The Beginning of Numerical Weather Prediction
Even though the first attempts at weather prediction were made more than 2000 years ago, the bulk of the knowledge about precipitation and its prediction has been acquired during the last century. Specifically, the succession of low and high pressure which accompanies the changing weather in the mid latitudes was only understood as recently as around 100 years ago. The atmosphere is a large dynamic system and its accurate description requires the knowledge of its state, which is only obtained by observations at multiple locations over a large area. These have to be suﬃciently dense in space and time (see, e.g., Bjerknes, 1919). Because of this, meteorology was one of the first disciplines which made wide use of the early means of telecommunication.
Vilhelm Bjerknes (1916) was the first to explain cyclones as resulting from disturbances in the westerly winds, which are often found in the mid-latitudes. His work was then validated by his son, who developed an empirical model of a mid-latitude cyclone based on surface observations (Bjerknes, 1919) and described rain as result of lifting processes along fronts and orographic barriers (Bjerknes and Solberg, 1921). They also explained mid latitude cyclones as resulting from disturbances in the polar front and provided the first schematic model of the mid-latitude circulation (Bjerknes and Solberg, 1922).
The idea and attempt of numerical weather prediction predate the advent of the first computers by more than two decades. Undergoing the process of discretizing the thermal and dynamical fields of the atmosphere and their governing equations in space and time requires a large number of calculations, making it impossible to do even in real time without the help of computers. The first attempt, however, was done by Richardson (1922). He attempted a 6-hour forecast of the surface pressure using a set of discretized equations. It took Richardson 6 weeks to calculate just two vertical columns and he estimated that for a horizontal grid size of 200 km ”64000 computers [referring to persons doing the calculations manual ly, author’s note] would be needed to race the weather for the whole globe” (Richardson, 1922, p. 219). Unfortunately, his forecast for the change in surface pressure was wrong by two orders of magnitude due to an imbalance of wind and pressure in his initial conditions. Removing these imbalances would take another 20 years. The upper level structure of the mid-latitude atmosphere was described by Rossby et al. (1939), who developed the theory of what we nowadays know as barotropic Rossby-waves. This theory was refined by accounting for the earth’s curvature (Haurwitz, 1940) and extended to a baroclinic atmosphere (Bjerknes and Holmboe, 1944). Based on their work, Charney (1947) presented a way to re-move acoustic waves and shearing-gravitational oscillations from the perturbation equations, eliminating the problems that prevented the success of Richardson in 1922. These equations formed the basis of later work (Charney, 1949; Charney and Eliassen, 1949), which led to the first successful computer-based numerical weather forecast (Charney et al., 1950), obtained by numerical integration of the barotropic vorticity equation. Over the following decades, computational power has grown exponentially, allowing smaller grid spacings and time steps, the use of more complete sets of equations and more sophisticated parametrizations for subgrid processes such as microphysics and turbulence. However, this progress has its challenges.
Atmospheric Scales – Synoptic, Meso- and Micro- scale
Weather models are based on the equations that govern the evolution of a given state (pressure, temperature, moisture, wind) of the atmosphere over time. Values of the fields are discretized onto a number of points which are distributed on a grid that covers either the entire globe or a limited region. Typically, the values at a certain grid point are then viewed as representative for the entire grid cell. A basic property of the computational grid is the distance between its points which equates to the grid cell size.
For global models, the grid spacing is often in the tens of kilometers while for localized weather models in research applications the horizontal grid spacing can reach less than 100 m. Atmospheric phenomena also have typical scales. Rossby waves span over thousands of kilometers and the surface low and high pressure systems can become equally large. On the other end of the scale, turbulent eddies are found everywhere in the atmosphere with sizes down to the fraction of a mil-limeter. Between the synoptic (large) and the microscale a range of phenomena can be found in the mesoscale (Orlanski, 1975), like frontal circulations, convec-tive systems, orographically induced circulations or sea and land breeze systems. Depending on the phenomenon, a grid spacing of few kilometers down to around 100 m is necessary to capture the relevant processes. As a result, certain mesoscale phenomena are sometimes represented by a limited number of grid points or they might fall entirely within just one grid cell. In order to fully capture all relevant motions of turbulent flow in a simulation, one would have to resolve all scales of motion. The minimum size of turbulent eddies which have to be resolved does have a lower limit (Kolmogorov, 1941), but unfortunately it is beyond any reasonable grid spacing currently achievable in weather models. The scale of these eddies, the Kolmogorov-microscale, depends on the kinematic viscosity ν and is given by 1 ν3 4 η = , (1.1).
The Physics of Heavy Precipitation Events
Deep moist convection (DMC) is involved in a large number of Mediterranean HPEs (see, e.g. Davolio et al., 2009; Doswell et al., 1998; Ferretti et al., 2000; Jansa et al., 2000, 2001; Lambert and Argence, 2008; S´en´esi et al., 1996; Tapiador et al., 2012; Trapero et al., 2013). For deep moist convection to occur, three ingredients are required: conditional instability, low level moisture, and lift (Doswell et al., 1996; Doswell, 1987).
Orography and its Eﬀect on Air Flow and Precipitation
Since the Mediterranean is surrounded by multiple high mountain ranges and some islands have mountains in excess of 2000 m, orographic eﬀects play an essential role in Mediterranean HPEs. The interaction between orography and air flow has been repeatedly studied for decades, but even idealized mountain shapes and constantly stratified layers of dry air introduce a number of diﬀerent phenomena. In the simple 2D case (an infinitely long ridge) and homogeneous cross-mountain flow the eﬀect is limited to relatively simple topographic waves. Variation of the cross-mountain wind or the stability with height allows the formation of lee waves which can extend hundreds of kilometers downstream of mountains (Durran, 1990). When air flow encounters a mountain, one primary question is whether the flow will traverse the obstacle or be blocked by it. The parameter that helps to determine the answer is the Froude number 2 u¯2 u¯2 F r = = , (1.9).
where u¯ is the mean environmental wind speed, c2 is the shallow water wave speed (see, e.g. Holton, 2004, p. 287), and Lc is the characteristic length. The Froude number F r can be understood as the ratio of kinetic and potential energy. For F r < 1 (subcritical) flow will tend to be blocked by an obstacle while for F r > 1 (supercritical) the flow will pass over the obstacle. For F r ≈ 1 the linear solution breaks down. The flow is subcritical upstream of the obstacle, turns supercritical above the obstacle and tends to form a downslope windstorm in the lee with a hydraulic-jump-like feature, where the flow adjusts back from super- to subcritical in a turbulent zone (Durran, 1990). In real case scenarios, the applicability of these concepts is somewhat limited, as the atmosphere is neither homogeneously stratified nor is the flow horizontally or vertically homogeneous. Reinecke and Durran (2008) presented a way to estimate the resulting flow regime for real cases. They use the mountain height normalized by a scale for the vertical wavelength of a linear 2D hydrostatic mountain wave, sometimes also called inverse Froude number (see also Smith, 1989a) ˆ N h h = u , (1.10).
where N is the Brunt V¨ais¨al¨ frequency, h is the mountain height and u is the cross mountain wind speed. One method to determine h proposed by Reinecke and Durran (2008) is to measure u and N below the mountain height and then take the average over the layer below h to calculate h. Even in dry homogeneous flow, simple setups can produce complex solutions, such as stagnation points (Smith, 1989b), lee vortices, wakes (Sch¨ar and Smith, 1993a) and vortex streets (Sch¨ar and Smith, 1993b). The above mentioned phe-nomena are also observed in the atmosphere, such as the wake of Madeira (Grubiˇsi´c et al., 2015), and they can also be relevant for regional weather phenomena, like the cyclogenesis supported by Alpine blocking (Egger, 1988; Pichler et al., 1990), which also occurs over the Gulf of Genoa (Trigo et al., 2002).
Taking moisture into account introduces a number of additional mechanisms, which happen primarily due to the conversion between latent and sensible heat. If the lifting is suﬃcient to produce clouds, latent heat is converted into sensible heat, changing the stability profile. If rain forms, it will fall out of the cloud into the unsaturated layer below and start evaporating, thereby cooling the air beneath the cloud and forming a cold pool. Even over an idealized 2D mountain a simple setup such as a moist nearly neutral flow with constant u can lead to complex eﬀects, such as downslope windstorms, convective cells and upstream mid-level drying (Miglietta and Rotunno, 2005). In conditionally unstable flow, rain was found upstream and downstream of the 2D mountain for weak and intermediate u (2.5 and 10 m s−1 ) and over the mountain for strong u (20 m s−1 ). Convection initiated along the windward slope produced a cold pool which propagated upstream when u was weak (Miglietta and Rotunno, 2009). The highest rainfall amount was seen for simulations where u balanced the upstream propagation of the cold pool, resulting in quasi-stationary convection which allowed large accumulations of rain (Miglietta and Rotunno, 2009, 2010). It was also found that a sheared profile with cross mountain wind in the boundary layer and weaker or no cross mountain wind aloft allows the formation of deeper and more intense convective cells (Miglietta and Rotunno, 2014). Real cases are vastly more complex because the terrain, airflow and moisture are inhomogeneous 3D fields which change over time.
Heavy Precipitation Events in the Mediterranean
Ricard et al. (2012) showed that long-lasting HPEs over southern continental France and Corsica are mostly associated with quasi-stationary trough-ridge pat-terns, high CAPE values over the western Mediterranean and a moist troposphere. Low level jets (LLJ) advect moisture from the sea toward the coast, where the HPEs occur. These unstable inflows together with lifting above orography or along convergence lines lead to DMC, which can either occur alone or embedded into larger, stratiform precipitation systems.
Duﬀourg and Ducrocq (2011) analyzed recent events over southern France in an attempt to explore the origin of the moisture supply. They found that the main sources of moisture for the studied HPEs were evaporation over the Mediter-ranean and advection from the Atlantic. Ducrocq et al. (2008) looked at three HPEs over southern France and analyzed the mesoscale ingredients for stationary events. They identified orographic lift and lifting along the edge of cold pools as primary lifting mechanisms. In all cases, a conditionally unstable LLJ was imping-ing on an obstacle, supplying the convective system with moisture and an inflow of potentially unstable air.
Numerical models can help tremendously in understanding single events as well as the involved processes. Before the wide availability of mesoscale models, Ducrocq et al. (2002) found that models with a grid spacing of 2.5 km are well capable of outperforming low resolution (10 km) models. However, this improve-ment required that the initial conditions were well captured. They even found that poorly captured initial conditions could reverse the results, causing the high resolution simulations to perform worse than the low resolution simulations. Since then, the availability of computational resources has increased drastically and grid spacings of 2.5 km and less have become feasible even for operational purposes. Nevertheless, small changes in initial conditions can cause large diﬀerences on the mesoscale, especially when convection is involved. Thus, large eﬀorts have been made to explore and improve the capability of such high resolution models. Hally et al. (2014a,b) explored the potential of a stochastic ensemble by adding random perturbations to model physics. They analyzed their results in terms of disper-sion of the precipitation forecast and found that this approach has the potential to assess the sensitivity of HPEs. However, they also found the initial conditions to be the most important criterion. Fresnay et al. (2012) used the same method, including tests with a grid spacing of 500 m. They found that at this higher res-olution the ensemble shows a larger sensitivity to perturbations in model physics. Instead of perturbing only one microphysical scheme, Tapiador et al. (2012) cre-ated an ensemble by using diﬀerent schemes not only for microphysics but also for cumulus parametrization and the land surface. In addition, they tested perturbed initial conditions. Their results show that using multiple schemes resulted in a larger spread than the perturbed initial conditions.
Numerous case studies using numerical models have been conducted to learn more about the details of HPEs in the Mediterranean region. Doswell et al. (1998) showed that heavy precipitation in the Mediterranean region can be associated with diﬀerent processes, such as DMC but also orographic enhancement of precip-itation below a relatively stable air mass. S´en´esi et al. (1996) studied the Vaison-La-Romaine flash-flood event in southern France. They found that a cut-oﬀ low and its slowly moving cold front led to a squall line. The slow movement of the system led to large precipitation accumulations. Trapero et al. (2013) studied a catastrophic 1982 flash-flood event in the Pyrenees, which aﬀected Spain, Andorra, and France. They found a quasi-stationary extratropical cyclone advecting moist air toward the Pyrenees. Buzzi et al. (1998) studied a HPE over the Piedmont in northwestern Italy in 1994. They determined the local orography as an im-portant factor, which influences precipitation by forcing orographic lifting. Buzzi et al. (1998) also conducted sensitivity tests by deleting parts of the orography and changing model physics. They found that removing the terrain caused the HPE to shift downstream while changes in evaporative cooling and latent heating controlled the formation of cold pools and the capability of the air to move over orography, respectively. Ferretti et al. (2000) confirmed the importance of orogra-phy and orographic lifting for that particular event. It was later found that the 1994 Piedmont flash flood was intensified by dryer air from the east which was blocked by the Alps and deflected westward, increasing convergence beneath the convective cells (Rotunno and Ferretti, 2001). Davolio et al. (2009) studied a HPE which occurred at the Adriatic coast. It was caused by convergence of a northeast-erly barrier jet along the Alps and a southeasterly moist LLJ from the Adriatic sea. In a comprehensive analysis of multiple events, Davolio et al. (2016) found that the precipitation distribution over northeastern Italy depended heavily on the thermodynamic profile of the incoming flow. Flow over the Alps tends to produce heavy precipitation over the orography whereas blocked flow leads to the forma-tion of a barrier jet and upstream convergence, displacing the precipitation and convection over the flat terrain of the Po valley. Further east, similar events can occur. Kotroni et al. (1999) studied a HPE which occurred in 1997 over Greece. They also found DMC as a result of orographic lifting ahead of the cold front to be responsible.
Heavy Precipitation Events over Corsica
From a composite analysis of 8 HPEs over Corsica, Ricard et al. (2012) showed that moisture and CAPE were generally high between Sardinia and continental Italy. According to their findings, the main source of moisture lies to the south of the island with southerly flow in the boundary layer being the dominant direc-tion during HPEs over Corsica. The island and its interaction with precipitating systems were the subject of several studies during the recent years. Lambert and Argence (2008) did a preliminary study of the HPE of 14 September 2006. They demonstrated one of the diﬃculties with current mesoscale case studies, namely that the verification of the simulation output is diﬃcult. While obtaining clearly diﬀerent results with two diﬀerent input data sets, no conclusion was reached as to which simulation was better than the other. They also encountered problems when trying to reproduce the fine scale features of the event even though the large scale was well captured in both their experiments.
A more in-depth analysis was performed by Barthlott and Kirshbaum (2013), who analyzed isolated convection which occurred on 26 August 2009. The event was characterized by DMC over Corsica and Sardinia. They simulated the case using diﬀerent stretching factors for the terrain height between 0 and 1.3 and also without islands. Their modeling experiments indicate that the mountains influenced the formation of convection via their diurnal circulation. However, even the temperature gradients between a flat island and the sea would have been suﬃcient for initiation of DMC due to convergence along the sea-breeze front. Only the complete removal of the islands from the simulation completely suppressed deep convection. This shows that diﬀerent factors contribute to the formation of convection, including but not limited to sea-breeze, land-breeze and orographic circulations.
The role of Sardinia in DMC over Corsica was investigated by Ehmele et al. (2015), who looked at six events and conducted tests with standard orography as well as flat and deleted Sardinia. They found a decrease in precipitation for cases with strong synoptic forcing and no systematic change for cases with weak synoptic forcing. The role of Sardinia consists of blocking or deviating the large scale flow and modification of convection over Corsica via cold pools generated by convection over Sardinia.
An idealized study was conducted by Metzger et al. (2014), who placed Corsica as an isolated island in homogeneous flow. They used vertical profiles to initial-ize their simulations and varied the wind direction in 15◦ steps. The tests were conducted using constant winds of 2 and 5 m s−1 . They also tested the eﬀect of increased instability and a reduced saturation deficit between 900 and 400 hPa. For the cases where DMC was simulated, it occurred on the lee side of the island, initi-ated by convergence. Metzger et al. (2014) found that lower wind speeds are more reliable in initiating DMC. For the higher (5 m s−1 ) wind speed they found that northerly and southerly winds are capable of producing convection while easterly and westerly winds were not. Their conditions were highly idealized. Nevertheless, their findings show that convection can form in the lee of Corsican orography.
Current Knowledge on the Climate of the Mediterranean
Precipitation in the Mediterranean follows a seasonal cycle. The summers are gen-erally dry and during the late summer precipitation increases in the west, where cyclogenesis is most often found over the Iberian peninsula (Trigo et al., 2002). During September, October and December, the heaviest precipitation moves grad-ually east (see, e.g. Kelley et al., 2012; Mehta and Yang, 2008; Trigo et al., 2002). For Corsica, the maximum is found from September to December. The region around Corsica also has an exceptionally high cyclone track density (Alpert et al., 1990; Nissen et al., 2010) with the Gulf of Genoa just north of the island being the most active cyclogenesis region from November to February (Trigo et al., 2002).
Mehta and Yang (2008) obtained a precipitation climatology for the Mediter-ranean basin based on 10 years (1998 – 2007) of TRMM measurements. They found that the highest precipitation is found over the mountainous regions of Europe, namely the Pyrenees, the Alps, the Apennines and the mountain ranges east of the Adriatic, in Slovenia, Croatia, Bosnia and Herzegovina, Montenegro and Albania. In these mountains, the average precipitation is between 2 and 4 mm d−1 . On the other end of the scale, north Africa receives only around 0.1 mm d−1 . However, the precipitation over the Mediterranean basin shows a seasonal cycle in intensity and location. Mehta and Yang (2008) found that the strongest precipitation oc-curs from September to March, with the peak months being October to January. While the peak month for the western Mediterranean (5-10◦ E) is in November, the peak occurs later further east (November and December at 10◦ E and December to January at 30◦ E). In meridional direction, precipitation is located further north in the Summer (values of >2 mm d−1 north of 45◦ N), the strongest precipitation moves south until it peaks around 37◦ N in November and December.
Seasonal Distribution, Frequency and Com- posite Meteorological Fields
From 1985 to 2015 (31 years), 173 HPEs were identified. The criterion for an HPE is chosen at 100 mm of 06 to 06 UTC 24 hour accumulated precipitation observed by at least one surface station on Corsica. The analysis is limited to the 24 hour accumulated precipitation because the greater number of 24-hourly reporting stations provides a substantially larger sample (120-125 stations, depending on the year and event) compared to the hourly reporting stations (only around 25 stations). Each year between 2 and 12 events occurred with an average of 5.6 events per year (Fig. 2.1a). When viewed monthly (Fig. 2.1b), the typical distribution for a location in the Mediterranean emerges. Most of the events are observed in autumn and early winter, with October showing 34 events (19.6%). Of all events, 95 (55%) were observed between October and December (consistent with the findings of Gao et al., 2006; Kelley et al., 2012; Ricard et al., 2012).
Table of contents :
1 General Introduction
1.1 Geographical Context – The Mediterranean Basin
1.2 The HyMeX Program
1.3 Numerical Weather Prediction
1.3.1 The Beginning of Numerical Weather Prediction
1.3.2 Atmospheric Scales – Synoptic, Meso- and Microscale
1.4 The Physics of Heavy Precipitation Events
1.4.1 Convective Instability
1.4.2 Orography and its Effect on Air Flow and Precipitation
1.4.3 Heavy Precipitation Events in the Mediterranean
1.4.4 Heavy Precipitation Events over Corsica
1.5 Goals and Outline of this Thesis
2 Climatology of Rainfall on Corsica
2.1 The Climate of the Mediterranean
2.2.1 EOFs and Principal Components
2.2.2 The k-means algorithm
2.3 Seasonal Distribution, Frequency and Composite Fields
2.6 Physical Interpretation of the Clusters
2.6.1 Mean Fields
2.6.2 Precipitation Distribution
3 Numerical Tools and Used Observations
3.1 Meso-NH Simulations
3.1.1 Model Configuration
3.1.2 Simulation Ensembles
3.1.3 Experiments with Modified Orography
3.2 Observational Data and Comparison Methods
3.2.1 Precipitation – Surface Stations and Radar
3.2.2 Satellite Data
3.3 Statistical Methods
3.4 A Simple Cyclone Tracking Algorithm
4 Case 1: 4 September 2012 – A Quasi-Stationary Cyclone
4.1 Synoptic Situation
4.2 Observed Evolution
4.2.1 Satellite Images
4.2.2 Observed Precipitation
4.3 Initial Condition Ensemble
4.3.1 Spatial Distribution of 24 Hour Accumulated Precipitation .
4.3.2 Quantitative Precipitation Verification
4.4 Cyclone Tracks
4.5 Evolution of the HPE in the Reference Simulation
4.6 Sensitivity to Horizontal Grid Spacing
4.6.1 Impact on Precipitation Distribution
4.6.2 Convergence Zones
4.7 Test over Flat Orography
5 Case 2: 31 October 2012 (IOP 18) – A Fast Moving Cyclone
5.1 Synoptic Situation
5.2 Observed Evolution
5.2.1 Satellite Images
5.2.2 Observed Precipitation
5.3 Initial Condition Ensemble
5.3.1 Spatial Distribution of 24 Hour Accumulated Precipitation .
5.4 Quantitative Precipitation Verification
5.5 Cyclone Tracks
5.6 San Giuliano Radiosoundings
5.7 Evolution of the HPE in the Reference Simulation
5.8 High Resolution Simulation
5.8.1 Impact on Precipitation Distribution
5.9 Test over Flat Orography
6 Case 3: 23 October 2012 (IOP 15c) – A Highly Localized Convec- tive Event
6.1 Synoptic Situation
6.2 Observed Evolution
6.2.1 Satellite Images
6.2.2 Observed Precipitation
6.3 Predictability and Sensitivity to Input Data Set and Initialization Time
6.4 High Resolution Simulations
6.4.1 Qualitative Comparison and Evolution of the HPE
6.4.2 Impact of the Mixing Length Formulation
6.5 Sensitivity to physical parametrizations
6.6 Physical Process Study
6.6.1 Analysis Departures
6.6.2 Role of the Corsican Orography
6.6.3 Role of the Gap Flows
6.7 Quantitative Precipitation Verification
7 Conclusions and Outlook
7.1.1 Climatology and Clustering
7.1.2 Results of the Case Studies