Research Collection
Doctoral Thesis
Performance and error diagnosis of global and regional NWP models
Author(s): Didone, Marco
Publication Date: 2006
Permanent Link: https://doi.org/10.3929/ethz-a-005294422
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ETH Library Diss. ETH No. 1C597
Performance and Error Diagnosis of Global and Regional NWP Models
A dissertation submitted to the
Swiss Federal Institute of Technology (ETH) Zürich
For the degree of
Doctor of Sciences
Presented by
Marco Didone Dipl. Phys. ETH born 18 May, 1977 citizen of Carabbia TI, Switzerland
Accepted on the recommendation of
Prof. Dr. Huw C. Davies, ETH Zürich, examiner Prof. Dr. Dino Zardi, University of Trento, co-examiner Dr. Daniel Lüthi, ETH Zürich, co-examiner
April 2006 Lontano lontano
come un cieco m'hanno portato per mano
Uiigaretti, 1917 Contents
Abstract viii
Riassunto x
1 Theorie, Models and Data 1
1.1 Theoretical Aspects 1
1.1.1 Basic Notions 1
1.1.2 Thermal Wind 2
1.1.3 Potential Vorticity 2
1.1.4 Properties of PV 4
1.1.5 Isentropic PV 5
1.1.6 Vertically Integrated PV 5
1.2 The 'Lokal Modell' G
1.3 Other Numerical Models 9
1.3.1 ECMWF Model and Data Set 9
1.3.2 The 'Climate High Resolution Model' 10
1.4 Lagrangian Trajectories 10
1 Errors of Large Scale Models 12
2 Case Study: ECMWF Model Errors 13
iii iv Contents
2.1 Introduction 13
2.2 The approach 14
2.3 Pacific Case Study 15
2.4 North Atlantic Case Study 17
2.5 Rationale 18
3 Nature of the 'Forecast - Analysis' Difference Fields 19
3.1 The Potential Vorticity Perspective 19
3.2 Prevalent Features of Error Fields 20
3.3 Time Evolution of the Forecast Errors 21
3.4 F-A Dynamics 26
3.5 High Resolution Simulations in the Pacific 27
3.6 Summary and Conclusion 28
4 Backtrajectories 31
4.1 Approach 31
4.2 Pacific Case 33
4.3 Atlantic Case 36
4.4 Summary and Conclusions 38
5 Idealized Simulations 41
5.1 Introduction to Countour Dynamics 41
5.2 Strong Negative Vorticity 46
5.3 Weak Negative Vorticity 47
5.4 Summary and Conclusions 49
6 Error Climatology 51
6.1 The approach 51
6.2 A Seasonal Climatology 52 Contents v
6.2.1 The Tiaditional View 52
6.2.2 The PV Perspective 54
6.3 The Nine Months Climatology 56
6.4 Evolution of PV Error Growth 58
II Studies with a Regional Model 59
7 Introductory Remarks and Case Description 61
7.1 Introduction 61
7.2 MAP IOP 8 64
7.3 MAP IOP 15 65
7.4 ECMWF Forecast 66
7.5 The Analysis Dataset 67
8 Horizontal vs. Vertical Resolution 69
8.1 Horizontal Resolution 69
8.2 Setting the Vertical Levels 70
8.3 Results - Comments 71
9 Error in Precipitation Field 73
9.1 IOP-15 74
9.2 IOP-8 75
9.3 Conclusions 78
10 Domain Study 81
10.1 Intioduction and Procedure 81
10.2 IOP-15 Case 82
10.3 IOP-8 Case 84
10.4 Conclusions 85 vi Contents
11 The Storm Lothar 87
11.1 Aim and Approach 88
11.2 Sensitivity to the Initial Conditions 89
11.3 A3 Dimensional PV Perspective 92
11.4 Conclusions 94
A Appendix to Chapter 5 97
B Appendix to Chapter 6 101
Bibliography 103
Acknowledgements 109
Curriculum Vitae 111 Seite Leer / Blank leaf
i Abstract
The new generation of supercomputers developed in the last years allow more and more sophisticated global and regional weather forecast models. Nonetheless deficiencies in modeling the atmosphere behavior will always be present due to its strong unpredictability. Thus, fundamental numerical modeling tasks include (i) the calibration of a model configuration to maximize the simulations quality and (ii) the investigation of systematic errors that lead to constant biases in the forecasts. These two aspects are considered in this thesis, where the latter is
explored within a global numerical weather prediction suite, and the former on a
regional scale at very high resolution.
The first part of the thesis is devoted to the analysis of forecast 'errors' of the ECMWF model (defined as the differences between forecast and analysis). Var¬ ious statistical methods have been applied in studies on systematic model er¬
rors, where the main interest was to quantify the deviation on classical fields as geopotential and temperature. Here the PV perspective is adopted, as intrinsic properties of this perpective have direct implications for the study of forecast error fields. Moreover the dynamics of rapid error growth is linked to distinctive PV features. Two cases have been selected for the analysis of the forecasts de¬ viations, one occurring in the Atlantic and the other one in the Pacific ocean. Single model runs as well as the time evolution of the forecasts are taken into account to identify the features characterising these fields and their dynamics. Back trajectories are calculated to detect differences in the flow advection gener¬ ated by the model and the analysis. Hints of an undorstimation in the analysis
of the negative PV regions along the southern flank of the jet that may enhance and even trigger the 'errors' are identified. Idealized simulations are generated with a contour-dynamics based model. They show the behavior of a positive vorticity region patially surrounded by a negative vorticity line. Strong similari¬ ties with the 'forecast minus analysis' fields are highlighted. Finally, to obtain a geographical distribution of the systematical deficiencies of the forecasts and to identify regions where the observation and/or data assimilations may have to be improved, a climatology of the 'errors' is produced.
The aim of the second part of the dissertation is to investigate the potential benefits and the problems involved with the increase in resolution of a regional high resolution model. Particular attention is devoted to the precipitation field, a key mesoscale phenomenon when forecasting extreme weather events. The Spe¬ cial Observing Period (SOP) of the Mesoscale Alpine Programme (MAP) that has taken place in autumn 1999 had among the scientific objectives to improve understanding of orographic precipitation, gap flows and foehn, providing also a Abstract ix
useful database for validating numerical models. For this occasion the ECMWF produced in addition to the operational analysis, a second dataset assimilating extra observations to be used as initial and boundary conditions: This opportu¬
nity is used here and two cases are selected among the MAP as case studies for the verification. The model adopted in this part is the 'Lokal Modell' developed by COSMO. Dif¬ ferent set-ups are tested, with particular interest in the horizontal and vertical resolution. Two distinct configurations are then identified: one for the coarse simulation, where the convection in parametrised, and the second for the nested convection resolving simulations, and are adopted for the sequent investigations.
A first application is to compare the observed data of the MAP database to the 24hrs precipitation accumulation over the Alpine Area of the coarse and of the high resolution simulations, using operational analysis and reanalysis as ini¬ tial and boundary conditions. The observed differences in the flow advection that lead to disagreement in precipitation amounts between model and analysis trigger the next study, where the influence of the domain size of the coarser sim¬ ulation on the large scale flow of the nested integration is examined on different fields. In the last application in the framework of high resolution modeling three hindcast simulations of the storm Lothar initialized at different times are con¬ ducted to evidence the extreme importance of the initial and lateral data time resolution in case of explosive cyclogenesis. The integration is performed only at 7km resolution due to the exceptional phase velocity of the storm. Moreover a dry simulation is also carried out to highlight (i) the fundamental contribution of diabatic processes to the explosive evolution of the storm and (ii) the difficulties of the model to simulate a violent condensation rate and therefore PV production to keep up with the observed intensification. Riassunto
Lo sviluppo dei modelli numerici a scala globale e regionale, dovuto alia nuova generazione di supercomputers costruiti negli ultimi anni, permette previsioni del tempo sempre pin particolareggiate e a lungo termine. Nonstante cid inesattezze e imprecisioni riscontrate cercando di modellare il comportamento deh"atmosfera
sono e saranno sempre presenti. Per questo motivo tra i compiti fondamentali di chi lavora nel campo dei modelli meteorologici si distinguono sprattutto (i) quello di configurare il modello numerico in modo da massimizzare la qualità della previsione e (ii) analizzare gli errori sistematici che portano ad una costante polarizzazione dei risultati. Nel corso di quest a, tesi sono affrontati entrambi gli aspetti: il primo su scala regionale ad alt a risoluzione, il secondo nell'ambito di una previsione numerica globale.
La prima parte della dissertazione è dedicata aH'analisi degli 'errori' di pre¬ visione (definiti corne la differenza tra modello ed analisi) del modello IFS del centro meteorologico europeo ECMWF. Vari metodi statistici sono stati appli- cati, in diversi studi, agli errori sistematici, cercando di quantificare la differenza di previsione attraverso grandezze classiche quali il geopotenziale e la temper- atura. In questo studio è adottata invece la prospettiva della vorticita Potenziale (PV) in quanto alcune sue propriété intrinsiche sono direttamente implicate nello studio degli 'errori' di previsione. Questa prospettiva evidenzia inoltre partico- lari caratteristiche collegate alla teoria degli errori ('rapid error growth'). Pr l'analisi di queste grandezze sono stati selezionati due casi avvenuti nell'oceano
Atlantico e rispettivamente nel Pacifico. Sono presi in considerazione sia sin- gole simulazioni ehe evoluzioni temporali delle previsioni per poi identificarc le caratteristiche principali delle differenze e le dinamiche coinvolte. Per individ- uare differenze di avvezione delle masse d'aria tra l'analisi e quelle generate dal modello, sono inoltre calculate delle traietturie dalle quali si possono intravvedere segnali riguardo una sottostima della magnitudine delle region! a PV negativa sit¬ uate lungo il lato sud delle correnti 'jet' che potrebbero provocare o anche solo amplificare gli 'errori'. Alcune simulazioni idealizzate generate con un modello basato sulla dinamica dei contorni mustranu il comportamento di una regione a vorticita positiva in funzione della magnitudine della striscia a vorticita negativa che la circonda parzialmente ed evidenziano forti somiglianze con le differenze tra analisi e modello dal punto di vista della vorticita Potenziale. Iiifine per avere indicazioni sulla distribuzione geografica di queste sistematiche differenze di pre- visione e per localizzare regioni dove le osservazione e/o l'assimilazione dei dati deve essere migliorata, e' proposta una climatologia degli 'errori'. Riassunto xi
Lo scopo della seconda parte della dissertazione è di indagaie tra i benefici ed
i problemi che si pongono con l'aiimento della risoluzione in un modello regionale ad alta definizione. Particolare attenzione e' inoltre data alle piecipitazioni, un
fenomeno chiave nella previsione a mesoscala di eventi meteorologici estremi. II periodo di osseivazione SOP (Special Observing Period) del piogiamma MAP (Mesoscale Alpine Program) effettuato nel 1999 aveva tia i vari obbiettivi scien- tifici quello di migliorare le conoscenze riguardanti le precipitazioni orografiche, il folm e i Aussi di compensazione (gap flows), fornendo al tempo stesso un database per testare modelli numerici. Per questa occasione l'ECMWF ha prodotto oltre
alle analisi per le simulazioni operazionali, una seconda série di dati compien- dent e osservazioni in phi, da utilizzare corne valoii iniziali e al contorno: i due
casi selezionati per la veiifica piovengono di conseguenza da questo piogiamma. Il modello adottato in questa seconda parte è il 'Lokal Modell', sviluppato dal
'COSMO', del quale sono stati testati difterenti set-ups con particolaie intéresse nella risoluzione verticale e orizzontale. Sono scelte due eonfigurazionr una per le riceiche ad una scala di 7km (dove la convezione è parametrizzata) e lispet- tivamentc una per quelle 'nested', ad alta risoluzione (2km) dove la convezione è risolta esplicitamente. In una prima applicazione si paragonano le osservazioni raccolte dînante il MAP con le piecipitazioni giornaliere previste dal modello sulla regione alpina, generate utilizzando sia le analisi che le rianalisi come valori iniziali e al contorno Le differenze osservate nell'avvezione delle masse d'aria, che portano ad un disaccordo nelle quantità di precipitazioni osservate e prodotte dal modello portano ad un altro studio, dove vengono esaminate le correnti a larga scala nel modello ad alta lisoluzione al variare della grandezza del dominio delle simulazioni a lisoluzione bassa (7km). NeU'ultimo capitolo vengono analizzate 3 simulazioni del ciclone 'Lothar' inizializzate cou 6 ore di scarto con lo scopo di evidenziaie l'estiema impoitanza della risoluzione temporale dei dati iniziali e al contorno in caso di una ciclogencsi esplosiva. Le siinula/ioni sono integrate solo a 7km di lisoluzione a causa dell'ectezionale velocità con la quale il ciclone ha attraversato il Centroeuropa. È inoltre effettuata una simulazione senza processi di condensa/ione con lo scopo di mettere in evidenza (i) il contiibuto fondamen¬ tale dei processi diabatici neU'evoluzione esplosiva del ciclone e (ii) le difficoltà del modello nel simulaie una condeiisazione tanto violenta da niant encre il passo deU'intensificazione osservata durante questo evento. Chapter 1
Theorie, Models and Data
1.1 Theoretical Aspects
1.1.1 Basic Notions
A set of three equations (the so-called primitive, equations) is used to describe the complexity of the dynamics of the atmospheric flow:
— + 2ÜAu=—Vp-V^ + F (1.1) Dt p |? + V •(,«)= 0 (1.2) ^=« (1-3) Dt
where is the time derivative an air u is the three-dimensional jyt following parcel, wind speed, Vt the angular speed of the Earth's rotation, p the mass density, p the pressure, <3? the geopotential gz, 0 the potential temperature, F the non- conservative friction term and 6 the diabatic source. This set of equations com¬ prises the momentum (1.1), continuity (1.2) and thermodynamic (1.3) equations. Note that most of the systems of equations ruling the motions of the atmosphere (i.e. geostrophic or quasi-geostrophic systems) can be derived from the set of primitive equations through suitable assumptions and scale analysis (e.g. Davies 1999).
1 2 Chapter 1. Theorie, Models and Data
1.1.2 Thermal Wind
The thermal wind relation is obtained by combining the geostrophic wind relation with the hydrostatic equation (Bluestein 1992, Section 4.1.6):
where R is the gas constant, / the Coriolis parameter 2Q,sirn/) (where (/) is lat¬ itude), and T and p the temperature and pressure, respectively. This relation describes the link between the vertical shear of the horizontal geostrophic wind and the horizontal temperature gradient. It yields, for instance, for the zonal component of the geostrophic wind:
{l-°} dp -fp\dy)P> i.e. a poleward decrease of temperature is linked with an increase with height of the westerly geostrophic wind component.
1.1.3 Potential Vorticity
The Ertel potential vorticity (PV hereafter) is defined as (Ertel 1942):
PV = -ff-$9, (1.6) P where p, fj and 6 are the density, the absolute vorticity and the potential temper¬ ature, respectively. Using the hydrostatic approximation, and casting in pressure coordinates on a spherical earth,(fig 1.6) after scale analysis becomes:
PVn-Qtt + f)^ (1.7) where £ is the vertical component of the relative vorticity and / the Coriolis parameter. To avoid the cumbersome units of PV, a terminology for PV units (pvu hereafter)1 is used. The relations 1.6 and 1.7 indicate that PV combines a kinematic field (absolute vorticity) with a thermodynamic one (static stability). Due to the high stability of stratospheric air, climatolgical distributions of PV (Fig. 1.1) exhibit high values in the stratosphere (values larger than 2 pvu) and lower values in the troposphere (typically smaller than 1 pvu). Moreover, the /^-effect also tends to distribute higher PV air in the polar regions and lower PV
11 pvu is defined as 10 6m2s :K kg ]. 1.1. Theoretical Aspects 3
9 0» tor 30*1 0 J05 G03 y>S
Figure 1.1: Mean January (averaged in the 1979-1989 period) vertical cross section of the zonal mean of Ertel's potential vorticity in pvu (clashed lines) and potential temperature in K (solid lines). The bold solid lines depict the dynamic tropopausc
(defined as 2 pvu in the Northern Hemisphere and -2 pvu in the Southern Hemisphere) and the dark grey shaded region depicts the stratosphere. Adapted from ßluestein (1993).
air in the subtropics. The dynamic tropopausc (DT) separating these two regions is collocated with a zone of enhanced PV gradient on isentropic surfaces. The 2-pvu surface is quite often used to define the DT (Hoskins et al. 1985). In the last 20 years, a large interest in the use of PV in the field of atmospheric dynamics was triggered by the combination of the paper by Hoskins et al. (1985) and the availability of large meteorlogical data sets. Moreover, the PV-Ö frame¬ work (lioskins 1991) has proved to be a powerful diagnostic tool, as the study of synoptic and global systems has been linked to the evolution and interaction of identified PV 'anomalies' (individual regions of anomalously low or high PV air compared to their surroundings)2. The attractiveness of the PV perspective lies in three aspects developed by Hoskins et al. (1985) and these are briefly reviewed below.
2The use of PV by weather forecasters may also be expected to increase in the coming years. 4 Chapter 1. Theorie, Models and Data
1.1.4 Properties of PV
Conservation
The potential vorticity of an air parcel is conserved, provided its motion is adia¬ batic and frictionless' ^fPV = 0. (1.8)
In this case, PV can be regarded as a passive tracer that can facilitate the study of complex flow configuiations. The adiabatic and frictionless assumption may prove to be a good approximation at upper-levels but is harder to justify at lowei- levels, where PV can be created or destroyed by diabatic sources and frictional forces:
jï-PV = -grjVà~gVd-(VAF). (1.9)
The first term on the right-hand-side of Eq 1 9 states that a positive (negative) material PV tendency will be induced below (above) a mid-tropospheric diabatic heating release region (Haynes and Mclntyre 1987). Furthermore, the symmetry of the distribution of the diabatically induced PV anomalies depends also on the time-scales of the condensation piocesses and advection of the air parcels (e.g. Fig 4 in Wernh and Davies 1997). The diabatic production of positive PV anomalies plays a major lole in the formation of PV towers (Rossa et al. 2000) that are in turn relevant foi the matiiie stage of extiatropical cyclones
Invertibility Principle
The invertibility principle (as suggested by Kleinschmidt 1950) states that the flow structure can be deduced from the PV distribution in the interior domain with appropriate boundary conditions and the specification of a reference state and of a balance condition:
az
(»,»;, Ö) = VW, where \I/ is the streamfunction. Mathematically, this pioblem consists in inverting a Laplacian operator and is analogous to electrostatics (Hoskins et al. 1985; Thorpe and Bishop 1995). 1.1. Theoretical Aspects 5
The Partition Principle
The whole PV distribution can be 'decomposed' into individual PV anomalies. The individual contribution of each anomaly to the flow field can then be infeiied by inverting each separately (the so-called piecewise PV inversion, e g. Davis and Emanuel 1991 and Davis 1992), provided that a suitable linearized balance condi¬ tion is used. Many studies have confirmed the utility of the piecewise PV inversion for atmospheric flow phenomena such as cyclogenesis (Davis and Emanuel 1991, Hakim et al. 1995, Stoelinga 1996), hurricanes steeling flows (determined by removing their intrinsic circulation, e.g. Henderson et al 1999, Koch 1999) or the sensitivity of Alpine1 rainstorms to mesoscale upper-level structure (Fehlmaim et al. 2000).
1.1.5 Isentropic PV
The use of this device relies upon the two physical principles introduced in the pievious section: the invertibility concept and the Lagrangian conservation of po¬ tential vorticity under adiabatic, frictionless and hydrostatic conditions When advective flow prucesses dominates frictional and diabatic ones, the conserva¬ tion principle also holds for potential temperature so that PV is simply advected on isentropic surfaces by the quasi-horizontal two-dimensional wind field. As a iesult, maps displying isentropic PV distribution facilitate the location of strato¬ spheric intrusion and hence of the most dynamically active and determinant le¬ gions of the atmosphere. They are as such succesful diagnostic analysis tool for the atmospheric dynamic behaviour.
1.1.6 Vertically Integrated PV
Whereas the isentropic PV distributions yield infoi mations upon the stiuctuie of the PV anomalies at one particular isentropic level, knowledge of the anomaly thiee-dimensional structure requires the consideration of several isentropic levels.
Practically however the concomitant inspection of several isentropic PV maps is cumbersome and fails to provide a quantitative picture of the three-dimensional anomaly intensity. Here we compute fields of the vertically integrated PV for the 400-200 hPa layei (cf. Shapiro and Grell 1994). This field constitutes a compact measure of the scale, intensity and structure of any stratospheric intrusion (PV-streamer, cut-off); its horizontal distribution (hereafter referred to as VIP) yields a two- dimensional portrayal of the three-dimensional that can serve, in conjunction with the display of other variables, as an indicator of the possible influence of the 6 Chapter 1. Theorie, Models and Data
upper-level feature upon the low-level dynamics of weather systems. The layer of integiation is defined in terms of pressure (400-200 h Pa) rather than potential temperature (300-340 K) to ensure the stratospheric origin of PV.
1.2 The 'Lokal Modell'
The LM is a limited-area model designed for numerical weather prediction on the mcso-/:? and meso-7 «cale as well as for different scientific applications. It can be operated on grid spacings from 50km down to about 50m. Besides the model itself, a number of additional components such as data assimilation, interpolation on boundary conditions from a driving host model and postprocessing is required to run a NWP system. This section piovides only a brief overview of the LM model (Steppeler et al. 2003). For a comprehensive description the reader is referred to the documentation of the LM package found on the COSMO website (http.//cosmo-inodel.cscs.ch/).
Dynamics and Numerics
The LM model is a non-hydrostatic moist and fully compressible high resolu¬ tion model, based on the primitive hydro-thermodyiiamical equations. The basic equations are written in advection form and the continuity equation is replaced by a prognostic equation for the pressure perturbation from the reference state. The coordinate system is a rotated lat/lon grid with coordinates (A, 0). The rota¬ tion of the system results hoin the tilting of the north pole. In the vertical a gen¬ eralized terrain-following height ( coordinate is used, constant in time. Therefore the system (A, 0, () represent a non-deformable coordinate system where constant
Ç surfaces are fixed in space, which is not the case for pressure based coordinate systems. The finite difference method is used to numerically solve the model equations. The lesult is that spacial differential operators are replaced by finite difference opeiatois, whereas the time integration by a fixed timestep Ax. The variables are staggered on a Arakawa-C/Lorenz grid for a better representation of some differential operators, scalar variables as temperature, pressure and humidity are defined at the center 011 a grid-box whereas velocity components on the box-faces.
Initial and Boundary Conditions
The LM model is driven per default by the global model GME of the DWD. Op¬ tionally, initial and boundary data from the IFS model at ECMWF can be also 1.2. The 'Lokal Modell' 7
Model Equations: Basic hydro-thermodynamical equations for the atmo¬ sphere:
- advcction form
- non-hydrostatic;, fully compressible, no scale approx¬ imation
- subtraction of horizontally homogeneous basic state at rest.
Prognostic Variables: Horizontal and vertical Cartesian wind components, tem¬
perature, pressure perturbation, specific humidity, cloud water content. Optional additional prognostic variables: TKE, cloud-ice, rain, snow and graupcl content.
Diagnostic Variables: Total air density, precipitation fluxes of rain and snow.
Coordinate System: Rotated geographical (lon/lat) coordinate system horizon¬ tally; generalized terrain-following height-coordinate verti¬ cally. Built-in options for the vertical coordinate arc:
- Hybrid reference pressure based cr-type coordinate
- Hybrid version of the Gal-Chen coordinate
- Hybrid version of the SLEVE coordinate
Grid Structure: Arakawa C-grid. Lorenz vertical grid staggering.
Spatial Discretiz.: Second order horizontal and vertical differencing.
Time Integration: Leapfrog (horizontally explicit, vertically implicit) time- split integration scheme by default: includes extensions proposed by Skamarock and Klemp (1992). Additional op¬ tions for:
- a two time-level split-explicit scheme (2nd order Rungc-Kutta scheme )
- a three time-level 3-d semi-implicit scheme
- a two time-level 3rd-ordcr Runge-Kutta scheme with various options for high-order spatial discretization.
Numerical Smooth. 4th order linear horizontal diffusion with option for a mono- tomic version including orographich limiter; Rayleigh-
damping in upper layers; 3-d divergence damping and off- centering in split steps.
Lateral Boundaries: 1-way nesting using the lateral boundary formulation ac¬ cording to Davies (1976). Options for:
- boundary data defined on lateral frames only
- periodic boundary conditions
Table 1.1: LM Model formulation: Dynamics and Numerics, taken from the LM Doc¬ umentation. 8 Chapter 1. Theorie, Models and Data
used. The lateral boundary conditions are treated by the Davies (197G) relax¬ ation tecnique, where the internal model solution is nudged against an externally specified solution within a narrow boundary zone by adding a relaxation forcing term to the equation.
For research applications the LM can also handle idealized cases using user- defined artificial initial and boundary condition data as periodic lateral bound¬ aries. In this dissertation the driving model is always the IFS model.
Physical Parametrization
The physics package of the LM model has been adapted from the former EM
(European Model) of the DWD. Since its birth a number of new optional schemes has been developed and implemented, as the prognostic treatment of rain and snow, the inclusion of graupel in the prognostic variables, a new scheme for vertical diffusion based on prognostic turbulent kinetic energy, a new surface scheme, a new multi-layer soil model including freezing of soil water and different moist convection schemes. Due to the continuous implementation of new schemes since the beginning of this thesis, a deadline was fixed for the update of the model version. The results proposed in this thesis take into account of all physics implementations up to LM Version v2.15. In addition the following facets were also tested.
External Parameters
As external parameters are joined all the data that cannot be derived from ini¬ tial and boundary conditions but are required by the parametrization and the adiabatic parts of the model, as topography, roughness length, soil type and many physiological data. For the simulations produced for this thesis, topogra¬ phy data have been geneiated from GTOPO30 Data (30" resolution) and filtered once with a Gauss-filter to avoid numerical problems on steep orography, whereas physiological data have been produced by the ISLSCP3 (1° resolution).
Data Assimilation
Since the synoptic scales are determined by the lateral boundary conditions of the driving model, the purpose of the data assimilation is to analyse the meso¬ scale features and to satisfy the needs of the operational LM, determined by
3The International Satellite Land-Suiiaco Climatology Project 1.3. Other Numerical Models 9
the high resolution and nowcasting purposes. Instead of the 4-diniensioiial vaii- ational (4DVAR) method, which offers potential advantages as the inclusion of
model dynamics in the assimilation process directly but is veiy expensive for an operational run. For the LM A scheme based on the observation nudging has been developed to define the atmospheric fields. It is based on a experimental nudging analysis developed previously and adapted to the nonychostatic mod¬ elling framework of the LM. This scheme runs on distributed memory machines using domain decomposition. Theiefoie the observational informations of the total domain is previously distributed to the sub-domains and then the analysis in computed at every grid-point of the subdomain.
1.3 Other Numerical Models
1.3.1 ECMWF Model and Data Set
The data for the analysis fields of the case studies are taken from the 6hrs op¬ erational analysis cycle running in Reading by the European Center for Medium Range Weathei Forecast (ECMWF). The numerical model for the analysis con¬ tinuously undergoes changes in the horizontal and vertical resolution as computer power increases. The analysis fields are calculated globally and incorporate past analysis fields, conventional surface and upper soundings as well as satellite-based informations.
The numerical model used for the case study is version T511L60. It is a hydro¬ static primitive equation spectral model (for a thorough model description see Simmons (1991)) with spherical functions up to the 511th order. This data is interpolated on a grid with a horizontal resolution of 0.5°, corresponding to an horizontal resolution of approximatevely 60 km in mid latitudes. The vertical res¬ olution is specified as 60 levels. They are hybrid levels that follow the topography in the boundary layer and lower troposphere and in the overlying atmosphere. The levels themselves are spaced logarithmically in the boundary layers, evenly in the lower troposphere and lower stratosphere and again logarithmically above the lower stratosphere up to the uppermost level of lOhPa, in an attempt to have high resolution in layers with stiong dynamic activity as the boundary layer or the tiopopause height. The ECMWF analysis data include as primary quantities specific humidity q, temperature T, vertical and horizontal wind fields («, (;, w) and surface pressure. Other quantities such as potential vorticity and potential temperature are derived from these. 10 Chapter 1. Theorie, Models and Data
1.3.2 The 'Climate High Resolution Model'
The numerical simulations conducted in Chapter 3 and by Wernli et al. (2002) are carried out on the Climate High Resolution Model (CHRM) that is based on the High Resolution Model (HRM) of the German Weather Service (DWD).
It is a numerical weather prediction model based upon the hydrostatic set of primitive equation, using a hybrid vertical coordinate system and operating on a rotated spherical Arakawa C-grid. Following a formulation by Davies (1976), the model variables aie lelaxed towards their initial state values. Foi the study in Chaptei 3 the model is run with 30 vertical levels, whereas in Wernli et al. (2002) the number is incieased to 40. The CHRM uses surface pressure, temperature, horizontal wind components, watei vapoi and cloud water as prognostic variables. The parameterised physi¬ cal processes include a surface-layer formulation, Kcsslei-type grid-scale micro- physics (Kessler 1969) and a mass flux convection scheme after Tiedtke (1989). Further details regarding the model set-up and the physical parameterisations as well as previous validation studies can be found in Majewski (1991) and Liithi et al. (1996)4.
1.4 Lagrangian Trajectories
The analysis of Lagrangian trajectories is presented in Chapter 4. In the La¬ grangian framework a physical vaiiable is obseived and characterized from a reference system moving with an elementary air volume in the atmospheric flow. The evolution of the physical properties of an air parcel can therefore be charac¬ terized along its trajectory in this fiamewoik. In Chaptei 4, the thermodynamic history of selected trajectories are calculated using the three-dimensional Lagrangian algoiithm, piesented in Wernli and Davies (1997) which follows a kinematic method introduced by Petterssen (1956). The required three-dimensional fields aie taken from the ECMWF analysis and Model data set Each trajectory step (t i—> t + At) is evaluated with the following iter¬ ative scheme:
n - rQ + Ata(fö,t)
= fo + + t + foi i > rt -y (u(r0, 0 ff(r,_i, At)), 2, where wis the three dimensional wind field and the f, aie the iteiative evaluations of the trajectory position at t + At, which are assumed to converge to the exact
4Sco also http://www.iac.ethz.ch/en/gioupfe/schaci/dimmod/dirm/maiii.html for a sum- maiy ot the chaiacteiistics of the CHRM 1.4. Lagrangian Trajectories 11
position f(t + At):
limf, = f(t + At).
Intergrid wind values are provided by linear interpolation of gridded values. Fol¬ lowing the recommendations of Seibert (1993), a time step of 30 minutes is adopted for the iterative process. Part I
Errors of Large Scale Models
12 Chapter 2
Case Study: ECMWF Model Errors
Nowadays global numerical weather prediction models operationally produce fore¬ casts up to 10 days. Their mean reliability has undergone notable year after year increase. However individual events can be and sometimes are, badly misfore- eastecl. One challenge is to interpret and account for these failures with a view to reducing the number of such events. Causes and effects of some such misforecasts will be examined in part I of this thesis.
2.1 Introduction
Performance verification of a model is itself a challenging task and various ap¬ proaches have been adopted, depending on the topic of most interest. Statistical analysis is the most common tool and provides information on the bias and vari¬ ance between model and analysis over a certain time-period. Again ensemble forecasts of a single event provides information on the spread between different runs, and estimates of the predictability of the atmosphere and the stability of the model under slightly different initial conditions. It therefore quantifies the reliability of the forecasts. In the case of a well performing model, probably the most pressing task is the study of misforecasted events and determine the cause of the model failure. Here the ECMWF model (version T511L60, operational until January 2006) has been selected for this examination. It is one of the best models in terms of fore¬ cast mean score. Moreover it is also the driving model for the operational high resolution simulations of LM at Meteoswiss (see part II), providing initial and boundary conditions for the forecast runs.
13 14 Chapter 2. Case Study: ECMWF Model Errors
To illustrate the nature and spatial structure of a misforecast we show heie one such example. The general features of a three day forecast foi October 10 2001 of the ECMWF model foi the noithein emisphere is shown in fig. 2.1. On the left side the foiecasted sea level pressure shows low pressure values towards the north pole (minimum of about 970hPa near Iceland) and ling of high piessure values around the globe at about 40° north (maximum of 1035 ovei noitheastern USA, the Japan sea and the Caspian area). This ring of high pressure is inter¬ rupted over or to the lee of major mountains ( Rockies, Hymalaya, ...) and related troughs are visible on the 500hPa field (to the light). Other notable structures are a cutoff (over Spain) and troughs (over central US and mid Atlantic).
The corresponding analysis for October 10 2001 is also shown in fig. 2 1 (black contour) for SLP and Z. Both seem well predicted in magnitude and geographical distribution. However a more careful look reveals some significant differences, in particular over the Pacific: A deep surface cyclone appeals over the central pa¬ cific in the analysis whereas on the forecast the SLP reaches a value only slightly smaller than lOOOhPa. The corresponding trough in the Z field is also deeper and wider in the analysis In the next sections these differences will be examined from diffeient peispectives and approaches (both Lagrangian and Eulerian). Two case studies (in the Pacific and in the Atlantic) aie selected foi the study.
2.2 The approach
Dataset
The dataset used for this study comes from the analysis and control forecast of the operational ECMWF prediction system. The diagnosis of the present study were performed by inteipolating analysis and ECMWF control forecasts (starting at 12UTC each day) on a l°-grid covering the Noithein Hemisphere, with a 6 hours time resolution. Moieovei foiecasts of 24, 48, 72 and 96 hours duration are consideied.
The Difference Fields
The verifications are based on the differences between the forecast and the ver¬ ifying analysis fields. However these aie refeired to as difference fields or for 2.3. Pacific Case Study 15
convenience as 'error' fields:
AS{x, t) = ShV{x, t) - SAN(x, t) (2.1)
where Spa and San denote respectively the forecasted and the observed value of a specific variable. To examine the features in the upper and the lower tropo¬ sphere, various variables for 8 have been considered:
• SLP
• ZmOOhPa
• PV@'i2QK, VIP (Vertical integration of PV)
• 0@85OA'
Considering not only one single level (PV@320K) but an average of over a vertical layer we lend weight to vertically coherent structures.
Credibility and Considerations
Notice that the definition of 'error' does not preclude deficiencies in the analysis and this complicates the analysis of the fields and their interpretation. Two exam¬ ples will be illustrated next, and later we adress the issue of their representativity by presenting a climatology of the errors (Chapter 6).
2.3 Pacific Case Study
The first case study selected develops over the Pacific and refers to October 2001, centered on the 10th of the month (same as fig. 2.1). During this period the ECMWF model exhibits weaknesses in predicting a series of deep cyclones that developed explosively in the northern Pacific. The large scale flow is an example of a strong and quasi-straight jet both in the model and in the analysis with embedded cyclones crossing the ocean within few days.
Plots of the difference on the 500hPa height (the difference is always obtained from the subtraction 'Forecast minus Analysis', fig. 2.2) show a very different and particular structure:
In the case of the geopotential the most significant errors are located along the jet with alternating positive and negative values and an amplitude between 100 and more than 200m. The positive errors (the heights simulated by the model are higher than the reality) are more frequent than negative, indicating that al¬ though the model predicts deep and fast moving troughs, it does not capture 10 Chapter 2. Case Study: ECMWF Model Errors
Fiqait i 1 Clobal 721ns foiecast foi the 10 10 2001 al 12 WVC ol th< FCMWF model
Sea level piessuie (SLP, left) and geopotential heiglit at 500hPa (Z right) shaded 1 lie black (ontoui is the analysis [oi th( 10 10 2001 plotted aie 1000 and IOlOliPa isobais foi SU' and r>2()(), r)l()(), 5600, 5800m isohnes foi Z
Fufuu J J 72his forecast minus analysis of SLP (coloui, left) and analysis (black coiitoms), wind at N50hPa ( vector max = 15m/s), geopotential at "jOOhPa (coloui, right) and analysis (black contour) for 10 10 2001 at 12UTC
Fhjuh i i %lns forecast minus analysis o[ SLP (coloui, left) and wind at
The errors illustrated above are an extreme example of how 'forecast minus analysis' field can look like and how decepting forecasts can be even on a relatively shoit time scale. The second case study will again illustrate the kind of error structures we aie inteiested on.
2.4 North Atlantic Case Study
Cases similar to the previous one occur also over the Atlantic ocean. For example consider the 'difference fields' between a 96his forecast and the analysis for in mid
January 2002. Again the large scale flow is dominated by a strong zonal jet from the central US to the UK (fig. 2.3, light). An alterning of stiong positive and negative 'differences' are visible along the jet, reaching values of more than 200m.
In this case positive and negative enois have the same magnitude and a structure similar to a dipole has developed over the northeastern US. The SLP plot tells us that this dipole error cannot be explained only with spatial shift of the cyclone: from a pressure point of view the structure is not symmetric, the positive part (30hPa) is much stronger that the negative (-16hPa). Moieover the wind error vectors report clockwise circulation for the positive and negligible difference for the negative, another sign of non symmetric configuration and therefore model underest imat ion.
Briefly, an inaccurate geographical placement of the low piessuie system can potentially account for this differences between foiecast and analysis but it's not the exclusive reason 18 Chapter 2. Case Study: ECMWF Model Errors
2.5 Rationale
The case studies intioduced above illustrate the reason for looking at forecast minus analysis difference fields.
We have seen that the geopotential heights are underpredicted and that the sur¬ face cyclones amplitude and phase errors are coherent. In general it's appropriate to say that difference fields are significant. The underlying aim is to improve de¬ terministic forecast and by default ensemble forecasts. Chapter 3
Nature of the 'Forecast - Analysis' Difference Fields
3.1 The Potential Vorticity Perspective
Instead of the classical view (geopotential, SLP) applied in the previous chapter and in numerous studies as Jung and Tompkins (2003), the adoption of the Po¬ tential Vorticity (PV) Perspective offers the possibility to analyse the errors from a completely different point of view. Indeed intrinsic properties of this perpective have direct implications for the study of forecast error fields. As an illustration, consider fig. 3.1 which shows a typical picture of the difference fields over the northern hemisphere. Feature of the figure is that the error is located where the PV gradient is large, i.e. along the PV wave-guide (this means again along the jet). To the south of this band of significant differences, no errors are found, while to the north of it some regions with low magnitude are present.
Another impressive aspect is the absolute value of these differences: up to more than 6 pvu! In fig. 3.1 extratropical cyclones with SLP lower than lOOOhPa are also indicated.
They are located ahead of troughs, in the region where the error gradient reaches its maximum. This implies that an inaccurate forecast of the jet path has strong influences in the further developement of the cyclone.
Another rationale for applying the PV perspective is the fact that the dy¬ namic of rapid error growth has beeen linked to distinctive PV-features of the error fields.
The main aspects of this theoretical facet are easily visualized in fig. 3.2. In the presence of a vertically sheared background flow (left), an alignment of the
19 20 Chapter 3. Nature of the 'Forecast - Analysis' Difference Fields
Figure 3.1: 72hrs forecast minus analysis of PV at 320K in colour, PV analysis (2pvu isoline at 320K, thick black line) and SLP analysis (thin black line, below lOOOhPa every 5hPa) for 10.10.2001 at 12UTC over the northern emisphere.
as in errors the center of the figure occurs (the error structure appears initially in tilted bands of positive and negative values). Due to the unshielding of the errors, a vertical realignment of the structure occurs, resulting in vertically ori¬ ented columns of alternating positive and negative errors. This means that the differences are consistent also in the vertical and not only on a particular surface.
In effect, these differences have a 3D structure, reach extreme values, are located in particular regions, and show always the same pattern and features. In the next section a closer analysis of these characteristics will be drawn.
3.2 Prevalent Features of Error Fields
With the help of the two ease studies introduced in the previous chapter, a closer analysis of the main features of the fields under the PV perspective is undertaken. The reproduction of the PV errors for the Pacific case (72hrs) and Atlantic case (96hrs) is visible in fig. 3.3 and fig. 3.4. They also indicate the wind errors on the same isentrope (320K). The two figures are very similar and share certain common features as:
• Amplitude deficiency of waves on PV wave-guide.
• Phase/Amplitude deficiency of parturated PV-streamers.
• Negative/positive difference fields associated locally with anticyclonic/cyclonic circulation.
• Negative/positive differences indicating troughs/ridges are weaker in the forecast. 3.3. Time Evolution of the Forecast Errors 21 %
Figure 3.2: Error realignment: back¬ ground flow (top, left), vertical realign¬ cz_ ""> ment (top, right), unshielding of the er¬ rors (left).
• The wind error circulation is not centered on the PV error due to the low level interaction
• Difference in flow advection between realised evolution and simulation.
We have already seen that an amplitude deficiency of waves typifies these fields. Streamer's forecast also incurs in errors alike (fig. 3.3 upper right corner). Moreover the phase speed of the structure is an important factor. The presence of the wind error vectors on the same surface as PV let us deduce new properties: The PV difference field behave like PV, where positive values are associated with cyclonic and negative with anticyclonic circulation. This implies that these errors have an intrinsic dynamic, given by the different flow advection between realised and forecasted evolution.
3.3 Time Evolution of the Forecast Errors
Hitherto a singular forecast has been compared with the analysed development of the atmosphere. Since the ECMWF model produces forecasts up to 10 days every day, it is possible to compare the error fields of different forecast lengths for a particular time, as it has been done next: Figure 3.5 shows the F-A fields for different runs (24, 48, 72, 96 hrs) at a spe¬ cific time for the Pacific case. Instead of plotting PV as in the previous figures, we introduce the vertical integration of PV. Its horizontal distribution (hereafter referred to as VIP) yields a two-dimensional portrayal of the three-dimensional structure and it gives a clear picture of the magnitude and location of the PV errors. A closer inspection shows that its 24hrs forecast exhibits substantial amplitude deficiency (up to 3pvu) along the PV wave-guide. The other forecast-days con¬ firm the spatial distribution. The pseudo growth rate is analysed in figures 3.7 22 Chapter 3. Nature of the 'Forecast - Analysis' Difference Fields
Figan 3.3: 72hrs forecast minus analysis of PV and wind at 320K foi 10.10.2001 at
12UTC over northern Pacific.
Figure 3Jt: Otihrs forecast minus analysis of PV and wind at 320K for 1(5.01.2002 at
12UTC over noithorn Atlantic.
(and 6.7 as a climatology). Also the wind errors confirm the circulation directions and spatial distribution observed previously. The Ailantie case (fig. 3.6) is not as extreme as the previous for the magnitude of the F-A field at least in the first 72hrs, but it supports well the indications of fig. 3.5: the VIP and wind errors grow from the 24hrs to the 96hrs foiecast and have the typical spatial distribution. This ease shows an explosive growth from 72 to 90hrs.
These representative figures (3.5 and 3.6 ) clearly indicate that at a specific time the F-A fields have a similar spatial structure but différent amplitudes. This pro¬ vides a hint for systematic diffeieuees/errors in capturing/representing synoptic development, which has implications for the design of ensemble procedures but does not single out causes (physic/numeric of assimilation) of error. 3.3. Time Evolution of the Forecast Errors 23
Figure 3.5: 24, 48, 72, OOhrs forecast minus analysis of the vertical integration of PV in the higher troposphere ( VIPV-UP, 200-400hPa) and wind at 300hPa for 10.10.2001 at 12UTC.
Figure 3.(1: 24, 4X. 72, 9(ihrs forecast minus analysis of the vortical integration of PV (VIPV-UP. 20()-400hPa) and wind at 300hPa for 10.01.2002 at 12UTC. 24 Chapter 3. Nature of the 'Forecast - Analysis' Difference Fields
VIPV-MI VIPV-DO SLP
Figure 3.7: RMS of the forecast differences integrated over the Pacific (P, solid line) and Atlantic: (A, dashed line) case regions for VIP-UP, VIPV-MT (500-600hPa), VIPV- DO (700-900hPa) (in pvu) and SLP (in hPa). The domains are defined as sectors (160E-100W, 40N-60N for Pacific and 100W-15E, 40-65N for Atlantic:)
Figure 3.7 offers a synthetic overview of the time evolution of the error dif¬ ferences of VIP-UP, -MI (500-600hPa), -DO (700-900hPa) and SLP. Evidently the RMS depends strongly on the forecast time: PV and SLP show a coherent behavior with a pseudo-growth factor larger than 2 in the 24-96 time period. We have already noticed that the main difference between the two eases is the magnitude of the errors, with the Atlantic being weaker, particularly in the first 72 hours. This is also visible is this figure: the R,MS of VIP-UP reaches about 1.4 (P) and OJpvu (A) after 72hrs while SLP 5.8 and 2.6hPa. There is a doubling factor from A to P case. Another interesting feature of this graphic illustration is the extremely similarity that VIP-UP (which is calculated between 200 und 400hPa) and SLP (surface) show. The inference is that there is a (strong?) relation between the upper and the lowermost part of the troposphere! VIPV-MI and VIPV-DO also show a strong relationship. Their behavior is almost identical as well as their values, which are significantly lower than aloft. Whereas the Atlantic case shows a monotone increasing RMS of VIP-UP and
SLP, in the other case the error growth evidences a step-like behavior with in¬ tervals of constant or even slightly decreasing RMS or strong increase. This is not the case in the mid and low atmosphere where the two cases are similar. To examine this aspect a different graphical illustration is needed. Instead of plotting the R,MS of different forecasts ending at a specific time as in figure 3.7, where every values belongs to a different forecast, we will take into account the complete forecast output until a given time.
The transient RMS evolution of the forecasts for the Pacific case is shown in figure 3.8 for the same variables as fig 3.7. If the forecasts were always of the same quality, we would see in this kind of plot a series of parallel lines. The initial conditions influence the score of a global forecast run and the predictability of 3.3. Time Evolution of the Forecast Errors 25
VIPV-UP VIPV-MI VIPV-DO SLP
Figure 3.8: RMS of 96, 72, 48 and 24hrs forecasts for October 10 2001 at 12UTC (located at 96his mark) integrated over the Pacific domain for VIPV-UP, VIPV-MI, VIPV-DÜ (in pvu) and SLP (in hPa)
VIPV-UP VIPV-MI VIPV-DO SI P
Figure 3.9: Same as 3 9 but for January 16 2002 at 12UTC integrated over the Atlantic domain.
the atmosphere.
As we can see in the four panels, VIP-UP and SLP show again a very similar behavioi, wheieas VIPV-MI and VIPV-DO are different. In the case of VIPV-UP and SLP the 241us forecast is by far the worse forecast producing an RMS value that the other model imis reach only after 48, wheieas suiprisingly the best is the oldest one. The 48hrs forecast crosses the 24hrs which results in a constant RMS in the previous plot and explaining the afore curious feature. This is not the case foi VIPV-MI and VIPV-DO. The former does not show any particular feature, wheieas the latter shows a particularly low RMS value at 72hrs and low quality 48 and 241us foiecasts. All the panels (apart from VIPV-DO) piesent a linear to exponential growth which indicates, along with the fact that the 24hrs foiecast is the worst, a strong unpredictability of the atmosphere. The comparison with the Atlantic case (fig 3.9) is striking and explains the con¬ tained magnitude of the second case in respect to the former. A first feature is that the RMS are always smallei. Secondly the giowth rate shows a satuiation of the RMS in time (apart from the 96hrs forecast of SLP). The different forecasts are often parallel to each other indicating that their quality remains constant.
This suggests that the atmosphere is well predictable and that the errors may be due to analysis/initial values failures. 26 Chapter 3. Nature of the 'Forecast - Analysis' Difference Fields
The explosion of the RMS of the 96hrs forecast in the SLP panel in the last 24hrs
(similar to the pacific case) may indicate that even for a case as predictable as this one at surface level the predictability is strongly reduced.
It is interesting to notice that both cases lead to extreme differences between analysis and forecast as seen in figures 3.3 and 3.4 and not only the Pacific one. To obtain a strong improvement in the forecast quality it is not sufficient to have a predictable case like the Atlantic. An improvement in the data assimilation might be another important key factor needed!
3.4 F-A Dynamics
What can we infer regarding the dynamics of the F-A fields? Let's consider the wave structure on the isentropic suiface (fig. 3.3 and fig. 3.4). The following dynamical features could account for the genesis and development of the difference fields:
• Large scale deformation
• Localized anomaly
• Baroclinic growth
• Endemic physics/numerics/analysis failure
Every feature participates differently to the dynamic: The large scale defor¬ mation of the jet can support and enhance the error growth but does not induce new patterns. The presence of a localized anomaly could induce a pattern con¬ sistent with the anomaly but it requires:
• an anomaly of finite amplitude. • that the analysis scheme misses its existance.
• an anomaly suitably located on successive days
The existence of baroclinic instability effects in the vicinity of the jet would require a comparable lower troposphere structure to the upper level PV/V1P. Fig. 3.10 illustrates for both cases the presence of a strong baroclinic instability pattern in the low atmosphere, where an increase in 9 of almost 10K piependic- ularly to the jet is available. The comparison between the PV@320K analysis and model fields suggests that theie is a conceivable misrepresentation of the anomalously low PV zone aligned 3.5. High Resolution Simulations in the Pacific 27
Figure 3.10: Forecast minus analysis of 0 at 850hPa (in colours) and analysis foi the
Pacific case- (72hrs FC, left) and the Atlantic case (901ns FC, right).
along the- jet. Idealised and NWP simulations suggest that it might account for wave structure and PV streamei error (see chapter 5).
3.5 High Resolution Simulations in the Pacific
Until now the1 focus has been set on the ECMWF operational model, which shows foiecasj minus analysis fields with a particular wave pattern and own dynamics.
Tn this section a simulation driven with the HRM model will show that they are 28 Chapter 3. Nature of the 'Forecast - Analysis' Difference Fields
not a pieiogative of the IFS global model and that a major resolution increase does not prevent the appearance of such 'errors'
Selected is the Pacific case, for 24, 48 and 72hrs high resolution simulations end¬ ing on October 10, at OOUTC. The HRM grid is set at 14km and 30 vertical levels, covering the whole northern Pacific from the Chinese to the Western U.S. coast The initial and boundary data are provided by the ECMWF model, interpolated on the HRM grid. Figure 3.1 f shows the VIP and the wind vectois for the HRM model. For a comparison, the ECMWF model figures 3.5 and 3.3 are available (notice that there is a 12hrs shift between ECMWF and HRM model, but the error fields are calculated at the same time span). The main features observed in the global model of the European Centie in the previous sections aie also visible in these high resolution runs: the main 'errors' appeal again as deficiencies of waves on the PV wave guide with weaker troughs and lidges in the forecast as well as phase deficiencies. Ditfeiences in the flow advection are also present (wind enois). The time evolution of the 'errors' is very similar to what observed in fig 3.5 with a very strong increase of the 'difference' amplitude at 72hrs. ft is also important to evidence that improvements due to the high resolution are also present, the differences aie reduced in magnitude at every foiecast span compared to the global model errors. Biiefly the coarse horizontal resolution of the IFS model cannot entirely account for the differences between simulation and observed evolution. An increase in resolution reduces the amplitude oi the 'enois' but the pioblems forecasting the exact location of the PV wave guide remain and may be lead back to misrepre¬ sentations in the initial conditions.
3.6 Summary and Conclusion
The PV perspective has been applied instead of the traditional view to examine the difference/error fields, since intrinsic properties of this perpective have direct implications for the study of forecast enoi fields. Moreovei the dynamic of rapid error growth has beeen linked to distinctive PV features of the error fields.The
PV perspective indicates prevailing features in the 'enoi' fields and a coher¬ ent time evolution in the two illustrated case studies. A deeper analysis of the
RMS of different forecasts reveals substancial differences between the two cases, characterized by a strong unpredictability in the pacific case (linear/exponential RMS growth and strong variability between different forecasts) and a bettei pre¬ dictability of the atlantic case (saturation or the RMS and similar behavior of different forecast runs) . A suggestion of the dynamic of the F-A difference fields is proposed in section 3.5.
This is developed in foui steps regarding the large scale deformation, a localized anomaly, the presence of baroclinicity and possible endemic failures of the model 3.6. Summary and Conclusion 29 and in the initial conditions regarding the misrepresentation of the anomalously low PV zone aligned along the jet, which can account for the wave structure and PV streamers 'error'. High resolution simulations confirm the difference field's structure and dynamics but point out that the magnitude of the 'error' can be reduced by a decrease of the gridspacing. In the next chapter a lagrangian view of the differences between model and anal¬ ysis will be introduced with the aim of comparing the flow advection and point out the main differences. Seite Leer / Blank Seat
i Chapter 4
Backtrajectories
Lagrangian trajectories have been calculated with the purpose of identifing dif¬ ferences in the flow advection between analysis and model. The trajectory tool and allows us to follow air parcels from one time step to the next (or the previous) therefore simulate the advection of the different air masses that interact in the extratropical Pacific and Atlantic and identify the source regions. The? absence or the predominance of a certain trajectory cluster can lead to totally different development in the low as well as in the higher troposphere. The approach that we followed and the results for the two cases will be discussed next.
4.1 Approach
The trajectory tool, Lagranto, (Wernli and Davies 1997) has been applied to calculate the trajectories of this part of the study. The aim is to trace back air parcels that satisfy some given conditions at a certain time in the model and in the analysis and thereby carefully capture the features that lead to the huge differences seen previously. The setup of the tool offers the specification of the following parameters:
• the length of the tracing: 96hrs • the origin of the trajectories: a strong positive PV error (target area, the coordinates depend on the case)
• the variables traced: p, Q, RH, T, TH, PV, VEL, 9 • condition: all trajectories must end with PV^ 2pvu
The tracing length of 96hrs is hopefully long enough to gather information, the whole development at the ground (SLP) and at tropopause height and there-
31 32 Chapter 4. Backtrajectories
PV along trajectories from 200110101200 to 200110061200 U1C
Figure 4-1' 96hrs backtrajectories for the Pacific case, analysis (top) and forecast (bottom) Plotted is the PV value along trajectories ending with PV ^ 2 and in of the the positive PV error region of fig. 3.3 (190W-160W, 45N-55N). Only the 10% trajectories is plotted.
PV along trajectories from 200201161200 to 200201121200 U TC
Figure 4-2. same as fig. 4.1 for the region in 60W-50W, 40N-50N Analysis (top) and foiecast (bottom) Only the 10% of the trajectories is plotted. 4.2. Pacific Case 33
fore have two independent evolutions (model and analysis). We also want a clear pictuie of the different air masses in play and their paths. Because of this the attention has been placed only on the positive PV errors (they show a more in¬ tense cyclonical circulation in the wind error vector field. The interest in PV is clearly correlated to the PV peispective whereas the con¬ dition has beeen set to decrease the number of trajectories and concentrate them
in the interval where it is more likely to find important differences. To highlight the diffeience in the advection of the air masses between model and analysis a clustering algorithm (thanks to H. Sodemann) has been also applied to divide the calculated trajectories in the most meaningful groupings. Plotted in figures 4.1 and 4.2 is about the 10% of the calculated trajectories, whereas in the following plots all the trajectories are illustrated.
4.2 Pacific Case
The target area identified in the Pacific (for coordinates see fig 4.1) is a legion in the vicinity of the jet characterized by extreme differences in PV, SLP and Z and a strong cyclonic circulation of the wind error vectoi field. The 4-days back trac¬ ing of the air parcels ending in this area does not evidence extreme differences in the advection in the analysis and the model, with PV values between 0 and 5pvu, source regions as the eastern Pacific, China, the Indian Ocean and the Western
Méditeranean, and a wave pattern between Eastern China and Japan, more ev¬ ident in the analysis. Nonetheless this is sufficient to lead to a very different evolution on the dynamical tropopause as well as on the surface. A closei view of the different advections taking place in this case can be given thanks to the clustering algorithm, which identifies three main groups of trajectories, plotted in figures 4.3 to 4.8.
The fiist ensemble represents tiajectories with origin in the Eastern Pacific, at below 50ühPa. In the model (fig. 4.6) as well as in the analysis (fig. 4.3) the air parcels descend for about 60 houis reaching less than 75()hPa. Then, sud¬ denly, they undergo to an extreme ascent to 250hPa. They are part of the warm conveyer belt (Browning 1990) related to the developing surface cyclone. During this ascent, condensational processes occur, which increases the PV values. Dif¬ ferences between model and analysis are found in the number of trajectories in this cluster (more in the analysis) as well as the slight different timescale of the rising motion: in the analysis the ascent is limited to the last 24hrs (with the maximum at 12hrs) whereas in the model it occurs from 48hrs on.
The second cluster groups air parcels traveling in the upper troposphere, be- 34 Chapter 4. Backtrajectories
Figure lh3: Pacific case, cluster 1 of the analysis.
Figure 4-4: Pacific case, clustei 2 of the analysis
Figure J,.5: Pacific case, clustei 3 of the analysis
lie- identified twoen 500 and lOOhPa. The source regions of these1 trajectories can
and as far as the1 Western as the Indian Ocean (Arabian Sea), Central Asia Mediterranean. Their path is characterized by weak vertical displacements and high horizontal velocities. They are part of the jet stream. Differences between forecast and analysis can be identified in the vcitical coherence' of the tiajectories. 4.2. Pacifie Case 35
Figure 4-(>: Pacific case, cluster I of the forecast
Figure J,.H: Pacific case, cluster 3 of the forecast whicli is much higher it the model (15()-40()hPa compared to l5()-()00hPa) and in the1 not the mean path which shows a wave-like character over Japan analysis, in present in the forecast. The presence in the analysis of a previous cve4ogeinesis the China Sea basin is probably the cause the wave-like de-formation of the jet. 36 Chapter 4. Backtrajectories
A last group of trajectories, depicted on fig 4.5 and fig 4.8, is identified for this case. These are mid-range parcels (for what it concernes the horizontal displace¬ ment) starting over China, China Sea basin and the Himalayan region. Their vertical coherence is low in the initial phase (1000-250hPa) clue to the origin di¬ versity but is high in the end phase (200-300hPa). In the analysis plot all the air parcels undergo to a rising (of different magnitude depending on the initial height) at 36hrs reaching 350-250hPa, similar to what happens in cluster 1. The evolution of the model instead shows the main part of trajectories travelling on a constant pressure level, whereas only few are subjected to a vertical updraft of a smaller vertical and different time scale. The presence in the analysis of the pre¬ viously mentioned upstream cyclogenesis triggers this second low level advection towards the target area.
Even if the first impression given by fig 4.1 evidences strong similarities be¬ tween the forecast and the analysis, a systematic comparison of single clusters composing the traced air parcels highlights differences that may explain the ex¬ treme values of the forecast minus analysis fields observed in this case study. These affect mostly the lower tioposphere, with a more intense wann conveyer belt and a previous cyclogenesis (misforecasted by the model in the low levels) that promoted a wave pattern in the jet and indirectly a second weaker advection of low level air parcels.
4.3 Atlantic Case
As seen in the previous chapter the main difference between this case and the Pacific is the intensity of the 'errors' and not their horizontal and vertical struc¬ ture, nor their time evolution. Therefore the same setup of Lagranto has been applied. For cooidinates of the target area see fig 4.2. The illustrations of fig. 4.2 show that the similarities in this case are fewer com¬ pared to the previous. The analysis-based plot shows trajectories originated in the Pacific as well as in the Gulf of Mexico area whereas in the model only the
Pacific part is present. Through clustering, three groups are individuated within the analysis trajectories whereas only one in the model.
The first cluster of the analysis (fig 4.9) is the only finding a comparison in the model (fig 4.f2). The trajectories are originated either off Japan or between California and Hawaii, where a weak upper level disturbance is located (cut-off in the analysis, part of a streamer streching from the continental U.S in the model). From the origin regions the two groups merge together off California, cross the 4.3. Atlantic Case 37
36 >J4 ?i fiO *£< Jtf {A i il
Figure J,.9: Atlantic Case, cluster 1 of the analvsis
Figure 4-10: Atlantic Case, cluster 2 of the1 analysis
G4 71 SD 4C & ja J! ij
Figure 4.11: Atlantic Case, cluster 3 of the analysis
go -84 n eo
Figure 4.12: Atlantic Case, forecast. 38 Chapter 4. Backtrajectories
U.S and reach the taiget area. These are low PV jet-stream air parcels, located between 250 and 450hPa The difference between forecast and analysis regards the number of these tiajectories, few in the model (the jetstieam is probably forecasted with higher PV values), common in the analysis.
A second group of air parcels (fig 4.10) is generated either across Central America (Gulf of Mexico, Caiabbean Sea, Pacific Ocean off southern Mexico) oi between California and Hawaii. In the vertical section two groups are well high- ligted: one between 400 and 850hPa while the second above 300hPa. The first group is related to the Central American region: the inital steps are characterized by veiy slow vertical and horizontal velocities whilst it is subjected to a lise up to 250hPa in the last 36hrs of the tracing when the second group, coming from
California and being faster and descending, catches up. These trajectories are not present in the forecast and since they represent the warm conveyer belt of the atlantic cyclogenesis, the difference is surprising.
A third cluster is evidenced by the algorithm in fig 4.11. These air parcels travel above 250hPa. They leave Japan towards the U.S, are deviated by the above mentioned upper level disturbance located between California and Hawaii which and finally reach the target area. These trajectories are absent in the model as well
In this case the number of trajectories ending with PV lowei than 2pvu fore¬ casted by the model is strongly underestimated. Apart from the deficiencies in the Hawaiian region highlighted above (no cut-off), the model misses completely the presence of the low level warm and moist air parcels which generate a moist and baroclinic environment in the Central America regions and interacting with an upper level disturbance tiaveling across the U.S. aie of extreme inpoitance for the development of stoims along the U.S. Atlantic coast.
4.4 Summary and Conclusions
The indications piovided by the PV perspective of the previous chapter hypoth¬ esized important differences in the flow advection predicted by the model and the actual evolution. We therefore computed model-based (for the FC96) and analysis-based backtrajectories of an parcels ending with a PV values lowei than 2pvu, in a strong positive region of the F-A field of PV(di320K. The results show important differences in the Pacific case wheieas in the At- 4.4. Summary and Conclusions 39 _^
lantic case the model failures are impressive. In both cases the main deficiencies concerne the low atmosphere with an underestimation (or even a complete mis- forecast) of the low level jet, related to the warm conveyer belt, a fundamental feature1 of the conveyer belt model, along with the cold conveyei belt and the and the diy intrusion, which is related to upper-level frontogenesis and tropopausc folding (Browning 1971, Carlson 1980). The presence of an upstream disturbance influences the air paicels trajectories in the analysis, inducing a wave pattern in the jet-stream aloft and a secondary advection of low level air towaids target area, whereas in the model such features are not present. Seite Leer / Blank leaf Chapter 5
Idealized Simulations
Among the possible reasons found for accounting for misforecasts, the quality of the analysis data, is of primary importance. Moreover any other improvement as in the model physics, dynamics and resolution are subject to the initial condi¬ tions. Comparing analysis and model outputs of different cases we have noticed that the representation of the PV distribution to the south of the jet is often un¬ derestimated. In this chapter an idealized model based on the contour dynamics will l)e used to show the importance of this rejgion and the influences that their misrepresentation has for the model development.
5.1 Introduction to Countour Dynamics
The mathematical model applied to run the idealized simulations illustrated in this chapter is based on Fluid and Contour Dynamics, often used for stratospheric circulation, polar vortex and even stratospheric chemistry (Juckes and Mclntyre 1987). It is therefore meaningful to develop next some aspect of this theory.
In an incompressible and two-dimensional fluid the velocity u = (v., v) is given bv
. u = _ v= — (5.1 ay ax
where $ is the streamfunction. The assumption of incompressibility and two- dimensionality in our case is resonable since:
• the geostrophic wind is divergence-free =£> incompressibility
41 42 Chapter 5. Idealized Simulations
t>0
B2 Ç=ÇJ = 0
Figure 5.1: The Contour C is the dividing line between a region B\ of vorticity ("i and
B2 and C2 for t — 0 (left). On the right hand side for t > 0.
• in case of an adiabatic flow, 9 is conserved. 9 is therefore constant following a fluid parcel =^> two-dimensionality
The change of the streamfuiiction along a streamline and the divergence of u are (due to A.l): cl# = 0 ; div u = 0 (5.2)
which means that ty is constant along a streamline and that the incompress¬ ibility assumption is automatically fulfilled. The vorticity ( is defined as:
dv du „9 T £ = — - — = V2\P = A* (5.3) ox ay
where A is tlio two dimensional Laplace operator. This means that knowing the vorticity ( (with boundary conditions) it is possible through inversion to obtain ^ and therefore also the velocity field u. The equation of motion of a fluid parcel neglecting friction R and viscosity r/ is
7-. -* -1 ;s.4) Dt Q
where g is the density, p the pressure and D/Dt the material derivative1. We can then reformulate 5.4 for a two dimensionale incompressible flow as:
0 5.5 Dt
(see Appendix A for the proof). This has some important implications for the contour dynamic. Figure 5.1 illustrates the implications of 5.5: The region B\ with vorticity (1 and contour C is surrounded by a region #2 of vorticity C, = 0 at t ~ 0. This vorticity 5.1. Introduction to Countour Dynamics 43
configuration induces a velocity field u = (u, v) by which the contour C will be deformed with time. From the equation of motion 5.5 we derive that
Ci = G ; C' = o (5.6)
and from the incompressibility of the flow that the surface Z?/ = B±. However the contour between Bi and B2 continuosly changes its shape since C ^ C. We want now an equation for change of C with time. We first make an Ansatz
and assume that
= — • r = + V(x,y) MO , s/x2 y2 (5.7)
is a solution of the two dimensionals Laplace operator, i.e. A^ = (5 (the Dirac delta function, see Appendix A for the proof). With this fundamental solution (5.7) it is possible to calculate the streamfunction for any arbitrary distribution of C, through superposition:
±- - = r = + - $>(x,y) / C(xf,y')\og(r)dx'dy' , y/(x .r')2 (y y'f (5.8)
We are interested in a particular C. distribution (fig. 5.1)
f Ci îov(x,y)eB1,B1Cl®:2 c= (59)
The streamfunction ^ can be then rewritten as
*(^?y) = ~ / ^ë(r)dx'dy'. (5.10)
With equation 5.1 and with the Green theorem for continuously differentiable vectorfields (sec appendix A) we obtain for any point x()(f) = (xa(t), lJo(t)) located on the contour C the velocity field
io (*) = u(xo(*)) =-~ i log|xo(t)-xVx' (5-11) ^ JdHi
which is a 1. order partial differential equation to be solved numerically and determines the temporal evolution of the contour. 44 Chapter 5. Idealized Simulations
B, c=o
Figure 5.2: A case of three different (a, in I£2, where B^ C B2 C M2
In case of n regions with vorticity values ^ (see fig. 5.2 for n = 2) and the following configuration
0. for (r,,
the streamfunction becomes
(5.13)
where Acjj = ^ — £„ and therefore the velocity field
u(,r, y) log(r) (dx',dt/) ;s.i4) 2tt EA<* A=l àBk
With this shoit theoretical introduction we have seen that it is possible to simulate the evolution of colitouis defoimation by numerically solving a set of partial differential equations. In the idealized model adopted here we have set the initial configuration to be similar to the potential vorticity distribution on the 320k isentrope (even if vorticity and potential vorticity aie different): a circular region of high vorticity partially surrounded by a thin line of negative vorticity (the values are set arbitrarily) In the next sections the results of two different vorticity setups at different tirnesteps will be analysed. 5.1. Introduction to Countour Dynamics 45
t=0.0 t=0.G t=1.4
t=2.2 t=3.0 t=3.8
Figure 5.3: Idealized Simulation: Vorticity ( is set to +10 in the positive region (inside the red contour) and -10 in the negative (blue region). Development from t=() to t=3.8.
t=11.0 t=118 t=12.6
^@t"-r^"^14' f ^
/ v 0
>ättS% êÉp t=13.4 t=14.2 t=15
0 %
I \ %
^ 1 4 i< i i L !> ib i- t
Figure 5.4'- Same as 5 3 but for t=ll to t—15. 46 Chapter 5. Idealized Simulations
5.2 Strong Negative Vorticity
The fiist simulation is performed with a negative voiticity value of —10 and a positive value of +10. Fig. 5.3 depicts in six panels the deformation of the con¬ tours of the positive and the negative regions at the beginning of the simulation. Keeping in mind that positive vorticity induces a cyclonic whilst negative vortic¬ ity an anticyclonic circulation, two main interactions can be identified in this set of plots. Whereas the whole structure rotates around the pole, at two ends of the negative vorticity line something occurs. At t ~ 0 6 the end of the blue region (which is located in the lower part of the panel at this time) originates an eddy and induces a deformation in the contour of the positive vorticity region which can be seen as a jet. This deformation is enhanced at t = 1.4 and by the next time step a small portion of negative £ is cut off from the main contour. Moreover a small streamer-like structure develops between the isolated contour and the original one. The same piocess is repeated at t = 3 0 and t = 3 8 when another small portion of negative Ç is released and the weak short-living streamer/wave develops.
What happens on the other end of the negative line is similar but slower and of larger amplitude. Due to the different position, the clockwise lotation of the negative £ induces a streamer this time ahead of the eddy, allowing both of them to grow longer instead of producing a sudden cut off The instability and the formation of the cut off occur by the time a second cut off is generated on the other end of the negative £ line. There is therefore a factor 2 between peiiods of the two processes.
This sequence of developments occurring on both ends of the negative voi¬ ticity line located to the south of the jet continues until the whole voiticity has encountered a cut off. Hereafter a irew configuration emerges, where the positive vorticity region, which is no longer circular due to the previous deformations, is surrounded by small portions of negative £. Whilst the whole structure con¬ tinues to circulate cyclonically around the pole, these vorticity anomalies also oscillate latitudinally approaching and moving away from the positive £ domain.
When one gets close enough to the contour as in figure 5.4 at t = 11.0, a new deformation of the jet takes place as shown in the successive panels. Due to the interaction between the negative anomaly and the positive contour, the former increases its angular velocity, the distance between the two different contours de¬ creases and a wave originates on the latter. The amplitude of the wave increases assuming a streamer-like character at t = 14.2 By this time the streamer's south elongation reaches its maximum, the influence of the negative anomaly already weakens and its angular velocity decreases. In the last panel the two structures are completely separated: the anomaly is far to the south and the streamer is moving fast downstream. 5.3. Weak Negative Vorticity 47
Since the small portions of negative; £ are usually located to far south to interact with the jet, the approach of a previously formed streamer as in the flrst panel of fig. 5.4 is often a key factor to advect a negative anomaly in the vfoinity of the jet (the same happens for the newly originated streamer of panel 6).
The idealized simulation considered so far can be easily linkend to the actual formation of wave patterns along the zonal jet and development of PV streamers recorded in the everyday weather. The presence; of negative potential vorticity anomalies triggers the genesis of such structures and is therefore fundamental.
Here the magnitude of the positive and the negative vorticity regions were iden¬ tical. Another simulation has been driven with the same geographical setup but different vorticity values and will be analysed in the next section.
5.3 Weak Negative Vorticity
In this second simulation the positive vorticity region is left unmodified while the negative has a weaker anomaly (+10 and -4). The first timesteps (t ~ 0.0 to t — 3.8) are depicted in Figure 5.5. The negative line is visibly thinner and its effects on the jet are reduced in comparison to the previous case. On the left end
(hi respect to t — 0.0) the genesis of a negative vorticity eddy and the consequent wave pattern, even if of reduced amplitude, occurs within the same period. On the right end instead apart from an initial wave pattern that propagates along the flow, the formation of the eddy is invisible even on panel G. Only from time t = 6.0 on its presence becomes visible. By t = 10.0 a weak streamer is generated and the entire negative £ is finally distributed in small portions around the high vorticity region (not shown). Later in the simulation (fig. 5.6) we see a small vorticity anomaly approaching the jet at t = 22.0. The interaction between the two structures is really weak: the anomaly induces just a slight bent on the positive contour at / = 22.6. In the last panel no more than a weak trough is formed on the jet, which is propagating zonally away from the negative vorticity region, ending the process.
In this second simulation we have seen that an asymmetric configuration with a negative vorticity anomaly weaker than the positive has influences in the am¬ plitude and the growth rate of the eddies and on the consequent wave activity developed on the positive contour. This influence is visible not only in the first timesteps. Its influences are extended troughout the whole simulation. These effects can be linked to an underestimation of the magnitude of the negative PV anomalies stretched along the southern flanks of the jet. 48 Chapter 5. Idealized Simulations
II ±_Q — KtW**UifP-Atfl(B-' IJ1U1U1UIUIU>UTIJ1U1 yiwiyiui^Uio'biepif
Figure 5.5: Idealized Simulation: the Vorticity £ is set to +10 in the positive region and -4 in the negative. The panels illustrate the development for t—0 to t=3.8.
V DI M Ç» W "UlUllHUlCtlVUIVIUIVI
Figure 5.6: Same as 5.3 but for t=22 to t=23.2 5.4. Summary and Conclusions 49
5.4 Summary and Conclusions
Two different idealized simulations are presented in this chapter with the aim of investigating the impact of negative PV anomalies and their misrepresenta¬ tion in the model's initial conditions. Some aspects of the contour dynamics are introduced as well, to understand the basis of the idealized model used for the simulations.
In the two cases the negative vorticity region aligned along the contour of the positive region is very unstable and numerous eddies are generated at cither of its ends activating a wave activity response on the positive contour. The amplitude and the growth rate of theîse structures are directly related to the strength of the negative vorticity as we have seen comparing the two runs. If the magnitude of the two vorticity regions is similar, strong cut off's and streamers are quickly generated whereas later in the simulation when a negative vorticity anomaly is advected in the vicinity of the jet, the interaction between the two structures produces a new streamer. Otherwise if the negative anomaly is weaker, the gen¬ eration of cut offs and streamers is minimised. Even later in the development, negative anomalies approaching the positive produce only a small deformation of the contour.
If we assume that the analysis underestimates the strength of the negative vorticity anomalies, even if the model does not present any particular lack in its physics and dynamics, it is impossible to simulate the proper wave activity along the jet. The amplitude and the phase velocity of troughs, ridges and streamers is underestimated in comparison to the actual evolution and the pattern obtained by subtracting the analysis to the model's field is similar to fig.3.3. Seite Leer / Blank Seal Chapter 6
Error Climatology
Until now the structure of 'Forecast minus Analysis' difference fields of singular cases have been examined under the traditional and PV peispective, and the eulerian and lagrangian views. To have a broader perception of the importance and frequency of these 'errors' a climatology has beeen produced, which let us draw a geographical distribution of these systematic 'errors' and point out regions where observations, assimilation and/or physics may need to be improved (see also 3.5).
6.1 The approach
As introduced above, a climatology over nine months was compiled (September
2001 - May 2002). Whereas some studies (e.g. Ferranti et al. 2002 ) focused on particular months over diffeient years, we chose a recent period of several months in order to avoid possible biases induced by the technical variations of the ECMWF forecasting system. Seasonal means (SON, DJF, MAM) weie also computed to have a hint of the seasonal variability of the F-A fields as well as the impact of diffeient forecast length (from 24 to 96 hrs)
Two different time-averages of the 'errors' were calculated for the climatology:
• The mean 'errors' (Bias): Äc^(f) = ^ J2tAS(.r,t)
• The root mean square 'errors': RMSt(A5) = (jj £, (AS)2(.r. f)) j
As in single cases (chapter 3), the presence of a positive and negative dipole would indicate a spatial mean displacement 'error', whereas an amplitude mean
51 52 Chapter 6. Error Climatology
'error' would yield a single signal in the error field. BMSt(AS) is the square root of the (time) average of the squared differences (model minus forecast) and is used in order to avoid the distinction between the sign of the difference field (compared with the mean), in particular in regions where the compensation effect between positive1 and negative differences may be important.
Notice that insight into the variability of the mean 'errors' can be optained by computing the standard deviation er,(Ac)) since for small ASt
at2(A5) = j^iBMSf - Ält2) k RMSt(AS)2
The method accounts some possible limitations regarding the definition of the 'enois' since deficiencies in the analysis cannot be excluded and is even inferred
(in chapter 5). Othei constraints may be the interdépendance between analysis and forecast and failures in the derived data as the vertical integration of PV in the low troposphere which suffeis of extiemely high and therefoie unrealistic values in the vicinity of steep orography A filter is therefore applied to these regions.
6.2 A Seasonal Climatology
Of the three seasonal climatologies compiled while producing the nine-months mean, we present heie the result for winter (DJF) 2001/2002 (see Appendix B for autumn 2001 and spring 2002). First the traditional view is illustrated (geopo¬ tential and SLP) followed by the PV perspective
6.2.1 The Traditional View
Figuies 6.1 and 6.2 illustrate the bias and the RMS distribution of the geopoten¬ tial at 500hPa and SLP foi the 96hrs forecast for the winter months. All panels show a concentration of the signal over the pole while to the south of 40N no sig¬ nals (or very weak in case of the bias) are present. The geopotential field bias (6.1 left) indicates some well delineated regions of positive difference as north-eastern
Canada, western Africa and Japan surrounded by a general underestimation of the values by the model, with maxima to the south-west of Iceland and in the
Gulf of Alaska, two regions of extreme cyclogenesis frequency. The presence of two opposite maxima close to each other (a dipole, between NE Canada and SW Iceland) can be explained by the compensation of the positive and the negative 6.2. A Seasonal Climatology 53
9
i
! ^
... \f*W\
- ^ """UTiÛ .... ji3T""""b ^
I ) .- 1.11 -i ?n
for DJF Fï.e/we 6.1: Winter-Season Error Climatology of Z@500hPa 'errors' 2001/2. The Bias (left) and the RMS (right) for the 96hrs forecast. (PV2@.'J20K analysis black thic:k contour)
>=j\ i-7? y"
Figure 6.2: Same as 6.1 but for SLP.
values between the two: the RMS panel illustrates that in the region where1 the
Gulf-Stream and the Labrador-sea merge together (off the Newfoundland coasts) of bias indicates there is a maximum of R.MS. This together with the minimum that, the compensation factor in this region is extremely high. The 'error' of the model compared to the analysis reaches in this region the highest values of the northern hemisphere;. Keeping in mind that this is an extremely active; eycol- that this has in the; forecasts genetic: region it is easy to imagine the; influences downstream of Newfoundland. A similar but weaker structure is present along 54 Chapter 6. Error Climatology
the north American Pacific coast.
Another feature visible on the geopotential RMS panel is the spiral-shape of the RMS signal, it staits to the west of Japan at about 40N and follows the jet (PV2 isoline) to the British isles wheie the jet shows a tilt to the north. Afterward while the jet continues along the 40N latitude, the band of high RMS increases its latitude reaching 60-70N over Siberia.
In the case of SLP even if the bias appears quite different from the geopotential climatology (the bias is positive along the 'spiral' feature and negative along the Asian jet), the RMS confirms what observed previously: the two regions of extremely high amplitude and frequency of the 'eirois' (the whole noithein Atlantic basin and Pacific) aie enhanced as well as the spiral behavior of the RMS.
6.2.2 The PV Perspective
Figures 6.3 and 6.4 illustrate the result of the bias and the RMS of PV for the winter climatology, for the 24 and 96hrs forecasts, which allow also to draw a possible time evolution.
The Bias
The bias of PV shown in Figure 6.3 is much clearer than in the case of SLP oi the geopotential field. The climatology shows predominantly an annular structure of mainly negative bias aligned along the PV wave guide at 24hrs as well as at 96hrs.
From this obseivation we can learn that:
• The model underestimates the PV values along the jet e.g. the jet is located further north in the forecast (Asia) or/and
• The analysis fails to lepresent correctly the negative regions stretched to the south of the jet.
• The negative difference is mainly located at the entrance to and along the north African-Asian jet
• A dipole is located across the Rockies in the left panel which is compatible with a reduced amplitude of the prevailing trough-ridge in the forecast field.
• Stieameis do not extend as far equatorward in the forecast as in the analysis
over the Meditenanean sea. Situated at the end of the Atlantic stoim track
this region shows an enhanced streamers development. 6.2. A Seasonal Climatology 55
Figun (>. 1; Wintei-Season Enoi Climatology of PV^330k 'errors' for DJF 2001/2. The Bias of KC24 (left) and FC90 (right). (PV2 Figure 6 4- Same as 6.3 but for RMS • There is a growth factoi of ^2 in the 24-06 hours time period. It is curious to observe the asymmetrical diffeiences bedwchui the Furoasian continent (mostly negative) and the rest of the northern hemisphere (weaker sig¬ nals both positive and negative). Moreover no particularly extencfod errors are found in the1 noithein Atlantic region/Labrador sea and in the Gulf of Alaska, which differs from what seen previously (SLP and Z). Again the compensation effect has also in the PV climatology a stiong impact as we will sex1 in the RMS plots. 56 Chapter 6. Error Climatology Root Mean Square Error The RMS panels of figure 6.4 reveal an opposite asymmetry in comparison to the bias as well as some similar characteristics. In this statistic the differences even if still aligned along the jet, are much weaker in the sector stretching from eastern Europe to the central Pacific, whereas it reaches its maximum across the Rockies. Moreover it is not confined to the conventional storm track regions at 24hrs range. As already pointed out the compensation effect is the cause of this asymmetry: where a lot of compensation takes places the bias is very weak whereas the vari¬ ance is strong (across the Rockies) and if little or no compensation takes place (the differences are systematically of the same sign), the bias is strong while the RMS is not particularly strong and does not appear in the RMS plot as a major feature. A growth factor of ~2 between 24 and 96hrs is still present. 6.3 The Nine Months Climatology This climatology has been compiled adding the previous and the following seasons to the climatology of the winter season of the previous section. It includes all the months from September 2001 to may 2002. The Bias The panels in figure 6.5 represent the bias of PV of the nine months climatology. The illustrations are similar to the three month climatology but the noise is reduced, in particular in the low latitude regions, and the extreme values are smoothed. At 24hrs range the negative bias is reduced to three regions: Europe, Mongolia and the U.S. Inbetween neutral (Caucasian region) or positive (eastern Pacific) regions are found. We can explain this configuration as before with the inadeguate streamers extention over Europe, the northward shift of the jet in the central Asia and a reduced wave amplitude of PV over America. The 96hrs plot differs from the previous mainly by the uniform band of negative bias found from Europe to Japan. As in the winter climatology there is a factor of ^2 between 24 and 96 hours. 6.3. The Nine Months Climatology 57 Figure 6 5: Same as (>.3 hut foi tlie nine-months period Scptembei 2001 - May 2002. Figure 6.6: Same as 6.4 but nine-months period September 2001 - May 2002. Root Mean Square Error The RMS panels of the1 climatology indicate a complete and a partial annulât structure at 24 and 96 hours. The1 central Asia region presents a break in the structure at 961ns. The cause of this is probably due to the jet which is sys¬ tematically forecasted to the north. This constant slight shift results in a strong bias (no compensation effects) and in a low magnitude RMS compared to other legions. The maxima of RMS aie observed over the northwestern US and ovei Euiope at 241ns and ovei the British isles region at 901ns. The north allant ie basin also 58 Chapter 6. Error Climatology VIPup ,< 013 VlPmi .... .* VIP mi--- 01 ***' VIPlo --- ..• VIPlo ... 008 ,•'" 0.0* ..••"•* ..*** ,*' •.* 004 ,.'*" —:vj mm* •*"""" --»•-' ? - —21Vi" •** Z,--» 002 • »A»»"' *>' «fays .days 01.234 01234 Figure 6.1: Atlantic-integrated RMS forecast 'errors' of VIP (in pvu) as a function of the forecast lange (adapted from Dirren et al. (2003)) presents high values of RMS. These legions correspond to the Pacific and Atlantic storm tracks. It is interesting to notice the error pattern's maximum amplitude shifts eastwaid during the 24-96his period; this is indicative of the inadequate replication of the eastward propagating PV ffow features in the forecast. 6.4 Evolution of PV Error Growth Finally figure 6.7 illustrates the vertical dependency of the PV error's tempoial evolution integrated over the atlantic region. Displayed is the four-days nine- months chmatological evolution of the VIP 111 the high mid and low troposphere. In the low and mid troposphere the bias and the RMS show a doubling time greater than 1 day in the initial 24-36 hours and an asymptotic behaviour af¬ terward. In contrast the upper troposphere error grows with a doubling time of about f 2 hours in the initial 24hrs and then shifts to a quasi-linear growth. A similai analysis has been computed foi the whole northern hemisphere and for the Pacific legion with similar results: 110 significant difference in the low and mid troposhere and a higher amplitudes and growth rates over the oceans than over the continents (whole emisphere). Part II Studies with a Regional Model 59 Seite Leer / Biank leaf Chapter 7 Introductory Remarks and Case Description Numerical weather prediction models will in the near future be operationally run at resolutions of the order of l-3km even at European scale. It is the purpose of this study to investigate the potential benefits and also the problems involved with this increase in resolution. To this end high resolution simulations (at 2km) with the Lokal Modell (LM) of the COSMO* are performed for selected MAP IOP cases and the results are examined in comparison with available high res¬ olution datasets from the MAP campaign and with operational simulations at meso-scale coarser resolution.The study develops in three directions: (i) study of structures with help of a new modeling tool (Dynamics), (ii) with a systematical analysis of the model behavior for a selection of MAP IOP case studies with particular attention to model errors in precipitation field (Prediction) and (iii) experiments with the numerical set-up of the model (Configuration) investigating the? influence of the domain size; on the high resolution simulation and adapting the number of verfiel levels of the model due to the increased horizontal resolution. 7.1 Introduction The continuing increase in computer power now renders it feasible to perforin numerical weather predictions using a regional NWP model operating at very high (2-8kin) resolution (Cotton et al. 2001, Benoit et al. 2002, Renfrew et al. 1999). The challenge is to forecast the space-time scale evolution of meso-a and meso-/:? scale systems such as passage of frontal systems, the occurrence of severe 1 Consortium for Smalt Scale Modeling 61 62 Chapter 7. Introductory Remarks and Case Description storms, the location of orographically-induced turbulence, and the break-up of a low-level stratus layer. A model's configuration will be constrained on the one hand by operational and computational limitations (e.g. availability of adequate measurements, desired forecast lead-time, available CPU-time), and on the other influenced by generic physical factors and modelling issues. It is the latter inter-related factors and issues, as they pertain to predictions for the Alpine; region, that constitute the focus of the present study. From the physical standpoint the relative importance of accurately capturing the synoptic- is scale forcing as opposed to better representing the meso-scale processes partic¬ ularly piquant for the Alpine region. There is strong evidence that the incident and ambient synoptic-scale flow at upper-level can e;xert a strong influence upon: of the timing of a frontal passage and the occurrence, timing and amplitude heavy Martius et al. precipitation on the Alpine south-side (Massacand ct al. 1998, 2006); turbulence above the Alps (Smith and Broad 2003); and lee cyclogenesis (Pichler and Lanziger 1990, Pichler and Hagenhauer 1995). Concomitantly the in-situ meso-scale processes are seminal for the evolution, strength and location of the meso-scale systems. From the modeling standpoint key issues are the sefoction of the domain size, the comparative advantages of nesting allied to increased spatial resolution, and the sensitivity to the specification of the initial and lateral boundary data. In relation to domain size the challenge is to balance the advantages of a large do¬ main yielding potentially better representation and development of meso-scale flow features against the accompanying increased computational costs and oper¬ ational constraints. For regional climate models with the focus on relatively small target area and longer-te;rm simulations, studies indicate that operating with as to large a domain as feasible delivers both more local detail and better fidelity and the mean climate (Bhashkaran et al. 1996, Jacob and Podzun 1997, Jones Noguer 1995, Seth and R,ojas 2003, Vannitsem and Chômé 2005, Diniitrijevic and Laprise 2005,). For weather prediction models with the focus again on a relatively small region but now for simulations of f-2 day time-span, studies have been undertaken with initial and lateral boundary data derived from either a global prediction model or analysis data. Studies with the former forecast-mode generally point to the efficacy of a relatively large integration area in allow¬ ing a less constrained development of the sub-synoptic and meso-scale flow (e.g. Warner and Treadon 1997, Chôme and Nicolis 2002) but with some indications of low sensitivity to the domain size (Steed and Mass 2000). Studies with the latter hindcast-mode indicate that better Root Mean Square (RMS) scores are obtained with smaller domains (Seth and Giorgi 1998, Tanajura and Bianco 2002). This dichotomy is not necessarily contradictory since the accuracy of the hindcast si- 7.1. Introduction 63 ululations is enhanced by the use of the analysis fields at the lateral boundaries. In relation to nesting the regional NWP suite can take the form of a single or multl-nested configuiation so as to stagger the jump in spatial resolution between the global and regional model(s) and to concomitantly provide greater resolution in the neighborhood of the target region (see e.g. Rife and Davis 2005). The challenge is again to balance the potential benefits of on the one hand smoother inter-model transitions and higher resolution with on the other computational and operational considerations. In relation to sensitivity to the specification and sensitivity to the initial and lateial boundary fields there ate two distinct issues One is fundamen¬ tal and relates to the level of intrinsic (un)predictability of meso-scale systems wheieby comparatively small mis-specification of the initial or lateial boundary the data might, even in a perfect model setting, exert a significant influence upon forecast (Walsei and Schär 2004, Eckel and Nas 2005). The other is pragmatic and relates to the lack of adequate mesoscale observational data sets to specify the initial and boundary conditions. Tn the latter note that, for the Intensive Observation Periods (IOPs) of the Mesoscale Aalpine Programme (MAP), there is available both the routine operational analyses fields and the MAP Reanaly- sis data set produced at ECMWF (Keil and Cardinali 2003) that incorporates a observational mea¬ range of additional conventional and non-routine mesoscale surements. The provision of the latter enriched data set was a major MAP objective ((Bougeault et al. 2001)) to aid the development of regional forecast¬ ing. The existence of these two data sets has already been exploited to conduct sensitivity studies for some of the IOPs. For example for IOP 15 it has been shown that the use of the reanalysis set improves the quality of the simulation (Buzzi and Davolio 2003, Buzzi et al. 2003, Buzzi et al. 2004 Hoinka et al. 2003), but this has not been the case for some other IOPs (Buzzi:2003b, Wang and Bazile 2004, Lascaux et al. 2004). Here the ovei ai clung goal is to co-examine the impact of the fore-mentioned physical factors and modeling issues to help guide the design of the next genera¬ tion high-resolution NWP models for the Alpine region. To this end one forecast and a series of hybrid hindcast simulations are performed for two MAP events (IOP 15 and IOP8) using a state-of-the-art mesoscale NWP model The model's performance is assessed in terms of its replication of the synoptic-scale flow, its generation of modified mcso-cv scale sub-structures, and its representation of the finer mcso-/? scale precipitation features. 61 Chapter 7. Introductory Remarks and Case Description In this chapte i we will se>t out details ol the e ases The model setup is discussed m chapter 1 and 8 The approach entails conducting a senes of experiments with different domain sizes at a fixed horizontal lesolution, operating an embedded hlghei resolut rem domain, and foiemg the* models with both the operational anal¬ ysis and the leanalysis data sets fn chapteis 9 and 10 results obtained foi TOPI5 and IOP8 are presented and disc ussed The eases chosen for this validation study arc* MAP-IOP 8 (19-22 October 1999) and MAP-IOP lr> (r)-10 november 1999) They both produced moderate intensity piecipitation but of different character I m aQ 1VA jt\. ST A vy TT O Tu this oetobei ease an atlantic depiession lavs at 12UTC of the 20th neat the1 coast of northern Spam with geopotential values of 5100m and T of -2T at 500hPa (Fig 7 I) After 121ns I he tiough has moved to the SE now strechmg bom Cataluuia (Spam) to western France approaching the alpine1 region from the W and triggering a stiong advec tion of moisture from the western Mochtenanearr sea to SE Tiance where stiong precipitations occur and dailv ac cumulations up to 150mm are measured m the Montpellier region Withm the following 12his 7.3. MAP IOP 15 65 the advection of moisture lotates to South-Noith direction and translates east affecting the southern side of the Alps with precipitations (Fig. 7.3, left) and triggering south-fdhn in noithern Alpine valleys like1 Wipptal and Rhine valley. This case was a good configuration for modéraie to stiong amounts of precipi¬ tations over noithern Italy and Ticino and records in this occasion up to 80mm rain on October 21 in the Milan area and up to 100mm within 18his from Ticino to Veneto (mostly stratiform precipitations) At OOIJTC of October 22 the sys- toin has moved towards central Italy and lost its strength and influence1 over the Alpine legion (not shown). Remarkable features of this case weie also a gravity wave breaking, a stationary PV banner over the Alps and a surprisingly broad ehy/waiui deep fohn which pushed northward into Swit/eilaud and Bavaria. 7.3 MAP IOP 15 This ease is another typical example of a front influencing the weather on the Alpine region: a lee1 cyclogenesis in the gulf ed' Genua A trough with geopotential heigth of 5280m and T of -32° at 500hPa lays over the1 North Sea on novembei 6 at OOUTC. A front related to it is moving towards 66 Chapter 7. Introductory Remarks and Case Description 21-10-11)'» ' ~ Sb I 06-11-1999 Figure 7.3: 21 liouis precipitation (starting on O(iUTC) ofoetobci 21 (left) and novem- ber 6 (light) taken from the Alpine High-Resolution Rain-Gauge Observations for the1 MA F Special Observing Period. the western Alps, reaching by that time the north of France (Fig. 7.2, top left). The W-SW winds over central Europe produce some orographic precipitations in the Jura and Geneva region as well as in northern Ticino (up to 20mm, not shown). After 12hrs the cold air lays to the1 west of Switzerland (-28" at 500hPa) wheieas the front approaches the Alps from the NW. Aliead of it the flow is now from tlie1 SW as in Fig. 7.2, top right) and the moisture is able1 to reach the southern alpine region causing moderate precipitations over the central Po valley and southern Ticino (up to 50mm, Fig. 7.3, right). Tn the meanwhile a strong Mistral event affects SW Fiance. The- development is extremely fast and after 6his a lee cyclone1 is fully developed in the Gulf of Genoa (Fig. 7.2, bottom). The target of the moisture advect ion translates from the central Alps to the eastern Alps (heavy precipitations over Veneto, up to lOOuim in few hours). The cyclone eventually translates SE towards Sicily and a north-fohn event oecuis over Ticino and northwestern Italy (not shown). The intensive observation period evidenced some characteristic features of the Alpine atmospheric dynamics as a strong Mistral and Bora, PV banners and gravity wave1 breakings. 7.4 ECMWF Forecast During the MAP campaign singular intensive observation periods (IOP) were mdivituated according to forecasts produced by different models. When at least one among the different model outputs predicted a potential interesting event at least 24hrs in advance, an TOP' was called. In tlie1 TOP8 as well as in the IOP15, the ECMWF model captured the evolution several days in advance. Figure 7.4 illustrates the1 mode] precipitation forecast for tlie two e ases during the most intense 6 hours interval. In the TOP8 the ECMWF medium-range forecast showed very favorable conditions for a heavy rain event in the Lago Maggiore area 7.4. ECMWF Forecast 67 Fig un 7 4: 6 hours precipitation accumulation foiecasted by the FCMYVKnioclel. rlb the left foi 10P8 on October 20 12UTC (init. 48his before). To the1 right foi IOP15 on November 06 at 1XUTC (mit. 421us before) with amounts up to 55 nun within 6 hours during the most intense phase. The precipitation area streaches from Cential Fiance (where intense precipitations were recorded the previous days) to the1 Tyrrhenian Sea wheieas a new Atlantic fiont approaches the1 Irish and Tberian coasts. In the IOP 15 ease instead the1 ECMWF run indicated the formation of a lee- cyclone, with the surface core1 located over the western Po Valley by Satur¬ day. The predicted lee cyclogenesis followed a classical scenario wherein a strong upper-level trough and assoe iated cold front deepens and progresses southeast¬ ward through central Europe, with a strongly asymmetric structure (northerly jet streak on tlie1 west side ed' the upper trough). Tire various models available this dav did not indicate much lainfall over the western and central Po Valley (or the 6th, while1 high rain was predicted over the Friuli target area in the eastern Alps. It was expected that the1 cold Iront would Irave difficulty getting over the Alps. 68 Chapter 7. Introductory Remarks and Case Description 7.5 The Analysis Dataset In addition to the standard analysis dataset assimilated by the ECMWF for the operational model, the Eurpean Centre produced specifically for the MAP Special Observing Period a leanalysis dataset, containing additional surface observations and wind profiler measurements (Keil and Cardinali 2003). In the following investigations the two sets have been used for the model initialization. It has beeen therefore possible to draw some conclusions on the quality of the two analysis. Chapter 8 Horizontal vs. Vertical Resolution As introduced in the model description, a useful characteristic of the non hydro¬ static model LM is the possibility of rising the horizontal resolution and adapting the corivective scheme parametrization to the new mesh. The motivation of this chapter is to give arr overview of the model set-up used in the second part of the dissertation, its benefits and its negative aspects. 8.1 Horizontal Resolution In the operational set-up of the aLMo model at Meteoswiss, the horizontal mesh is fixed at 7km. Diabatic processes like convection and turbulence are parametrized since they occur at such small scale that a model is unable to take them into ac¬ count at this resolution (they are subgrid processes with a scale-length of about 1-3 km in case of convection and 10-30m for turbulence), where as others as con¬ densation are resolved at gridscale. According to Durran and Klenip (1983) a second order smother has to be applied to the variables perturbation at gridpoints near the boundaries with a coefficient that matches the interior smoothing for 2Ax scale disturbances. In the absorbing layer the horizontal smoothing increases to the value at which 2Ax are completely removed at each time step. This to improve the short wavelength absorption, whose behavior cannot be accurately represented by the finite difference method. The result of this smoothing is that the first not damped mode has a wavelength of 21km for a 7km mesh and of 6km in case of a grid of 2km. Fig. 8.1 shows the improvement in the model orography thanks to the higher den- 09 70 Chapter 8. Horizontal vs. Vortical Resolution /. FigiiK S. 1 : Repiesentatiou of the ,_? model orography of Km ope* whole1 do¬ main at 7km (left), whole domain at ' (**' r'w 2km (below) and at 7km ewe1! the 2km domain si/e (below, left) 0 J}/ i#l ,L ff 'Jf* .Um.*/ u.j$ A'l ii sity of giid-points. On a European scale (large scale flow. Fig. 8.1. fold) the Alps appear already well defined but zooming on the1 alpine regiorr it becomes clear that for more reliable regional forecasts a better representation of the alpine ridge may be1 fundamental. In fact an increase from 7 to 2km rises the alpine1 peaks from a maximum of about 3200m to 3800m, which is still lowei than reality (up to 4800m on Mont Blanc) but it allows a much better visualization of the intri¬ cate structure that the alpine valleys have. Notice that a filter has to be applied to the topography no matter what the resolution to avoid numerical problems on stoop orography: this also accounts for the smoothing of the orography. 8.2 Setting the Vertical Levels The1 number of veitical levels that aie set in the1 operational set-up is 15 with the lowest at about 3 lui above the ground and the top at almost 21'000m. Is this still appropriate for simulations at 2km or should the vertical resolution also be increased due to the higher density of hoiizontal gi id-points.^ This question is investigated with a ease study: two 24hrs binde ast simulations of the MAP TOP 15 case at 2km mesh size1 nested on the operational run, with different vertical layers set-ups (Fig. 8.2) are1 pen-formed: one with the usual 15 levels and the second one 8.3. Results - Comments 71 Figure 8.2: North-south cross section trough the Alps showing the verical levels below lO'OOOm. Left for 45 layers set-up, right for 64. (Top at 23000m) with a new 64-layers structure, whith a higher density of layers specifically in the lower troposphere (the lowest at 25m above the ground, a number of 35 levels below 3000m and 50 below lO'OOOm. (compared to 24 below 3000m and 36 below lO'OOOm of the former). The important aspects to check are the following: • Are there differences produced by the new vertical structure, according to the wave theory? • If yes, how are these related to real data? • CPU costs increase. 8.3 Results - Comments The plots in Fig. 8.3 illustrate the result of the two 24 his hindcast simulations for IOP15, showing the 24hrs rain accumulation on november 6, 1999. Even af¬ ter a close look, it is very hard to notice any variation between the two plots. Insignificant shifts or differences of accumulations are randomly present but the general picture is exactly the same (in chapter 9 a model-reality comparison will be discussed). Other fields (GPT, winds, PV, ...) have been plotted (not shown) with the same result. Since the increase in the number of vertical layers does not affect the CPU time needed for a 2km mesh simulation more than 5% of real time, we decided to mantain the operational setup at 7km and operate at 64 layers for the very high resolution to mantain coherence to the horizontal resolution increase even if the Chapter 8. Horizontal vs. Vertical Resolution p. -\ "\ Figure 8 3- 241us lain accumulation for IOP 15 stalling on november 00, 1090 at OOUTC. Cndspace 2km, 45 layeis m the vertical test simulation didn't show any improvement in the foiecast. Chapter 9 Error in Precipitation Field The reliability of a precipitation forecast is another issue of great importance when judging a high resolution model. Hier a comparison between real data and model (hindcast) simulation (initialized with ECMWF operational data and RE data) at two different horizontal resolution (7 and 2km) for the MAP cases IOP8 ane 15 will be shown. One method used for analysing precipitation amounts of forecast arrd real data is to select single rain gauges. An interpolation of the model values of some grid- points around the rain gauge is needed and the comparison is then performed between measured data and interpolated model data. The positive aspects of this method is that two statistics can be extrapolated: the presence of rain in the model and in reality and a comparison of the? forecasted arid measured quantités or precipitations. The negative aspect is that a slight phase shift of the precipitating system can result in a very poor score for the model. Moreover the forecast is not seen as a whole: just single gridpoints are taken into account. A less statistical but more fair method is to analyse daily precipitation charts covering the whole domain, individualising the dominant features and comparing their location and magnitude with the observed data and within other simula¬ tions. This is the method applied in this chapter. The observed data used for the comparison have been produced in a joint effort of tlie Institute for Atmospheric and Climate Science at ETH Zurich and the MAP Data Centre. The analysis is based on observations at about 6500 rain-gauge stations, covers the entire Alpine region (2.1-18.9W and 42.18-49.ON), including the ridge and the foreland, has a time resolution of one day and a space resolution of about 25 km (Frei and Schär 1998 and Frei and Häller 2001). 73 74 Chapter 9. Error in Precipitation Field Figure 9.1. 21 hours precipitation from november 00, 1900 at OGUTC* LM Model at 7km (lop left) and at 2kni (top right) initialized with AN; at 7km (bottom, left) and at 2km (bottom, light) inittali/ed with RE. Highlighted are the- two legions where an avegaie is computed. 9.1 IOP-15 The1 Analysis of Alpine High-Pesolution Rain-Gauge Observations foi Noveurbei 06 1999 (Fig. 7.3) shows a heavy precipitation event over the noithein adriatic coast and Veneto region in Italy with daily precipitation amount up to 80mm, a secondary maximum ovei the1 central Po plain (near Milan) up to (it) mm. a local precipitation minimum over tlie extreme NW Italy and a regular distibution of about 20mm ovc1! the1 Alps. The simulation at 7km initialized with opeiational data (Fig. 9.1 top left) does not show the adriatic precipitation maximum (but the very stiong maximum present over Croatia could indicate a horizontal shift of about 200km). This fore'cast also pictures no precipitations over a large area ed'the Italian NW region. The nested 2km inn is veiy similar even if no cou¬ vée tion paiainetrization has been used, with a peculiar difference over the Swiss Plateau, where little precipitation is properly predicted. More interesting aie the 9.2. IOP-8 75 mm/24hrs 7km-AN 2km-AN 7km-RE 2km-RE Appenines 28.5 29.2 30.6 29.1 Ticino 18.4 16.1 22.2 22.6 Table 9.1: Averages of the 24 hours precipitation over the two domains pointed out in fig. 9.1 (upper left panel): the Ligurian Appcnnins and the Ticino Area. results when the initialization is performed with RE data (Fig. 9.1 bottom left and right). The maxima over northern Adriatic is well forecasted (sligthly to the south-east of the exact location) as well as the dry region over NW Italy. In particular the 2km resolution run pictures precisely the strong precipitation max¬ imum (overestimating the amplitude) and improving significantly the prediction over the central Po valley whereas the Swiss Plateau appears wet with 10-20mm of rain, which is not the case according to the observations. Interesting is also a quantitative analysis of domain averages of the precipitation depending on the horizontal resolution and on the initial conditions used. This is provided in table 9.1 for two separate subdomains as the Ligurian Appennines and Ticino (highlighted in fig. 9.1). According to the table the RE data produce a slight to moderate increase of the precipitation amounts over the two domains. In particular- over the Appennines an increase is noticeable only at 7km (+7%) whereas at 2km the mean accumulated rain is constant. Over the Ticino area instead the increase is much stronger, about +20% for the 7km and up to +40% for the 2km. The influence of the increase in the resolution is not unique: it can result in an increase or a decrease of the precipitation amounts or even remain constant. The use of RE data for the model initialization has an strong impact on pre¬ cipitation forecasts, ameliorating significantly the precipitation distribution. The benefits from the use of the 2km horizontal resolution instead are less eviderrt (but present) in this November case, a period of low convection and the characteristic features of the model at very high resolution (no convection parametrization) may not be totally visualized. 9.2 IOP-8 The IOP8 case as already mentioned in chapter 7, occured in the second half of October. In October convective processes can still be very strong thanks to the advection of very warm and moist air from the Mediterranean sea towards 76 Chapter 9. Error in Precipitation Field F/gtiK 9.2: 24 hours precipitation from october 21, 1909 at 0GUOT: LM Model at 7km (top left) and at 2km (top right) initialized with AN; at 7km (bottom, left) and at 2km (bottom, light) initialized with PE. the1 Alps. As we can see in Fig. 7.3 in this case the whole south alpine regions received between 10 and 80mm in 24hours with a maximum located over south Ticino and western Lombardia and a minimum ovei southern Tirol. The TAT forecasts shown in Fig. 9.2 took very similar, independently from the initialization data and from the resolution but very different from the observation data. The biggest precipitation amounts are located in northern Piedmont and along the coastal region from Nice to Gonova and the1 predicted amounts are extreme: up to 150mm per day for the 7km runs and even more1 for the 2km simulations. It is now interesting to see why in this case1 the LM mode1! has not been able to improve the forecast of the1 precipitation field by a resolution increase nor by the use1 of RE data.. With the help of Fig. 9.3, whcTe tlie model and the analysis low levé large scale flow are compared, it is possible to have an explanation of the model behavior in case of the precipitation field. The main diff'eiene-es in the wind-vector field at 850hPa are: 9.2. IOP-8 77 Figure 9.3: 85()hPa horizontal wind at 06UTC, October 21 1999 (vmax = 15m/s). On the left the LM at 2km initialised with ECMWF analysis and on the right the analysis itself. The black dot represents the location of Milan (cf. Fig. 9.4). • Lower wind velocity over the Po valley in the analysis. • The presence of a wind minimum with a cyclonic circulation to the NW of Genova irr the rrrodel (rrot related to a pressure minimum on the ground). • This changes considerably the flow direction in the upper Po valley with a rotation of the low levés winds and a shift of the convergence regions towards the NW. The effects on a mountain terrain are visible in Fig. 9.2 and Fig. 7.3: it results in a very different advection of the moisture towards the Alps. A more intense flow carries the humidity nearer to the alpine crest and the different flow direction shifts the 'stau' effect where the convergence between mountain range and flow is at its maximum: in this case the "Lago Maggiore" area, a region where the orography has an extreme risirrg within few km wich enhances even more "stau" and corivective effects. Thanks to the Milan radiosounding Fig. 9.4 it is possible to have real time com¬ parison with the observation. It shows a saturated atmosphere up to 600-650hPa, a low level flow from the E (at 900hPa) to SE (at 800hPa) with intensity between 10 and 25m/s and a strong SW flow aloft. The analysis field in Fig. 9.3 is more coherent to the radiosounding, with a E-SE wind direction with intensity at about 15m/s, than the model (S-SE direction with almost 20m/s intensity). 78 Chapter 9. Error in Precipitation Field SITE FIXED MIL [18030] TIME 21 OOT-1399 06 00 00 (MLANO] TEMP/WINDS DEWPOtNT Figure 9.4- Milan radiosounding at 0GUTC October 21 1999 (from the map database) 9.3 Conclusions The daily precipitation forecasts of the LM model for two MAP cases have been compared to the High-Resolution Rain-Gauge Observations for the MAP Special Observing Period and in one case to a radiosounding. In the KJP15 case the model showed an increase in the forecast quality introduc¬ ing a higher horizontal (and vertical) resolution and using MAP reanalysis data as initial and boundary conditions which contain more observation data. The benefits of these improvements are quite impressive when comparing the simula¬ tion in Fig. 9.1 top left and bottom right to Fig. 7.3. A different result is obtained in the IOP8 case: the simulated daily precipitation amounts differ significantly from the observations both in intensity (heavier in the model) and in geographical distribution, no matter the resolution and the initial and boundary conditions that were adopted. The origin of this lies in the different low level windfield in the upper Po valley and therefore in the advection of moisture towards the Alps reproduced by the model compared to the observa¬ tions. The introduction of a higher horizontal resolution produces a fragmentation of the signal in the precipitation as well as in other fields and the genesis of substruc- 9.3. Conclusions 79 tures. In the two cases illustrated in this section the main features of the model simulation were already present in the 7km integration and the new informations produced by the nested run modifies only slightly the forecast. Moreover due to the coarser resolution of the observations/analysis it is not easy to establish if all these substructures developed really. Some certainly did, as the drier forecast for the Swiss Plateau in IOPf 5, which is confirmed by the observations. The level of predictability of the atmosphere plays a fundamental role in the ca¬ pability of a model to simulate its evolution as well as the analysis used as initial condition. The benefits from the increase of the horizontal lesolution instead are less evident (but piesent) irr a period (october and november) of low convection and the characteristics of the model at very high resolution (convection scheme) may not be totally visualized. Seite Leer / Biank leaf Chapter 10 Domain Study As seen in the previous chapter, differences between observed precipitation data and forecasted amounts occurred in some cases may be caused by differences in the large scale flow (see fig. 9.3) and not due to failuies in the model physics and dynamics. To see if these1 discrepancies are influenced by the model configuration and therefore can be minimized, a study on the impact of the model domain size on the forecast in piesented next. 10.1 Introduction and Procedure The aim of this part of the study is to investigate how the large scale flow on the nested 2km simulation is influenced by the domain size of the coarser simulation. To this purpose three different domains have been arbitrary chosen along with an Alpine domain foi the high resolution simulation (fig. 10.1). Since for MAP cases ECMWF provides also Re-analysis data (RE, which include additional observa¬ tions) it is a suitable chance to also have indications on the effects of initial data on the model (and give some issues on the quality of ECMWF Analysis (AN) and RE). This is the procedure that fias been followed: The case studies selected for the investigation are the MAP fOPs introduced in chapter 7 initialized with the ECMWF analisys (AN) and re-analisis (RE). Six 7km resolution simulations integrated on three different domains (L,M,S have domains,fig. 10.1) been performed for every case, three for every analy¬ sis dataset. Then from every simulation a new 2km resolution simulation has been nested on the Alpine Area. We ended up having 24 simulations (12 for every case) that were low pass filtered before calculating the difference between model run and its analysis dataset over the Alpine domain for the 2km as well 81 82 Chapter 10. Domain Study Figuit 10.1: In this figure vou can see the tlnee selected domains foi the 7km Simulation (Laige1, Medium and Small domain) along with the alpine domain [2km|. as foi the 7km simulations. The root mean square (RMS) integiatod ovei the domain was also produced. Before pioceeding to the results, some comments must be pointed out and discussed: ECMWF piovides MAP PE data with 31us time resolution instead of the1 operational Ohrs, an important aspect that could contribute for bettor simu¬ lations. Since the mode1! is operated with 'perfect boundary conditions' (hindcast sim.), the simulated huge scale flow should follow the1 analysis closely. We there¬ fore apply a low pass filter to both analysed and modeled fields and use1 the PMS difference of the geopotential as a measure for the deviation ed' the simulation from the1 analysis. The RMS of tlie1 temperature field is also taken into account, since this field gives an indication of the representation of the thermal structure of the1 simulated large se ale flow 10.2 IOP-15 Case Beginning witli the geopotential in the lower atmosphere (850hPa), we can see in fig. 10.2 (top left and right) the PMS foi the 7km run on the Ht and the 2km run on the right. Tire fiist impression is that in both cases the PMS values aie extremely low (on average PMS (at)out 20 %). an indication that RE data could belter reproduce the1 lower tropospheie (along with 31us time resolution). Differences can be found in the divergence with time of RMS values for L,M and S (gierte1! in 2km runs then in 10.2. IOP-15 Case 83 IOP15-ZLAY850 IOP15-ZLAY850 Time Time Figure 10.2: IOP15. RMS of geopotential field at 850 hPa (top) and 500hPa (bottom) for 7km (left) and 2km (right) on alpine domain. Solid lines initialized with AN, dashed lines with RE. 7km). The lower part of fig. 10.2 for the middle troposphere shows a different behavior The RMS values are still low with a remarkable coherence but it is evident that RE-mitiahzed simulation values are not lower (at least in the first f2-15 hrs) than the AN-initialized, indicating that RE data are not better in the higher tropo¬ sphere than the operational data. Another important difference is the exponential character of the RMS for AN-initialized simulations, while the RE-initialized runs seem to be moie stable. As can be seen from fig. 10.2 the RMS difference generally decreases as we go from the large to the small domain (there are few exceptions thow). This can be interpreted as follows: in the laigei domain the model has more freedom to develop its own flow structure, whereas in the smallei domain it is much more restricted by the lateral boundary conditions. To see if the evolution shown by the geopotential field is common to other vari¬ ables we look at RMS of the temperature field (fig. 10.3)• the most noticeable feature is the similarity of the plots: between the high and low tioposphere at 7 and 2 km resolution. The size of the domain influences very sligthly the values of the RMS and there is no particular improvement in using RE data instead of AN data as initial and boundary conditions. There is only a quasi-linear increase 84 Chapter 10. Domain Study IOP15-T850 - - MES SEc 3 S * LR* 20 LT 1 0 /y^^=^^ 3 6 0 — LEl 5Eo 30 -*- MRU • Sfly CO q: 1 s - Time Time Figure 10.3: IOP15: RMS of Temperature field at 850 hPa (top) and 50()hPa (bottom) for 7km (left) and 2km (right) on alpine domain. Solici lines initialized with AN, dashed lines with RE. of the RMS with time, more accentuated in the first 6 hours and a hint of expo¬ nential trend at the end of the 24hrs interval. The RMS difference still decreases as we go from the large to the small domain but the spread remains very small compared to the geopotential case. 10.3 IOP-8 Case As confirmation for the characteristics of the 'domain issue' observed in the MAP IOP15, it is useful to have a look at the second case study, IOP8. As in the previous case the geopotential PMS is very low (even lowei) and in the low troposphere simulations initialised with RE data show on average lower values (fig. 10.4, top) than with AN. On the SOOhPa surface the initialisation data has very little impact on the development of the model as also seeen in the previous case. The influence of the domain size is small for the first 18hrs (0-5m on average) and becomes noticeable (>10m) afterwords with the characteristic growth going from S to L size. However the time evolution does not show a specific trend other than an increase in RMS arrd irr the spread between L,M,S. 10.4. Conclusions 85 IOP8-ZLAY850 IOP8-ZLAY850 20 — LEl - MEt 3F -»- LRo -- Mn- *- MR« * SRC 20 CO CO LT \ J*-*-n- ,--" - CE o •r //^ 3 flu ^ n ? 24 3 0 0 2 j S 2 24 Time IOP8-ZLAY500 IOP8-ZLAY500 — LEe - - MF - - MEc 30 -*- LRc -m- MR« _#_SRs Ho S1. to2° cl rx s 7?^v^^:^lJ^tr^JE^;^*' ^^tt* > s Time ifyunr? 70.^; IOP8: RMS of Geopotential field at 850 hPa (top) and SOOhPa (bottom) for 7km (left) and 2km (right) on alpine domain. Solid lines initialized with AN, dashed lines with RE. The temperature field is rrot shown due to the extieme similarity do the IOP15 case. 10.4 Conclusions The aim of this study was to investigate how the large scale flow on the nested 2km simulation is influenced by the domain size of the coarser simulation. Moreover the availability of diffeient sets of initial and boundary conditions allowed to examine othei issues like their quality and the time evolution of the RMS. The following features have been obseived: • The influence of the domain size is minimal in the first f2hrs and grows afterwords reaching in some cases RMS differences betweeen L and S up to 20m for the heights field (fig. 10.2 bottom) and 0.5K for the temperature (fig. 10.3) • The RMS values increases in time and decreases as we go from the large to 86 Chapter 10. Domain Study the small domain • The RE data appear more reliable in the lower atmosphere than AN data in the geopotential case. No influences are recorded higher (SOOhPa) and for the temperature field This can be partially explained by the fact that the diffeience between RE and AN data is to be found on the surface (due to the additional surface data) • The time evolution of the RMS varies from case to case and if you look in the low or high troposphere. It can be exponential (fig. f0.2 bottom), stable (fig. 10.2 top) or a quasi-linear growth (fig. 10.3) • A greater time resolution and more surface observations in the initial data aie do not determine a particular increase in the quality of the simulations. Instead it amplifies the vaiiabihty, introducing peaks of RMS orr the 850hPa suiface at time 3 (model spin-up?) and f5hrs. To conclude, we have seen that in a larger domain the model has a lot of freedom to develop its own flow structure, whereas in a smaller one the restric¬ tions due to the lateial boundary conditions damp its independent developmerrt. This needs to be kept in mind when setting the outei domain size. Depending on the application of the model a balance between the freedom to develop and the correct representation of the large scale flow rreeds to be fourrd. Chapter 11 The Storm Lothar At the end of December 1999, one of the most severe winter storms of the last decades crossed Central Europe causing major damage and destruction in north¬ ern France, southern Germany, Switzerland and Austria. Lothar was character¬ ized by an extreme translation speed (and indeed was embedded in an unusually intense upper-level jet), an explosive development, and extremely high surface winds that caused the most of the damages, with millions of mA of forest dam¬ aged and more than 50 people; killed (Wernli et al. 2002). Maxirrrum wind speed of 158km/h were measured in Zürich, 134km/h in Bern, 147km/h in Basel and 130km/h at Zürich Airport, whereas in the alpine crests, even though very strong (204km/h on the Jungfraujoch), the wind speed were not particularly stronger than in other winter storms cases. The dynamical aspects of Lothar have been deeply investigated by Wernli et al. (2002) under the PV perspective, with the help of an HRM2 hindcast sim¬ ulation with ECMWF analysis data as initial and boundary conditions. The most important aspects regarding Lothar captured by this study involve the transla¬ tion and the intensification of the storm, whereas the decay docs not present any exceptional feature other than a rapid decay, caused by the ending of the moist air advection due to the increasing distance from the Atlantic. Lothar originated in the western Atlantic as a shallow low-level instability and intensified due to the continuous and intense condensational heating (diabatic process) causing a constant production of positive PV (see eq. f .9). Located at the beginning to the south of an intense upper-level jet, the storm intensified explosively when the two structures converged. At this point the circulation in- 1 Named Lothar by the German Weather Service, DWD 2High Resolution Model, the new version of the former Modell' used until 2000 " 'Europa by DWD 87 88 Chapter 11. lothar FigtiK 11 1 Suiface piessuie of Lothai at 0(>tJ 1 (1 of Decenibei 2(> when the minimum of SIT is obseivtd EC'MWr Analysis (top left) and the tin c c moist simulations, stalling at 0(>U I C (top light) at 12U I C (bottom le ft) and at 18U I C (bottom light) of dee enibei 2r) due cd by the upper -level positive1 PV anomaly clue to the steep isentropic surfaces that intersect the upper-level jet significantly helped the genesis of a narrow and deep stiatospheiic an intrusion The whole sti ire true (diabatic allv geneiated PV and tropopause (old) results in a PV tower by the1 time of maximum intensifica¬ tion, that is ovei Confiai Europe (see figure 111) 11.1 Aim and Approach lire majoi interest in operational models miming at veiy high resolution in very lecent years lias made binde a st simulations of past cases a verification tool (or resolution increases 1 her ofore, a cential aim of this last chapter is to compare the runs of the two models (HPM and LM) and sen1 i( the numeric al improve¬ ments reflect m a bettor represent at rem of the instability growth and the cyclone life-cycle The1 accent will be set on the1 tiauslation and on the intensification 11.2. Sensitivity to the Initial Conditions 89 A second interesting aspect to be investigated is how a short range hind- cast simulation (24-48hrs) is influenced by the initial conditions and the forecast length. Three moist runs have beeen performed with the LM model, starting at different times: the first on December 25 1999 at 06UTC, the second at 12UTC arrd the; last at 18UTC (we will refer to the 06UTC, 12UTC and 18UTC simulation). At Ü6UTC Lothar stands outside of the LM domain, at 12UTC on the boundary, whereas at 18UTC it is placed well inside the model area. This approach may evidence important features on the model behavior and the influence of the initial conditions on the forecast. As initial and boundary conditions ECMWF data have beeen used. An horizon¬ tal and a vertical resolution of 7Km and 45 levels were adopted, that compared to the HRM it means an increase factor in the horizontal of 4 (28km for HRM) and an almost constant resolution in the vertical (40 for HRM). Tn the previous chapters the LM have been applied up to 2km horizontal res¬ olution. At this mesh the domain size has to be kept relatively small due to computational power. In a case as Lothar, where the upper level jet is so intense that the storm would be in the typical nested domain only for few timesteps, it would have been impossible to adopt a domain suitable for the whole time period with a limited increase of gridpoints. Even on a resolution of 7krn the domain setup rreeds to be adjusted due to the translation speed. To minimize possible problems and be sure that the storm remains in the domain as long as possible, we increased the domain size in the E-W direction (500x364 gridpoints instead of the operational 385x325), in particular upstream of the Alps and Central Europe. 11.2 Sensitivity to the Initial Conditions What we expect from a short-range forecast (24-48hrs) is arr accurate representa¬ tion of the short-term development of the atmosphere in a particular part of the world (e.g the Alpine region). As we have seen previously this is not always the case due to the variable atmospheric predictability. Since the Lothar case shows an extaordinary active dynamics, it is a good opportunity to test the sensitivity of the model under extreme conditions. Three short-range hindcast simulations ini¬ tialized at different times (with 6hrs gap in-between) of the Lothar development have been therefore performed with the 'Lokal Modell' as mentioned previously. As in (Wernli et al. 2002) a 'dry simulation' has been also performed to check the influence of the condensation processes for the growth of the cyclone. Figure 11.2 shows the time evolution of the pressure minimum in the core of the cyclone for different sources. The minimum of pressure that was observed by DWD and that is recorded in the Berlin Weather Charts during this event 90 Chapter 11. lothar ___ LOTHAR - SLP - 2513 ' - - 2506 dry -O- ECMWF An * DWD Obs Time Figure 11.2: Time evolution of the minimum sea-level pressure in the cyclone Lothar from observations, ECMWF Analysis, LM dry and moist with different forecast lengths. The '0' time label refers to December 25 at 00UTC and 12 refers to dec 25 at 12UTC. is 962hPa on December 20 at 06UTC. The pressure distribution over Central Europe forecasted by the moist simulations and assimilated by in the ECMWF analysis at this time is shown in fig 11.1. It is remarkable that the ECMWF analysis displayed Lothar in its initial condition data set as a 976hPa low at the same time, which is a 14hPa difference to from the observations! The LM model is represented on fig. 11.2 by the dry and the three moist simulations and all of them record a higher minimum of pressure about 3 hours after the observations, which means at 09UTC Dec 26. Moreover the pressure maintains its lowest value for 3-4 hours, whereas the observations show a rapid decay of the cyclone with a sudden increase of the pressure value. Within the moist simulations the main difference is found mainly between the 06UTC and the two others. if Even the intensification occurs very similarly with a pressure drop of about 20hPa in the 15 hours before the minimum is reached in all of the three simulations, the 06UTC run shows a difference of about +7hPa from the observations early in the; intensification phase, whereas the; 12 and the 18UTC runs are very accurate and remain accurate for the following 10 hours. Later, when the minimum of pressure is observed, the difference between the 06 and the 12 an 18UTC runs is still of about +7hPa, while; it is of +15hPa in comparison to the observed value (+8hPa for the 12UTC and 18UTC runs). The observed pres¬ sure value increases dramatically after setting its minimum and after six hours the difference between observation and 12UTC and 18UTC runs is reduced to 0. The 06UTC simulation is however still about 5hPa to high. This difference 11.2. Sensitivity to the Initial Conditions 91 diminuishes at the end of the simulations, when observed data, ECMWF analysis and the three moist LM runs display the same pressure value. As already mentioned in the previous section, on December 25 at 06UTC, Lothar is located outside, at 12IJTC on the boundary, whereas at 18UTC it is placed well inside the model domain This explains the pressure behavior of fig. 11.2. In the 06UTC simulation the initial data does not contain any informations about the approaching storm and when the new boundary data are advect ed into the model (6 hours later) the cyclone should already be present on the western boarder of the domain and is therefore missed At this time the intensity of the cyclone compared to the observations is already of 0-7hPa too weak and will stay too weak. Thus the development is similai to the other simulations. The initial con¬ ditions for the two simulations irritialized 6 and 12 houis afterwards contain all the up-to-date informations about Lothar. The model can therefore develop its physics/dynamics and better simulate Lothar even if the time resolution of the boundary data is the same, inadequate, as in the 06UTC. Apart from the problems evident within the boundary data, even the two simu¬ lations receiving all the informations of Lothar from the initial conditions are not able to completely simulate the storm in its fully and explosive development (the usual criterion for 'explosive development' is accepted to be -24hPa within 24hrs (Sanders and Gyakum 1980) and Lothar shows about -35hPa within the last 24hrs). In the last Öhrs of intensification the pressure decreases of about 22hPa, while the model can account for a decrease of 13hPa. Even the 06UTC with the initial difference shows an intensification of 13hPa, which shows that the initial bias does not effect the mode] physics/dynamics. To better understand the model behavior, a sensitivity study has been performed as in Wernli et al. (2002): we simulated Lothar with the LM initialized at 06UTC with no condensational effects. The results foi the pressure tendency plotted in 11.2 fig. state that the effects of this change in the model dynamics are visible immédiat ly with a strong signal in the pressure field. A difference of 3-4hPa is recorded between moist and diy runs until 6 hours before the minimum of pres¬ sure is reached in the model. When the intensification growth increases in the moist 06UTC, the pressure in the dry run decreases constantly until the mini¬ mum is set. At that time the difference between dry and moist is about 7hPa and this values is maintained until the end of the simulations. This sensitivity study shows that the diabatic effects play a basic role for the development of the storm. Condensational effects in the LM model can produce an acceleration of the storm intensification but are still too weak in comparison to the observed explosive development. The 12UTC and the 18UTC simulations reproduce well the observed intensification of the storm until the intensification rate increases, from this point on the diabatic forcing of the model is not sufficiently strong to keep up with the observed explosive deepening of 92 Chapter 11. lothar Figure 11.3: 3D plot of the 4pvu isosurface and wind vectors at 850hPa for the three LM moist (top left and right for 06UTC and 12UTC, bottom left for 18UTC) and the dry simulation (bottom right). Lothar. 11.3 A3 Dimensional PV Perspective In the previous section we have illustrated how important the diabatic effect (condensation) can be in the development of a cyclone. Equation 1.9 relates the material rate of change of the; PV and the production of diabatic heating. The release of latent heat in saturated regions in the lower and middle troposphere diabatically generates so-called 'low-level positive PV anomalies' (Wernli et al. 2002, Wernli and Davies 1997, Stoelinga 1996). The following vertical realign¬ ment of the upper-level and the low-leve PV anomalies leads to the creation of a 'PV tower' (Rossa et al. 2000). This structure corresponds to a quasi-barotropic vortex with a strong cyclonic wind field troughout the whole troposphere. Figure 11.3 illustrates the structure of Lothar under a 3D potential vorticity per¬ spective for the three moist and the dry LM simulations on December 26 06UTC, the moment of nraximal intensity of the storm. At this time the low level PV anomaly in the three moist simulations is similar: an immense amount of ver¬ tically aligned PV is located over the centre of Lothar and rises up to the mid troposphere. Notice that the 18UTC panel shows the most vertically extended 11.3. A3 Dimensional PV Perspective 93 tower of low level PV and that the 4pvu isosurface is plotted instead of usual the 2pvu due to the strong background signal generated at this horizontal res¬ olution. In the upper troposphere though the differences are more significant: the anomaly that generates the PV fold is veiy weak in the 06UTC simulation and gains in intensity and vertical extension in the 12UTC and even more in the 18UTC simulation. This is probably another key factor for the pressure behavior seen in fig. 11.2. The upper level and the low level PV anomalies generate a unique PV tower only in the 12UTC and 18 UTC simulations, leading to the formation of the quasi-baiotiopic vortex associated with a strong cyclonic wind field mentioned previously, whereas in the Ü6UTC only the low level anomaly in sufficiently developed and the structure remains only partially developed. The effects of this differences are visible in the pressure tendency, in fig. 11.2 The wind field (at 850hPa) also plotted in fig. 11.3 shows as well a weaker wind inten¬ sity ahead of the storm in the first simulation and a more meridional and intense advection in the last run. In the case of the sensitivity study, where all condensational processes are elimi¬ nated, the low level PV anomaly is completely absent, wheieas the upper tropo- spheric configuration is very similar to the simulation with condensation. The differences between the moist simulations aie also evident from the verti¬ cal sections across the centre of the cyclone (see fig. 11.4). The low level anomaly is well present in the three moist runs showing considerable values (8 to 10 pvu) and absent in the dry. The upper level PV fold (2pvu isoline) reaches 450, 480 and 530hPa in the three moist and 350hPa in the dry panel. Only when the upper and lower troposphere anomalies are well developed at the same time, the cyclonic wind-field can develoj^ through the whole troposphere and induce an acceleration of the intensification visible at the surface as a sud¬ den and strong pressure decrease. According to the surface pressure observation, the PV towei foimed on December 26 1999 must have been more extreme than what simulated by the 18UTC run. If we compare the LM simulations with the HRM model pioduced in Wernli et al. (2002) (24hrs hindcast simulation from dec. 25 12UTC to dec. 26 12UTC) we see that both models are unable to capture the exact intensity of the storm. The LM run initialized at the same time as the HRM produces a more accru ate minimal surface pressure (970hPa versus 972hPa, observed 962hPa) and a more extreme low level PV anomaly (> lOpvu vs ~ 6pvu) whereas in the HRM re¬ production the upper level PV anomaly is more intense and well confined in the fold. Even if the stiong increase of the hoiizontal resolution results in a bettei repro¬ duction of the intensity of the stoim compared to the HRM, it is not sufficient 94 Chapter 11. lothar Figure 11.4.: Vertical S-N oriented cross-sections trough the center on the storm for the moist (top left and right for OGUTO and 12UTC, bottom left for 18UTC) and flic dry LM runs (bottom right). Plotted are PV, in colours, 6 (solid black line) and zonal wind if larger than 80in/s (dashed). to reduce considerably the difference between simulation and observed evolution. The sensitivity study evidences once; again the extreme importance of the conden¬ sational processes in the; development of Lothar and hints of an underestimation of tlie diabatic forcing in short range; numerical models as the LM. 11.4 Conclusions A sensitivity study has been conducted to investigate the influence of tlie initial condition and of tlie diabatic heating on a high resolution model during an ex¬ treme ea.se such as the Lothar storm that hit Central Europe on boxing day 1999. Three simulations have been performed at a horizontal resolution of 7km, initial¬ ized on December 25 at 06UTC. 12UTC and 18UTC. A fourth simulation started on 06UTC has been driven without condensation effects. Two main differences 11.4. Conclusions 95 have been noticed within the three moist runs and compared to the observations: if at the initial time no irrformations of the storm are present in the initial con¬ ditions, due to the coarse time resolution of the boundary data (6 houis) and to the extremely intense large scale flow, the lepioduction of the cyclone evolution will be strongly underestimated for the entire simulation (06UTC). Else, if the storm is already in the model domain at the initial time, its evolu¬ tion is well reproduced until few hours before the minimum of surface pressure is reached. At this time the observed storm intensification is subjected to an acceleration that is not captured by the model, oven at this resolution. The dry simulation confimrms the importance of the condensation processes for an accurate representation and hints that the diabatic forcing is underestimated in (high resolution) models. Seite Leer / Blank leaf Appendix A Appendix to Chapter 5 Vorticity Conservation Theorem In an incompressible and two-dimensional fluid the velocity u = (u, v) is given by u = _ v= A.l) ox ox where ty is the streamfunction. Then, the vorticity ( is defined as: dv du 2 , . ( = _ = V2* - A* (A.2) ox ay where A is the two dimensional Laplace operator. This mearrs that knowing the vorticity ( (with boundary conditions) it is possible trough inversion to obtain $ and therefore also the velocity field u. The equation of motion of a fluid parcel neglecting the friction R and the viscosity 77 is DÛ 1 ^ /A o\ — = - • Vp (A.3) Dt Q where g is the density, p the pressure and D/Dt the material derivative. We; can then reformulate A.3 for a two dimensional incompressible flow as: ^ = 0 (A.4) Dt For the proof of this theorem consider a loop C in a fluid, moving within the large scale flow. Then according to the; Stokes: 97 98 Appendix A. Appendix to Chapter 5 M-*-d*=ïïiç-ia (A-5) on the other hand r r r d .. . d Du _ _ ^ _ _ = • as (b a —- -7— é u ds The equation of motiorr by neglecting the viscosity 7/ is Dit 1 - / a -\ = — .Vp (A.7) Dt Q — — By replacing A.7 and jyjds = ^f ^ — u,2 u\ = dit in A.6 we obtain: È£"-d"=-£*yds+£!t-d!!=-liO+ld&=0 (A-8) and therefore §tl<-da-lix-da+£<-m'"' = 0 (A-9) due to the assumed incompressibility of the fluid, D(da)/Dt = 0 and therefore jf£ «*. = <> (A.1Ü) since the loop C is arbitrai, we obtain that ^=0 (A.ll) v ; Dt 99 Fundamental Solution of the 2 Dimensional Laplace Operator We want to prove that *(.r, y) = — - log(r) ; r = s/x2+y2 (A.12) 27T is a solution of the 2 dimensional Laplace operator, that is A* — Ö, where S is the Dirac delta function. f. We have to show that A$> — 0 for r/0 For lotation-symmetric function the 2D Laplace operator is defined as: 02 1 ö A = ^ + - • (A.13) orz r or and therefoie by substitution- *>=<£ + ;•£}£ MO =0 (A.14) 2. For ^ to be considered a fundamental solution, a second condition must be fulfilled: / A* dxdy = 1 ; B,= {(.r, y) \ x2 + y2 ^ R2} (A.15) It is sufficient to demonstrate that §dB V\T/ -dn = l because then according to the 2 dimensional Gauss theorem: / AÜdxdy= Thus* f - f2n ö* 1 i'2n 0 ~.rd(ß=— i V* -dfî = — • = ^ log(r)6V ; r dxf>V 1 K(A. 17)' Lb, Jo or 2tt J0 dr therefoie is fy a fundamental solution of the 2D Laplace Operator 100 Appendix A. Appendix to Chapter 5 Green's Theorem for Continuous and DifFeren- tiable Vectorfields For continuous and differentiable vectorfields as K(x,y) — (P(x,y),Q(x,y)) the vector identity known as the Green's Theorem assesses that / (-^ - — ) dxdy = I P-dx + Q-dy (A.18) JB V dx dy ) JdD In our case the vectorfield is 5.10: *(x,y) = £- i \og(r)dx'dy> (A.19) applying the vector identity A. 18 we can calculate the velocity field u = (v, v). With Q = 0 and P = - log(r), we obtain that — / log(r) dx'dy1 = -J> log(r) dx' ; r = y/(x - x')2 + (y - y')2 (A.20) and therefore u(x,y) = ~ = -^ jf log(r)^ (A.21) = — Analogously with Q log(r) and P ~ 0 we obtain for v(x,y) v(.r, y) = -^ = -f- / log(r) dx' (A.22) oy 2^ Job This means that we can reproduce the velocity field trough the informations about the contourline and that the velocity field itself determines the temporal evolution of the contourline. Then at any point on the contour dB, the velocity is given by x0 (t) - u(x0(f)) =-^i log |xo(t) - x'l dx' (A.23) ^7r JdB Appendix B Appendix to Chapter 6 Seasonal Climatology: RMS of SON and MAM SON: September, October, November 2001 DJF: December, January, February 2001/02 MAM: March, April arrd May 2002 101 102 Appendix B. 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Dynamical aspects of the life cycle of the winter storm 'Lothar' (24-26 December 1999). Quart. J. Roy. Meteor. Soc. 130, 405 - 429. Seite Leer / Blank leaf Acknowledgements f would like to adress some thanks to the various persons who, consciously or not, were fundamental for the succeeding of this thesis. In the more than four years spent at the Institute I appreciated in particular the relaxed (hopefully non- changing...) climate, the (extra-) scientific conversations, advices and of course the professional competence among the dynamical group. A particular mention to Huw, the main contributor to my work, who besides adopting me as a PhD student, initiated and conducted me wisely through the obstacles of scientific research, with his contagious enthusiasm, forging continu- osly new ideas, encouraging when necessary and providing an essential construc¬ tive criticism, always with pleasure. A great thank you! Another thank you goes to Dani, who introduced me into the (for me unknown) modeling world, smoothing my way through the different tools and model ver¬ sions, solving problems, supplying hints. In other words for being so patient with me, thank you! A further thank you to Dino Zardi for accepting the position of co-examiner for my thesis, challenging himself with potential vorticity forecast error helds as well as with very high resolution modeling and finally undertaking an exhausting one- day return trip from Verona to Zürich. Thank you! A special thank also to whom I shared the office with, Sarah and Harald, Rich, Seb, Patrick, as well as to the rest of the group members, Mischa, Olivia, Michael, Sandro, Johannes, Thomas, Kassiein, Conny and Heirri. 1 wish you all the best for future achievements. ... and a last thank to Claudia 109 Seite Leer / Blank laaf Curriculum Vitae Marco Didone Haldenstrasse 27 Born on 18 May 1977 CH-8904 Aesch in Lugano (TI) [email protected] Citizen of Carabbia (TI) Education and Professional Training January 2003 - April 2006: PhD thesis at the ETH, Institute for Atmospheric and Climate Sciences in the group of Dynamical Meteorology of Prof Dr. H.C. Davies. Title: 'Performance and Error Diagnosis of Global and Regional NWP Models'. May 2002 - December 2002: Scientific collaborator at ETH, Institute for Atmospheric and Climate Science. October 1996 - April 2002: Physics studies at the ETH Zürich, Switzerland. Diplorrra Thesis in Environmental Physics under the Supervision of Prof Dr. H.C. Davies. Title: 'Insights into Upper-Level Induced Cyclogenesis' Dipl. Phys'. ETH 1993-1994: High School in Wisconsin Rapids, Wisconsin, USA as exchange student. Ill 112 Curriculum Vitae 1992-1993 and 1994-1996: High school studies at Liceo Cantonale of Lugano (TI), Switzerland (Scientific Graduation) 1983-1992: Secondary and secondary school in Lugano (TT), Switzerland Publications • Insights into Upper-Level Induced Cydogenesis(2Q02). Diploma thesis in Environmental Physics under the Supervision of Prof Dr. H.C. Davies. • Diagnosis of 'Forecast-Analysis' Differences of Weather Prediction System (2003), S. Dirren, M. Didoiie and H.C. Davies, Ge oph. Res. Letters, VOL. 30, NO. 20, 2060. • Influence of Domain Size on Large Scale Flow (September 2006). M.Didoiie, D. Liithi, H.C. Davies. Submitted to Meteorologische Zeitschrift. International Conferences and Workshops • Numerical Methods and Adiabatic Formulation of Models Meteorological Training Course at ECMWF. Reading, UK, March 2003. • Summer School on Mountain Meteorology 2003: Thermally Driven Winds in Mountainous Terrain Trento, Italy, August 2003. • Parametrization of Diabatic Processes Meteorological Training Course at ECMWF. Reading, UK, April 2004. • Summer School on Mountain Meteorology 2003: Orographic Effects on Pre¬ cipitation Trento, Italy, July 2004. • Diagnosis and Dynamics of the 'Forecast Minus Analysis' PV Fields The First THORPEX International Science Symposium. Montreal, Canada, December 2004. • Diagnosis and Dynamics of the 'Forecast Minus Analysis' PV Fields European Geosciences Union General Assembly 2005. Vienna, Austria, April 2005. • Exploring and Validating LM Performance at Very High Resolution International Conference on Alpine Meteorology and Mesoscale Alpine Pro¬ gram (MAP) 2005. Zadar, Croatia, May 2005. Curriculum Vitae 113 • Diagnosis and Dynamics of "Forecast minus Analysis" PV Fields" Cyclone Workshop, Monterey, CA, USA, October 2006.