCSs’ cloud and precipitation properties from two perspectives. First, by separating the MCSs into ice-phase layer and liquid-phase layer, this dissertation will investigate each layer’s microphysical properties with different emphases. For ice-phase layer, the major issue is the correct estimation of IWC, because almost all the instruments have the issue in collecting efficiency of ice particles. For liquid-phase layer, the insufficient collection of raindrops also exists. However, the parameterization of DSDs is the more important issue because it is directly related to the cloud-to-precipitation process and is the key assumption in radar-based rain rate estimation. Based on the comprehensive aircraft/surface in-situ cloud/precipitation microphysical property measurements during MC3E, a series of new

PSD/DSD parameterization formulas have been developed, providing the theoretical basis for the retrievals of cloud ice/liquid-phase properties from radar observations.

After the study of cloud microphysical properties, this dissertation will focus on the evaluation of the long-term MCSs simulation generated by NSSL WRF over the SGP and NGP domains, from the perspectives of precipitation intensity, spatial distribution, diurnal cycle, as well as their correspondence to different synoptic schemes.

As a result, this dissertation consists of two major sections addressing the abovementioned issues. In sections 2.1 and 2.2, the estimation of cloud microphysical properties is conducted using aircraft in situ measurements from MC3E field campaign. In section 2.3, the quantitative analyses of convective rain (CR)’s intensity, coverage, amount, and diurnal cycles are conducted over two selected regions: SGP and NGP. Finaly the future research direction is discussed in section 2.4.

CHAPTER 2: PRESENT STUDY

2.1 INVESTIGATE ICE CLOUD PROPERTIES OF MCSs FROM AIRCRAFT IN-SITU

MEASUREMENTS

DCSs play an important role in both the atmospheric radiation budget and hydrological cycle.

The accurate simulation of DCSs greatly depends on the understanding of cloud microphysical properties, especially the particle size distribution (PSD) for ice-phase layer and raindrop size distribution (DSD) for liquid-phase layer. During the MC3E field campaign, more than 7 hours in-situ microphysical observations in SR ice-phase layer were collected by the University of North

Dakota Citation II research aircraft, providing a “groun-truth” for validating the ground-based and satellite remote sensing retrieved cloud properties.

In this part of dissertation, the SR ice-phase cloud properties are investigated based on the continuous aircraft in-situ measurements of six selected DCS cases, namely 27 April 2011 (08: 02:

07 – 11: 22: 45), 1 May 2011 (16: 28: 39 – 18: 42: 13), 11 May 2011 (16: 02: 09 – 19: 27: 06), 18

May 2011 (07: 20: 10 – 09: 21: 56), 20 May 2011 (13: 05: 39 – 17: 02: 04), and 23-24 May 2011

(20: 18: 25 – 22: 27: 50). First, cloud phase separation is conducted using multi-sensor detection of super-cooled liquid water droplet. Whenever there is a drastic decrease in Rosemount icing detector (RID) vibrating frequency (indicating the ice coating on the surface of sensor), a surge in

Cloud Droplet Probe (CDP) measured number concentration or King/Nevzorov liquid water content (LWC) sensors, those samples are considered as potential contamination of super-cooled liquid water and discarded for the ice-phase layer study. The correction of Nevzorov measured ice water content (IWC) is performed using the newly developed mass-dimensional relationship with the assumption that Nevzorov probe only responses to ice crystals smaller than 4 mm. Lastly, the Gamma function is fitted to the observed PSD, and the empirical relationships are established among the shape parameters (intercept: N0, dispersion: μ, slope: λ), providing theoretical basis for the radar-based PSD reconstruction and cloud property retrievals.

This part of study has been published in the Journal of Geophysical Research, Atmospheres:

Wang, J, X Dong, and B Xi (2015), Investigation of ice cloud microphysical properties of DCSs using aircraft in situ measurements during MC3E over the ARM SGP site. J. Geophys. Res. Atmos.,

120, 3533–3552. doi: 10.1002/2014JD022795.

2.2 INVESTIGATE LIQUID CLOUD AND PRECIPITATION PROPERTIES of MCSs FROM

AIRCRAFT AND SURFACE MEASUREMENTS

As a companion study of SR ice-phase layer cloud properties, the aircraft in-situ measurements of eight DCS cases are investigated for the characteristics of liquid-phase layer

DSD. Compared to the surface disdrometer measurements, the aircraft optical array probes (OAPs)

39 feature much larger sampling volume (400 L s-1 for HVPS vs. 0.05 L s-1 for RD-80), providing comprehensive in-cloud DSD measurements those cannot be observed by the surface disdrometers.

A total of 1126 five-second in situ measured DSDs were fitted into exponential size distributions, and then parameterized as a function of radar reflectivity according to its theoretical definition.

In order to assess the new parameterization scheme incorporating the dependencies between

DSD parameters, the rain rates were calculated using the retrieved DSDs from NEXRAD reflectivity at cloud base, and then compared with surface rain rate measurements. The excellent agreement in surface rain rate between the retrievals from this study and the surface rain gauges measurements has indicated that the new DSD parameterization scheme is robust, which provides a solid basis for calculating bulk liquid cloud microphysical properties of DCS in the future.

Compared to the retrieved and measured surface rain rates, the NEXRAD Q2 precipitation estimates demonstrate severe overestimation for heavy rain events. These comparisons have revealed that the Q2 products based on Marshall-Palmer Z-R relationship, where a constant DSD intercept parameter (N0) was used, need to be improved for heavy precipitation cases.

This part of study has been published in the Journal of Geophysical Research, Atmospheres:

Wang, J., X. Dong, B. Xi, and A. J. Heymsfield (2016), Investigation of liquid cloud microphysical properties of deep convective systems: 1. Parameterization of raindrop size distribution and its application for stratiform rain estimation, J. Geophys. Res. Atmos., 121, 10,739–10,760, doi:

10.1002/2016JD024941

In addition to SR liquid-phase layer study, the convective rain (CR) portion of DCSs are investigated using the intensive disdrometer measurements during MC3E, since the aircraft intentionally avoided the penetration of convective core regions. By comparing long-term surface disdrometer measurements, the CR and SR samples demonstrate almost no overlap in N0-λ

relationship, and SR features more variation in λ direction along a constant N0, but the trend is reversed for CR which is more scattered in N0 direction than λ direction. Together with the well- known “N0 jump” issue (Waldvogel, 1974), the distinction between SR and CR DSD characteristics poses a question mark to the power-law CR Z-R relationship that is still based on the constant N0 assumption. Following the same procedure of SR DSD study, the CR DSDs are parameterized using the constant λ instead of constant N0, resulting the CR rain rate estimated from cloud-base radar reflectivity matches better well direct surface observation, while the Q2 product based on traditional Z-R relationship demonstrates severe overestimation.

This part of study has been submitted to the Journal of Geophysical Research, Atmospheres:

Wang, J., X. Dong, and B. Xi (2018), Investigation of liquid cloud microphysical properties of deep convective systems: 2. Parameterization of raindrop size distribution and its application for convective rain estimation.

2.3 EVALUATE WRF SIMULATED PRECIPITATION

The third major focus of this dissertation is the evaluation of NSSL WRF simulated warm season convective systems over the SGP and NGP. Through the examination of cumulative distribution function (CDF) during the period 2007-2014, cases that account for the upper 90 % regional total precipitation are considered over each region (SGP: 387 out of 1370 cases, NGP:

421 out of 1370 cases), and the SOM results of synoptic pattern analysis are shown in Figures 6 and 7. Each region’s 6 SOM classes are further simplified into two categories: Type 1

(extratropical cyclone related) vs. Type 2 (subtropical ridge related), and evaluation of NSSL WRF simulation is performed accordingly.

As shown in Table 1, the scatter statistics are calculated for each region under different

41 synoptic patterns, where the Stage IV observations serve as x-axis and NSSL WRF as y-axis

(scatter plots are not shown). For the SGP, as the precipitation accumulation intervals increase from 1-hr to 24-hr, the valid grid-point sample number decreases drastically from 107 to 106.

Meanwhile, in response to more collocated grid-points as the result of temporal accumulation, the fitted linear slope increases for both Type 1 and Type 2, and the correlation coefficients between the two datasets increase as well. However, at different time intervals, Type 1 storms all demonstrate persistent better performance than Type 2 with fitted linear slopes closer to 1 and higher correlation coefficient values. Similar conclusions can also be drawn from the NGP regions.

Table 1. The statistical comparisons between NSSL-WRF simulations and Stage IV observations based on grid-points at the precipitation accumulation intervals of 1-hr, 3-hr, 6-hr, and 24-hr over the SGP and NGP regions Type 1/Type 2 1-hour 3-hour 6-hour 24-hour Sample number 1.64 / 1.20 ×107 7.95 / 6.24×106 5.06 / 4.25×106 1.96 / 1.98×106 SGP Slope 0.016 / 0.004 0.094 / 0.086 0.164 / 0.155 0.354 / 0.273 Correlation 0.017 / 0.004 0.097 / 0.083 0.172 / 0.153 0.362 / 0.269 Sample number 1.51 / 1.08 ×107 7.04 / 5.35×106 4.40 / 3.54×106 1.65 / 1.58×106 NGP Slope 0.059 / 0.004 0.159 / 0.093 0.243 / 0.176 0.407 / 0.335 Correlation 0.050 / 0.003 0.138 / 0.078 0.214 / 0.147 0.354 / 0.274

The annual accumulated precipitation fields are compared for the overall distribution, zonal and meridional variations for the SGP as shown in Figure 9, where the Type 1 (Figure 9a) storms feature more zonal variation as the west-east precipitation gradient dominates the domain and the maximum precipitation occurs at the northeast corner. In contrast, the Type 2 (Figure 9d) has the precipitation core more horizontally oriented which is center around the 37o N parallel.

In order to facilitate the analysis of directional variations in spatial precipitation distribution, the zonal (meridional) mean is calculated along each latitude (longitude) parallel, then weighted

42 by the maximum precipitation value over the entire domain, and finally shown as the function of longitude (latitude) for the Type 1 (Figure 9c) and Type 2 (Figure 9f). For the SGP, NSSL WRF captures the overall zonal precipitation trend increasing from west to east, both the zonal slope

(69.88 mm deg-1 for Stage IV vs. 68.61 mm deg-1) and normalized standard deviation (standard deviation weighted by the mean value, 0.19 vs. 0.18) are well simulated. However, on the meridional direction with less variation (0.05 for Stage IV vs. 0.04 for NSSL WRF), the observed increasing trend (meridional slope of 14.63 mm deg-1) from south to north is flipped in simulation

(-4.66 mm deg-1).

In summary, the differences in spatial pattern between Type 1 and Type 2 are well simulated by NSSL WRF (Figures 9b and 9e), but better performance is still found for the Type 1 storms.

First, although NSSL WRF has slight undersimulation for both synoptic patterns, the former is less biased (246 mm for Stage IV vs. 239 mm for NSSL WRF) than the latter (219 vs. 209 mm).

Secondly, by comparing the directional variations (Figures 9c and 9d), simulated Type 1 storms match well with the Stage IV observations in both zonal and meridional directions, but the Type 2 meridional trend corresponds to the largest error where the location of the peak is shifted southward by 1 degree (37.5o N to 36.5o N).

By comparing the accumulated precipitation fields between observations and simulations for both Type 1 and Type 2 over the NGP (Figure 10), the oversimulation is the most prominent issue. Different from the SGP which features more prominent zonal variation than meridional, the

NGP has similar variations on each direction (i.e., 0.04 for zonal and 0.06 for meridional), which are competently simulated by NSSL WRF (0.06 for both). However, as the simulated precipitation maximizes at the southeast corner of the domain, NSSL WRF almost triples the zonal slope (6.45 vs. 17.01 mm deg-1) while the decreasing meridional slope is not strongly impacted (-13.72 vs. -

16.80 mm deg-1). In the zonal direction, Type 1 features the homogeneous distribution with a

44 southwest-northeast oriented precipitation band centered at the 46o N (clockwise rotation angle of

~ 35o), which results in the decreasing meridional trend from south to north. With the majority of precipitation distributed to the southwest of the domain, NSSL WRF has difficulty to represent the observed precipitation decay towards both the east and the north. Despite those differences in spatial distribution, the averaged trends in zonal and meridional directions are comparable between observations and simulations in Figure 10c. Although the simulated trends both decrease eastward and northward, they still roughly follow the observed trends with slight deviation.

Figure 10. Same as Figure 9 but over the NGP.

Compared to the Type 1, larger discrepancies in spatial precipitation distribution can be found for the Type 2. First, Type 2 corresponds to larger oversimulation of accumulated precipitation both in absolute value (24 vs. 22 mm) and relative value (18 vs. 12 %). Secondly, there is a slantwise heavy precipitation band collocated with Type 1 observation, which is greatly

45 shifted northward in simulation. Moreover, the heaviest precipitation simulation occurs at the southeast corner of the domain (200 mm year-1), where a deficit region is found in observation (80 mm year). In response to those distinctions in spatial distribution, the simulated zonal trend (13.27 mm deg-1) increases faster than observed (5.95 mm deg-1), and in the meridional direction the meridional peak is shifted northward by 0.6o.

Figure 11. The diurnal cycle comparison between Stage IV observations (solid lines) and NSSL WRF simulations (dash lines) for Type 1 (a, b) and Type 2 (c, d) synoptic patterns over the SGP (a, c) and the NGP (b, d). The local night is shaded gray from 2000 to 0600 LST, and the total bias between the two datasets are also calculated for each time period as shown below the diurnal curves.

Lastly, the precipitation diurnal cycles are evaluated over both regions for different storm

46 types (Figure 11). From the perspective of observation, the Type 1 precipitation rates over both regions (Figures 11a and 11b) demonstrate the compliance to the typical diurnal pattern commonly observed over the GP with nocturnal maximum at the night and minimum at the noon. Over the

SGP, the Type 2 precipitation rates (Figure 11c) still preserve the diurnal pattern found in Type 1, but the peak precipitation occurs at 0300 LST with a 3-hour delay relative to the Type 1 (0000

LST). Similarly, there is also a 3-hour delay in minimum precipitation when comparing the two synoptic patterns (1500 vs. 1200 LST). The phase shift is also observed over the NGP, where the

Type 2 precipitation peaks at 0400 LST (4-hour delay compared to the Type 1).

The delayed precipitation peak observed over both regions suggests that the Type 1 and

Type 2 patterns have different dependence on the strength of LLJ. As revealed in previous studies

(e.g., Bonner 1968; Bonner and Paegle 1970; Paegle and Rasch 1973; Jiang et al. 2007), the LLJ peaks around 0000 to 0300 LST over the central states (95o W to 100o W). Under the Type 1 condition, the extratropical cyclone aids the eastward propagation of cold and day air from the lee side of Rocky Mountains towards the GP. Then this air mass encounters the local warm and moist air, forming a frontal boundary which favors for the convection initiation. As a result, the moisture injection by the LLJ can easily precipitate out in this scenario, so the maximum precipitation can be generated (at 0000 LST) before the strongest LLJ forms (0000 to 0300 LST). The Type 2 synoptic pattern (subtropical ridge related) produces subsiding air over the southern part of the study domain, whereas the northern part is dominated by the cold and dry air. Consequently, the convections formed around the periphery of the high pressure are often associated with a west-east oriented stationary front or warm front. In order to generate precipitation, the stronger LLJ is required to bring the moisture to the cool side of the boundary, which explains why the Type 2 precipitation maximizes after the strongest LLJ.

Different from the SGP where overall match in diurnal pattern between the two synoptic conditions, the NGP Type 2 precipitation rates (Figure 11d) demonstrate more interesting features in addition to the delayed precipitation peak. First, its diurnal variation is greatly suppressed (at the magnitude of 0.1 mm compared to 0.3-0.4 mm for the rest of the conditions). The meridional vapor flux is already very weak over the NGP, and the moisture availability is further constrained by the subtropical high, which generates an unsaturated environment along the path of the water vapor transport. As a result, the weakest precipitation is produced there. Secondly, the typical GP diurnal features are totally disappeared, and a bimodal distribution is observed with an afternoon peak around 1700 LST. In response to the widespread descending air, the NGP is more exposed to clear sky with less clouds, thus the cloud shortwave radiative cooling effect is minimized and the surface solar heating becomes the major triggering mechanism for convection (Lee et al., 2010) which destabilizes the atmosphere with increasing Convective Available Potential Energy (CAPE).

As a result, the afternoon convection could occur under the influence of the subtropical ridge.

In order to facilitate the evaluation of NSSL WRF diurnal cycle simulation, the separation of local day and night is conducted with the average sunrise time at 0600 LST and sunset time at

2000 LST. From 0000 to 0600 LST, there exists a common nocturnal underestimation issue for both regions under both synoptic patterns, but the NGP corresponds to less negative biases overall.

By comparing the Type 1 and Type 2 precipitation during that period, a slight better performance is found under the Type 1 pattern for both regions. For the rest of the day, NSSL WRF demonstrates oversimulation over both regions, but different from the period from midnight to sunrise, less positive biases are found over the SGP than the NGP. The most prominent oversimulation issue occurs for the NGP Type 2, when the afternoon convection is greatly magnified. Again, despite of the regional difference, the Type 1 precipitation is still better

48 simulated than the Type 2 in general over both regions.

In summary, over both regions, the NSSL WRF simulated Type 1 precipitation cases outperform those from the Type 2 from different perspectives. Detailed evaluation studies have been submitted to Weather and Forecasting in two companion papers:

Hagenhoff, B., A. Kennedy, X. Dong, J. Wang, and M. Gilmore (2018), Evaluation of Northern and Southern Great Plains Warm Season Precipitation Events in WRF. Part I: Objective

Classification of Meteorological Regimes.

Wang, J., X. Dong, B. Xi, A. Kennedy and B. Hagenhoff (2018), Evaluation of Northern and

Southern Great Plains Warm Season Precipitation Events in WRF. Part II: Analysis of Observed and Simulated Precipitation.

2.4 FUTURE RESEARCH DIRECTIONS

In addition to the MC3E, a series of field campaigns were conducted over the North America by the joint force of DOE and NASA. Namely, the GPM Cold-season Precipitation Experiment

(GCPEx, January 17 – February 29, 2012), the integrated Precipitation and Hydrology Experiment

(IPHEx, May 1 to June 15, 2014), the Olympic Mountain Experiment (OLYMPEX, November,

2015 – February, 2016), etc. During these experiments, the UND Citation II research aircraft played a major role in the cloud microphysical properties in situ observation, and more than 200 hours cloud samples were collected. With the comprehensive aircraft observations available, future work should focus on creating a comprehensive dataset through the synthesis of the aircraft data collected from multiple field campaigns, providing the ground-truth cloud microphysical properties for the evaluation of model simulation and satellite retrieval.

For the NSSL-WRF evaluation and model improvement, based on the research discussed in

49 section 2.3, the simulated daily precipitation accumulation is in good agreement with observation

(less than ± 10% difference in average value). However, prominent issues are found for the simulation of precipitation diurnal cycle. Over both study regions, at least 60% of MCS simulations demonstrate difficulties in capturing the nocturnal convection featuring upscale growth, among which half of simulations end convection too soon, whereas the other half start the convection initiation process by 2-hour earlier. Moreover, those different model behaviors are proven to be highly related to the dominant synoptic patterns classified by SOM method, which deserves further investigation as the MCSs’ evolution demonstrates strong connection to the environmental conditions in the early stage.

To facilitate the MCS life cycle study, Feng et al. (2012) developed a tracking algorithm based on satellite and radar data. By separating a MCS into initiation, mature, and dissipation stages, future work should focus on the evaluation of model performance based on different life stages. Inspired by the improvement in cold pool simulation by introducing intensive raindrop break-up efficiency by Feng et al. (2015), we expect to reveal the weakest link in simulating MCS life cycle, and to provide insightful suggestions for the model improvement. Moreover, after the tracking of MCS objects from multiple years, the future work should extend to the construction of a comprehensive MCS tracking database. By doing that, we expect to reveal the MCS characteristics in the temporal dimension which haven’t been thoroughly studied previously, and address the following questions for each specific MCS object:

a. Where and when does the system originate?

b. What is the environmental scenario (synoptic pattern and underlying surface conditions)

during the convection initiation?

c. How long does the system last and when the maximum coverage/intensity occur?

Although this unique MCS database is designated for the NSSL-WRF evaluation, but it is expected to serve as the ground-truth observation for the broader modelling communities.

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APPENDIX A: INVESTIGATION OF ICE CLOUD MICROPHYSICAL PROPERTIES OF DCSS USING AIRCRAFT IN-SITU MEASUREMENTS DURING MC3E OVER THE ARM SGP SITE

(Published in the Journal of Geophysical Research: Atmospheres)

Jingyu Wang, Xiquan Dong, Baike Xi

Department of Atmospheric Sciences, University of North Dakota, Grand Forks, North Dakota

Wang, J, X Dong, and B Xi (2015), Investigation of ice cloud microphysical properties of DCSs using aircraft in situ measurements during MC3E over the ARM SGP site. J. Geophys. Res. Atmos.,

120, 3533–3552. doi: 10.1002/2014JD022795.

ABSTRACT

Six deep convective systems (DCSs) with a total of 5,589 5-s samples and a range of temperatures from -41 oC to 0 oC during the Midlatitude Continental Convective Clouds Experiment (MC3E) were selected to investigate the ice cloud microphysical properties of DCSs over the DOE

Atmospheric Radiation Measurement (ARM) Southern Great Plains (SGP) site. The ice cloud measurements of the DCS cases were made by the University of North Dakota Citation II research aircraft and the ice cloud properties were derived through the following processes. First, the instances of super-cooled liquid water in the ice dominated cloud layers of DCSs have been eliminated using multi-sensor detection, including the Rosemount icing detector, King and CDP probes, as well as 2DC and CIP images. Then the Nevzorov-measured ice water contents (IWCs) at maximum diameter Dmax < 4,000 μm are used as the best estimation to determine a new mass- dimensional relationship. Finally the newly derived mass-dimensional relationship (a = 0.00365, b = 2.1) has been applied to a full spectrum of particle size distributions (PSDs, 120-30,000 μm) constructed from both 2DC and HVPS measurements to calculate the best-estimated IWCs of

DCSs during MC3E. The averages of the total number concentrations (Nt), median mass diameter

-3 (Dm), maximum diameter (Dmax), and IWC from six selected cases are 0.035 cm , 1,666 μm, 8,841

μm, and 0.45 g m-3, respectively. The gamma-type-size-distributions are then generated matching the observed PSDs (120-30,000 μm), and the fitted gamma parameters are compared with the observed PSDs through multi-moment assessments including first moment (Dm), third moment

(IWC), and sixth moment (equivalent radar reflectivity, Ze). For application of observed PSDs to the remote sensing community, a series of empirical relationships between fitted parameters and

Ze values has been derived and the bullet rosette ice crystal backscattering relationship has been suggested for ground-based remote sensing.

1. INTRODUCTION

Deep Convective Systems (DCSs) have traditionally been divided into a deep convective precipitating portion and a non-precipitating anvil canopy (Feng et al., 2011, 2012). The former is important to the atmospheric hydrologic cycle because intense precipitation is common with

DCSs, while the latter is important for the atmospheric radiation budget due to the extensive spatial coverage of anvil canopies (Feng et al., 2011, 2012). The magnitude of the interactions between radiation and clouds primarily depends on the DCS’s macrophysical (e.g., cloud fraction and height) and microphysical properties (e.g., median mass diameter (Dm), ice water content (IWC), particle size distribution (PSD)) (Liou, 1986; Stephens et al., 1990; Protat et al., 2007; McFarquhar et al., 2014). Many previous studies of cloud microphysical properties focused primarily on synoptically generated cirrus clouds due to their high altitudes (>5 km) and low ambient temperatures (< -20 oC), which provided an ideal environment to study the ice cloud microphysical properties. A series of field experiments were carried out to investigate cirrus cloud microphysical properties including the First International Satellite Cloud Climatology Project (ISCCP) Regional

Experiment (FIRE) and the Cirrus Regional Study of Tropical Anvils and Cirrus Layers - Florida

Area Cirrus Experiment (CRYSTAL-FACE), using multiple ground- and space-based remote sensors, and aircraft in situ measurements (Heymsfield et al., 2002, 2007, and 2010). As a result, numerous datasets have been produced through these field campaigns, which help us to further understand the microphysical properties and processes of anvil and cirrus clouds.

Among all ice cloud microphysical properties, IWC is one of the most important parameters for radiation budgets and surface precipitation. There are three primary techniques to estimate cloud IWC from aircraft in situ measurements. The first technique is based on the relative amount

62 of power needed for melting and evaporating ice crystals collected by a hot-wire sensor, such as the difference between Nevzorov measured Total Water Content (TWC) and Liquid Water Content

(LWC) (Sky Tech Research) (Korolev et al., 1998b). The second one is based on the increased water vapor density by evaporating ice particles, which can be collected by the counterflow virtual impactor (CVI) (Noone et al., 1988) and cloud spectrometer and impactor (CSI). The last technique involves the calculation of IWC from PSD measurements, which is based on a mass- dimensional relationship (e.g., Brown and Francis, 1995, BF95 hereafter; Mitchell, 1996;

Heymsfield et al., 2002, 2007, and 2010). The PSDs can be measured by either one optical array probe (OAP), such as 2DC and HVPS for a partial spectrum of PSDs, or a combination of two

OAPs (2DC + HVPS for a full spectrum of PSDs in this study). The mass-dimensional relationship can be derived by summing over the PSD for each bin with the Nevzorov measured IWC ∝ aDb

(where a is the coefficient, b is the exponent, and D represents ice particle size). Note that different values of a and b can be derived from different field campaigns, and even for different cases within a campaign itself (e.g., Locatelli and Hobbs, 1974; BF95; Heymsfield et al., 2010).

PSD plays an important role in the study of ice clouds because most of bulk ice cloud microphysical properties, including IWC, bulk density, median mass diameter (Dm) etc., are determined from the PSD measurements. Furthermore, the PSD should have a strong relationship to ice formation and growth processes including aggregation, accretion, deposition, melting, and autoconversion of droplets to raindrop sizes (Lin et al., 1983). In this study, the gamma-type-size- distributions have been generated matching the observed 5-s averaged PSDs during MC3E, that can be applied by the remote sensing and modeling community to retrieve or simulate bulk ice cloud microphysical properties of the DCSs.

Compared to synoptically generated cirrus clouds, the ice cloud microphysical properties of

DCSs may be complex because DCS clouds include at least three parts: the ice-phase layer, mixed- phase layer, and the liquid or precipitation layer below the melting band (Korolev et al., 2006).

The ice cloud microphysical properties of DCSs share some characteristics of cirrus clouds, but have distinguishable differences, such as different particle size spectra, ice crystal shapes, and IWC

(Heymsfield et al., 2010). To investigate the formation-dissipation processes and microphysical properties of continental DCSs, the Department of Energy (DOE) Atmospheric Radiation

Measurement (ARM) conducted a field campaign, the Midlatitude Continental Convective Clouds

Experiment (MC3E), at the ARM Southern Great Plain (SGP) site from April-June 2011 (Jensen et al. 2010). The campaign consisted of the most comprehensive cloud observing infrastructure currently available in the central United States combined with an extensive sounding array, ground-based remote sensors, aircraft in situ observations, and updated ARM radar instrumentation. The overarching goal of MC3E was to provide the most complete characterization of convective cloud systems, precipitation, and their environment, such as convective initiation, updraft and downdraft dynamics, and precipitation and cloud microphysics (Jensen et al., 2010).

In a series of papers by the authors, all the DCS cases during MC3E will be categorized into ice, mixed-phase, and liquid layers, and investigations will be focused on the microphysical properties of each category. As the first paper of the series, six DCS cases during MC3E (Figure

A. 1) were selected to investigate the microphysical properties of DCSs measured by the

University of North Dakota Citation II research aircraft and the ground-based remote sensors. This study will focus on the ice cloud microphysical properties of DCSs, excluding liquid-phase conditions and most of mixed-phase conditions using multi-sensor detection which will be discussed in section 2.3. However, contamination from a small portion of mixed-phase clouds is still inevitable in this study. In detail, we will discuss the instrumental limitations of the Nevzorov

64 hot-wire TWC probe measured total condensed water content (TWC) within ice dominated cloud layers, which is treated as IWC in this study. We also propose the best-estimated IWC and PSD using a combination of the two-dimensional Particle Measurement System (PMS) cloud probe

(2DC, 30-3,000 µm) and the SPEC Inc. High Volume Precipitation Spectrometer (HVPS, 300-

30,000 µm) measurements. Finally the gamma-type-size-distributions have been generated matching the observed 5-s averaged PSDs, and the fitted gamma parameters have been compared with the observed PSDs through multi-moment assessments including first moment (median mass

퐷푚 푏 퐼푊퐶 diameter, Dm, ∫ 푛(퐷)푎퐷 = , where D is the representation of particle size, and n(D) is 0 2

퐷 corresponding number concentration), third moment (IWC, 퐼푊퐶 = 푚푎푥 푛(퐷)푎퐷푏), and sixth ∫0

퐷 moment (equivalent radar reflectivity Z , 푍 ∝ 푚푎푥 푛(퐷)퐷6푑퐷). e 푒 ∫0

2. DATA

The University of North Dakota (UND) Citation II research aircraft was one of the primary research aircraft deployed during the ARM MC3E field campaign, and was fully equipped for cloud physics research. The UND aircraft probes used in this study and their associated measurements and accuracies are listed in Table A. 1. In summary, the Rosemount icing detector,

King and Droplet Measurement Technologies (DMT) Cloud Droplet Probe (CDP) probes, as well as 2DC and DMT Cloud Imaging Probe (CIP) images, were used to detect the super-cooled LWC in the ice dominated cloud layers of DCSs. The Nevzorov TWC/LWC sensor and OAP 2DC and

HVPS probes were used to study the ice cloud IWC and PSD of the DCSs during MC3E.

Table A. 1. The University of North Dakota Citation II aircraft probes used in this study.

Instrument name Description Nevzorov TWC/LWC sensor Deep cone (60o), range of measured LWC/TWC 0.003 – 3.0 g m-3, accuracy ± 10%.

King LWC sensor Model KLWC-5, range of measured LWC 0.05 – 3.0 g m-3, accuracy ± 15%.

Rosemount icing detector Model 0971LM, causing a sharp drop in the frequency of oscillation due to accrete and glaciate SLW droplets on the sensing cylinder.

CDP 1-50 µm

2DC 30-3,000 µm (bins of 1 - 3, from 30 to 90 µm were not used in this study)

HVPS 300-30,000 µm

2.1 PSD MEASUREMENTS

The measurements by three probes carried by Citation II can be used to retrieve a full spectrum of PSDs during MC3E. The CDP can measure cloud particles smaller than 50 µm (1 to

50 µm), the 2DC probe can measure a range of particle sizes from 30 to 3000 µm, and the HVPS

67 probe observes a broad range between 300 and 30,000 µm. Data were collected and pre-processed using a Model 300 Data Acquisition and Playback system (manufactured by Science Engineering

Associates), and the PSDs were calculated using software developed by Aaron Bansemer at the

National Center for Atmosphere Research (Field et al., 2006). Cloud particle sizes measured by

OAPs were sorted into bins accordingly based on the diameter D of smallest circle that encloses the particle (Heymsfield et al., 1978; Field et al., 2006; Korolev et al., 2007). Cloud particles were not used in this study with the following conditions: (1) the area ratio (the ratio of the projected area of the particle to the area of a circumscribed circle (McFarquhar and Heymsfield, 1996)) is less than 0.1, and (2) the area ratio is less than 0.2 and the particle size is twenty times greater than the resolution of the probe (Field et al., 2006).

As pointed out from previous studies (Heymsfield, 2007; McFarquhar et al., 2007a), there are large uncertainties in the 2DC measurement for particles with size less than 500 µm due to the contamination from small crystals generated by the shattering of larger crystals on the probe tips.

Suggested by Jackson et al. (2014a, b), both the anti-shattering tips of the 2DC and the inter-arrival time based shattering removal algorithm provided by Aaron Bansemer (Field et al., 2006) were used to reduce the effect of artifacts during MC3E. Although it is commonly believed that most of the shattered artifacts have been eliminated through the combination of two shattering removal methods, there are no ways to know how many undetected artifacts are still present (McFarquhar

2015, personal communication). Since this issue affects more on quantities that are dominated by lower order moments of PSD, we did a sensitivity study of Nt with a 10% uncertainty in number concentration for each size bin from 120 to 500 µm, and found a 8% uncertainty in Nt.

Uncertainties in gamma fitted parameters will be discussed in section 3.2.

In this study, the PSD covers the full spectrum from 120 µm to 30,000 µm through a

68 combination of 2DC (excluding the first three channels because of the issue of depth of field and errors involving the digitization of small ice crystals (Korlev et al., 1998a)) and HVPS measurements. For the overlapping spectral region (from 900 µm to 2800 µm) between the 2DC and HVPS, the frequency of occurrence for particles recorded by each size bin was calculated.

The differences in the frequency of occurrence between 2DC and HVPS increase from 9% at 900

μm to 39% at 2,800 μm because the HVPS probe is capable of measuring more large particles than the 2DC probe (particles were reconstructed for D > 1000 µm). Over the overlapping region, the

-3 -3 averaged ratio of the Nt calculated from HVPS (0.211 cm ) to that (0.185 cm ) from 2DC

-3 -3 measurements is 1.14, while their IWC ratio is 1.12 (0.183 g m and 0.163 g m ). Both Nt and

IWC have indicated a consistency between the 2DC and HVPS measurements over the overlapping region with differences around 13%. As a result, the HVPS measurements were used for D > 900

μm, while the 2DC measurements were used for D = 120-900 μm in our constructed PSDs. Both the 2DC and HVPS probes were well calibrated by manufacturers before the field campaign, and performance check and quality control were carried out before and after each flight. When analyzing data, we found that both probes functioned well throughout the entire project with the exception of 24 May 2011 when the 2DC malfunctioned after 21:30 UTC. Hence, part of 24 May

2011 was excluded from the analysis. To further control the quality of the data, 15% of the OAP records were rejected due to either insufficient sampling or non-simultaneous recordings between two OAPs.

2.2 IWC/LWC MEASUREMENTS

For cloud water content measurement, the Citation II was equipped with a Nevzorov hot wire TWC/LWC probe (CWCM-U2) (Korolev et al., 1998) and a PMS King hot-wire LWC probe

(King et al., 1978, 1985). From the operating manual, the Nevzorov TWC sensor (shallow cone version, 120o) can measure a range of TWC from 0.003 gm-3 to 3 gm-3 with a 10% uncertainty, which was proved in wind tunnel test. Korolev et al. (1998) also found the uncertainties of 10% to 20% for small frozen droplets with median volume diameter around 20 μm. However, for the modified Nevzorov TWC sensor (deep cone, 60o) used in this study, its accuracy is still under investigation (details for calibration and treatment of baseline drift will be discussed in appendix).

The main component of the Nevzorov TWC sensor is a conical collector with a diameter of 8 mm, which works under the assumption that all ice particles tend to remain inside the conical hollow region of the sensor until they completely melt or evaporate (Korolev et al., 1998). Because of its fixed diameter and limited sampling area (0.5 cm2), it is probably that the Nevzorov TWC sensor underestimates the IWC, especially for large particles (Korolev et al., 2013). The magnitude of underestimation for IWC with large particles occurring will be investigated in this study.

Previous studies found that the Nevzorov TWC sensor may collect most of the ice particle mass when their sizes range from a couple hundred up to 4,000 μm (e.g., Korolev et al. 1998;

Strapp et al., 2005; Korolev et al. 2013). However, snow and ice crystals are generally large in nature and their sizes can be up to a few millimeters. Therefore, it is most likely that the Nevzorov

TWC probe underestimates the IWCs for these large particles due to its low collection efficiencies resulted from particle bouncing, pooling and subsequent shedding of water before complete evaporation (Strapp et al., 2005). Korolev et al. (2013) compared the IWCs measured by the modified Nevzorov TWC sensor (deep cone, a 60-degree angle, which was used during MC3E) and DMT Counterflow Virtual Impactor (CVI), as well as the IWC calculated from the PSD. In

Korolev et al. (2013), they found that the IWCs measured by the modified Nevzorov TWC sensor are nearly the same as the CVI measurements and PSD calculations for D < 4,000 μm, but their

70 differences increase with increased particle size when D > 4,000 μm.

The King probe operates under the same principle as the Nevzorov TWC/LWC sensor where the cloud LWC can be calculated from the measurement of the heat release of a cylinder exposed to an air stream that intercepts evaporating cloud droplets. The uncertainty of King LWC measurements is around 15% for cloud droplet diameters D < 30 µm, and may be greater than 15% when D > 30 µm, with a reliable detection threshold about 0.05 g m-3 (Biter et al., 1987; Strapp et al., 2003). As a result of poor response to D > 50 µm (Biter et al., 1987) and data calibration issues due to the occurrence of some negative LWC values, as well as its potential response to small ice crystals, the King probe cannot be used to quantitatively measure the actual LWC in super-cooled regions (SLWC). However, the King LWC measurements can still be used to identify the existence of SLWC in the ice dominated cloud layers of DCSs in this study.

2.3 PHASE DETERMINATION

Contamination by SLWC is a major issue in estimating the IWC in a DCS because any super-cooled liquid water (SLW) droplets misinterpreted as ice crystals would cause an order-of- magnitude mass shift. For example, the water mass IWC or LWC was calculated using the mass- dimensional relationship (~ aDb, in cgs units) where a = 0.5233, b = 3 for SLW droplets, and a =

2.94×10-3, b = 1.9 for aggregate ice crystals (BF95). Given a particle with D = 3,000 µm, the difference in water mass could be up to 30 times between the SLW droplets and ice crystals.

Therefore, it is critical to eliminate the contamination of SLWC when calculating the IWCs in a

DCS.

In this study, multi-sensor detection, such as the Rosemount Icing Detector (RID), King and

CDP probes, as well as 2DC and CIP images, has been adopted to eliminate the SLWC in the ice dominated cloud layers of DCSs. The RID (Baumgardner and Rodi, 1989) is very sensitive to super-cooled liquid water droplets because they can be accreted and glaciated on the sensing

72 cylinder causing a sharp drop in the frequency of oscillation as demonstrated in Figure A. 2b.

When a high concentration of SLW droplets becomes glaciated on the surface of the RID cylinder and the accumulated ice on the RID probe exceeds 0.5 mm, a heater is turned on to sublimate the coated ice. This process normally takes about 10-15 seconds. Since there is little to no response to ice crystals (Heymsfield and Miloshevich, 1989), the RID probe is extremely useful in segregating the different cloud phases qualitatively. However, the RID probe is not suitable for detecting liquid water at a temperature range from -3 to 0 oC because of the dynamic heating of the probe by the flight speed of the aircraft. As a result, the RID records were not included in the phase identification process in that temperature range in this study (Heymsfield, 2015; personal communication).

In addition to the RID measurements, previous studies show that when the air temperature is below 0 oC, SLWCs are to a large extent dominated by small super-cooled liquid water droplets

(e.g., Stewart et al., 1994; Rosenfeld et al., 2013), which can be directly measured by King Probe and calculated from CDP measured PSDs, as shown in Figure A. 2b. However, when D > 50 μm, the King and CDP LWC measurements are no longer useful due to their measurement limitations

(Biter et al., 1987). Therefore, a large number of 2DC and CIP images were visually examined to verify the existence of large SLW droplets. Figure A. 2c shows two images containing SLW droplets sampled by the 2DC (upper panel) and CIP (lower panel), and simultaneous RID frequency measurements and CDP LWC records at 21:15:40 UTC. As demonstrated in Figure A.

2b for the case of 24 May 2011, the occurrence of SLW can be detected by multiple sensors with sudden drops in frequency (RID) and/or corresponding LWC peaks (CDP and King probe), as well as the peaks in CDP concentration. Table A. 2 lists the criteria using multiple sensors to detect super-cooled liquid water, and the contamination periods were marked when one or more criteria

73 were satisfied. For the selected MC3E cases, there is a threshold of 0.24 cm-3 in CDP concentration that corresponds to SLW events recorded by other sensors. This conclusion is similar to the results of Rosenfield et al. (2013). After eliminated these SLWCs, all ice particles from six selected cases during MC3E have been processed to generate the ice cloud microphysical properties of DCSs in the following section.

Table A. 2. The criteria of using multiple sensors to detect supercool liquid water content Instrument/Measurement Criteria for detecting SLWC Criteria for detecting non- eventsa SLWC events RID Causing a sharp drop (more than 40 Frequency remains constant Hz) in the frequency of oscillation (no icing detected) due to accrete and glaciate SLW droplets on the sensing cylinder CDP_LWC CDP_LWC ≥ 0.1 g m-3 CDP_LWC < 0.1 g m-3 (varied case by case) (varied case by case) King_LWC King_LWC ≥ 0.1 g m-3 King_LWC < 0.1 g m-3 (varied case by case) (varied case by case) 2DC/CPI image reading Complete spherical particles or No complete spherical smooth-edged incomplete particles particles or smooth-edged were visually found incomplete particles were found a For strict exclusion, SLWC event was marked even one criterion was satisfied.

The design of the Nevzorov LWC probe suggests that it usually records small amount of

LWC during collision with ice particles due to the residual effect of small ice crystals (Korolev et al., 1998). As the result, the Nevzorov LWC measurements are questionable in ice dominated cloud layers because of undistinguishing the SLW droplets and small ice crystals from its measurements. Therefore, the Nevzorov LWC probe was not used in this study.

3. RESULTS AND DISCUSSION

Table A. 3 summarizes the aircraft flight date, time, altitude, temperature, and Next-

Generation Radar (NEXRAD) radar reflectivity along the aircraft track for the six selected DCS

74 cases during MC3E. The total flight time for these six selected cases is about 18 hours with an altitude of 237 m to 9,572 m, temperatures ranging from -41 oC to 31 oC, and NEXRAD reflectivities ranging from 1.89 to 44.82 dB. A total of 5,589 5-s samples (7.76 hours) with a range of temperatures from -41 oC to 0 oC from the six selected cases have been used to investigate the ice cloud microphysical properties of DCSs over the DOE ARM SGP site.

Table A. 3. The summary of aircraft flight date, time, altitude, temperature and NEXRAD radar reflectivity along the aircraft track for the six selected DCS cases during MC3E.

Temperature Datea Timeb (UTC) Altitude (m) Z (dB) (oC) e 110427 080207 – 112245 411 – 6213 -24 to 12 1.89 – 40.35 110501 162839 – 184213 237 – 7702 -28 to 10 3.00 – 37.05 110511 160209 – 192706 253 – 7385 -29 to 29 3.56 – 38.54 110518 072010 – 092156 363 – 7364 -27 to 16 5.29 – 28.81 110520 130539 – 170204 360 – 7660 -23 to 20 5.00 – 44.82 110524 201825 – 222750 421 – 9572 -41 to 31 4.03 – 30.87 all cases 18 hours 237 – 9572 -41 to 31 1.89 – 44.82

a YYMMDD format b HHMMSS format

3.1 RECALIBRATION OF MASS-DIMENSIONAL RELATIONSHIPS

The relationship between the particle mass and diameter was measured and fitted by

Locatelli and Hobbs (1974) to the following equation:

푚푎푠푠 = 푎퐷푏, (A1) where D is the diameter of smallest circle that encloses the ice particle (Heymsfield et al., 1978;

Field et al., 2006; Korolev et al., 2007), a is the coefficient, and b is the exponent. Subsequent studies have been published with different sets of parameters a and b depending on the hydrometeor shape and density (e.g., BF95; Mitchell, 1996; Heymsfield et al., 2002, 2007, 2010) with a range of values from 2.94×10-3 to 6.30×10-3 for coefficient a and from 1.9 to 2.4 for

75 exponent b suggested by Heymsfield et al. (2007), even a broader range from 1 to 3 (Fontaine et al., 2014). The mass-dimensional relationship (a = 2.94×10-3, b = 1.9 from BF95) has been widely used for calculating cloud IWC and parameterizing ice cloud bulk microphysical properties.

However, the BF95 method was initially derived by Locatelli and Hobbs (1974) and investigated and evaluated by Brown and Francis (1995) using aircraft in situ measurements in cirrus clouds, thus it is questionable to apply its coefficients to MC3E campaign. Though the ice cloud microphysical properties of DCSs and cirrus clouds share some similarities, the differences are significant and will be discussed below.

First, the range of the particle size spectrum between MC3E and BF95 is significantly different. Most of ice cloud particles in BF95 ranged from 200 to 800 µm, while during MC3E the maximum diameters could be up to 30,000 µm, and for some cases the mass contributed by large particles with D > 1,000 µm could be more than 50% of the total mass. Secondly, the mass- dimensional relationship in BF95 was based on ice crystals with habits of aggregates of un-rimed bullets, columns, and side planes. During MC3E, aggregates of different types of ice crystals, including bullet rosettes, planes, and columns etc., were found from CPI images and the backscattering properties using the assumption of a bullet-rosette ice crystal habit exhibited good agreement with NEXRAD radar reflectivity measurements (further discussion and validation in habit will be in section 3.3). As pointed out by previous studies (e.g., Heymsfield et al., 2010), the mass-dimensional relationships should be significantly different from different ice crystal shapes.

Finally, the air temperature ranges between BF95 and this study are also different. In BF95 study, the air temperatures were typically between -20 oC and -30 oC whereas for this study, the air temperature ranged from -41 oC to 0 oC. Considering all of these differences between the BF95 and this study, it is necessary to develop a new mass-dimensional relationship for the ice cloud

76 microphysical properties of DCSs from aircraft in situ measurements during MC3E.

The essence of the mass-dimensional relationship is the conversion from 3D data (time series, spectra, and number concentrations) to 2D data (time series and IWCs) (Figure A. 3). Using

( ) ( ) 2 2 푁 [퐼푊퐶푝푟표푏푒 푖 − 퐼푊퐶푁퐸푉 푖 ] least-square fitting (χ = ∑푖=1 ), the coefficient a and exponent b can be 퐼푊퐶푁퐸푉(푖) derived by fitting the IWCs calculated from PSD to the Nevzorov IWC measurements. In order to derive the appropriate mass-dimensional relationship, the exponent b should be varied within the range from 1.9 to 2.4 as suggested by Heymsfield (2007). Once the exponent b is determined, values of a can be derived from either a full or partial spectrum depending on the segment that can be represented by the direct measurement in a specific temporal resolution (e.g., 1 s, 5 s, or 1 min).

Thus, the IWC calculated through the summation of the PSD (right side of Eq. 2) should yield the same IWC as measured by Nevzorov probe (IWCNEV). The parameters a and b can be derived using least-square method that provides the best match with the Nevzorov–measured IWCs by

77 satisfying the following equation:

푖=퐷푚푎푥 푏 퐼푊퐶푁퐸푉 = ∑푖=퐷푚푖푛 푁푖 × 푎 × 퐷푖 (A2)

Heymsfield et al. (2010) compared the CVI-measured IWCs with the IWCs calculated from

PSDs and determined b = 2.1 because the IWC ratios are nearly independent of median mass diameter (Dm) and air temperature. They also used 2D particle images with different habits

78 sampled by Cloud Particle Imager (CPI) probe to calculate median fractal dimension values (the exponent b of mass-dimensional relationship) and found that b = 2.1 can be broadly applied to a variety of habits including aggregate, bullet rosette, needle, plate, and dendrite. Korolev et al.

(2013) used the CVI-measured IWCs as the best estimation (because CVI can measure a full spectrum of PSDs) and compared the CVI-measured IWCs to the Nevzorov-measured IWCs.

They concluded that the averaged ratio of CVI-measured IWC to Nevzorov-measured IWC is 1.03 with a correlation of 0.94 at Dmax < 4,000 μm, for Dmax > 4,000 μm it is 1.84 with a correlation of

0.81. Therefore, they concluded that the Nevzorov probe can accurately measure IWCs at Dmax <

4,000 μm, but severely underestimate IWCs for Dmax > 4,000 μm.

Following the conclusions of Heymsfield et al. (2010) and Korolev et al. (2013), we apply b = 2.1 and the BF95 relationship to a total of 1,097 5-s samples for Dmax < 4,000 μm. As demonstrated in Figure A. 4a, the ratios of the IWCs calculated from mass-dimensional relationship with b = 2.1 to the Nevzorov-measured IWCs were peaked around 1.0, while using

BF95, they were skew at around 1.1. Using the Nevzorov-measured IWCs at Dmax < 4,000 μm as the best estimation, we can determine the coefficient a values for each 5-s sample during MC3E, and the averaged a value is 3.65×10-3. Finally we apply the newly derived mass-dimensional relationship (a = 0.00365, b = 2.1) during MC3E to the full spectrum of PSDs and calculate the best-estimated IWCs. As expected, the averaged ratio of IWCprobes to IWCNEV is 1.035 and a

2 correlation (R ) of 0.89 at Dmax < 4,000 μm, however, their ratios increase and correlations decrease with increased Dmax values as shown in Figure A. 4b. To quantitatively determine the underestimation of the Nevzorov-measured IWCs with D > 4,000 μm, we plot Figure A. 4c. As illustrated in Figure A. 4c, the Nevzorov-measured IWCs increase with increased Dmax from 0.155

-3 -3 g m at Dmax = 4,000 μm to 0.311 g m at Dmax = 13,000 μm, but their underestimations also

79 increase from 2.2% to 23.8% when comparing to the calculated IWCs from PSDs. To further investigate the mass contribution from particles greater than 4,000 µm to the total mass, we apply the newly derived mass-dimensional relationship to the averaged full spectrum of PSDs from the six selected cases. As listed in Table A. 4, the integrated mass contribution from D = 4,000 μm to

Dmax to the total mass is 19.75%.

Table A. 4. The mass contribution from particles with D > 4,000 μm to the calculated total IWC

-3 Dmax (μm) IWC (D < Dmax) (g m ) Mass contribution (4,000 μm to Dmax) (%) 4,000 0.358 0.00 4,400 0.371 2.85 4,800 0.382 5.32 5,500 0.403 10.08 6,500 0.417 13.35 7,500 0.427 15.52 8,500 0.433 16.97 9,500 0.438 17.94 11,000 0.443 19.01 13,000 0.445 19.46 15,000 0.445 19.64 17,000 0.446 19.71 19,000 0.446 19.73 22,500 0.446 19.75 27,500 0.446 19.75

The calculated IWCs using the new mass-dimensional relationship for the full spectrum of

PSDs are treated as the best-estimated IWCs during MC3E. Although we did not have the CVI- measured IWCs, when determining the mass-dimensional relationship, the exponent b = 2.1 and the size threshold Dmax < 4,000 μm agreed well with the conclusions from both Heymsfield et al.

(2010) and Korolev et al. (2013) respectively, where they used the CVI-measured IWCs as the best estimation. Notice that the derived mass-dimensional relationship was established for D <

4,000 um, it is highly possible that the calculated IWCs with D > 4,000 um could have a relatively large uncertainty (Heymsfield, 2014; personal communication).

To demonstrate the best-estimated IWCs calculated using the new mass-dimensional relationship along with their comparisons with the Nevzorov-measured IWCs, we present an example of the ice cloud microphysical properties on 20 May 2011 in Figure A. 5. To further demonstrate detailed ground-based and in-situ measurements, Figure A. 5a shows the NEXRAD radar reflectivity cross-section along the aircraft flight track with the classified stratiform (SR) and

Anvil (AC) regions (Feng et al., 2011, 2012) and the corresponding aircraft altitude and

temperature. During the period 14:15-14:45 UTC, the aircraft flew near the cloud top at 7.3 km

(Figure A. 5a) with the occurrence of most Dmax < 4,000 µm (Figure A. 5c and Figure A. 6) where the best-estimated IWCs (red line in Figure A. 5b) are almost the same as the Nevzorov-measured

IWCs (blue line in Figure A. 5b). Before 14:15 (and after 14:45) UTC, the aircraft ascended from

4 km to 7.3 km (descended from 7.3 km to 4 km) where the Dmax values are greater than 4,000 µm as shown in Figures A. 5c and A. 6, the best-estimated IWCs are much larger than the Nevzorov- measured IWCs, and their ratios can reach up to 2. This result is anticipated because we applied the coefficients a and b derived at Dmax < 4,000 µm to the full spectrum of PSDs. The total number concentration (Nt, 120-30,000 μm) derived from the full spectrum of PSDs mirrors the variation of ice crystal diameter (Figure A. 5d).

Table A. 6 lists the means and standards of Nt, Dmax, Dm using the observed PSDs and the calculated IWC using newly developed mass-dimensional relationship for each case and all six

-3 - cases. The mean Nt values vary from case to case, ranging from 0.014 cm on 27 April to 0.07 cm

3 on 18 May with an average value of 0.035 cm-3 and standard deviation of 0.004 cm-3 from all samples. The average and standard deviation of Dm are 1,666 μm and 1,188 μm with a range of mean values from 1,422 μm to 2,731 μm. The maximum diameters, on average, are five times as large as their corresponding median diameters with an average of 8,841 μm from all samples. The mean calculated IWCs, depending on both ice particle size and concentration as demonstrated in

Figure A. 5, range from 0.12 gm-3 on 1 May to 0.72 gm-3 on 18 May with an average and standard deviation of 0.45 gm-3 and 0.33 gm-3, respectively.

3.2 FITTING THE OBSERVED PSDS

A total of 5,589 5-s PSDs have been fitted to the gamma-type-size-distribution as follows

(in cgs units):

휇 −휆퐷 푁(퐷) = 푁0퐷 푒 . (A3)

-(4+µ) -1 In (A3), N0 is the intercept (cm ), µ is the dispersion (unitless), λ is the slope (cm ), D is used as the binned particle size from OAPs (cm), and N(D) (cm-4) is the corresponding number concentration at each bin (Heymsfield et al., 2010). As a result of the fact that measurements of ice crystals with size less than 500 µm contain unknown amount of uncertainties as discussed in

83 section 2.1, given a 10% uncertainty in number concentration for each size bin from 120 to 500

µm would result in a 43% uncertainty in µ and an 8% in λ (uncertainty in N0 cannot be quantified due to its large variation range in the fitting scheme). The non-linear Levenberg-Marquardt method was used in the fitting process to minimize the difference between the observed dataset and the fitted dataset generated from (3) (Press et al., 1992; McFarquhar et al., 2007b).

Figure A. 6 shows a series of typical fits to the averaged PSDs observed from different aircraft legs with a range of temperatures from 0 oC to -22 oC (note that the x-axis is evenly spaced rather than following the actual tick values for displaying). At each individual time, the gamma- type-size-distribution fitted result (red line) agrees well with the observed PSDs (blue bars). Note that the maximum diameters decrease from 27,500 µm to 4,000 µm, whereas the total number concentrations increase about 100 times when the aircraft ascended from 4 km to 7.3 km as demonstrated in Figure A. 6. These ice cloud microphysical features have been fitted to the gamma-type-size-distributions represented by equation (3) for general application purposes.

3.3 MULTIMOMENT ASSESSMENTS OF FITTED PSD PARAMETERS

Bulk properties and radiative properties of clouds are widely used in ground-based and satellite remote sensing communities, as well as in model simulations, which are directly or indirectly related to PSDs. These bulk properties correspond to different moments of PSDs. For example, the number concentration distribution and total number concentration are zeroth moment of PSDs, median mass diameter is the first moment, extinction coefficient is the second moment,

IWC is the third moment, radar reflectivity is the sixth moment, etc. Many techniques have been developed to fit gamma-type-size-distribution to the observed PSDs, like incomplete gamma fitting technique (IGF), discrete version of the IGF (DIGF), etc. (more details are available in

McFarquhar et al., 2014). However, the essence of those different fitting schemes is the same: to best matching the PSDs constructed from fitted parameters to the PSDs from in situ observations.

By giving the best-fitted PSD parameters, different fitting schemes have reached a good agreement in zeroth moment with the observed PSDs. However, the agreements between the observed PSDs and the fitted PSDs for quantities dominated by higher-order moments, such as ice water content and radar reflectivity, have not been thoroughly discussed.

In this study, multi-moment (first, third, and sixth) assessments have been performed in order to check the consistency between the 5-s fitted gamma-type-size-distributions and the 5-s observed PSDs. Figure A. 7 shows the comparisons of multi-moment variables generated from

85 the observed and fitted PSDs for the 20 May case. The results were first expressed in the form of median mass diameter Dm (first moment), which can be generated using observed PSDs by locating the D that splits its corresponding IWC distribution in half. The Dm can also be calculated from the fitted PSDs using

푏+휇+0.67 퐷 = , (A4) 푚 휆 where b (value of 2.1) is the exponent in mass-dimensional relationship, µ is the dispersion, and λ is the slope (Mitchell et al., 1992). As demonstrated in Figure A. 7a, the calculated Dm values using the fitted PSDs in (A4) are identical to those using the observed PSDs. For the evaluation of the third moment (Figure A. 7b), the calculated IWCs using the fitted PSDs also agree well with those using the observed PSDs. Both calculations used the newly derived mass-dimensional relationship in Section 3.1 (a = 3.65×10-3, b = 2.1). The excellent agreement and high correlation between two calculated IWCs indicate that the third moment evaluation is as good as the first moment evaluation.

For the assessment of the sixth moment equivalent NEXRAD radar reflectivity (Ze), an assumption of radiative properties of particles needs to be made as

휎 = 푠퐷푡, (A5) where σ is the backscatter cross section area, D is the particle size, s and t are fitting coefficients.

For this study, a series of σ-D relationships according to different ice crystal habits at the wavelength of the NEXRAD radar (10 cm) has been generated (Hong, 2014; Liu, 2014; personal communication). Because the CPI malfunctioned during most of MC3E experiment, only partial

CPI images from the cases of 23 and 24 May 2011 were available for this study. Based on a number of the CPI-observed ice crystal images (0 oC to -41 oC), aggregates of bullet rosettes, planes, and columns were observed to be the dominant ice crystal habits, which is consistent with

86 the conclusion in Heymsfield et al. (2002) that aggregation was observed to be a primary growth process in the convective and stratiform regions of tropical ice clouds. Note that there are different definitions of habits in different studies. In this study, a bullet rosette is depicted as an aggregation with six hexagonal columns’ pyramid tips attached at the center (Hong, 2007a), and coincidentally, the σ-D relationships provided by both Hong and Liu groups have excellent agreement for the habit of bullet rosette (Liu: s = 1.66×10-9, t = 4.6; Hong: s = 1.02×10-9, t = 4.6). The equivalent

6 -3 NEXRAD radar reflectivities Ze (in units of mm m ) have been calculated using the observed

PSDs and Hong’s (Liu) bullet rosette σ-D relationship, and then compared with the NEXRAD observations.

Using the equation for radar reflectivity factor for ice particles, Zi (Donovan et al., 2004;

Sato and Okamoto, 2006; Hong, 2007b) is given by

휆′4 ∞ 푍푖 = 5 2 ∫ 휎(퐷)푁(퐷)푑퐷, (A6) 휋 |퐾푖| 0

′ where 휆 is the wavelength (10 cm), and Ki (= 0.1768) is the dielectric factor of ice for NEXRAD.

For the relationship between Ze and Zi (Smith, 1984; Atlas et al., 1995), it is defined as

2 |퐾푖| 푍푒 = 푍푖 2 , (A7) |퐾푤| where Kw (= 0.93) is the dielectric factor of liquid water for NEXRAD (Wang et al., 2002). The final form for equivalent NEXRAD radar reflectivity is given by

휆′4 ∞ 푍푒 = 5 2 ∫ 휎(퐷)푁(퐷)푑퐷. (A8) 휋 |퐾푤| 0

Because the integral to infinite could add a lot to the calculated Ze values, in the actual calculation, the lower and upper limits were set to the observed minimum and maximum diameters.

As shown in Figure A. 7c, the Ze values calculated using (A8) with the observed minimum and maximum diameters from both the observed and fitted PSDs are almost identical. During the

period 13:30-14:00 UTC, most of the calculated Ze values are only a few dB lower, some within 1

dB, than the NEXRAD observations. However, the differences between the calculated Ze values

and NEXRAD observations are ~10 dB around 14.5 UTC at 7.3 km level. These differences are

probably due to the following reasons. 1) Different ice crystal shapes from 13.5 UTC to 14.5 UTC

as aircraft climbed from 4 km to 8 km, and its PSDs also changed as shown in Figure A. 6.

Therefore it is difficult to use only one ice crystal shape to fit the NEXRAD reflectivities. 2) Ice

mass density also increased from 4 km to 7.3 km, and 3) the NEXRAD sampling volume became

worse towards to higher levels (from 250 to 2000 m from ground to higher levels).

N (cm-(4+µ)) µ (unitless) λ (cm-1) Z (dB) Z * (dB) Datea 0 e e Mean Stdev Mean Stdev Mean Stdev Mean Stdev Mean Stdev 110427 4.27e6 7.02e7 0.71 1.88 27.34 22.04 16.92 7.15 15.61 8.58 110501 4.84e4 4.64e5 -0.52 1.28 16.86 10.52 18.32 6.32 11.50 6.98 110511 1.69e6 2.38e7 -0.10 2.37 10.75 10.35 21.40 4.89 24.35 3.93 110518 1.82e5 2.84e6 -1.52 1.19 7.99 6.48 20.13 3.72 22.07 5.57 110520 3.90e5 1.33e7 -1.00 1.05 19.35 17.21 17.50 7.75 14.36 8.29 110524 1.01e5 1.16e6 -0.13 1.53 13.59 8.27 16.41 4.38 18.85 3.12 all cases 1.09e6 3.06e7 -0.58 1.66 17.24 16.96 18.12 6.70 17.27 8.05

-3 -3 -3 Nt (cm ) Dmax (µm) Dm (µm) Dm* (µm) IWC (g m ) IWC* (g m ) Date Mean Std_dev Mean Std_dev Mean Std_dev Mean Std_dev Mean Std_dev Mean Std_dev 110427 0.014 0.012 6284 5210 1422 1247 1132 533 0.23 0.17 0.41 0.20 110501 0.012 0.022 6673 3336 1482 1114 942 461 0.12 0.16 0.43 0.14 110511 0.029 0.057 12626 2876 2731 1305 1818 281 0.63 0.37 0.60 0.07 110518 0.070 0.059 11331 3379 1816 853 1741 385 0.72 0.41 0.59 0.10 110520 0.035 0.020 7708 4053 1474 1173 1294 578 0.42 0.23 0.53 0.11 110524 0.049 0.060 8905 2135 1721 661 1667 260 0.43 0.23 0.61 0.10 All cases 0.035 0.044 8841 4539 1666 1188 1399 554 0.45 0.33 0.52 0.16

For 20 May 2011 case, the averaged NEXRAD reflectivity is 17.5 dB, the calculated equivalent NEXRAD radar reflectivity using Hong’s (Liu) bullet rosette σ-D relationship, on average, is 14.36 dB (16.42 dB) with an RMSE and correlation of 4.29 (3.10) and 0.94 (0.94). For more details for each case and summary for the six selected cases, see Table A. 5. Although the bullet rosette σ-D relationship can’t apply universally, it outperforms other crystal shapes from both Hong and Liu’s σ-D relationships when comparing with NEXRAD observations during

MC3E. Therefore we used Hong’s bullet rosette σ-D relationship as an example to derive

89 empirical relationships for application to the remote sensing community. Application of other σ-

D relationships to the remote sensing, such as aggregate, snow, column, plate etc. will be done in the future because a good parameterization scheme should take into account of different ice crystal habits under different altitudes and temperatures.

Multi-moment (first, third and sixth) assessments for other cases are also performed and their results are shown in Figure A. 8 where the performance of multiple moments for other five cases is as good as the case of 20 May with high correlations (> 0.9) and nearly the same standard deviations as observed ones. Table A. 5 lists the means and standard deviations of fitted parameters (intercept N0, dispersion µ, slope λ) and the observed Ze and calculated Ze* for each case and all samples. The Ze values were observed from the NEXRAD, while the Ze* values were calculated using the observed PSDs and Hong’s bullet rosette habit. In the following section, we will derive the empirical relationships between fitted parameters and Ze* values.

* 3.4 EMPIRICAL RELATIONSHIPS BETWEEN FITTED PARAMETERS AND Ze

For application of the observed PSDs to the remote sensing community, such as retrieving cloud microphysical properties using NEXRAD Ze, we parameterize the originally fitted slope λ values (5,589 5-s samples) as a function of calculated equivalent NEXRAD radar reflectivity Ze*.

As shown in Figure A. 9, the original λ values were binned into every 2.5 dB and the parameterized

λ* exponentially decreases with increased Ze*. The results in Figures A. 6 and A. 7 have indicated that at the upper layers of DCSs, ice crystal PSDs are narrow, slope λ values are large with a broad

o range, Ze values are small and temperatures are low. Towards to melting band (T ~ 0 C), the PSDs are different from those at upper layers with broader distribution, smaller λ, larger Ze and higher temperature, which can be attributed to aggregation and deposition processes (Gamache, 1990). It

90 is interesting to note that as the aircraft penetrates through the middle layers of DCSs (above 20 dB), the variation in λ is very small (within 10%), whereas at the upper layers (0 to 10 dB), there is a broad range of λ values (50% to 200%). The small variation in λ with Ze > 20 dB corresponds well with the steady decrease in Nt as shown in Figures A. 5a and A. 5d, suggesting a sub-saturated environment near the melting layer. This conclusion is consistent to the results from McFarquhar et al. (2007) and Smith et al. (2009) where little to no change in λ with decreasing Nt indicates a subsaturated environment and sublimation is an important process in this layer. Finally, the empirically fitted λ* - Ze* relationship is given by

∗ ∗ 휆 = 51.465 exp(−0.091푍푒). (A9)

The correlation between original λ values and parameterized λ* values is 0.79.

Found by Heymsfield et al. (2002) and also hypothesized by McFarquhar et al. (2007b), the other fitted parameters N0 and µ are not independent of λ. Therefore, Figures A. 10a and A. 10b are generated to demonstrate the N0 - λ and µ - λ relationships from a total of 5,589 5-s samples.

As shown in Figures A. 10a and A. 10b, contrary to the earlier study (McFarquhar et al., 2007b) of N0 - λ and µ - λ relationships for stratiform region of mesoscale convective systems and bow echoes using single equations, there are clearly two separate trends in both N0 - λ and µ - λ scattering plots in this study. The similar results were also found in the N0 – λ scattering plot from

Heymsfield et al. (2002, Figure 15b) over tropical stratiform precipitation and anvils regions.

Their results showed that the N0 values of the 22 August 1999 case (with calculated Ze values between -10 and 22 dB) started to significantly diverge from those of the 19 August 1999 case

-1 (with calculated Ze values between 12 and 22 dB) at λ = 20 cm with increased λ. In order to generate more robust empirical relationships for N0, µ, and λ, we have tried different Ze values to fit these two separate trends and finally chosen a threshold of 12 dB. As shown in Figures A. 10c and A. 10d, the empirically fitted N0 – λ and µ - λ relationships for Ze* > 12 are given in (A10) with correlations of 0.74 and 0.83, respectively. For Ze* ≤ 12 dB, the relationships are given in

(A11) with correlations of 0.94 and 0.83, respectively.

∗ −4 푁0 = 1.187 × 10 exp(0.508휆), (A10a) and

휇∗ = (0.131휆1.042) − 2.5. (A10b)

∗ −5 푁0 = 5.131 × 10 exp(0.292휆), (A11a) and

휇∗ = (0.028휆1.225) − 2.5. (A11b)

Substitution of (A9) into (A10) and (A11), N0* and µ* becomes only dependent on the calculated equivalent NEXRAD radar reflectivity Ze* values. Substitution of (A9), (A10b) or

(A11b) into (A4), Dm* can be estimated from Ze* values only. Insert (A9), (A10), and (A11) into

(A3), the fitted PSDs can be reconstructed, and finally the IWC* can be directly calculated from

(A2). These empirical relationships, i.e., (A9-A11), are very important for ground-based remote sensing because the Dm and IWC of ice cloud layer in a DCS can be directly retrieved from

NEXRAD radar reflectivity. Table A. 6 lists the means and standard deviations of Dm* and IWC* for each case and all cases. The average difference between the observed Dm and calculated Dm* is only 267 µm, but for individual case, the differences are relatively large, ranging from 54 µm on 24 May to 913 µm on 11 May. In addition to their means, the calculated standard deviations are, in general, about half of observed standard deviations. The IWC comparisons are similar to

-3 -3 the Dm comparisons, i.e., the averages of IWC and IWC* are 0.45 g m and 0.52 g m , respectively, while their standard deviations are 0.33 g m-3 and 0.16 g m-3. Also for individual case, their mean

IWC differences range from 0.03 to -0.31 g m-3.

Previous studies (e.g., Sassen et al., 2002; Heymsfield et al., 2005) show the relationship between Ze and IWC using power law in the form of

푑 퐼푊퐶 = 푐푍푒 , (A12) where c is the coefficient and d is the exponent. Heymsfield et al. (2005) used the equivalent 9.7

GHz radar reflectivity to generate the IWC-Ze relationship for convectively generated stratiform

0.39 6 3 0.29 6 3 ice clouds: IWC = 0.143 Ze (Ze < 8.09 mm /m ), 0.179 Ze (Ze > 8.09 mm /m ). Independent of empirical relationships involving fitted gamma parameters above, merely using the best- estimated IWCs and calculated equivalent NEXRAD radar reflectivities Ze*, the similar

0.43 6 3 relationships have been derived in this study with IWC = 0.135 Ze (Ze < 10 mm /m ), 0.158

0.24 6 3 Ze (Ze > 10 mm /m ). The differences in Ze threshold, coefficient, and exponent between this study and Heymsfield et al. (2005) could be attributed to a few factors, such as different field experiments, radar wavelengths etc.

4. SUMMARY AND CONCLUSIONS

In this study, six DCS cases using the University of North Dakota Citation II research aircraft in situ measurements during MC3E were selected to investigate the ice cloud microphysical properties of DCSs. The data used in this study were mainly sampled within the stratiform regions of DCSs which were nearly adjacent to convective cores, with a detailed study describing the distribution and variation of PSDs, IWC, Dm, and fitted parameters using gamma-type-size- distribution (intercept N0, dispersion µ, and slope λ), as well as comparison with the NEXRAD radar reflectivity. The main conclusions are as follows:

1) Multi-sensor detection has been adopted to eliminate the super-cooled liquid water (SLW) in the ice dominated cloud layers of DCSs. The RID is very sensitive to SLW droplets and is extremely useful in segregating the different cloud phases. In addition to the RID measurements, the LWCs measured by the King Probe and calculated from the CDP were also used as another indicator for small SLW droplets, and 2DC and CIP images were visually examined to verify the existence of large SLW droplets. Therefore, the occurrence of SLW can be detected by multiple sensors with sudden drops in frequency (RID) and/or corresponding LWC and Nt peaks (King and

CDP).

2) Followed the conclusions of Heymsfield et al. (2010) and Korolev et al. (2013), the Nevzorov- measured IWCs at Dmax < 4,000 μm are used as the best estimation to determine the coefficient a values for each 5-s sample during MC3E. The mean a value is 3.65×10-3 averaged from a total of

1,097 5-s samples for Dmax < 4,000 μm. Finally, the newly derived mass-dimensional relationship

(a = 0.00365, b = 2.1) has been applied to the full spectrum of PSDs (120-30,000 μm) constructed from both 2DC and HVPS measurements to calculate the best-estimated IWCs of DCSs during

-3 MC3E. The Nevzorov-measured IWCs increase with increased Dmax from 0.1546 g m at Dmax =

-3 4,000 μm to 0.311 g m at Dmax = 13,000 μm, but their underestimations also increase from 2.2% to 23.8% when comparing to the calculated IWCs from PSDs. The integrated mass contribution from D = 4,000 μm to Dmax to the total mass is 19.75%.

3) The statistical results calculated from the six selected cases are as follow. The Nt (D = 120-

30,000 μm) vary from case to case, ranging from 0.014 cm-3 on 27 April to 0.07 cm-3 on 18 May with an average value of 0.035 cm-3 and standard deviation of 0.004 cm-3 from all samples. The average and standard deviation of median mass diameter (Dm) are 1,666 μm and 1,188 μm with a range of mean values from 1,422 μm to 2,731 μm. The maximum diameters (Dmax), on average, are five times as large as their corresponding median diameters with an average of 8,841 μm from all samples. The mean calculated IWCs range from 0.12 gm-3 on 1 May to 0.72 gm-3 on 18 May with an average and standard deviation of 0.45 gm-3 and 0.33 gm-3, respectively.

(4) For application of the observed PSDs to the remote sensing community, the gamma-type-size- distributions are then generated matching the observed PSDs (120-30,000 μm), and the fitted gamma parameters are compared with the observed PSDs through multi-moment assessments including first moment (Dm), third moment (IWC), and sixth moment (equivalent radar reflectivity,

Ze). For the six selected cases, the excellent agreements in Dm, IWC, and Ze (correlation above

0.9 and normalized standard deviation around 1.0) between those calculated from the observed

PSDs and the fitted gamma parameters were found, indicating the robustness of fitting scheme used in this study. Although the bullet rosette σ-D relationship can’t apply universally, it

96 outperforms other crystal shapes from both Hong and Liu’s σ-D relationships when comparing with NEXRAD observations during MC3E. Finally, a series of empirical relationships including

λ - Ze, N0 - λ and µ - λ have been derived for application of the observed PSDs to the remote sensing community.

These results can serve as a baseline for studying the ice cloud microphysical properties of

DCSs over the continental US. These aircraft in situ measurements can also serve as the best estimation for validating ground-based and satellite retrievals, as well as model simulations. The empirical relationships developed in this study (Eqs. 9-11) were applied in our recent study to retrieve ice cloud Dm and IWC using the NEXRAD radar reflectivity measurements during MC3E.

The conclusions reached here are based only on six selected DCS cases, more aircraft in situ measurements are required to generate a firm conclusion. Future analyses of this series will report on the liquid and mixed-phase cloud microphysical proeprties of DCSs during MC3E.

ACKNOWL.EDGEMENTS

The data were obtained from the Atmospheric Radiation Measurement (ARM) Program sponsored by the U.S. Department of Energy (DOE) Office of Energy Research, Office of Health and

Environmental Research, Environmental Sciences Division. This study was primarily supported by DOE ASR project at University of North Dakota with award number DE-SC0008468 and the

NASA CAN project at University of North Dakota project under Grant NNX11AM15A. Special thanks to Dr. Jensen, PI of MC3E, and UND flight crew who calibrated and operated all airborne instruments, and processed the Citation II raw data during MC3E experiment. Special thanks to

Aaron Bansemer who provided OAP processing algorithm, and Drs. Heymsfield and McFarquhar who provided insightful comments and suggestions to improve this manuscript. We would like to thank Dr. Logan and Mr. Stenz to proofread the manuscript.

APPENDIX A: CALIBRATION AND TREATMENT OF BASELINE DRIFT FOR

NEVZOROV TWC PROBE

The power loss in flight on the collector sensor due to convective heat loss is related to the aircraft speed, air temperature, and air pressure (Korolev et al., 1998). The sensor then compensates for this heat loss by providing more power to the collector sensor to maintain a constant sensor temperature. The collector sensor power is related to the reference sensor power by:

푃푐표푙푙 = 푘 × 푃푟푒푓, (AA1) where, Pcoll is the collector sensor power, Pref is the reference sensor power, and k is a coefficient.

During a flight that undergoes changes in air speed and/or air density, the k coefficient will change, which is called the baseline drift. During periods of clear air, k can be calculated directly, but when the aircraft is in cloud or precipitation, k must be estimated.

The k is calculated using a multi-variable linear regression equation in the following equation:

푘 = 푇푊퐶푝푐표푛푠푡 × 푃푟푒푠푠푢푟푒 + 푇푊퐶푖푐표푛푠푡 × 퐼퐴푆 + 푇푊퐶푐푐표푛푠푡, (AA2) where k is the sensor power calibration variable, TWCpconst is the total water content sensor pressure coefficient, Pressure is the air pressure, TWCiconst is the total water content sensor indicated air speed coefficient, IAS is the aircraft indicated air speed, and TWCcconst is the regression equation constant term.

For the selected cases during MC3E, the calibration coefficients were calculated from the

April 22, 2011 flight from 81260 to 83460 sfm UTC (clear air takeoff and ascent to 9.5 km MSL), and the values are: TWCpconst = -2.097104e-4, TWCiconst = -0.00207234, TWCcconst = 1.074499

(Neumann, 2015; personal communication).

The power loss due to precipitation is calculated by:

푃푝푟푒푐푖푝 = 푃푐표푙푙 − 푘 × 푃푟푒푓, (AA3) the power loss due to precipitation (Pprecip) is then used to calculate the liquid or total water content.

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APPENDIX B: INVESTIGATION OF LIQUID CLOUD MICROPHYSICAL PROPERTIES OF DEEP CONVECTIVE SYSTEMS: 1. PARAMETERIZATION OF RAINDROP SIZE DISTRIBUTION AND ITS APPLICATION FOR STRATIFORM RAIN ESTIMATION

(Published in the Journal of Geophysical Research: Atmospheres)

Jingyu Wang,1 Xiquan Dong,1 Baike Xi,1 and Andrew J. Heymsfield2

1University of North Dakota, Grand Forks, North Dakota

2National Center for Atmospheric Research, Boulder, Colorado

10.1002/2016JD024941.

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ABSTRACT

To investigate liquid-phase (T > 3 oC) cloud and precipitation microphysical properties within

Deep Convective Systems (DCSs), eight DCS cases sampled by the UND Citation II research aircraft during Midlatitude Continental Convective Clouds Experiment (MC3E) were selected. A full spectrum of raindrop size distribution (DSD) was constructed from 120 μm to 4000 μm through a combination of 2DC (120 to 900 μm) and HVPS (900 to 4000 μm) data sets. A total of

1,126 five-second DSDs have been used to fit to Gamma and Exponential functions within the stratiform rain (SR) regions of DCSs. The Gamma shape μΓ and slope λΓ parameters are then compared with those derived from surface disdrometer measurements. The similar μΓ - λΓ relationships but different μΓ and λΓ value ranges from two independent platforms at different elevations may represent the real nature of DSD shape information in clouds and at the surface.

To apply the exponentially fitted DSD parameters to precipitation estimation using NEXRAD radar reflectivity factor Ze, the terms N0E and λE have been parameterized as a function of Ze using an empirical N0E – λE relationship. The averaged SR rain rate retrieved from this study is almost identical to the surface measurements, while the NEXRAD Q2 precipitation is twice as large. The comparisons indicate that the new DSD parameterization scheme is robust, while the Q2 SR precipitation estimation based on Marshall-Palmer Z-R relationship, where a constant DSD intercept parameter (N0E) was assumed, needs to be improved for heavy precipitation cases.

1. INTRODUCTION

Deep Convective Systems (DCSs) with radar-echo top altitudes from 500 hPa (~ 6 km) to the tropopause can be separated into a deep convective precipitating portion and a non- precipitating anvil canopy (Feng et al., 2011, 2012). The former dominates much of the warm

109 season intense rainfall over the midlatitudes, while the latter plays a significant role in the atmospheric radiation budget due to its extensive spatial coverage. DCS systems strongly affect local climate, and provide important feedbacks to the global climate system through their radiative effects and distribution of moisture (Futyan and Del Genio, 2007; Feng et al., 2011, 2012).

Feng et al. (2011) developed a hybrid classification method to objectively identify components of DCSs into the convective core (CC), stratiform region (SR), and anvil clouds (AC), using a combination of ground-based (NEXRAD) and spaceborne (GOES) data. The hybrid classification algorithm builds upon a previous convective-stratiform algorithm (Steiner et al.,

1995), by incorporating anvil classifications and satellite data, providing a thorough means for studying the life and diurnal cycles of DCSs, as well as their associated precipitation (Feng et al.,

2012). They also found that precipitation comes almost exclusively from the CC and SR regions of DCSs, and that the probability density function (PDF) of the averaged CC rain rates (RRCC) is similar to that in the SR regions (RRSR), except the magnitude of averaged RRCC is 10 times higher than that of averaged RRSR.

The characteristics of stratiform rainfall in DCSs have been intensively investigated through a variety of platforms, including satellite (e.g., TRMM precipitation radar, Liu et al., 2007;

Schumacher and Houze, 2003; Xu, 2013), ground-based radar (e.g., National Mosaic & Multi-

Sensor Quantitative Precipitation Estimation, also known as NMQ or Q2, Chen et al., 2013; Stenz et al., 2014, 2016), surface rain gauge network (e.g., Oklahoma Mesonet observations, Brock et al., 1995; video disdrometer, Zhang et al., 2001, 2003; Cao et al., 2008, 2009), and airborne remote measurements (e.g., Multichannel Cloud Radiometer, Heymsfield et al., 1988; 10- and 94-GHz airborne radars, Boudala et al., 2006; Tian et al., 2007). Because aircraft in situ measurements have better collocations with radar observations and larger sample volumes than surface

110 disdrometer measurements, aircraft can provide more accurate raindrop size distribution (DSD) information for cloud and precipitation studies. However, to the best of our knowledge, there are no precipitation retrieval methods developed through an integrative analysis of aircraft in situ, collocated radar reflectivity and surface rain rate measurements. The goal of this study is to derive an improved DSD retrieval method for SR regions of DCSs using aircraft in situ measurements.

By applying this improved DSD retrieval method to horizontally polarized radar reflectivity prior to the dual-polarization radar upgrade, regional surface precipitation estimation and in-cloud DSD data products will be generated to further understand cloud and precipitation processes in DCSs.

The DSD is one of the most important factors in the study of DCS cloud and precipitation properties, because most cloud bulk microphysical properties are determined from the retrieved or measured DSD (Sempere-Torres et al., 1994 and 1998; Lee et al., 2004; Fan et al., 2015). In addition, the DSD bridges the transition processes from cloud to precipitation (Pruppacher and

Klett, 1978; Kumjian and Prat, 2014), an area which has been widely studied through modeling collisional coalescence and breakup processes in DCSs. However, in most previous studies, the initial DSD values aloft were either fixed or simplified (McFarquhar, 2004a, 2004b). The

Experiment (MC3E), at the ARM Southern Great Plains (SGP, 36° 36' 18" N, 97° 29' 6" W) site from April to June 2011 (Jensen et al., 2015). The goal of MC3E was to characterize convective cloud systems, including convective initiation and updraft and downdraft dynamics, precipitation and cloud microphysics, and their environment. The campaign consisted of the most comprehensive cloud observing infrastructure currently available in the central United States,

111 combined with an extensive sounding array, ground-based remote sensors, aircraft in situ measurements, and updated ARM radar instrumentation.

For the DCS modeling and forecasting community, an accurate precipitation product is needed to serve as the data set for validating model output (Clark et al., 2014; Fan et al., 2015).

Limited by the number of surface rain gauges, the regional precipitation product is usually estimated from observations with weather surveillance radar network. The accuracy of precipitation estimation depends primarily on the choice of power-law Z-R relationships, which are literally hundreds in existence developed using different datasets for different precipitation types (Marshal and Palmer, 1948; Rosenfeld et al., 1993; Nelson et al., 2010; Giangrande et al.,

2014). Nonetheless, those power-law Z-R relationships, even without explicit clarification, all assume DSDs following an Exponential function with the constant intercept (N0). Since natural

DSD rarely follow Exponential functions, a fixed N0 even further constrained the applicability of power-law Z-R relationships. Completed in 2013, the nationwide dual-polarization radar upgrade made multi-variable radar observations available (e.g., differential reflectivity, specific differential phase) (Zrnic and Ryzhkov, 1999; Ryzhkov et al., 2005; Kumjian, 2013; Zhang et al., 2015), which resulted in new precipitation estimation techniques. For example, by using a 3-parameter Gamma function, Bringi et al. (2002) proposed a DSD retrieval method with inputs of radar reflectivity, differential reflectivity (ZDR), and specific differential phase (KDP). In order to further reduce the degrees of freedom in the DSD estimation, the normalized Gamma function was developed

(Testud et al., 2001; Zhang et al., 2001; Cao et al., 2008 and 2009), where the DSD can fully be represented by Nw (normalized parameter) and D0 (median volume diameter). However, more than one radar observation is still required as input.

112

During the MC3E campaign in 2011, precipitation estimation was still based on Z-R relationships, with the use of horizontally polarized radar reflectivity due to the lack of operationally gridded polarimetric radar observations. The commonly used National Centers for

Environmental Prediction (NCEP) Stage IV Quantitative Precipitation Estimation (QPE) product lacks necessary temporal information due to its hourly update cycle (Baldwin and Mitchell, 1998;

Lin and Mitchell, 2005), while the 5-min NEXRAD Q2 product demonstrates a non-negligible overestimation compared to surface rain gauge measurements (Stenz et al., 2014). Motivated by the demands to accurately estimate surface precipitation and in-cloud DSD, we will focus on investigating an alternative DSD parameterization scheme and its application in radar-based precipitation estimation. Further, we hope to better understand cloud-to-precipitation transition processes through an integrative analysis of aircraft in situ measurements in clouds and disdrometer measurements at the surface.

A total of 15 DCS cases were sampled by the University of North Dakota (UND) Citation

II aircraft during MC3E and those were categorized into ice, mixed-phase, and liquid layers (Wang et al., 2015). In this companion study, in order to develop a new DSD parameterization and retrieval scheme, eight DCS cases during MC3E were selected to investigate the liquid-phase (T >

3 oC) cloud and precipitation microphysical properties within DCSs. The eight selected DCS cases are 25 and 27 April, 1, 11, 18, 20, 23, and 24 May 2011, in which sufficient liquid-phase cloud samples were collected. This paper is organized as follows: Section 2 describes various datasets, including aircraft in situ measurements, ground-based NEXRAD observations and surface rain rate measurements. Section 3 will present the newly developed DSD parameterization scheme based on aircraft in situ measurements and their application to precipitation estimation, as well as

113 the comparison of surface rain rates among NEXRAD Q2, surface measurements and new retrieval from this study. Finally section 4 summarizes our findings and conclusions from this study.

2. DATA

The in situ measurements of DCS microphysical properties were carried out by the UND

Citation II research aircraft, which was fully equipped with state-of-the-art instruments for cloud physics research. A detailed discussion about airborne probes can be found in Wang et al. (2015).

The surface rain rates were measured by one Distromet model RD-80 disdrometer deployed at the

ARM SGP site, five two-dimensional video disdrometers (2DVD) in the surrounding area of the

ARM SGP site, and eight Mesonet tipping-bucket sensors scattered within a 1o × 1o domain centered on the ARM SGP site (Figure B. 1a). In addition to these datasets, surface rain rate measurements from a total of 17 APU (Automatic Parsivel Unit) sites for the entire MC3E

114 campaign (from 22 April to 6 June, 2011) were collected and processed as an independent dataset to evaluate the different Z-R relationships (a brief summary of APU stations is listed in Appendix

B).

2.1 AIRCRAFT IN-SITU MEASUREMENTS

A full spectrum of DSDs in this study was constructed from the combination of Particle

Measurement System (PMS) two-dimensional cloud probe (2DC, 30-3,000 µm) and the SPEC Inc.

High Volume Precipitation Spectrometer (HVPS, 300-30,000 µm). All DSDs collected within the liquid-phase layer of the DCSs at cloud temperatures above 3 oC were used in this study. The cloud properties with a range of temperatures from 0 oC to 3 oC were eliminated from this study mostly to rule out melting layer cases. It is important to note that no hail was reported within the study domain for the selected cases. This temperature range is consistent with the altitude of the radar bright band where ice particles fall just below the 0 oC level (Fujiyoshi, 1986; Oraltay and

Hallett, 2005; Heymsfield et al., 2015). As a result, a temperature of 3 oC was chosen as the criterion to distinguish liquid-phase from mixed-phase clouds.

The first three channels of the 2DC were discarded because of the issue of questions about the depth of field and errors involving the digitization of small particles (Korolev et al., 1998). For large raindrops measured by the HVPS, elongated “artifacts” with sizes greater than 10 mm were sometimes observed, presumably due to probe errors, and were eliminated from the dataset.

Another important source of artifacts is the recorded splash pattern when raindrops hit the probe tips. After careful examination of the in situ measured particle images, we concluded that there are no raindrops greater than 5.5 mm within the regions sampled in this study. This conclusion is also consistent with the previous studies of breakup processes of raindrops (Low and List, 1982a,

115

1982b; McFarquhar and List, 1991a, 1991b; McFarquhar, 2004a, 2004b; Seifert et al., 2005;

Barros et al., 2008; Schlottke et al., 2010; Emersic and Connolly, 2011), where distinct collisional breakup types were observed and parameterized, and the raindrops larger than this size could not be sustained.

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By conservation of mass, using the ice mass-dimensional relationship (mass = aDb, a =

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0.00365, b = 2.1) established during MC3E (Wang et al., 2015), Figure B. 2a shows an independent investigation of possible equivalent melted diameters based on aircraft in situ measurements above the melting layer during the campaign. In other words, the majority of ice crystal aggregates above the melting layer can melt to an equivalent diameter of less than 4 mm. The 4 mm size threshold coincides with previous in situ measurements (Szumowski et al., 1997; Szumowski et al., 1998), where they concluded that the raindrops with D > 4 mm are more likely to be associated with strong updrafts, but also possible from melting graupel and hail outside of strong updrafts.

However, we do not rule out the aggregation process within the melting layer. As demonstrated in previous studies (Barthazy et al., 1998; Troemel el al., 2014), the aggregation process can lead to larger than expected raindrops from the melting process

In addition, this result is further confirmed by the probability of raindrop diameters measured by the ARM SGP RD-80 disdrometer as shown in Figure B. 2b, where most of the raindrop diameters are less than 4 mm. By considering the aircraft in situ measurements and surface disdrometer measurements, the limit of the maximum raindrop diameter is set to 4 mm in this study for the following reasons. First, there are no algorithms to date that are capable of removing all these large elongated artifacts, which are more likely to occur at the large size of the spectrum. Second, the cumulative probability in Figure B. 2b shows that the surface measured raindrop diameters greater than 4 mm only represent 1.3 % of the entire distribution, which will not have a strong impact on the calculation of bulk properties. Finally, excluding the portion of

D > 4 mm benefits the DSD fitting process by reducing the uncertainties from artifacts. This is also consistent with the results of Wang et al. (2015), where the maximum diameter of the ice crystal aggregates is 30 mm (equivalent to the maximum raindrop diameter of ~4 mm in Figure B.

2a).

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For the overlapping spectral region (DSD = 900 - 2800 μm) measured by both the 2DC and

HVPS, the frequency of occurrence for particles recorded by each size bin was calculated. Their differences increase from 42% at 900 μm to 49% at 2800 μm because the HVPS probe is capable of measuring larger raindrops than the 2DC probe (raindrops were reconstructed for D > 1000 μm,

Heymsfield and Parrish, 1978; Korolev, 2007). One possible reason for the discrepancy is the difference in sample volume between the two probes. Further investigations were also carried out for bulk properties of total number concentration (Nt) and liquid water content (LWC). The averaged ratios of Nt and LWC (2DC over HVPS) are 1.41 and 1.24, respectively, showing general consistency between the two optical array probes. As a result, in this study we use the DSD spectrum ranges from 120 μm to 4000 μm through a combination of 2DC (120 to 900 µm) and

HVPS (900 to 4000 µm) probe data. Both the 2DC and HVPS probes were well calibrated by the manufacturers before the field campaign, and performance checks and quality control procedures were carried out before and after each flight. To further control the quality of the data, 20% of the optical array probe (OAP) records were rejected due to either insufficient sampling or non- simultaneous recordings between two OAPs.

2.2 GROUND-BASED RADAR OBSERVATIONS

Based on the Next-Generation Radar (NEXRAD, S-band) network of Weather Surveillance

Radar-1988 Doppler (WSR-88D) radars, the NOAA National Severe Storms Laboratory (NSSL) produces a national (CONUS) 3D gridded radar mosaic coverage with 1-km horizontal resolution,

31 vertical levels (resolution varies from 200 m to 2,000 m), and 5-min temporal resolution

(https://www.nssl.noaa.gov/projects/q2/nmq.php). As a key component in the NMQ system, the

NEXRAD Q2 precipitation product was generated to quantitatively estimate the surface rain rate

119 by choosing an appropriate Z-R relationship (Zhang et al., 2011). The high resolution 3D gridded radar mosaic was used to extract the large volume cloud bulk properties (the equivalent reflectivity factor Ze) collocated with the UND aircraft flight track, which served as an independent data source to evaluate the representation and calculations of in situ measurements.

Figure B. 3 illustrates the comparisons between the calculated equivalent radar reflectivity

* factor (Ze ) using the in situ measured DSDs (5-second averaged, a flight distance of ~500 m) and

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the collocated NEXRAD radar reflectivity observations (Ze, sampled along the aircraft track). The black circles in Figure B. 3 represent the calculated results using the size spectral range mentioned in Section 2.1 (120 to 4,000 µm) and the red circles were generated from the full spectrum. The radar equation is given by:

∗ 6 −3 12 퐷푚푎푥 6 푍푒(푚푚 푚 ) = 10 ∫ 푁(퐷)퐷 푑퐷, (B1) 퐷푚푖푛 where Dmin (120 µm) and Dmax (4,000 µm) are the integral limits, D is the diameter of the smallest circle that encloses the raindrop image (Heymsfield and Parrish, 1978; Field et al., 2006; Korolev,

* 2007), and N(D) is number concentration of corresponding D (all parameters except Ze are in cgs units, and the aircraft bin scheme is shown in Appendix A, which will also be used in rain rate derivation). Apparently, the black circles converge much closer to the collocated NEXRAD Ze observations than the red circles, suggesting the existence of elongated artifacts recorded by the

HVPS at D > 4 mm and those artifacts could be easily removed using the designated size threshold

D ≤ 4 mm in this study.

Another important assumption used in calculating reflectivity factor is the constant axis ratio of 0.7, in which axis ratio is defined as vertical dimension over the horizontal dimension of the raindrops (Jameson and Beard, 1982). As suggested by Chandrasekar et al. (1988), by eliminating the influence of the rotation angle of raindrops, the axis ratio can be equivalent to the aspect ratio

(the ratio of maximum dimension of raindrops along and across the scan direction). In addition, with the assumption of an oblate shape, the aspect ratio of raindrops defined by Korolev and Isaac

(2003) (i.e., Dw/Dmax_d, where Dmax_d is the maximum dimension of raindrops, and Dw is the maximum dimension of raindrops in the direction perpendicular to Dmax_d), is equal to the well- accepted area ratio (the ratio of the projected area of raindrops to the area of a circumscribed circle,

McFarquhar and Heymsfield, 1996) according to the following derivation:

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휋 퐷 퐷 퐴푟푒푎 표푓 퐸푙푙푖푝푠푒 4 푚푎푥_푑 푤 퐷푤 퐴푟푒푎 푟푎푡𝑖표 = = 휋 = = 퐴푠푝푒푐푡 푅푎푡𝑖표, (B2) 퐴푟푒푎 표푓 푀푎푥푖푚푢푚 퐶푖푟푐푙푒 퐷2 퐷 4 푚푎푥_푑 푚푎푥_푑

As a result, by assuming an oblate shape and disregarding the discrepancy in definitions of aspect ratio, the area ratio could serve as a good approximation of the axis ratio. In this study, the

* averaged area ratio (0.7) was used in calculation of Ze for simplicity.

It is worthwhile to note that some outliers shown in Figure B. 3 may be attributed to the mismatch in sample volumes between aircraft in situ and radar observations as discussed in Mace et al. (2002) and Dong et al. (1998 and 2002). The sample volume of the radar is a few orders of magnitude larger than in situ probes, which makes the representativeness of in situ measurements greatly depend on the homogeneity of large-volume samples observed by radar (Ryzhkov et al.,

2005 and Ryzhkov 2007). In addition, a minor error could also be introduced by interpolating radar data from coarse to high temporal resolution.

The NOAA Earth System Research Laboratory Physical Sciences Division S-band precipitation profiler (Ecklund et al., 1999) was deployed at the ARM SGP site during MC3E.

This instrument measured the vertical structure of DCSs at 1-min temporal resolution and 62-m vertical resolution ranging from 200 m to 1,600 m above the ground. With an adequate sensitivity in reflectivity factor (-14 dBZ at 10 km) and finer resolutions, the NOAA S-band radar reflectivity serves as the “ground-truth” to evaluate the performance of NEXRAD mosaic data.

2.3 SURFACE RAIN RATE MEASUREMENTS

A brief summary of the instruments used for measuring precipitation characteristics and rainfall is listed in Table B. 1. In addition to precipitation properties including rain rate, radar reflectivity, etc., the RD-80 disdrometer also provided the most continuous DSD measurements at high spectral and temporal resolutions along with routinely fitted DSD exponential parameters, at

122 the ARM SGP site during MC3E. Taking advantage of the detailed DSD information, the intercomparisons of cloud-base reflectivity factors between the radar observations and the RD-80 reconstructions, as well as the NEXRAD retrieved and RD-80 provided exponentially fitted parameters, were conducted for the ARM SGP site, which will be discussed in Section 3. As for quality control of the surface measurements, both the spurious raindrops (e.g., likely caused by splash or insects) and sparse observations (fewer than 10 raindrops or rain rate less than 0.01 mm hr-1 per minute), were eliminated in this study (Tokay et al., 2001; Jaffrain and Berne, 2011). Note that the data provided by the RD-80 were not used for DSD parameterization, but for validating retrieved precipitation. In addition, the correction for dead-time (underestimation for the number concentration at small drops in heavy precipitation events, Waldvogel, 1974; Sheppard and Joe,

1994) was not performed during this study. The 2DVDs had a considerable amount of time intervals with missing data (e.g., more than 3 hours of void values for the SN35 site on 20 May

2011 from 10:40 to 14:56 UTC). Due to intrinsic instrumental limitations, the unheated tipping- bucket rain gauges used in the Oklahoma Mesonet network have a coarse detectability of 0.254 mm (one tip) with a temporal resolution of 5 minutes.

In order to temporally match the observations from different instruments, i.e., NEXRAD (5 minutes), NOAA S-band radar (1 minute), RD-80 disdrometer (1 minute), 2DVDs disdrometers

(1 minute), and the Mesonet tipping-bucket (5 minutes), the temporal resolution was set to 5 minutes for the surface rain rate measurements in this study. That is, the 1-min rain rate measurements from the RD-80 and 2DVDs disdrometers were resampled with each 5-min interval to match the 5-min Mesonet tipping-bucket measurements. To avoid spatial mismatches between in situ measurements, ground-based radar observations, and surface rain rate measurements, the study domain was confined to a 1o × 1o grid box centered on the ARM SGP site (Figure B. 1a),

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where the disdrometers and Mesonet tipping buckets, as well as aircraft flights, were all located

(Figure B. 1b).

Table B. 1. Summary of surface rain rate measurements

Precipitation Location Amount DSD Temporal Data Source (longitude, latitude) Detectability Observations Resolution (mm) 20 size bins https://www.arm.gov/ -97.485, 36.605 (SGP RD-80 0.0001 0.3 to 5.4 1 minute instruments/disdromet CF) mm er -97.532, 36.624 (SN25) ftp://gpm.nsstc.nasa.g -97.480, 36.618 (SN35) 0.00017 41 size bins ov/gpm_validation/mc 2DVDs -97.479, 36.581 (SN36) (0.01 mm 1 minute 0.1 to 10 mm 3e/disdrometers_and_ -97.481,36.633 (SN37) -1 hr ) gauges/2dvd/data/ -97.445, 36.578 (SN38) -97.254, 36.754 (BLAC) -97.694, 36.412 (BREC) -97.286, 36.147 (CARL) -97.213, 36.064 (MARE) https://www.arm.gov/ Mesonet 0.254 N/A 5 minutes -97.607, 36.119 (MARS) instruments/okm -97.746, 36.792 (MEDF) -97.153, 36.356 (REDR) -97.095, 36.121 (STIL)

3. NEW DSD PARAMETERIZATION SCHEME AND ITS APPLICATION FOR

PRECIPITATION ESTIMATION

In this section, a full spectrum of rain DSDs was constructed through a combination of 2DC

(120 to 900 µm) and HVPS (900 to 4000 µm) measurements. A total of 1126 five-second in situ

measured DSDs were fitted with exponential size distributions, and then parameterized as a

function of the radar reflectivity, according to its theoretical definition (Eq. 1). In order to assess

the new parameterization scheme incorporating the dependencies between DSD parameters, the

rain rates were calculated using the retrieved DSDs from NEXRAD reflectivity at cloud base, and

then compared with the surface rain rate measurements. Lastly, the NEXRAD Q2 precipitation

estimate is compared with the calculated and measured surface rain rates.

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125

Figure B. 5. (a) Gamma fitted DSD shape parameter μΓ as a function of slope parameter λΓ. (b) Gamma fitted DSD intercept parameter N0Γ as a function of slope parameter λΓ. (c) Exponentially fitted DSD intercept parameter N0E as a function of slope parameter λE.

3.1 FITTING TO THE IN-SITU MEASURED DSDS

The Exponential function has been commonly used in representing DSD for its simplicity in connecting DSD-based bulk properties for different moments (e.g., sixth-moment radar reflectivity and roughly third-moment rain rate (Marshall and Palmer, 1948)). Since the publication of the classic paper (Ulbrich, 1983), a 3-parameter Gamma function has drawn more attention. Following the same fitting techniques used in ice cloud properties of DCSs (Press et al.,

1992; McFarquhar et al., 2007; Wang et al., 2015), a total of 1,126 five-second DSDs have been used to fit to the gamma function as follows (in cgs units):

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휇 −휆퐷 푁(퐷) = 푁0퐷 푒 . (B3)

-(4+µ) -1 In (3), N0 is the intercept (cm ), µ is the shape (dimensionless), λ is the slope (cm ), D is the raindrop diameter (cm), and N(D) (cm-4) is the corresponding number concentration at each bin

(Heymsfield et al., 2010). Besides the Gamma function, a 2-parameter Exponential function

(where µ = 0) was also performed to facilitate precipitation estimation from radar reflectivity, because the operationally gridded polarimetric radar observations were not available during MC3E.

Figure B. 4 shows a series of typical Gamma and Exponential fits to the averaged DSDs with collocated NEXRAD Ze, ranging from 30 to 26 dBZ. At each individual time, the Gamma fitted results (red solid lines) demonstrate better agreement with the observed DSDs (blue bars), especially for drop sizes greater than 2 mm. However, for certain cases like Figure B. 4b, no significant differences in the overall shape, as well as the values of N0 and λ parameters, were found between Gamma and Exponential fits, indicating that the Exponential function can capture most of the DSD shape information except for some of the large drops.

For Gamma parameters, Zhang et al. (2001) and Brandes et al. (2004) concluded that shape parameter (μΓ) is strongly related to the slope parameter (λΓ). Refined by Cao et al. (2008 and

2009) using surface 2DVDs observations in Oklahoma, an applicable shape-slope (μΓ - λΓ)

2 relationship was generated as μΓ = -0.0201 λΓ + 0.902 λΓ – 1.718 (black dash line in Figure B. 5a).

Similarly, a second-order polynomial regression was fitted from the aircraft data (black solid line in Figure B. 5a). Figure B. 5a clearly demonstrates that the two trends from Cao et al. (2008 and

-1 -1 2009) and this study are nearly the same for the λΓ values ranging from 0 mm to 6 mm (note that the cgs units were not used in μΓ - λΓ relationship for consistency with previous studies). For

-1 λΓ > 6 mm , these two trends start to deviate and their differences increase with increasing λΓ.

These differences can either be attributed to the 2DVDs’s undersampling issue for drop sizes

127 greater than 3 mm as discussed in Cao et al. (2008), or that sorting and averaging methods based on the two parameters were not employed in aircraft data processing due to limited number of samples. Nonetheless, by applying the equation from Cao et al. (2008) to aircraft data, the coefficient of determination (R2) is 0.532, which is comparable to the new fitting result (R2 =

0.561). The similar μΓ - λΓ relationships generated from aircraft in situ data aloft in this study and surface disdrometer measurements in Cao et al. (2008) have demonstrated that two independent platforms at different elevations can capture similar DSD attributes.

In addition to the shape-slope relationship, Figure B. 5b exhibits the intercept-slope (N0Γ -

λΓ) relationship for the Gamma fits. Similar to the finding of Ulbrich (1983), N0Γ values fluctuated by several orders of magnitude (in this case from 10-5 to 106 cm-(4+μΓ), not completely shown in

Figure B. 5b), which limits the utility of the N0Γ - λΓ relationship in studies of cloud and precipitation microphysics. However, for the parameters from the Exponential fits (Figure B. 5c),

-3 -1 -4 most of the N0E values fall within a range from 10 to 10 cm , indicating that setting μΓ = 0 is the simplest assumption from the perspective of constraining the variation in the intercept parameter (Tian et al., 2007; Liao et al., 2014; Williams et al., 2014). To verify the validity of μΓ

= 0, the probability density function (PDF) of μΓ values generated from aircraft in situ data is shown in Figure B. 6, where it basically follows the Gaussian distribution with a mean value of

0.58 and a standard deviation of 1.15. This result has demonstrated that the approximation of the

Gamma function using an Exponential function with the assumption of μΓ = 0 is valid and reasonable. Note that the μΓ - λΓ relationship generated in Figure B. 5a cannot be applied to the λΓ

-1 values greater than 6 mm , and the N0E – λE relationship shown in Figure B. 5c cannot be applied

-1 to the λE values greater than 60 cm .

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Figures B. 5 and B. 6 exhibit additional information about the ranges of μΓ and λΓ values

-1 -1 from this study and from Cao et al. (2008). The λΓ values range from 0 mm to 20 mm , and the

μΓ values are from -3 to 15 in Cao et al. (2008), whereas both the λΓ and μΓ values in this study have limited ranges (with 95% tolerance interval of [-1.72, 2.88] for μΓ). The different ranges from these two studies using two independent platforms at different elevations may represent the real nature of the DSD shape information in clouds and at the surface. These aircraft in situ data can directly provide statistical information of the DSD shape parameters during MC3E for the

129 study of cloud-to-precipitation processes (e.g., breakup and collision), where the initial DSDs aloft in most of the previous studies were either fixed or simplified (McFarquhar, 2004a, 2004b). In summary, the similar μΓ - λΓ relationships but different μΓ and λΓ value ranges generated from two independent platforms at different elevations have demonstrated that it is helpful to study DSD changes from clouds to precipitation, using a combination of aircraft in situ measurements in clouds and disdrometer measurements at the surface.

3.2 SEMIEMPIRICAL RELATIONSHIPS BETWEEN FITTED DSD PARAMETERS AND Ze

Compared to surface disdrometer measurements which are several hundreds of meters below the radar echo base, aircraft in situ measurements and radar observations can be easily collocated both spatially and temporally. Using aircraft in situ measurements does reduce the problem of the variation of the DSD from cloud base to the surface. More importantly, aircraft in situ probes can provide much larger sample volume (400 L s-1 for HVPS at the flight speed of 100 m s-1) and better temporal resolution compared to surface disdrometers (0.05 L s-1 for RD-80 with 50 cm2 s-1 sample area and a 10 m s-1 assumption of fall speed). For application of the fitted DSD parameters to precipitation estimation using NEXRAD Ze, the N0E – λE relationship is generated and presented in Figure B. 5c from a total of 1,126 five-second samples. The new power-law relationship is presented as:

1.49 푁0퐸 = 0.000141휆퐸 , (B4)

2 with coefficient of determination (R = 0.48). Note that the N0E – λE relationship derived from the

RD-80 disdrometer measurements may introduce larger uncertainties than that derived from aircraft in-situ measurements, due to the limited sample volume. This is another major reason that the N0E – λE relationship was established here using the aircraft in situ measurements rather than

130 from RD-80 disdrometer measurements. Substituting (B3) into (B1) (with µ = 0 and integral limits

* from 0 to ∞), Ze becomes:

∞ 푍∗(푚푚6푚−3) = 1012 푁 푒−휆퐸퐷퐷6푑퐷. (B5) 푒 ∫0 0퐸

∞ Following the Euler integral of the second kind (Jeffrey and Dai, 2008) (Γ(푡) = 푥푡−1푒−푥푑푥), ∫0

* Ze can be expressed in the product of N0 and λ:

∗ 6 −3 12 −7 푍푒(푚푚 푚 ) = 10 푁0퐸휆퐸 Γ(7). (B6)

Finally, by substitution of (B4) into (B6), the slope parameter λ can be directly calculated from

* radar reflectivity Ze :

0.10152×1012 1 5.5 휆퐸 = ( ∗ 6 −3 ) . (B7) 푍푒(푚푚 푚 )

The major concern of this derivation is the substitution of the complete Gamma function

(CGF, integral from 0 to ∞) with an incomplete Gamma function (IGF, integral from Dmin to Dmax), whose differences were thoroughly discussed by McFarquhar et al. (2015). For the xth moment

(Mx) of a DSD,

퐷푚푎푥 휇 −휆퐷 푥 푁0 푀푥 = ∫ 푁0퐷 푒 퐷 푑퐷 = [Γ(푥 + 휇 + 1, 휆퐷푚푎푥) − Γ(푥 + 휇 + 1, 휆퐷푚푖푛)], (B8) 퐷푚푖푛 휆푥+휇+1 and

푣 Γ(푢, 푣) = 푥푢−1 푒−푥푑푥. (B9) ∫0

* In this study, we evaluated the influence of partial integrations (0 to Dmin and Dmax to ∞) in Ze

* calculation compared to the Ze values integrated from Dmin to Dmax, which we considered as the

* ground truth. The corresponding Ze uncertainties are 0% for the integral portion from 0 to Dmin and 7% for the portion from Dmax to ∞.

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3.3 APPLICATION OF NEWLY PARAMETERIZED DSDS FOR PRECIPITATION

ESTIMATES AND ASSESSMENT

Based on equations (B4) and (B7), the DSD variables can be parameterized as a function of radar reflectivity according to its theoretical definition. Therefore, the rain rate can be retrieved from the DSD parameters and NEXRAD cloud-base observed Ze values. To evaluate the

NEXRAD cloud-base reflectivity measurements within the SR regions of DCSs, a performance

132 check was conducted using collocated NOAA S-band radar observations at the NEXRAD cloud

* bases, as well as calculated Ze values from the RD-80 disdrometer at the ARM SGP site. As shown in Figure B. 7a, there is an excellent agreement in cloud-base radar reflectivity between

NEXRAD and NOAA S-band for the 20 May 2011 case, with averages of 27.0 and 28.7 dBZ

* during a 10-hr period. Another interesting result is that the average of the calculated Ze values using surface RD-80 disdrometer measurements is 26.7 dBZ, which is nearly the same as the

NEXRAD cloud-base radar observations. The mean differences of 0.3 dBZ and 1.7 dBZ indicate that the NEXRAD cloud-base reflectivity measurements are reliable for precipitation retrieval. As for all cases, a Taylor diagram (polar coordinate system) was generated in Figure B. 7c, where the correlation coefficients (shown as the rotation angle from the vertical axis) between NEXRAD and

NOAA S-band reflectivity measurements range from 0.44 to 0.85, and the normalized standard deviations (standard deviation of NEXRAD divided by standard deviation of NOAA S-band, shown as the distance from coordinate origin) range from 0.68 to 1.00.

Figure B. 7b shows another comparison in slope λE between calculated values from equation

(B7) using NEXRAD cloud-base Ze values and the ones provided by RD-80 measurements, for the SR regions of the 20 May 2011 case. There are no λ values between 1000 and 1100 UTC because the convective region passed directly over the ARM SGP site. Notice that prior to 1000

UTC, there are relatively large variations in both Ze and λE values, and their differences are also large, while after 1100 UTC (except 1530-1600 UTC), both Ze and λE values are nearly invariant and their differences are almost indistinguishable. These discrepancies could be attributed to the convection types before and after the overpass of the convective system. Prior to the squall line passage, there was isolated convection over the SGP region, whereas afterwards, there was widespread stratiform precipitation.

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Similar to Figure B. 7c, Figure B. 7d shows the correlation coefficients and normalized standard deviations of λE values from selected cases with most correlation coefficients ranging from 0.6 to 0.7, and normalized standard deviations from 0.75 to 1.5, except for the 1 May 2011 and 11 May 2011 cases. The large discrepancies for these two cases may result from the error propagated from the input (Ze), the uncertainty from the RD-80 DSD measurements, and the

Exponential fitting scheme used to calculate slope parameters. It is necessary to note that the statistical information was generated from a limited number of classified SR cloud samples directly over the ARM SGP site. For example, the 18 and 24 May 2011 cases were not shown in Figure

B. 7, because there were less than 10 5-min SR samples. However, more than 80% of the total

SR samples (27 April 2011 and 20 May 2011) showed good agreement with other independent observations (correlation coefficients greater than 0.8 for Ze and greater than 0.6 for λE).

Finally, the rain rate can be calculated as follows:

퐷 휋 6 푚푎푥 −휆퐸퐷 3 푅푅(푚푚/ℎ푟) = 3.6 × 10 ∫ 푁0퐸푒 퐷 푉(퐷)푑퐷. (B10) 퐷푚푖푛 6

Substituting equations (B4) and (B7) into (B10), it becomes

1 1.49 0.10152×1012 5.5 퐷 0.10152×1012 5.5 −( ) 퐷 휋 6 푚푎푥 푍푒(푚푚6푚−3) 3 푅푅(푚푚/ℎ푟) = 3.6 × 10 ∫ 0.000141 ( 6 −3 ) 푒 퐷 푉(퐷)푑퐷, (B11) 퐷푚푖푛 푍푒(푚푚 푚 ) 6 where V(D) (in unit of m s-1, and D is in unit of m) is the terminal velocity calculated following the method of Gunn and Kinzer (1949),

4 퐷푔(휌 −휌 ) 푉 = √3 푤푎푡푒푟 푎푖푟 , (B12) 퐶휌푎푖푟

-2 3 where the sea level condition is assumed with g = 9.8 m s , ρwater = 1000 kg/m , ρair = 1.225 kg m-3, C = 0.5, at the standard atmospheric pressure of 1013.25 hPa. All units in equations (B10) and (B11) are in cgs except for special notations.

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Figure B. 8 shows the time series of NEXRAD and NOAA S-band radar reflectivity factors, and three rain rates for the SR regions measured by the surface RD-80 disdrometer, extracted from the Q2 product, and retrieved from this study for the ARM SGP site. It is necessary to note that the UND CSA algorithm was performed for cloud classification and only the rain rates for SR regions were extracted and compared in the following discussion. Compared to the NOAA S-band radar observations, NEXRAD suffers severe artifact issues above 10 km, which is consistent with the conclusion from Homeyer (2014) and Homeyer and Kumjian (2015). Those artifacts could

135 result from the limited vertical sampling issue of the NEXRAD radars. However, for the near- surface observations, as discussed above and shown in Figures B. 8a and B. 8b, NEXRAD cloud- base reflectivity measurements are compatible with NOAA S-band measurements in the SR regions of DCSs. For SR rain rate comparisons, the averaged Q2 estimation (Figure B. 8d) is much larger (2.605 mm hr-1) than the corresponding surface disdrometer measurement (1.228 mm hr-1, Figure B. 8c, serve as the best-estimate in this study). On the contrary, the averaged SR rain rate retrieved from this study (1.218 mm hr-1) is almost identical to the best-estimate as illustrated in Figure B. 8, as well as in Figures B. 9 and B. 10. These comparisons also reveal that the Q2 SR precipitation estimation based on Marshall-Palmer Z-R relationship (Marshall and Palmer, 1948), where a constant DSD intercept parameter (N0E) was assumed, needs to be improved for heavy precipitation cases.

136

137

In addition to the SR rain rate comparisons over the ARM SGP site, the results from five

138 more surface sites are extracted and presented. Figure B. 9 shows NEXRAD reflectivity (left column) and rain rate comparisons (right column) among Q2 product, surface measurement, and retrieval from this study at the sites of 2DVD-SN25 (Figure B. 9a and B. 9b), BREC (B. 9c and B.

9d), CARL (B. 9e and B. 9f), MARE (B. 9g and B. 9h), and STIL (B. 9i and B. 9g). Similar conclusions can be drawn from these comparisons, that is, over these five additional surface sites the Q2 product severely overestimates the rain rates, especially for heavy rain cases, while the retrieval from this study is nearly identical to the surface rain rate measurement.

139

To further assess the Q2 product and retrieval from this study, the surface rain rate measurements from all disdrometers and Mesonet stations listed in Figure B. 1a are used as the best-estimate. As shown in Figure B. 10, the averaged ratios of Q2 product to the best-estimate are 2.12 at the ARM SGP site (Figure B. 10a), 1.38 at five 2DVD sites (Figure B. 10b), and 1.93 at eight Mesonet stations (Figure B. 10c) with corresponding correlation coefficients of 0.546,

0.42, and 0.595, respectively. The averaged ratios of the retrieval from this study to the best- estimate are 1.02, 0.68, and 1.00 for different sites, with ~0.05 higher correlation coefficients. The comparison over five 2DVD sites is not as good as expected, primarily due to the missing data issue as discussed in Section 2.3.0020

Based on the available disdrometers and rain gauges in Figure B. 1a, the spatial distributions of daily accumulated SR precipitation amount are presented over a 1o × 1o domain in Figure B. 11.

The third column (Figure B. 11c, B. 11h, B. 11m, and B. 11r) exhibits the daily accumulated SR precipitation amount extrapolated from 14 scattered surface measurements on 1, 11, 20 and 24

May 2011. Similarly, the second column (Figures B. 11b, B. 11g, B. 11l, and B. 11q) was generated by extrapolation for the locations of 14 surface sites using the data extracted from original Q2 estimation (Figure B. 11b, B. 11g, B. 11l, and B. 11 q, first column), and the fourth column (Figures B. 11d, B. 11i, B. 11n, and B. 11s) represents the extrapolated results using the data from the original retrieval in this study (Figure B. 11e, B. 11j, B. 11o, and B. 11t, fifth column).

Apparently, the extrapolated Q2 results (second column of Figure B. 11) are much higher than the surface best-estimate (third column of Figure B. 11) across the entire study domain, especially over the heavy precipitation regions, which is consistent with the findings in Figures B. 8-10. On the other hand, similar spatial precipitation patterns between the surface best-estimate and the retrieval from this study (fourth column of Figure B. 11) are found from four cases. Note that by

140 comparing the extrapolated results with their original high resolution ones, the spatial extrapolation is not always optimal in capturing all detailed features because of the limited number of surface sites. The purpose of comparisons in Figure B. 11 is to demonstrate that the overestimation issue in Q2 product can become more problematic spatially than site-by-site, which can significantly impact the local hydrological cycle by the large positive bias in areal rainfall. However, the retrieval from this study exhibits good agreement with direct measurements in spatial precipitation patterns.

3.4 EVALUATION OF MARSHALL-PALMER Z-R RELATIONSHIPS USED IN Q2

PRECIPITATION ESTIMATES

The Q2 SR precipitation estimates are based on the Marshall-Palmer Z-R relationship

(Marshall and Palmer, 1948), while this study uses newly generated DSD parameterization scheme to retrieve SR precipitation. Therefore, it is necessary to have an in-depth investigation of the similarities and differences between the two methods. As suggested by Khain et al. (2015) and

Patade et al. (2015), using fixed DSD parameters is not an optimal approximation and may lead to a substantial misrepresentation of the cloud microphysics. In Marshall and Palmer (1948), the

-4 assumption of constant N0 (0.08 cm ) was applied to construct the power-law Z-R relationship, which ignored the natural relationship between N0E and λE. On the other hand, the fitted N0E – λE relationship (Equation B4) was used to develop a new Z-R relationship over the SR regions in this

6 -3 study. Figure B. 12a compares the Z-R relationships from Marshall-Palmer (Ze (mm m ) =

200R1.6, R in mm hr-1) and this study (Equation B11), where the differences between these two Z-

R relationships are indistinguishable for Ze < 20 dBZ, but the differences start to increase with increased Ze values for Ze > 20 dBZ. This helps to explain the severe overestimation in Q2 precipitation estimates shown in Figures B. 8-11.

141

Figure B. 12a probes the following two questions: (a) is the Q2 classification consistent with the UND Convective-Stratiform-Anvil (CSA) classification for SR regions of DCSs and (b) what

142 if other Z-R relationships were used in precipitation estimation for those regions? To answer these two questions, Figure B. 12b presents four more operational Z-R relationships (Nelson et al., 2010) in addition to Marshall-Palmer for the SR precipitation estimation (Figure B. 12a). They are

1.4 1.2 2.5 convective (Ze = 300R ), tropical (Ze = 250R ), stratiform-east (Ze = 130R ), and stratiform-

2.5 west (Ze = 75R ). Figure B. 12b clearly demonstrates that the retrieval from this study agrees well with the Q2 rain rate estimation using Marshall-Palmer Z-R relationship for Ze < 20 dBZ, and outperforms other Z-R relationships. For example, with a given radar reflectivity of 15 dBZ, the rain rate retrieved from this study is 0.273 mm hr-1, which is close to the value of 0.316 mm hr-1 using Marshall-Palmer Z-R relationship. However, severe underestimation can be found using the

Z-R relationships for convective (0.200 mm hr-1) and tropical (0.179 mm hr-1), as well as an overestimation for stratiform-east (0.568 mm hr-1) and stratiform-west (0.708 mm hr-1). This comparison has confirmed that both Q2 and UND CSA algorithms have correctly identified the

SR regions of DCSs in this study, otherwise the differences between Q2 and this study would be much larger than the current ones.

Unlike all other power-law Z-R relationships shown as straight lines in Figure B. 12b, the one developed in this study (red line) deviates more from the straight line pattern as Ze increases beyond 20 dBZ. Figure B. 12c shows two other power-law SR Z-R relationships developed from

Darwin, Australia (Tokay and Short, 1996) and TRMM precipitation (Iguchi et al., 2000), along with the Z-R relationships from Marshall-Palmer and this study. This comparison illustrates the

“see-saw” patterns found using different samples based on power-laws, and the choice of intercept and linear slope may be, to a great extent, influenced by the distribution of rain rate intensity sampled in their experiments. Figures B. 12b and B. 12c clearly demonstrate that linear Z-R relationships on logarithmic axes cannot accurately represent the actual nonlinear relationship

143 found in this study, due to the intrinsic nature of the power-law relationship, whereby the downward curvature becomes increasingly prominent as Ze increases above 20 dBZ.

To further test the newly developed Z-R relationship developed in this study, the surface rain rate measurements and corresponding reflectivity measurements for SR regions from a total of 17

APU (Automatic Parsivel Unit) sites during the entire MC3E (from April 22 to June 6, 2011) experiment were collected and processed as an independent dataset to evaluate the different Z-R relationships. As demonstrated in Figure B. 12d, the rain rates calculated from our Z-R relationship (red solid line) have the best agreement with surface measurements, and outperform those from power-law fits (red dash line) and the Marshall-Palmer relationship (blue solid line).

More importantly, the APU data samples in Figure B. 12d show a nonlinear trend on a logarithmic scale, and the absolute slope difference relative to linear regression line (red dash line) seems to increase from 0 dBZ to 20 dBZ, and decrease from 20 dBZ to 45 dBZ, forming a downward curve.

Coincidently, the Z-R relationship from this study (red solid line) can capture the feature of downward curvature staring from 20 dBZ, while the other two straight lines demonstrate overestimation to different extents. For the portion from 0 dBZ to 20 dBZ, the rain rates estimated from Marshall-Palmer and new relationship are nearly the same, but both are overestimated. As shown in Figure B. 12d, the rain rates estimated from 0 dBZ to 20 dBZ are less than 0.5 mm hr-1, which falls into the uncertainties of detectability and has insignificant contribution to overall DCS precipitation. Figure B. 12d also illustrates that coefficients of determination (R2) are -0.04, 0.81 and 0.75, respectively, for the Z-R relationships from Marshall-Palmer, this study, and direct regression to the APU data for a typical SR reflectivity range from 0 dBZ to 45 dBZ. Based on the comparisons with other Z-R relationships and independent APU data, we can conclude that the newly developed Z-R relationship (Equation. 11) in this study exhibits the best representation of

144

APU data in both overall Z-R distribution’s shape and quantitative analysis.

4. SUMMARY AND CONCLUSIONS

In this study, eight DCS cases sampled by the University of North Dakota Citation II research aircraft during MC3E were selected to investigate the liquid-phase (T > 3 oC) cloud and precipitation microphysical properties within DCSs. The in situ measurements were carefully processed and examined, and semi-empirical relationships between DSD parameters and radar reflectivity were established. These relationships were then applied to estimate the rain rates from

NEXRAD cloud-base radar reflectivity, and were compared to the surface rain rate measurements.

The main conclusions can be summarized as follows:

1) A wide spectrum of the raindrop size distribution (DSD) was constructed, from 120 μm to 4000

μm, through a combination of 2DC (120 to 900 μm) and HVPS (900 to 4000 μm). A total of 1,126 five-second DSDs have been fitted to the Gamma (3 parameters) and Exponential (2 parameters) functions within the SR regions of DCSs. The Exponential function can capture most of the DSD shape information except for some of the large drops, indicating that the approximation of the

Gamma function by an Exponential function with μΓ = 0 is valid and reasonable.

2) Comparing the Gamma shape μΓ and slope λΓ parameters from aircraft in situ measured DSDs with those derived from surface disdrometer measurements reported in Cao et al. (2008 and 2009), the ranges of overlapping μΓ and λΓ values are limited but having similar trends. Similar μΓ - λΓ relationships with different ranges from two independent platforms with different elevations may represent the real nature of the DSDs in clouds and at the surface. It is helpful to study changes in the DSD from clouds to precipitation using a combination of aircraft in situ measurements in clouds and disdrometer measurements at the surface.

145

3) For application of the exponentially fitted DSD parameters to precipitation estimation using

NEXRAD radar reflectivity factor Ze, N0E and λE have been parameterized as a function of Ze with an empirical N0E – λE relationship. Thus, the rain rate can be retrieved the NEXRAD cloud-base observed Ze values, and then compared with the NEXRAD Q2 precipitation product and surface disdrometer/tipping bucket measurements over the SR regions of DCSs. The averaged SR rain rate retrieved from this study is almost identical to the surface measurements, while the NEXRAD

Q2 precipitation is twice as large. These comparisons indicate that the new DSD parameterization scheme is robust, while the Q2 SR precipitation estimation based on Marshall-Palmer Z-R relationship, where a constant DSD intercept parameter (N0E) was assumed, needs to be revised for heavy precipitation cases.

4) Further evaluation of the Marshall-Palmer power-law Z-R relationship and the Z-R relationship based on the new DSD parameterization scheme was conducted using an independent dataset from a total of 17 APU (Automatic Parsivel Unit) sites for the duration of the MC3E experiment.

Comparisons show that the differences between the rain rates calculated using the Marshall-Palmer

Z-R relationship and retrieved from this study are indistinguishable for Ze < 20 dBZ, but the differences start to increase with increased Ze values for Ze > 20 dBZ. The major reason for the discrepancy is that the power-law Z-R relationship’s linear relationship on a logarithmic scale does not represent the actual nonlinear relationship exhibited by the APU observations, while the downward curvature feature can be fully captured by the Z-R relationship developed in this study.

The excellent agreement between the retrieved rain rates from this study and the surface rain rate measurements has revealed that the DSD retrieval algorithm developed in this study is more advanced than the constant N0E assumption commonly used in power-law Z-R relationship.

Application of the N0E – λE relationship may shed light on the need for the development of a

146 regional in-cloud DSD product and thereby more accurate precipitation estimation, from radar reflectivity. This new DSD parameterization scheme and its application for precipitation estimation will also benefit the DCS modeling and forecasting communities, to whom the validation fields of in-cloud DSD and surface precipitation are needed, especially for the simulations of field campaigns before 2013 when the dual-polarization radar products were not available. It is worthwhile to note that the specific N0E – λE relationship was obtained for the

MC3E campaign, and adjustment of this relationship is necessary for different precipitation types, locations, and climatology, using observations. For precipitation estimation, the calculated rain rate could also be slightly impacted by the choice of the V(D) relationship and DSD bin scheme.

For the convective core precipitation retrieval and cloud microphysical properties, the power-law Z-R relationships based on the assumption of constant N0E seem more problematic due to the well-known N0E jump issue (Waldvogel, 1974) caused by drastic environmental changes associated with updrafts in the microscale. Future analyses in this series will report on a more detailed DSD parameterization scheme using surface disdrometer measurements, focusing on the

DCS convective cores during MC3E. Taking advantage of the improved DSD parameterization schemes for different regions of DCSs, the overarching goal of this paper series is to provide regional surface precipitation estimation and in-cloud DSD data products for evaluating the modeled cloud and precipitation properties.

147

ACKNOWLEDGEMENTS

The data were obtained from the Atmospheric Radiation Measurement (ARM) Program sponsored by the U.S. Department of Energy (DOE) Office of Energy Research, Office of Health and

Environmental Research, and Environmental Sciences Division. This study was primarily supported by DOE ASR project at University of North Dakota with award number DE-

SC0008468 and the NOAA R2O project at University of North Dakota project under grant

NA15NWS4680004. Dr. Andrew J. Heymsfield was supported by NASA GPM Project

NNX13AH73G at NCAR. Special thanks to Dr. Jensen, PI of MC3E, and UND flight crew who calibrated and operated all airborne instruments, and processed the Citation II raw data during

MC3E experiment. Special thanks to Aaron Bansemer who provided OAP processing algorithm.

We would like to thank Dr. Logan for proofreading of the manuscript and Mr. O’Brien for particle image interpretation. The data used in this study were downloaded through ftp://gpm.nsstc.nasa.gov/gpm_validation/mc3e/ on April 2015, and the processed cloud microphysical properties through aircraft in situ measurements during MC3E can be obtained from

Dr. Xiquan Dong ([email protected]).

148

APPENDIX A

For SR rain rate calculation, a full spectrum of raindrop size distribution (DSD) was constructed from 120 μm to 4000 μm through a combination of 2DC (120 to 900 μm) and HVPS (900 to 4000

μm) data sets. The central diameter and bin width for each bin are shown in Table B. A1.

Table B. A1. Aircraft probes’ diameter and width for each bin used in SR rain rate calculation Diameter (µm) Bin Width (µm) 120 30 165 60 225 60 285 60 345 60 405 60 465 60 522.5 55 600 100 700 100 800 100 900 100 1100 200 1300 200 1500 200 1700 200 2000 400 2400 400 2800 400 3200 400 3600 400 4000 400

149

APPENDIX B

In order to assess different precipitation retrieval methods, additional surface rain rate

measurements from a total of 17 APU (Automatic Parsivel Unit) sites for the entire MC3E

campaign (from 22 April to 6 June 2011) were collected and processed as an independent

validation data set. A brief summary of APU stations is listed in Table B. B1.

Table B. B1. Summary of 17 NASA GPM GV Automatic Parsivel Unit (APU) measurements Precipitation Location Amount DSD Temporal Data Source (longitude, latitude) Detectability Observations Resolution (mm hr-1) -97.472, 36.608 (APU01) -97.506, 36.608 (APU02) -97.499, 36.633 (APU03) -97.466, 36.608 (APU04) -97.517, 36.635 (APU05) -97.543, 36.637 (APU06) -97.552, 36.615 (APU07) ftp://gpm.nsstc.nasa.g -97.516, 36.615 (APU08) 32 size bins ov/gpm_validation/mc APU -97.489, 36.594 (APU09) 0.01 0.06 to 25.2 1 minutes 3e/disdrometers_and_ -97.507, 36.594 (APU10) mm gauges/parsivel/data/ -97.499, 36.578 (APU11) -97.480, 36.569 (APU12) -97.463, 36.579 (APU13) -97.426, 36.600 (APU14) -97.427, 36.578 (APU15) -97.453, 36.564 (APU16) -97.485, 36.604 (APU17)

150

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APPENDIX C: INVESTIGATION OF LIQUID CLOUD MICROPHYSICAL PROPERTIES OF DEEP CONVECTIVE SYSTEMS: 2. PARAMETERIZATION OF RAINDROP SIZE DISTRIBUTION AND ITS APPLICATION FOR CONVECTIVE RAIN ESTIMATION

(Submitted to the Journal of Geophysical Research: Atmospheres)

Jingyu Wang, Xiquan Dong, and Baike Xi

Department of Hydrology and Atmospheric Sciences, University of Arizona, Tucson, AZ

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ABSTRACT

Since convective rain (CR) has characteristics in raindrop size distribution (DSD) and precipitation that are distinct from stratiform rain (SR), its properties are investigated by using 20 hours of CR samples collected by 17 Automatic Parsivel Units (APUs) disdrometers during the Midlatitude

Continental Convective Clouds Experiment over the ARM Southern Great Plains (SGP) site. A full spectrum of DSDs are constructed based on 23 size bins of raindrop volume-equivalent diameters ranging from 0.321 mm to 9.785 mm, and both Gamma and Exponential fitted functions are applied to extract the DSD shape parameters. Compared to SR properties in Wang et al. (2016),

CR has distinct features including broader size range and narrower exponential slope parameter

(λE). These results indicate that the constant N0E assumption is inappropriate for CR rain rate estimates. Additionally, the subset of the CR DSD spectrum also has a strong impact on the

Gamma/Exponential functions. Therefore, by choosing the appropriate spectrum subset and using the constant λE instead of constant N0E, a new CR DSD parameterization scheme is developed, which intrinsically connects the radar reflectivity to the CR rain rate. By applying the new parameterization scheme to the cloud base reflectivity, the newly calculated CR rain rates match well with the collocated surface rain gauge measurements (127 Mesonet stations and 17 APUs), while the rain rates calculated using traditional Z-R relationship are 3-4 times larger, indicating constant λE is a better assumption for CR DSD.

1. INTRODUCTION

Deep convective systems (DCSs) play a significant role both in the global climate and local hydrological systems (e.g., Futyan and Del Genio, 2007; Feng et al., 2011, 2012). Through the combination of NEXRAD radar and GOES satellite observations, a hybrid cloud classification

164 method was developed by Feng et al. (2011), and the DCSs were objectively separated into components of convective core (CC), stratiform rain (SR), and anvil clouds (AC) regions. The SR region accounts for light and moderate rainfall, while the CC region accounts for the most intense precipitation over the midlatitudes. The AC region plays an important role in the atmospheric radiation budget due to its large coverage.

By incorporating aircraft in situ measurements and surface disdrometer measurements, the microphysical properties of ice and liquid layers of the SR region were thoroughly studied in the previous companion papers (Tian et al., 2016, Wang et al., 2015, 2016). However, due to the lack of direct aircraft penetration, the CC clouds were rarely sampled and the cloud properties were largely unresolved. As a result, over decades, the characteristics of convective rainfall (CR) have been intensively investigated through either the combination of surface-based observations, including disdrometers and radar (e.g., Joss and Waldvogel, 1990; Sauvageot, 1994; Cao et al.,

2008; Cao and Zhang, 2009; Zhang et al., 2011, 2016), or the spaceborne satellite observations

(e.g., Tropical Rainfall Measuring Mission precipitation product (TRMM, Schumacher and Houze,

2003; Houze et al., 2015); Self-Calibrating Multivariate Precipitation Retrieval (SCaMPR,

Kuligowski, 2010; Stenz et al., 2014)). Inspired by the exponential function with constant

-4 intercept (N0E, in unit of cm ) assumption (e.g., Marshall and Palmer, 1948), the most popular representation of raindrop size distribution (DSD) for different precipitation types, and the corresponding Z-R relationships can be easily generated relating the surface rain rate to cloud-base

1.6 reflectivity factors (Ze) (i.e., Marshall-Palmer Z-R relationship: Z = 200R , where Ze has the unit of mm6 m-3 and R is in mm hr-1).

Built on this assumption, a series of Z-R relationships targeting different precipitation types were developed by empirically relating surface rain rate measurements and near-surface radar

165 observation (e.g., Z = 300R1.4 for convective rainfall by Doviak and Zrnic (1984); Z = 250R1.2 for tropical rainfall by Rosenfeld (1993)). However, similar to the overestimation issue by using the

Marshall-Palmer Z-R relationship for SR rain rate as discussed in Wang et al. (2016), there also exists a notable positive bias in CR rain rate estimate by using the default Z-R relationship. As a result, in the newer operational NEXRAD-based national precipitation product, Multi-Radar-

Multi-Sensor (MRMS) Quantitative Precipitation Estimation (QPE) system (Zhang et al., 2016), the convective rain rate is capped at 103.8 mm hr-1.

In order to mitigate the overestimation issue presented by the default CR Z-R relationship, numerous efforts have been made on calibrating radar rainfall with gauge measurements (e.g., Xin et al., 1997; Fulton et al., 1998; Hossain et al., 2004; Kalinga and Gan, 2006; Haberlandt, 2007), and newly developed Z-R relationships have been proven to be more accurate for CR rain rate estimation. For example, Z = 250R1.2 (Xin et al., 1997) is reported with optimal performance for fast moving convective storms. Using a fixed exponent of 1.4, Amitai (2000) found CR at different locations and time periods features varying coefficients. Although these studies suggest different parameters in the CR Z-R relationship, the application of those parameters is greatly constrained because they were generated for specific cases, while there exist extensively spatial and temporal variations in CR (Xiao and Chandrasekar, 1997; Chiang et al., 2007). That is, no unique set of Z-

R parameters based on empirical fitting can provide a good rain rate estimate for a broad range of situations (Trafalis et al., 2002). This brings the question back to the optimal way of DSD parameterization, especially for the CR.

Given the important role of DSD in the studies of cloud-to-precipitation transition, as well as the overestimation issue associated with constant N0E assumption in surface precipitation estimation, Ulbrich (1983) presented a 3-parameter Gamma function for better approximation of

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DSD. Unlike the retrieval of exponential DSD merely from radar reflectivity, the Gamma function requires multiple inputs (differential reflectivity, specific differential phase, specific attenuation, etc.). It is necessary to note that those dual-polarization radar variables can also directly serve as

b the input of power-law relationship to calculate rain rate (e.g., R = aAH , where AH is the specific attenuation (Giangrande et al., 2014; Ryzhkov et al., 2014; Diederich et al., 2015), a and b are the coefficient and exponent). The normalized Gamma function has been widely applied to active remote sensing precipitation retrieval (e.g., TRMM), especially the dual-frequency precipitation radars on board of Global Precipitation Measurement (GPM) mission. Nonetheless, for CR regions, the dual-frequency technique suffers from severe attenuation issues due to the existence of oversized raindrops, making the retrieval more applicable to SR regions where the maximum raindrop size does not exceed 4 mm (Seto and Iguchi, 2015; Wang et al., 2016).

Since the surface disdrometer is the sole data source for the most direct and accurate CR

DSD measurement, the criterion for testing the performance of DSD assumptions relies on whether the closure study can be achieved by comparing the retrieved rain rate with direct measurements, which also rely on a large number of CR samples for statistical significance. By using the intensity surface DSD measurements deployed during the Midlatitude Continental Convective Clouds

Experiment (MC3E, Jensen et al., 2015), instead of using traditional Z-R relationship based on constant N0E assumption, this study proposes an alternative approach to parameterize the CR DSD, to reduce the uncertainty in radar reflectivity-based rain rate retrieval.

2. DATA

As a joint field program involving the National Aeronautics and Space Administration

(NASA) Global Precipitation Measurement (GPM) Ground Validation (GV) program, and the

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Department of Energy (DOE) Atmospheric Radiation Measurement (ARM) Climate Research

Facility, the MC3E was conducted in north-central Oklahoma during the period of April to June

2011. Focusing on improving the understanding and representation of cloud and precipitation interactions, an unprecedented combination of multi-platform observations was deployed around the Southern Great Plains central facility (SGP, 36° 36' 18" N, 97° 29' 6" W), including aircraft, ground-based cloud/precipitation radars, as well as an extensive sounding array. A focused effort was also made to collect the accurate characteristics of precipitation related to deep convective systems. As shown in Figure C. 1a, by using the hybrid Convective-Stratiform-Anvil (CSA) cloud classification algorithm (Feng et al., 2011) with the input of 5-minute 3D NEXRAD mosaic, the entire state of Oklahoma experienced more than 70 hours of convective core (CC) overpasses during the 2-month campaign, which were effectively recorded by the dense Mesonet tipping- bucket rain gauge network (Figure C. 1b, 127 stations). Moreover, as shown in Figure C. 1c, one

Disdromet model RD-80 disdrometer and 17 Automatic Parsivel Units (APUs) were deployed around the SGP central facility for raindrop size distribution measurements, and more than 20 hours of valid convective rain (CR) samples were collected. A detailed location information of those surface instruments can be found in Wang et al. (2016).

The distinction in DSD between SR and CR is well known for the phenomenon called “N0 jump” (Waldvogel, 1974), which reveals the discontinuity in the change of exponentially fitted intercept parameter (N0E) with convective activity from no convection (SR dominated precipitation, corresponds to lower constant N0E values) to convection (CR dominated precipitation, corresponds to higher varying N0E values). This feature was also captured by the RD-80 disdrometer as shown in Figure C. 2, where one year of SR samples (794 valid records) and 5 years of CR samples (8450 valid records) classified by CSA are displayed in the form of an exponentially fitted intercept

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parameter (N0E) as a function of slope parameter (λE). In Figure C. 2, the CR and SR samples demonstrate almost no overlap, and SR features more variation in λE direction along a constant

N0E, but the trend is reversed for CR which is more scattered in the N0E direction than λE direction.

Figure C. 2, together with the well-known “N0 jump” issue, has demonstrated that there is intrinsic distinction in DSD between SR and CR, which poses a question mark to the power-law CR Z-R relationship that is still based on the constant N0E assumption.

Figure C. 1. (a) The accumulated convective rain duration during MC3E, and the distributions of (b) Mesonet rain gauges and (c) disdrometers.

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Although the long-term RD-80 observation can serve as an indicator revealing the distinction between SR and CR, the new parameterization of CR DSD cannot be built on it because

RD-80 has very limited raindrop size range up to 5 mm (Joss and Waldvogel, 1967, 1969; Kinnel,

1976). This threshold is very close to the upper limit of SR raindrop size (4 mm), thus unsampled larger particles are excluded from the CR parameterization. Compared to the traditional disdrometer measurements which base on a pressure transducer, the OTT APUs employ more advanced laser optical technology and extend the maximum measureable particle size up to 24.5 mm (Brawn and Upton, 2008; Kathiravelu et al., 2016). Figure C. 3 compares the probability and cumulative probability of the APUs measured maximum raindrop volume equivalent diameter between SR (a total of 34518 1-min samples) and CR (a total of 1226 1-min samples) during

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MC3E, where no SR samples exceed the 4 mm threshold whereas 15% CR samples have drop size greater than 5 mm, which is consistent with previous observations from the CC region (e.g., Cao et al., 2009). Although only deployed during the field campaign for a short period, the APUs are chosen as the reliable measurements for CR, which can be used to develop a new CR DSD parameterization.

Figure C. 3. Probability and cumulative probability of maximum raindrop diameter measured by the APUs during MC3E for (a) stratiform rain (SR) and (b) convective rain (CR).

Without the capacity of DSD measurements, the 127 Mesonet tipping-bucket measurements are collected and used to validate the Z-R calculated CR rate. The rain rate comparison between the operational National Mosaic and Multi-Sensor Quantitative Precipitation Estimates (NMQ Q2)

(Zhang et al., 2011; Chen et al., 2013) and collocated measurements at Mesonet stations for the

CSA classified CC (corresponding to the precipitation type of CR) during the MC3E is shown in

1.4 Figure C. 4. On average, the Q2 CR estimates based on the power-law relationship of Ze = 300R are almost 4 times as large as the collocated Mesonet measurements with a low correlation coefficient.

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Figure C. 4. Rain rate comparison between Mesonet measurements and collocated Q2 estimates for all collocated convective rain (CR) samples.

Before moving on to the new CR parameterization, it is necessary to match the measurements from different instruments with different sampling frequencies. As a result, the 1- minute APU measurements are resampled with each 5-minute interval to match the NEXRAD Q2 retrievals and Mesonet rain rate measurements. After matching the temporal resolution, another question arises: how can we correctly identify the CR samples from different measurements? The

RD-80 disdrometer is at a single point and its cloud classification can be coarsely extracted from the neighboring NEXRAD CSA result (at spatial resolution of 1 km), while the 17 APU observation stations are densely distributed within a 0.05o by 0.07o grid box (Figure C. 1c), which pose a high demand on the accuracy of NEXRAD in such small scale. As shown in Figure C. 5, the APUs calculated radar reflectivity, on average, is 20% larger than NEXRAD observation and the coefficient of determination (R2 = 0.7) is not optimal. As a result, the CSA classification based

172 on NEXRAD radar reflectivity may discard valuable CR samples. Therefore, the rainfall-rate criterion (RRC) (Tokay and Short, 1996; Nzeukou et al., 2004; Giangrande et al., 2014) method is introduced for the identification of CR overpasses over the APU stations in this study, which simply assumes all rain rate ≥ 10 mm hr-1 as CR samples.

Figure C. 5. Comparison of radar reflectivity (Ze) between NEXRAD observations and collocated APU calculations.

Using the RRC method, a total of 238 5-min CR samples have been collected from 17 APUs during MC3E. As abovementioned, the theoretical design of the APU can measure raindrop sizes up to 25 mm, which is unrealistically large for raindrops even for CR. The maximum valid measured raindrop size is 9.18 mm (Adirosi et al., 2016) based on the statistical results from all available GPM GV field campaigns related to warm season convection including the Hydrological

Cycle in the Mediterranean Experiment (HyMeX, 2012, (Ferretti et al., 2014)), the Iowa Flood

Studies (IFloodS, 2013, https://pmm.nasa.gov/ifloods), and the Integrated Precipitation and

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Hydrology Experiment (IPHEx, 2015, https://pmm.nasa.gov/IPHEx). Moreover, as clarified in the APU user manual, the first two channels (average particle size of 0.064 and 0.193 mm) lack evaluation because they are outside the measurement range

(https://www.esrl.noaa.gov/psd/data/obs/instruments/OpticalDisdrometer.pdf). Thus, this study constrains the APU measured DSD spectrum to 23 size channels ranging from 0.321 mm to 9.785 mm based on the shape-corrected (Beard, 1976) volume-equivalent diameter

(ftp://ghrc.nsstc.nasa.gov/pub/doc/gpmgv/parsivel/DataFormat_parsivel_fieldCampaign.pdf).

Detailed APU DSD spectrum information is listed in Table C. 1. The CR DSD fits using

Exponential and Gamma functions (Ulbrich, 1983) are carried out accordingly employing the same algorithm used in SR region (Press et al., 1992; McFarquhar et al., 2007; Wang et al., 2016) as follows (in cm-gram-second units):

−휆퐸퐷 푁(퐷) = 푁0퐸푒 , (C1)

휇훤 −휆훤퐷 푁(퐷) = 푁0훤퐷 푒 . (C2)

The fitted results are discussed in Section 3.

Table C. 1. The shape corrected raindrop volume-equivalent diameter classification for the APU

Channel Number Average Diameter (mm) 1 0.064 2 0.193 3 0.321 4 0.450 5 0.579 6 0.708 7 0.836 8 0.965 9 1.094 10 1.223 11 1.416 12 1.674 13 1.931 14 2.189 15 2.446

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16 2.832 17 3.347 18 3.862 19 4.378 20 4.892 21 5.665 22 6.695 23 7.725 24 8.755 25 9.785 26 11.330 27 13.390 28 15.450 29 17.510 30 19.570 31 22.145 32 25.235

3. RESULTS

3.1 SENSITIVITY OF FITTING SPECTRUM SUBSET TO THE PRECIPITATION

ESTIMATION

As suggested by McFarquhar and List (1993), the fitted DSD spectra are very sensitive to the manners of fitting. Conventionally, almost all the DSD fitting practices take into account all the available measured raindrops starting from the minimum to the maximum detectable sizes (e.g.,

Zhang et al., 2001, 2003; Bringi et al., 2002, 2003; Gorgucci et al., 2002). Note that the variability of DSD is greatly determined by the small raindrops (featuring orders of magnitude higher in droplet number concentration than larger raindrops). In order to overcome the uncertainty caused by small raindrops, higher moments of DSD representation (e.g., Kozu and Nakamura, 1991;

Ulbrich and Atlas, 1998; Vivekanandan et al., 2004) are introduced into the DSD fitting to balance the contribution of larger raindrops, and the nth moment is calculated as follows:

퐷 푀(푛) = ∫ 푚푎푥 푁(퐷) 퐷푛푑퐷, (C3) 퐷푚푖푛

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where Dmin and Dmax are the minimum and maximum raindrops, liquid water content is proportional to M(3), rain rate is approximately represented by M(3.67), and M(6) is for Ze, etc.

Different combinations of moments are investigated for the best fitting of DSD (e.g., Kozu and

Nakamura, 1991; Testud et al., 2001; Zhang et al., 2001). The representation of DSD containing large raindrops is still not optimal due to the relatively larger errors in higher moments measurements (for example the inconsistent collocated Ze values shown in Figure C. 5), as well as the disdrometers’ intrinsic undersampling issue of large raindrops (Cao et al., 2008).

As revealed in previous studies (e.g., Tokay et al., 2013; Chen et al., 2017), APUs tend to severely underestimate the number of small particles especially for heavy precipitation. With the focus of accurate retrieval on CR rain rate, instead of using the multi-moment fit of DSD, this study proposes an alternative approach of only utilizing the APU measured rain rate as a constraint to evaluate the 0th moment fit of the DSD. In order to get rid of the influence of small raindrops and examine their impacts on rain rate calculation, different subsets of the DSD spectrum

(changing the Dmin in fitting) have been selected in this study. Figure C. 6a demonstrates an example of Gamma fitted results using three different subsets of the spectrum. The fitted curve

(red dotted line) starting from APU channel 3 conforms to the observed DSDs (blue bars) at the first few channels but soon suffers from severe underestimation in number concentration towards the end of the spectrum. On the contrary, the red dashed line starting from APU channel 19 has an excellent match for the last few channels but with severe underestimation in number concentration in the smaller size bins. According to the sensitivity test of different subsets of the spectrum in Figure C. 6b, the best match between calculated rain rate and directly measured rain rate is found at the middle of the spectrum.

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Based on the sensitivity study, the optimal starting channels should lie between channels 3 and 19, and channel 14 is selected in this study based on the method of mean normalized error

(MNE) which is defined as follows:

1 푛 |푅푚푒푎푠푢푟푒−푅푐푎푙푐| 푀푁퐸 = ∑푖=1 , (C4) 푛 푅푚푒푎푠푢푟푒 where Rmeasure and Rcalc are the measured and calculated rain rates. The latter uses the pristine terminal velocity assumption defined by Gunn and Kinzer (1949) which is also used for the removal of spurious APU DSD measurements by default (Tokay et al., 2001; Jaffrain and Berne,

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2011). The fitted Gamma curve using the subset from channel 14 is shown in Figure C. 6a (red solid line), which outperforms the other two alternatives in the overall representation of the observed DSD.

As revealed in previous studies (e.g., Zhang et al., 2001; Brandes et al., 2004; Cao et al.,

2008), the Gamma dispersion (μΓ) and slope (λΓ) parameters are highly related, which can serve as the constraint for the dual-polarization or dual-frequency DSD retrieval. The relationships between Gamma parameters using three different subsets of the spectrum in Figure C. 6 are examined, where an interesting clockwise rotation of the fitted μΓ – λΓ curves is observed as demonstrated in Figure C. 7a. Starting from channel 3, the scatter points demonstrate great similarities to the classic μΓ – λΓ curve found by Cao et al., 2008. However, the trend from the channel 14 subset follow a horizontal line, and the scatter points from channel 19 demonstrate a flipped trend compared to those from channel 3. This variation is not only supported by the three selected subsets of spectrum, smooth transition in rotation angle is also observed by using the continuous increment in subset channels (not shown). For convective precipitation featuring large raindrops, this study proposes an alternative approach to reduce the uncertainty associated with small raindrops by subsetting the spectrum in the DSD Gamma fit, and the choice of subset scheme has a tremendous impact on the resulting μΓ – λΓ relationship.

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Although the Gamma size distribution is commonly used in DSD parameterization, the constant dispersion parameter μΓ is always assumed in operation for simplification. For instance,

μΓ = 2 in both TRMM and GPM precipitation radar rain rate retrieval (Kozu et al., 2009), and the surface observed μΓ mode values are believed to be around 4 – 6 (Kozu and Nakamura, 1991;

Tokay and Short, 1996; Illingworth and Blackman, 2002). As shown in Figure C. 7b, by subsetting from channel 14, the probability distribution of μΓ follows the Gaussian distribution with a mean value of -0.17 and standard deviation of 0.60, making the DSD fit using Exponential function a reasonable assumption which is equivalent to set μΓ = 0 in Gamma fit. This conclusion is also supported by the Zhang et al., 2017, where convective rainfall is found to be more exponentially distributed than SR due to small μΓ values. Similar to Figure C. 6b, Figure C. 8b examines the sensitivity of DSD spectrum subset to rain rate calculation using Exponential fitting, where the least MNE is also found in the middle channels (channel 13 in this study). Moreover, the subset

179 of channel 13 can best represent the observed DSD as shown in Figure C. 8a.

Figure C. 8. Similar to the Figure C. 6 but using Exponential fitting.

It is necessary to note that by using different criteria of error evaluation methods (e.g., mean square error, root mean square error, mean absolute error, correlation coefficient etc.), the optimal channel subset scheme always falls in the middle of the spectrum. The MNE is chosen for the largest contrast among the channels, and the result could vary using different error evaluation approaches.

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3.2 COMPARISON BETWEEN DIFFERENT PARAMETERIZATION SCHEMES

Since we have confidence in the DSD spectrum subset scheme using Exponential fitting, the next step is to determine the best approach to establish the empirical relationship between the fitted parameters. Figure C. 9a demonstrates two alternatives in the curve fitting schemes based on all

-1 the APU-observed CR samples. Using the constant λE = 12.2 cm assumption (red solid line) along with the power-law regression (red dash line) given by:

−8 4.75 푁0퐸 = 3.38 × 10 휆퐸 , (C5) and substituting those assumptions into the pristine radar equation in Wang et al. (2016), the direct relationships between N0E and Ze can be established as

푍 (푚푚6푚−3)×12.27 푁 = 푒 , (C6) 0퐸 훤(7)×1012 and

2.4336×107 1 −8 0.47 푁0퐸 = 3.38 × 10 ( 6 −3 ) . (C7) 푍푒(푚푚 푚 )

Although (C7) outperforms (C6) in capturing the N0E – λE variation as shown in Figure C. 9a, it also generates a biased N0E distribution (Figure C. 9b), as well as an incorrect N0E (Figure C. 9d) variation with the input of the APU calculated Ze. In Figure C. 9b, the observed N0E (black bars)

-2 -4 values have the mode of 10 cm , which is well preserved by the constant λE assumption, but the peak is skewed to the larger N0E value when using the fitted N0E – λE relationship. For the λE – Ze relationship comparisons shown in Figure C. 9c, no significant difference in λE retrieved from Ze is found based on different approaches. However, the observed increasing trend in the N0E – Ze relation is captured by the constant λE assumption, whereas it becomes a decreasing trend by using

N0E – λE relationship as illustrated in Figure C. 9d. It is necessary to note that from the original

“N0 jump” theory, after the drastic increase in N0E from SR to CR, N0E tends to decay with increasing convective activity, which is strongly reflected in the Gamma function fitting. For

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8 -4.3 example, the relationship N0Γ = 4 × 10 R was established by Maki et al., 2001 to address this issue. In this study, the observed N0E – Ze trend does not follow the expected decrease in N0E with increasing convective activity, which mainly results from the spectrum subsetting in DSD fitting.

By using the default full spectrum, the descending N0E – Ze trend is still observed.

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3.3 EVALUATION OF THE NEW CR PRECIPITATION ESTIMATION

-1 Similar to the equation (11) in Wang et al. (2016), by applying λE = 12.2 cm , the new CR rain rate can be calculated as follows:

퐷 푍 (푚푚6푚−3)×12.27 휋 푅푅(푚푚 ℎ푟−1) = 3.6 × 106 ∫ 푚푎푥 푒 푒−12.2퐷 퐷3푉(퐷)푑퐷, (C8) 퐷푚푖푛 훤(7)×1012 6 where the terminal velocity V(D) still follows the pristine assumption by Gunn and Kinzer (1949).

Figure C. 10. The scatter plot of measured rain rates (Mesonet and APUs) vs. their collocated Ze

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(NEXRAD observed and APU calculated) at cloud base during MC3E, overlain by the newly developed Z-R relationship (red solid line) and the traditional Z-R relationship (red dash line).

To evaluate the performance of the newly developed Z-R relationship, in addition to the 17

APU disdrometer measurements, an independent dataset of CR rain rate measurements from 127

Mesonet rain gauges and their collocated cloud base Ze values during MC3E (2941 valid samples) are also examined in Figure C. 10. The newly developed relationship provides a more reasonable rain rate estimation, compared to the traditional power law CR Z-R relationship, which indicates that the constant λE could potentially be a better assumption instead of constant N0E for CR rain rate estimation.

Although lower CR rain rates are generated using the newly developed Z-R relationship, many critical issues are either overlooked or over-simplified in this study. For instance, the deformation of large raindrops is not fully considered. As shown in Figures C. 11a and C. 11b, the CSA classified CC regions (red color) all correspond to high ZDR values (> 2 dB), indicating that the observed raindrops are highly deformed with lower axis ratios (McFarquhar and

Heymsfield, 1996). In contrast, the vast SR regions feature much lower ZDR, where spherical raindrop assumptions can work better. Moreover, the V(D) follows the pristine assumption developed by Gunn and Kinzer (1949) for stagnant air, in which the impacts of vertical air motion and particle deformation are overlooked. In recent studies, more sophisticated raindrop fall velocity approximations are developed in the forms of polynomial (e.g., Edward et al., 2002; Cao et al., 2008), power law (e.g., Atlas and Ulbrich, 1977; Pei et al., 2014), and exponential (e.g.,

Atlas et al., 1973). However, the actual raindrop fall velocity cannot be segregated from environmental conditions, especially the vertical air motion, which could vary drastically within small temporal and spatial scales for the CR region.

184

Figure C. 11c attempts to summarize the relationships among the three simplified variables relevant to the best estimate of CR rain rate. First, large deformed raindrops have drag effects on the ambient air, which is in the opposite direction to the CR updraft. Meanwhile, stronger updrafts enhance the raindrop deformation. Secondly, large raindrops exhibit faster fall velocities, which is directly related to raindrop deformation. However, when deformation happens, raindrops expose more contact area to the updraft which slows down the falling with more air resistance.

Lastly, the fall velocity and updraft are negatively related as they are in opposing directions.

Nonetheless, all three factors indicate higher rain rates, so the robust estimation of CR rain rate can only be based on an in-depth understanding of those relationships with more observations. In addition to these three factors, multiple transition processes from cloud to precipitation (e.g.,

Pruppacher and Klett, 1996; Kumjian and Prat, 2014; Fan et al., 2015, 2018), including collision- coalescence, breakup, evaporation, etc., also play important roles in CR precipitation estimation, which warrant further joint investigation.

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4. SUMMARY AND CONCLUSIONS

In this study, a total of 20 hours of CR DSD samples that were measured by 17 APU disdrometers and deployed during MC3E were selected to investigate the CR precipitation properties. The surface in situ measurements were carefully processed and examined, and an alternative CR DSD parameterization scheme was developed, which was further applied to the CR rain rate estimation. The main conclusions can be summarized as follows:

1. Based on a large amount of disdrometer measurements over the SGP region, two distinctive

features of the CR DSD are observed and compared to the SR DSD which show (a) broader

spectrum distribution (maximum raindrop size can be up to 8 mm vs. less than 4 mm in

SR) and (b) more variation on N0E direction in CR vs. more variation on λE direction in SR

in N0E - λE relationship.

2. For the CR DSD, both the Gamma and Exponential DSD function fits demonstrate a large

sensitivity to spectrum subsetting. As the starting channel of the DSD is shifted towards

the larger raindrop sizes, an interesting clockwise rotation in the N0Γ - λΓ curves is observed,

where the curve of default full-spectrum fitting resembles to the classic N0Γ - λΓ relationship.

However, with the measured rain rate as a constraint, the best representation of CR DSD

is found by subsetting from the middle of the spectrum, where μΓ is close to 0, making the

fitting using Exponential function a reasonable assumption.

3. Rather than assuming constant N0E, the assumption of constant λE is more capable in

-1 capturing the natural N0E- λE variation observed by the APUs. By applying λE = 12.2 cm

to the intrinsic definitions of radar reflectivity factor, CR rain rates can directly be retrieved

from the observed Ze values. Compared to the severe overestimation using the traditional

power-law CR Z-R relationship (Z = 300 R1.4), the newly estimated rain rate is more

186

reasonable and close to the direct CR rain rate measurements.

Although many critical factors related to CR rain rate estimation are overlooked or over- simplified, and the conclusion was merely based on intensive observation during one field campaign, this study attempted to explore the alternative approach of CR DSD parameterization.

By changing to the assumption of constant λE, the overestimation issue in CR rain rate calculation is greatly mitigated. It is worthwhile to note that the new Z-R relationship was established for the

MC3E campaign, and the adjustments of optimal spectrum subsetting, as well as the choice of constant λE could vary for different climatic regions by different observations. For CR precipitation estimation, the calculated rain rate could also be impacted by choosing different V(D) relationships.

ACKNOWLEDGEMENTS

The data were obtained from the Atmospheric Radiation Measurement (ARM) Program sponsored by the U.S. Department of Energy (DOE) Office of Energy Research, Office of Health and

Environmental Research, and Environmental Sciences Division. This study was primarily supported by DOE CMDV project at University of Arizona with award number DE-SC0017015 and the NOAA R2O project at University of North Dakota project under grant NA15NWS4680004.

The disdrometer in situ measurements during MC3E can be obtained from Xiquan Dong

([email protected]).

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APPENDIX D: EVALUATION OF NORTHERN AND SOUTHERN GREAT PLAINS WARM SEASON PRECIPITATION EVENTS IN WRF. PART II: ANALYSIS OF OBSERVED AND SIMULATED PRECIPITATION

(Submitted to the Weather and Forecasting)

Jingyu Wang1, Xiquan Dong1, Baike Xi1, Aaron Kennedy2, and Brooke Hagenhoff2

1. Department of Hydrology and Atmospheric Sciences, University of Arizona, Tucson, AZ

2. Department of Atmospheric Sciences, University of North Dakota, Grand Forks, ND

197

ABSTRACT

Following the classified synoptic patterns based on Self-Organizing Maps (SOMs) in Part I of this study, the 2007-2014 warm season (April-September) precipitation events simulated by the

National Severe Storms Laboratory (NSSL) are evaluated in Part II over the Southern and Northern

Great Plains (SGP and NGP) using National Centers for Environmental Prediction (NCEP) Stage

IV observations. In Part II of this study, we have examined and discussed the heavy precipitation events from two perspectives: the primary precipitation type (convective rain CR vs. stratiform rain SR) and the dominant atmospheric synoptic pattern (extratropical cyclone vs. subtropical ridge). By separating the precipitation types into CR and SR, simulated CR intensity and coverage match well with the observations, whereas the simulations of their SR component are more problematic with weaker intensity and larger coverage. By grouping the SOM nodes through 500 hPa synoptic features, the higher performance scores are always associated with extratropical cyclone condition than the subtropical ridge. Of the six classes over both regions, the largest oversimulation of precipitation is found for SR dominated classes, whereas a nocturnal negative bias for precipitation exists for classes featuring upscale growth of convection. The distinctive characteristics of diurnal cycle, intensity/coverage, and precipitation types among different SOM classes further prove the capability of the objective classification technique. In addition to the similarities, there also exist notable regional differences where the SGP features larger overall intensity but smaller coverage compared to the NGP, but NSSL-WRF demonstrates less bias in the former region.

198

1. INTRODUCTION

This set of papers investigates characteristics of precipitation within a deterministic

Convection Allowing Model (CAM) run daily at the National Severe Storms Laboratory (NSSL) in support of National Oceanic and Atmospheric Administration (NOAA) Hazardous Weather

Testbed (HWT). In Part I of this study (Hagenhoff et al. 2018), 1370 days of 4 km Weather

Research and Forecasting (WRF) runs at NSSL (hereafter NSSL-WRF) from 2007 to 2014 were analyzed. Following the study of Goines and Kennedy (2018) that demonstrated spatial variability in precipitation bias in NSSL-WRF, two regions of interest were identified: the Northern and

Southern Great Plains (NGP and SGP, respectively). The long-term nature of these simulations facilitated the use of an unsupervised classification technique, the Self Organizing Map (SOM,

Kohonen et al. 1996) to classify synoptic patterns from the North American Regional Reanalysis

(NARR, Mesinger et al. 2006) for these two regions. Large-scale synoptic patterns were classified for days that fell within the upper 90% of all precipitating days as identified by the National

Centers for Environmental Prediction’s (NCEP) Stage IV multisensory analyses, and regime- dependent biases were found.

This work follows a line of studies that have investigated model forecast skill (for precipitation) in NSSL-WRF. For example, Herman and Schumacher (2016) examined extreme precipitation events over the continental United States (CONUS), and found that most skillful predictions were associated with less extreme events (lower return period) and performance was best from 1200 to 1800 UTC. Regarding the convection initiation process, a systematic eastward shift in NSSL-WRF forecasts was found by Coffer et al. (2013), and this issue was more prominent for cases with propagating, large-scale precipitating systems. In addition to these studies, broader evaluations of precipitation have been performed for different CAMs (e.g., Kain et al. 2008, 2010a,

199 b; Lean et al. 2008; Roberts and Lean 2008; Weisman et al. 2008; Clark et al. 2011) with different emphases on precipitation characteristics including timing, duration, evolution, distribution, and probabilistic properties. What hasn’t been considered is how these properties vary with the synoptic-scale environment. In Part II of this study, this issue will be addressed using the SOM classifications developed in Part I to segregate observed and simulated precipitation events by meteorological regime.

Besides the ramifications of this study for forecasters and other users of NSSL-WRF, there are additional benefits. Stretching across the mid-latitudes (30o N to 60o N), the entire Great Plains is considered as a whole without latitudinal discrimination for some applications. For example,

Geostationary Operational Environmental Satellites R Series (GOES-R) cloud properties and precipitation retrieval algorithms are segregated into four latitudinal regions (60o - 30o S, 30o S -

Equator, Equator - 30o N, and 30o - 60o N, Kuligowski 2010; Kuligowski et al. 2016). With latitudinal variations in mind, this study will quantitatively evaluate the NSSL-WRF simulated precipitation over the SGP and NGP to provide a robust statistical information with respect to large-scale synoptic patterns that can be of use to the broader modeling and satellite retrieval communities.

This paper is formatted as follows. In Section 2, additional methodology is provided to describe how NCEP Stage IV hourly precipitation data are separated into convective rain (CR) and stratiform rain (SR) components following a rainfall-rate criterion (RRC) method. In Section

3, NSSL-WRF simulations and Stage IV observations are analyzed to investigate the diurnal cycle, averaged precipitation intensity and coverage, and separation of CR vs. SR over the SGP and NGP regions, respectively. Four performance indices are developed to quantitatively evaluate the performance of NSSL-WRF simulations for all six SOM classes over both regions. Lastly, the

200 conclusions and suggestions for model improvement are discussed in Section 4.

2. DATA AND METHODOLOGY

Briefly summarizing the methodology of Part I, synoptic patterns were obtained from

NARR for a 19°×15° (longitude by latitude) region surrounding a point within the SGP (36.6°N,

97.5°W) and the NGP (47.0°N, 98.3°W, see Figure. 1). Quantitative evaluation of NSSL-WRF simulated precipitation was then conducted over smaller, 5°×4° regions centered for these points.

Precipitating periods were identified on a daily basis ranging from 1200 to 1200 UTC, and were associated with the atmospheric pattern at 00 UTC on the 2nd day, halfway through the precipitation period. Observed precipitation came from the NCEP Stage IV analysis, and SOMs were generated from days that fell within the upper 90% of the Cumulative Distribution Function (CDF) of regionally averaged, accumulated precipitation. To understand whether simulated precipitation and associated biases are SR or CR in nature, this study separates these categories within NCEP

Stage IV and describes as below.

Through the combination of the NEXRAD radar and GOES satellite observations, Feng et al. (2011) developed a hybrid cloud classification algorithm which objectively separates the convective systems into the components of convective core (CC), stratiform rain (SR), and anvil clouds (AC). The SR regions have the largest coverage of warm season rainfall over the mid- latitudes, while the CC regions account for the most intense precipitation. Feng et al. (2012) also found that the rain rate of CC is almost an order of magnitude higher than SR, causing a surge in accumulated precipitation within a short time period and possible resulting in flooding events.

Differences in statistical characteristics of CR and SR have been investigated through a variety of datasets, including space-borne satellite observations (e.g., Tropical Rainfall Measuring Mission,

201

Yang and Smith, 2008; GOES, Behrangi et al. 2009), ground-based radar observations (e.g.,

National Mosaic and Multi-Sensor Quantitative Precipitation Estimation, Stenz et al. 2014, 2015;

Feng et al. 2011 and 2012), direct surface rain gauge measurements (Giangrande et al. 2014; Wu et al. 2013; Tao et al. 2013), and aircraft in-situ measurements (Beard et al. 1986; Wang et al. 2015,

2016).

Since the differences between CR and SR are so obvious, separation can be performed using the rainfall-rate criterion (RRC) method where CR grid-points within hourly precipitation can be identified using a threshold greater than 10 mm hr-1, typically at a spatial grid spacing of 1 km

(Tokay and Short, 1996; Nzeukou et al. 2004; Giangrande et al. 2014). The 10 mm hr-1 RRC threshold is suitable for hourly data with a spatial grid spacing of 1 km but cannot be directly applied to Stage IV data with 4 km grid spacing. Rosenfeld et al. (1990) suggested the optimal convective rain rate cutoff should fall between 4-6 mm hr-1 at this lower resolution. In this study, grid-points in Stage IV data greater than 5 mm hr-1 are identified as CR.

3. RESULTS

3.1 THE SOUTHERN GREAT PLAINS

Examples of precipitation cases for each class within the SGP SOM (Figure 6) are shown in Figure D. 1. For the sake of clarity, only 500 hPa heights are shown, but it is important to recognize that SOMs were created from not only 500 hPa height anomalies, but also additional two-dimensional fields including mean sea level pressure (MSLP), relative humidity (RH) and wind (u and v components) at 900 and 500 hPa. As a result, good agreement isn’t necessarily expected across all fields. That said, examples were chosen that broadly encompass the noted upper-level features discussed in Part I.

202

With this discussion in mind, Figure D. 1 demonstrates that Classes 1-3 have a common feature of southwesterly wind with an upper-level trough or low in the vicinity of the SGP analysis domain. Evidence of the surface extratropical cyclone can be seen with the most intense precipitation occurring east of this feature, forming a widespread precipitation band over or near the study domain. As noted in Figure 8, these classes are most common in April to June and

September, which is in line with the climatology of extratropical cyclones. In the broadest sense, these patterns are tied to the location of the polar jet over this region. As discussed in many previous studies (e.g., Maddox 1978, Wash et al. 1990, Schumacher 2017), the polar jet stream plays a significant role for the cyclogenesis over the mid-latitudes. As the jet stream intensifies in spring and early fall, a jet streak forms with upper level divergence, which efficiently pumps air out of the vertical air column. In response to the aloft divergence, a low pressure system is generated at the surface level in order to draw in air. The configuration of low-level convergence with upper-level divergence favors the upward motion in the whole air column, thus the extratropical cyclone pattern is generated for Classes 1-3.

Classes 4-5 are characterized by northwesterly flow at 500 hPa over the west of the SGP domain and changed to near-zonal flow over the east of the SGP domain that is also occurred in

Class 6 (Figure D.1f). In addition to the difference in prevailing wind direction between the upper and lower classes, differences in the morphology of daily accumulated precipitation are also obvious. The examples shown for Classes 4-5 have less-intense precipitation around the periphery of a subtropical ridge/high center, which is commonly known as a “ring of fire” pattern (Galarneau and Bosart, 2006). In the early efforts that synthesize heavy precipitation events with synoptic conditions (e.g., Maddox et al. 1978, Mitchell et al. 1995), the pattern of “meso-high” has been associated with severe weather. Dominated by the subtropical high pressure system, the air is most

203 stable towards the center of the high pressure, where a subsidence inversion layer (capping inversion) is formed as a result of widespread descending air. The near-surface layer is heated and compressed by the high pressure but also trapped by the subsidence inversion, so the formation of thunderstorm is prohibited even with aloft cold air. However, this inversion becomes weaker towards the edge of the high pressure, which allows convection to occur with sufficient moisture supply, thus a ring precipitation can form at the periphery of the high pressure. Compared to the storms associated with extratropical cyclone (Classes 1-3), which is mainly driven by large-scale frontal forcing, the initiation of “ring-of-fire” convection more relies on the disturbance aloft (e.g., the advection of maximum vorticity by a short-wave trough or weather systems at finer scope) or mesoscale forcing (e.g. convergence along outflow boundaries). Similar to these bottom tier of classes, Class 6 also has less intense precipitation and there is some evidence of a weak shortwave trough at 500 hPa. As noted in Part I, these type of features can be washed out within the SOM, and as a result, the SOM displays zonal flow for this class.

204

3.1.1 Analysis of the diurnal cycle

The diurnal cycles of daily average precipitation rate over the SGP study domain are compared between Stage IV observations and NSSL-WRF simulations for each SOM class (Figure

D. 2). From the left to right (i.e. Classes 1-3 and Classes 4-6), the diurnal cycles increase in amplitude. A bimodal distribution is found for Classes 1 and 4 with a primary peak at sunrise

(0600 LT) and the secondary peak at sunset (1800 LT). In contrast, the remaining classes have the typical diurnal pattern documented over the Great Plains (e.g., Kincer, 1916; Wallace 1975;

Maddox, 1978; Colman, 1990a and 1990b) with peak precipitation rate around midnight. This region receives the majority of precipitation and convective activity at night during the warm season, which is not observed in other regions globally (e.g., Dai, 2001; Nesbitt and Zipser, 2003;

205

Lee et al. 2007; Weisman et al. 2008). The lack of diurnal variation in Classes 1 and 4 implies that the predominant forcing mechanism for these classes could be widespread SR precipitation.

This argument can be supported by synoptic patterns shown within Figure 6 where these classes are associated with higher relative humidity, residing underneath a 500 hPa trough.

Comparing the NSSL-WRF simulations with Stage IV observations, regime and time dependent biases are seen (Figure D. 2). A negative bias during night is found for all Classes, and a positive bias during the daytime and early evening is found for all Classes except for Classes 3 and 5 where both simulations and observations agree perfectly during the day. For Class 1, the nocturnal bias is negligible, and thus the model oversimulates precipitation over the entire day. In

Class 2, the positive bias carries over into the evening, and this offsets a negative bias that begins at approximately midnight local time. This characteristic is common in the majority of the classes that demonstrate a large negative bias during the night, which was also noted in the study of Goines

206 and Kennedy (2018). Even with explicit convection, proper simulation of the nocturnal maximum in precipitation remains a challenge in this CAM.

The timing of the bias provides insight into the forcing mechanism. Focusing on the similarities between Classes 3 and 5, the peaks at 0200 LT correspond to the largest nocturnal negative bias. The earlier precipitation peaks in the NSSL-WRF simulations indicate that the continuous upscale growth of convection during the night may be to blame, and this is supported by the Hovmöller diagrams shown in Goines and Kennedy (2018) that had propagating streaks that ended too early. Despite the negative biases of precipitation at night, Classes 3 and 5 have excellent agreement during the day. That said, most of the classes (such as Class 2) have a well- defined phase shift with simulated precipitation peaking two hours early. The Classes 2 and 6 serve as the transitional patterns connecting presumed SR precipitation (Classes 1 and 4) and those with nocturnal upscale growth (Classes 3 and 5).

To visualize the contrast in diurnal precipitation variation, the daytime and nighttime averaged 12-hour accumulated precipitation amounts and biases are shown in Figure D. 3 and listed in Table D. 1. By comparing Figures. D. 3a and D. 3d, no significant difference is found between the day and night observed precipitation for Class 1 (5.74 vs. 5.30 mm) and Class 4 (4.38 vs. 4.32 mm), whereas classes with more convective activity have lower daytime but higher nocturnal precipitation amount (e.g., Class 2: 4.43 vs. 7.09 mm; Class 6: 3.08 vs. 6.61 mm).

Moreover, the largest day/night contrast is found in Class 3 (2.46 vs. 6.96 mm) and Class 5 (2.38 vs. 5.55 mm), which indicates notable upscale growth in the night (Figures. D. 2c and D. 2e).

These pieces of information reveal that the well-documented GP nocturnal maximum precipitation diurnal pattern is not always true especially for events dominated by SR (taking up to 28 % of all heavy precipitating events), but only works for classes that have more convection. For the NSSL-

207

WRF simulations, they generally have positive biases during daytime but negative biases at night.

Figure D. 3. Daily averaged, 12-hour accumulated precipitation amount for Stage IV (a, d), NSSL-WRF (b, e), and bias (c, f, NSSL WRF - Stage IV) during the day (a, b, c) and night (d, e, f) for each class in the SGP SOM.

In addition to the contrast among the three sub-categories of SOM classes, difference can also be found regarding the synoptic pattern. From left-to-right across the SGP SOM, precipitation transitions from SR dominant (Classes 1 and 4), to CR dominant (Classes 3 and 6). As revealed in

Figure D. 1, Classes 1-3 are strongly impacted by the extratropical cyclone while subtropical ridge plays a significant role in Classes 4-6. In general, extratropical cyclone is more efficient in generating precipitation than subtropical ridge, and the NSSL-WRF performs better under the extratropical cyclone than the subtropical ridge, which will be discussed in Section 3c.

208

Table D. 1. Daytime and nighttime 12-hour accumulated precipitation from Stage IV observations, NSSL-WRF simulations, and their differences for each class of the SGP and the NGP SOMs. Class 1 Class 2 Class 3 Class 4 Class 5 Class 6 Stage IV 5.74 4.43 2.46 4.38 2.38 3.08 Day NSSL WRF 6.72 4.92 2.34 4.60 2.35 3.65 Difference 0.98 0.49 -0.12 0.22 -0.03 0.57 SGP Stage IV 5.30 7.09 6.96 4.32 5.55 6.61 Night NSSL WRF 5.27 6.96 4.49 3.77 4.69 6.38 Difference -0.03 -0.13 -2.47 -0.55 -0.86 -0.23 Stage IV 1.28 2.47 4.09 0.92 2.79 4.45 Day NSSL WRF 1.50 3.00 5.00 0.91 3.84 5.36 Difference 0.22 0.53 0.91 -0.01 1.04 0.92 NGP Stage IV 5.10 5.50 5.31 3.84 2.26 1.51 Night NSSL WRF 4.71 5.85 6.72 3.41 2.57 2.55 Difference -0.39 0.34 1.41 -0.44 0.31 1.04

3.1.2 Analysis of precipitation type, intensity, and coverage

As mentioned in Section 2, the rainfall-rate criterion (RRC) method was used to segregate

CR (≥10 mm hr-1) and SR (<10 mm hr-1) portions, and these results are split by SOM class for intensity and coverage (Figure D. 4, Table D. 2). Note that these results are based on hourly totals and only precipitating grid-points within the analysis domain. For all precipitating grid-points,

Classes 1 and 4 have the lowest intensity but the largest coverage where their CR intensities and coverages are smallest while SR coverages are greatest as illustrated in Figure D. 4 and listed in

Table D. 2. Their CR and SR results further verify earlier statements that meteorologically, these two classes are more dominated by SR precipitation. Moving across the SOM, trends from Classes

1 to 3 and from Classes 4 to 6 are seen in these properties. The CR intensities and coverages for

Classes 3 and 6 appear to be maxima while their SR coverages decrease to minima, indicating that

209 convective activity plays a more important role in these two classes which grow upscale during the night. These results also provide a strong support of the higher amplitude diurnal cycles for these two classes observed in Figure 2. The averaged CR and SR intensities for all six classes are

10.54 and 1.11 mm hr-1, respectively, which is consistent to the finding in Feng et al. (2012) where

CR intensity is an order magnitude higher than SR one. On the other hand, the averaged CR and

SR coverages are 3.35% and 12.50% of the study domain, respectively, where the SR coverage is almost four times as large as the CR one.

Results for NSSL-WRF are shown in Figures. D. 4b and D. 4d along with mean values and

210 biases listed in Table D. 2. For total precipitation, the issue of lower intensity but broader coverage exists for each SOM class except for Class 5 which will be discussed later. This issue is even more prominent for SR, where larger negative biases in precipitation intensity and positive biases in precipitation coverage are found. For the CR component, deviations from observations still exist, but the overall magnitudes of intensity and coverage match better than total precipitation and SR portion. In summary, although the simulated precipitation amounts have good agreement with the observations as shown in Figure 4, NSSL-WRF has weaker precipitation intensity but larger coverage, and this discrepancy is more prominent for the SR portion. In contrast, the CR intensity and coverage are better simulated for each SOM class.

As mentioned above, Class 5 differs from the other classes by having a negative bias in precipitation coverage for total (-2%), CR (-5%), and SR (-1%), whereas the remaining classes of simulations have large positive biases in both the total and SR coverages. As a result, Class 5's undersimulated nocturnal precipitation amount (Figure 2e) can be attributed to the missing precipitation coverage where the CR component (-5%) is more to blame than SR (-1%). Another interesting category is Class 3, which also has a lack of nocturnal precipitation (Figure 2c) but with a larger deficit. Similar to the Class 5, this class also undersimulates CR intensity (-17%) and coverage (-27%). Thus for these two classes, the undersimulated CR precipitation is the major error source for the deficit in nocturnal precipitation, and this is in agreement with earlier discussions based on Figure 2c and prior studies.

211

36% 63% 98% 18% 63% 42%

30% / / 30% / 32% / 41% / 32% / 30% / 34% / 32%

------

Difference Difference

WRF

26.77 22.91 18.88 16.35 10.05 14.82 17.70

0.74 / / 0.74 / 0.76 / 0.66 / 0.74 / 0.79 / 0.77 / 0.75

NSSL NSSL

9.54 9.10

19.70 14.03 13.91 10.12 12.50

1.05 / / 1.05 / 1.11 / 1.12 / 1.09 / 1.13 / 1.16 / 1.11

Stage IV Stage

3% 5%

27% % 4

1% 3%

3% / / 3%

- -

2 % / % 2

13%

8% / / 8% / 1% / 7% / 3%

- -

17% / 17%

Difference Difference

) / Coverage (%) Coverage / )

WRF for each class of the SGP SOM. Precipitation is separated the of SGP class is SOM. each separated Precipitation WRFfor

3.32 3.80 3.04 2.41 2.74 3.97 3.21

WRF

9.94 / / 9.94 / 9.69

NSSL NSSL

10.35 / / 10.35 / 10.46 / 10.44 / 10.94 / 10.33

2.96 3.85 4.14 2.49 2.88 3.86 3.35

9.18 / / 9.18 / 9.80

10.46 / / 10.46 / 11.61 / 10.75 / 11.28 / 10.54

Stage IV Stage

Precipitation Intensity (mm hr Precipitation Intensity

33% 52% 67% 15% 48% 33%

16% / / 16% / 24% / 52% / 21% / 20% / 26% / 26%

------

Difference Difference

Total

WRF

29.40 25.81 20.82 18.33 12.06 17.72 20.10

1.62/ 1.94/ 1.54/ 1.77/ 2.08/ 2.30/ 1.91/

NSSL NSSL

rain (CR), and stratiform rain (SR) stratiform components. rain(CR), and

22.11 17.00 12.46 16.00 12.29 12.01 15.06

1.94 / / 1.94 / 2.55 / 3.21 / 2.23 / 2.60 / 3.12 / 2.61

Stage IV Stage

Precipitation intensity and coverage from Stage IV and NSSL and from IV coverage Stage and intensity Precipitation

. .

1 2 3 4 5 6 Class

Mean

into total, convective intoconvective total, TableD 212

3.2 THE NORTHERN GREAT PLAINS

Similar to the SGP, the NSSL-WRF simulations in the NGP are evaluated for each SOM class (Figure 7) from the perspectives of diurnal cycle, precipitation intensity/coverage, and the separation of CR vs. SR. As shown in Figure D. 5, specific examples of precipitation cases are shown for each SOM class. As discussed in Part I, Classes 1-3 feature southwesterly flow at 500 hPa level with surface patterns ranging from southerly flow ahead of an approaching surface cyclone (Class 1), to the warm sector just NE of a cyclone (Class 2), to the warm front N of the cyclone (Class 3). Class 6 can also be grouped with these types of cases as the domain of interest is located just NW of the surface low underneath the upper-level trough, a typical pattern associated with Colorado Lows. In contrast, subtropical high pressure centers in Classes 4-5 are located at the south of the study domain with precipitation occurring at the peripheries of the high pressure centers.

Figure D. 5. Examples of precipitation cases for each class within the NGP SOM (a) Class 1:

213 storm on June 11 2008, (b) Class 2: May 23 2007, (c) Class 3: April 15 2011, (d) Class 4: July 19 2011, (e) Class 5: July 15 2011, (f) Class 6: April 1 2014.

Figure D. 6 shows the diurnal cycles of domain averaged precipitation rates from Stage IV observations and NSSL-WRF simulations for each class within the NGP SOM. Classes 1, 2, and

4 demonstrate different diurnal patterns compared to Classes 3, 5, and 6. The former is consistent with the typical GP diurnal pattern with nocturnal precipitation maxima, which resemble the SGP

Classes 2-3 and 5-6. The latter cases have less diurnal variability and their peaks occur around

1800 LT, which is similar to the SGP Classes 1 and 4 (Figures D2a and D2d), and the lack of day/night contrast may indicate the dominance of SR.

Figure D. 6. As in Figure D. 2, but for the NGP.

For the visualization of the day and night contrast, the daytime and nighttime averaged 12- hour accumulated precipitation amounts and biases for each SOM class are present in Figure D. 7 and listed in Table D. 1. Similar to the conclusions drawn in the SGP (Figure D. 3), strong positive

214 biases are found for SR dominated Classes (3 and 6, counterparts of SGP Classes 1 and 4) for both day and night. Classes 1 and 4 (counterparts of SGP Classes 3 and 5) correspond to the best daytime match (difference of 0.22 and -0.01 mm) and also the largest negative nocturnal biases (-

0.39 and -0.44 mm). In addition to the similarities, regional differences still exist. For example, compared to the SGP Classes 1 and 4 with the lack of day and night contrast, the NGP's SR dominated Classes (3 and 6) have notable diurnal variations (slightly increase and significant decrease, respectively), and almost no diurnal variation in Class 5 whose SR component is not as pronounced. As mentioned previously, these differences probably result from the limited number of final SOM classes in the NGP, which cannot fully account for other variabilities in addition to the CR vs. SR separation as explicit as the SGP.

Figure D. 7. As in Figure D. 3, but for the NGP.

215

Figure D. 8. As in Figure D. 4, but for the NGP.

To understand how precipitation is partitioned between CR and SR, box plots of precipitation are shown for the NGP SOM (Figure D. 8). Stage IV observations demonstrate that

Classes 3 and 6 correspond to the lowest total/CR/SR intensity (Figure D. 8a and Table D. 3) and the largest total/SR coverage (Figure D. 8c), which confirms that SR is the primary precipitation component for these two classes. Since these two classes include the strongest mid-latitude cyclones and a well-defined 500 hPa trough, this makes meteorological sense as these environments support widespread and longer-lasting SR precipitation. Classes 1, 2, 4, and 5 have higher overall intensity and their total and SR coverages are almost half of Classes 3 and 6 (mean values are shown in Table D. 3), which suggests that convection is more important for these four

216 classes. Comparing the mean values in Table D. 3 with those in Table D. 2, the Stage IV observed total, CR, and SR precipitation intensities are 1.54, 8.57 and 0.94 mm hr-1, about 1.07, 1.97 and

0.17 mm hr-1, respectively, lower than those at the SGP region. The averaged precipitation coverages at the NGP are 2.9% and 4.06% more in total precipitation and SR, but 0.88% less in

CR than those at the SGP.

From the perspective of NSSL-WRF simulations, the SR dominated Classes 3 and 6 have strong positive biases during both day and night (Figures D6c and D6f), which is different to the

SGP Classes 1 and 4. The positive biases are further investigated by separating the components of CR vs. SR (Figures D8). Compared to the slight positive biases in CR intensity/coverage, the largest positive biases of 51% and 71% in SR coverage are not seen from the SGP Classes 1 and

4. As a result, the incorrect simulation of SR precipitation is a more prominent issue in the NGP than in the SGP.

217

/ /

7% 6%

50% 51% 26% 71% 40%

31% / / 31% / 33% 23% / 29% / 27% / 24% / 29%

------

Difference Difference

WRF

21.90 17.53 42.39 11.82 14.86 36.82 23.17

0.67 / / 0.67 / 0.67 / 0.69 / 0.67 / 0.68 / 0.65 / 0.67

NSSL NSSL

14.88 16.35 28.08 11.18 11.80 21.50 16.56

0.96 / / 0.96 / 1.00 / 0.90 / 0.94 / 0.93 / 0.86 / 0.94

Stage IV Stage

5% 4%

11% 29% 35% 27% 17%

6% / / 6% / 4% / 8% / 1% / 9% / 1% / 5%

Difference Difference

) / Coverage (%) Coverage / )

3.50 2.69 3.72 2.33 2.75 2.21 2.89

WRF

9.32 / / 9.32 / 9.43 / 8.14 / 9.69 / 9.48 / 7.48 / 9.00

NSSL NSSL

3.16 2.56 2.89 2.43 2.03 1.74 2.47

8.82 / / 8.82 / 9.04 / 7.52 / 9.61 / 8.68 / 7.43 / 8.57

Stage IV Stage

Precipitation Intensity (mm hr Precipitation Intensity

7% 4%

9% / / 9%

43% 50% 27% 70% 38%

12% / / 12% / 19% / 15% / 17% / 25%

16 % / / % 16

- - - - -

Difference Difference

for the NGP SOM. NGP the for

Total

WRF

24.05 19.06 44.22 13.08 16.50 37.85 24.79

1.40 / / 1.40 / 1.45 / 1.02 / 1.47 / 1.47 / 0.82 / 1.30

NSSL NSSL

16.85 17.83 29.50 12.56 13.02 22.30 17.96

1.59 / / 1.59 / 1.80 / 1.20 / 1.77 / 1.61 / 1.09 / 1.54

Stage IV Stage

As in Table D. 2 but 2 D. Table in As

. .

1 2 3 4 5 6 Class

Mean

TableD 218

The NSSL-WRF simulations for Classes 1 and 4 peak at 0000 LT and 0400 LT, respectively.

These simulations are similar to the SGP Classes 3 and 5 with following characteristics: 1) delayed precipitation maxima compared to other classes, 2) notable undersimulated precipitation during the night, and 3) good agreement during the day. Different from their counterparts in the SGP where the negative bias is caused by simulated convection ending too soon, the NSSL-WRF simulation is in phase with the observation. As shown in Figure D. 8 and listed in Table D. 3, the

NSSL-WRF simulated CR intensities and coverages, as well as SR coverages, for all NGP classes, have positive biases, but moderate negative biases in SR intensities. Thus, the SR portion is the major error source for the nocturnal deficit. With -29% negative bias in the SR intensity, Classes

1 and 4 correspond to the least positive biases for the SR coverage (7% and 6% compared to 71% for Class 6), which further proves that missing SR precipitation causes the negative bias for cases with nocturnal upscale growth. In addition, Class 4 is unique as it corresponds to the only deficit in daily total precipitation over the NGP and this difference is statistically significant (Figure 6d and Table 4 in Part I). Both Classes 1 and 4 have evidence of the upscale growth of convection, but Class 4 peaks four hours later than Class 1. These differences are not seen by comparing SGP

Classes 3 and 5, which may reveal the SGP and NGP have different response to the atmospheric state.

The transitional Classes (2 and 5) with moderate positive bias (Figures D6b and D6e) are more similar to Classes 2 and 6 in the SGP as they connect the Classes dominated by SR (3 and

6, strong positive bias) and the Classes with upscale growth (1 and 4, negative bias). Note that

Class 5 has the least diurnal variation (Figure D. 6e) but is still classified as CR dominant class according to the precipitation intensity/coverage comparison. The abnormal diurnal cycle probably suggests that the SOM Class 5 includes too many cases (91 events) that cannot be

219 simply separated into CR vs. SR dominated precipitation. Moreover, as shown in Figure S5 of

Part I (6 nodes in bottom-central), Class 5 contains the largest inner variability and serves as the transitional class connecting the extratropical cyclone nodes (bottom-right) to the subtropical ridge dominated nodes (bottom-left), and errors could be aroused by including multiple synoptic patterns in one class.

3.3 EVALUATION OF NSSL-WRF SIMULATION USING STANDARD PERFORMANCE

INDICES

To quantitatively evaluate the simulations, each region's 2-D 24-hour accumulated precipitation field are examined through a series of standard performance indices, including

Correlation Coefficient (CC), Normalized Standard Deviation (NSTD), Agreement Index (AI), and ratio between simulation and observation:

∑푁 (푆 −푆̅)(푊 −푊̅ ) 퐶퐶 = 푖=1 푖 푖 , (D1) 푁 ̅ 2 푁 ̅ 2 √∑푖=1(푆푖−푆) ∑푖=1(푊푖−푊)

1 푁 ̅ 2 √ ∑푖=1(푊푖−푊) 푁푆푇퐷 = 푁 , (D2) 1 √ ∑푁 (푆 −푆̅)2 푁 푖=1 푖

푁 2 ∑푖=1(푆푖−푊푖) 퐴퐼 = 1 − 푁 ̅ ̅ 2, (D3) ∑푖=1(|푆푖−푆|+|푊푖−푆|)

푁 ∑푖=1 푊푖 푅푎푡𝑖표 = 푁 , (D4) ∑푖=1 푆푖 where Wi and Si represent the simulated and observed rainfall over each grid-point, and a perfect simulation would be one in the above variables. The mean values of these indices separated by

SOM classes over the SGP and NGP regions are shown in Table D. 4. To facilitate comparisons, these statistical results are illustrated in Taylor diagrams in Figure D. 9, where the CC and AI are shown as the rotation angle from the vertical axis, and NSTD and ratio are shown as the distance

220 from the coordinate origin for the SGP (Figure 9a and 9b) and the NGP (Figures. D. 9c and D. 9d).

By comparing the SGP Classes 1-3 (southwesterly flow aloft), the best performance (highest

CC and AI) is found for SR dominant Class 1, which corresponds to the largest positive bias

(highest ratio) and spatial variation (highest NSTD). Meanwhile, Class 3 (CR with upscale growth) has the worst performance due to missing nocturnal convection, while Class 2 falls between these two classes. These results are expected because both the CC and AI scores emphasize the collocation between simulations and observations. Since Class 1 has the largest all/SR coverage

(Figure D. 4, Table D. 2), collocation is reached more easily. Similar conclusions can also be drawn from the Classes 4-6 in the SGP SOM (northwesterly to zonal flow at 500 hPa), where the

CC and AI scores range from the highest in Class 4 to lowest in Class 5. In general, the averaged ratio from six classes over the SGP region is 1.065, suggesting that the NSSL-WRF simulated precipitation is comparable to the Stage IV observation. In the NGP (Figures. D. 9c and D. 9d), the best performance is also found for SR dominated regimes (Classes 3 and 6). There are positive biases for all six classes with an average ratio of 1.23, which is 15.5% greater than the SGP average.

In addition to the performance contrast regarding the dominant precipitation type, another interesting finding from Figure D. 9 is that the extratropical cyclone impacted classes (SGP: 1, 2,

3; NGP: 1, 2, 3, and 6) always outperform their counterpart classes (SGP: 4, 5, 6; NGP: 4 and 5) under the influence of subtropical ridge for both regions. Through the synthesis of all cases within different synoptic schemes (extratropical cycle vs. subtropical ridge), the former has higher CC and AI values than the latter (SGP: 0.266/0.486 vs. 0.209/0.458; NGP: 0.258/0.479 vs.

0.226/0.445). Moreover, the Kolmogorov–Smirnov (K-S) test results (Kolmogorov A., 1933) is also performed between the two samples over the SGP and NGP respectively. By comparing the

Cumulative Distribution Functions (CDFs) of two samples with the null hypothesis that the two

221 samples are drawn from the same distribution, both CC and AI can pass the test with significant level of 0.05, indicating the better performance of the upper classes is truly significant for both regions.

Figure D. 9. Taylor diagrams for normalized standard deviation vs. correlation (a, c) and ratio vs. agreement index (b, d) for each class in the SGP (a, c) and the NGP (b, d).

222

Table D. 4. The performance indices of NSSL WRF simulation for each class over both the SGP and the NGP.

Indices Class 1 Class 2 Class 3 Class 4 Class 5 Class 6 CC 0.294 0.259 0.249 0.249 0.176 0.224 NSTD 1.180 1.052 0.769 1.057 0.961 1.059 SGP AI 0.496 0.488 0.473 0.473 0.441 0.470 Ratio 1.296 1.153 0.776 1.069 0.914 1.187 CC 0.273 0.201 0.334 0.164 0.198 0.352 NSTD 1.079 1.153 1.217 1.047 1.341 1.248 NGP AI 0.485 0.451 0.518 0.399 0.426 0.533 Ratio 1.042 1.178 1.347 1.063 1.355 1.398

4. SUMMARY AND DISCUSSIONS

In Part I of this study, atmospheric states were classified using SOMs for warm season precipitation events over the SGP and NGP from 2007 to 2014. This work has demonstrated that precipitation biases within the NSSL-WRF simulations are dependent on the synoptic patterns and different regions (SGP vs. NGP). In Part II, the detailed characteristics of these events are evaluated between this model and NCEP Stage IV precipitation observations for each SOM class over both the SGP and NGP regions.

Following the SOM classes generated in Part I, precipitation events over both the SGP and

NGP regions were examined from two perspectives: the primary precipitation type (CR vs. SR) and the dominant synoptic pattern (extratropical cyclone vs. subtropical ridge). From Stage IV observations, distinct characteristics are found regarding the diurnal cycle and precipitation intensity/coverage. Some of those features can be well simulated by NSSL-WRF, while others have more significant disagreements. These results can be briefly summarized as follows.

1) For the SGP, of the six SOM classes, four classes with more convective activity have lower

daytime but higher nocturnal precipitation amount. Moreover, the largest day/night contrast is

found in Classes 3 and 5, indicating notable upscale growth in the night. These results provide

223

a strong support to the well-documented GP nocturnal maximum precipitation diurnal pattern.

However, this conclusion only works for the classes with more convection, and is not valid for

the events by SR dominated Classes (1 and 4, taking up 30% of all heavy precipitation events).

The averaged CR and SR intensities from all six classes are 10.54 and 1.11 mm hr-1, and their

averaged coverages are 3.35% and 12.50% of the study domain, respectively. Therefore, we

conclude that the CR intensity is an order magnitude higher than the SR one, but the SR

coverage is four times as large as for CR.

2) For the NGP, half of the classes have the typical GP diurnal pattern with nocturnal precipitation

maxima while other half have less diurnal variability with peaks occurring around 1800 LT.

In combination with the conclusion drawn for the SGP, the correct simulations of the nocturnal

maximum precipitation remains a challenge in NSSL-WRF. From the perspective of regional

difference, based on the results listed in Tables 1-3, we conclude that the Stage IV observed

daily accumulated precipitation, and total, CR, and SR precipitation intensities at the SGP are

much greater than those at the NGP.

3) Comparing the NSSL-WRF simulations with Stage IV observations from the perspective of

diurnal cycle, both regions’ SR dominated classes are well simulated by NSSL-WRF, while

classes with nocturnal upscale growth correspond to the largest negative at night. This along

prior studies that NSSL-WRF ends convection too soon. Transitional classes connecting SR

to CR dominated cases match the observations in overall magnitude, but instead of missing

nocturnal convection, simulated precipitation peaks too early, causing a daytime positive bias

and nocturnal negative bias. From the comparison of precipitation intensity/coverage

regarding the separation of CR vs. SR, we found that the simulated CR intensity and coverage

have good agreement with the observations for both regions, but NSSL-WRF simulates weaker

224

SR precipitation intensity but larger coverage.

4) To quantitatively evaluate the NSSL-WRF simulations, four standard performance indices:

Correlation Coefficient (CC), Normalized Standard Deviation (NSTD), Agreement Index (AI),

and Ratio between simulation and observation, are used in this study. In general, the averaged

ratio from six classes over the SGP region is 1.065, suggesting that the NSSL-WRF simulated

precipitation is comparable to the Stage IV observation. Whereas positive biases exist for all

six classes with an average ratio of 1.23 over the NGP region, indicating that there is an overall

oversimulation over the NGP region. Through the synthesis of all cases within different

synoptic schemes (extratropical cycle vs. subtropical ridge), the former has higher CC and AI

values than the latter (SGP: 0.266/0.486 vs. 0.209/0.458; NGP: 0.258/0.479 vs. 0.226/0.445).

This result further proves the finding from this study: the extratropical cyclone impacted

classes always outperform their counterpart classes under the influence of subtropical ridge for

both regions.

Based on the 8-years of simulations, NSSL-WRF demonstrates notable differences in simulating precipitation with different CR/SR proportion, as well as under different dominant synoptic patterns. The persistent better performance is strongly associated with the SR dominated cases, whereas the missing nocturnal precipitation remains the major issue for the simulation of convection with nocturnal upscale growth. Additionally, it is surprising that the CR intensity/coverage is well simulated for each SOM class over both regions, while the enlarged SR coverage and weakened intensity is more problematic. By comparing the influence of different synoptic patterns, cases impacted by the extratropical cyclone always have higher performance scores than those under the influence of subtropical ridge, indicating more emphasis should be placed on the improvement of precipitation simulation influenced by the subtropical ridge.

225

ACKNOWLEDGEMENTS

The 4-km gridded Stage IV data were downloaded from National Center for Atmospheric Research

(NCAR)/University Corporation for Atmospheric Research (UCAR) Earth Observing Laboratory

(EOL) using the link http://data.eol.ucar.edu/dataset/21.093 accessed on 20 November 2016. This research was supported by the NOAA R2O project with award NA15NWS468004 at the

University of North Dakota and subcontracted to the University of Arizona. The statistical data generated by this study can be obtained from Dr. Xiquan Dong ([email protected]).

226

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