Convection-Resolving Precipitation Forecasting and Its Predictability in Alpine River Catchments

Journal of Hydrology 288 (2004) 57–73 www.elsevier.com/locate/jhydrol

Convection-resolving precipitation forecasting and its predictability in Alpine river catchments

Andre´ Walser*, Christoph Scha¨r

Institute for Atmospheric and Climate Science, ETH, Zurich, Switzerland

Received 14 December 2002; accepted 20 November 2003

Abstract Predictability limitations in quantitative precipitation forecasting arising from small-scale uncertainties in the initial conditions are investigated for Alpine river catchments, with particular consideration of their implications on hydrological runoff forecasting. To this end, convection-resolving ensembles of limited-area simulations are performed using a nonhydrostatic numerical weather prediction (NWP) model, and results are analysed in terms of catchment-averaged precipitation. The applied ensemble strategy uses slightly modiﬁed initial conditions representing observational uncertainties, but identical lateral boundary conditions representing a perfectly predictable synoptic-scale forcing. A total of four case studies is carried out for different synoptic conditions leading to heavy precipitation. Ensemble integrations of 12 members are analysed for 24-h forecasting periods, with particular attention paid to precipitation in the Po basin and in its sub-catchments in the Lago Maggiore area. The simulations exhibit a large variability in the predictability of precipitation amounts, both from case to case and from catchment to catchment. It is demonstrated for an episode of thermal convection, that the predictability may be very low even in large-scale catchments of ,50,000 km2. In more synoptically dominated cases, predictability limitations appear to be restricted to catchments smaller than ,10,000 km2, while in one case predictability is found to be high in catchments as small as 200 km2. Overall, the simulations show that precipitation forecasts for alpine river catchments may on occasions be critically affected by predictability limitations, even though the NWP model and the synoptic-scale forcing are assumed to be prefect. It is demonstrated that a substantial fraction of the predictability limitations is due to the scattered and unpredictable occurrence of convective cells, but the presence of convective precipitation alone does not necessarily limit predictability. It is also shown that the predictability is systematically higher in mountainous catchments. q 2003 Elsevier B.V. All rights reserved.

Keywords: Ensemble simulation; Probabilistic forecast; Quantitative precipitation forecasting; High-resolution numerical weather prediction

1. Introduction

The Alpine region is frequently affected by ﬂood events due to exceptional precipitation amounts and * Corresponding author. Present Address: MeteoSwiss, Zurich, Switzerland. Tel.: þ41-1-256-94-43; fax: þ41-1-256-92-78. intensities. Some of these events are devastating E-mail address: [email protected] (A. Walser). and inﬂict loss of life and large property damage

(Frei et al., 2000). Experience suggest that appropriate are based on many parallel NWPs (ensemble warnings could substantially mitigate the conse- members), starting from slightly different initial quences of such events. Flood forecasting and conditions. In addition, uncertainties in the model warning systems in intermediate-scale catchments formulations are taken into account by the use of (,50,000 km2) best employ both an atmospheric and stochastic perturbations to physical tendencies a hydrological numerical model. In order to improve (Buizza et al., 1999) or multi-model approaches such systems, much research has been undertaken in (Grimit and Mass, 2002). Ideally, ensemble predic- the last years towards the use of coupled numerical tions should span the entire space of possible weather prediction (NWP) and hydrologic models solutions. In practice, however, the atmosphere has (Miller and Kim, 1996; Yu et al., 1999; Benoit et al., too many degrees of freedom to fully cover its 2000; Droegemeier et al., 2000; Jasper and Kauf- probabilistic behaviour. EPSs were originally devel- mann, 2003). oped for the evolution of baroclinic perturbations and For the prediction of critical river stages, quanti- designed for medium-range weather forecasts. In the tative precipitation is the most decisive variable last decade, studies have been devoted also to among the external inputs of hydrologic models. mesoscale predictability of precipitation using lim- However, forecasts of precipitation have an inherent ited-area models (Stensrud et al., 2000; Marsigli et al., uncertainty, since deterministic NWPs are intrinsi- 2001; Frogner and Iversen, 2002) and have accounted cally limited by the chaotic nature of the atmospheric for moist physics in detecting strong error growth dynamics. Already in the 1960s, Lorenz (1963) (Ehrendorfer et al., 1999). Nevertheless, the step demonstrated in a seminal study that small errors in towards short-range high-resolution EPS forecasts for the initial conditions of a weather forecast can grow hydrological applications still requires a further rapidly, leading to highly diverging solutions. The increase in spatial resolution. degree of this divergence, and hence the uncertainty, Runoff forecasts for typical alpine river catchments varies from one occasion to the next. In order to take are often affected by the spatiotemporal occurrence as this uncertainty into account, probabilistic river stage well as the intensity of convective systems and squall forecasts (PRSF) have been proposed in the past lines. Such meso-b scale precipitation systems have decade (Fritsch et al., 1998; Krzysztofowicz, 1998). short time-scales and their evolution is highly non- However, most hydrological forecasting systems still linear. It is still unknown at what catchment scale a produce deterministic forecasts, finding a single prediction of such systems is skilful. In a recent study, estimate without quantifying the uncertainty. The we found that the range of scale affected by small- currently available short-term PRSF are based on a scale predictability limitations may extend up to the statistical quantification of both the precipitation scale of several hundred kilometres (Walser et al., uncertainty (Kelly and Krzysztofowicz, 2000) and 2004), even when the synoptic-scale forcing is the hydrologic uncertainty (Krzysztofowicz and Herr, perfectly known. This result implies that, at least on 2001). It is expected that in future the input of occasions, NWPs may be unable to provide a useful precipitation for PRSF will be derived from high- area-mean representation of convective precipitation resolution ensemble simulations of NWP models even in major alpine river basins. which provide a quantitative dynamical approach for The main purpose of this study is to examine the probabilistic precipitation forecasts. uncertainty in mean-catchment precipitation arising In the last decades, much research has been from small-scale observational uncertainties. Predict- devoted to estimate the prediction of the uncertainty ability is thus investigated in the absence of larger- in numerical weather forecasts (see the reviews by scale uncertainties, assuming perfectly predictable Ehrendorfer, 1997 and Palmer, 2000). Only in the synoptic-scale conditions. Following earlier studies in 1990s, computing resources have become sufficient to short-range ensemble forecasting (Du et al., 1997; implement probabilistic atmospheric forecasts into Stensrud et al., 1999), we assume a perfect model, and operational practice (Molteni et al., 1996; Houteka- the resulting estimates will thus be referred to as mer et al., 1996; Toth and Kalnay, 1997), using global potential predictability. Our study quantifies the ensemble prediction systems (EPSs). Such systems potential predictability of precipitation in selected A. Walser, C. Scha¨r / Journal of Hydrology 288 (2004) 57–73 59

Alpine river catchments in four case studies, using a variant of the ensemble methodology. In order to simulate the small-scale processes as reliable as possible, the underlying simulations were performed in a convection-resolving setup with 3 km horizontal grid spacing. The paper is structured as follows: the relevant features of the model and the experimental setup are described in Section 2, complemented by background information on the process of deep convection in the simulations. Section 3 presents the results of our ensemble experiments on the basis of four case studies, including an intercomparison with radar observations. Finally, conclusions of the study are presented in Section 4.

2. Experimental design Fig. 1. Computational domains of the HRM (outer box), MC2 with 14 km grid spacing (middle box), and MC2 with 3 km grid spacing 2.1. Model chain (innermost box) superimposed on the HRM topography.

The model chain and simulation strategy used in formulated in a semi-implicit, semi-Lagrangian this study has been introduced in Walser et al. (2004). scheme (Tanguay et al., 1990; Benoit et al., 1997). The numerical weather simulations were undertaken The model was used during the special observing with a model chain that includes two limited-area period of the Mesoscale Alpine Programme (MAP NWP models and that is driven by the operational SOP; Bougeault et al., 2001) in a quasi-operational European Centre for Medium-Range Weather Fore- setup (Benoit et al., 2002; Scha¨r et al., 2003). The casts (ECMWF) analysis. This analysis assimilates all same physical setup (MC2 version 4.9) is used for this available observations in a spatially and temporally study. Nested in the HRM run, a MC2 simulation with consistent fashion with the help of a global NWP 14 km horizontal grid spacing and 35 vertical levels is model. The driving analyses of the year 1999 have a first conducted for an integration period of 34 h. This ; horizontal mesh size of about 0.58 ðTL ¼ 319Þ 50 MC2 simulation on a slightly smaller domain and with vertical levels (60 since November) and a six hourly basically the same resolution as the HRM simulation temporal resolution. allows a smooth transition to the height-based Gal- The High Resolution Model (HRM) is a hydro- Chen Somerville coordinates (Gal-Chen and Somer- static limited-area model developed at the German ville, 1975) and the different physical schemes used in Weather Service. For this study, it is used with a the MC2. It provides the initial and lateral boundary horizontal grid spacing of 0.1258 over Central Europe conditions for MC2 ensemble simulations over the (Fig. 1), and 31 vertical levels in a hybrid sigma European Alps (innermost domain in Fig. 1). In order coordinate system. In the present model chain, the to resolve convection explicitly (discussed later in operational ECMWF analysis provides the initial and Section 2.4), a 3 km grid spacing and 50 vertical lateral boundary conditions for the HRM simulation. levels are used for these ensemble simulations, The Canadian Mesoscale Compressible Commu- yielding a horizontal domain of 343 £ 293 grid points. nity (MC2) limited-area model is based on the compressible set of nonhydrostatic equations which 2.2. Ensemble strategy govern the atmospheric dynamics. The model is thus suited for the simulation of atmospheric flow at Ensemble forecasting makes use of a series of very high resolution. The prognostic equations are model integrations that slightly differ from one 60 A. Walser, C. Scha¨r / Journal of Hydrology 288 (2004) 57–73 another in terms of initial conditions. The spread of below an hour), the assumption of a linear system the ensemble members during the integration period appears poorly justified. then represents a measure of the predictability. As The present study uses an ensemble method- typical atmospheric models have a huge number of ology based on a lagged initialisation technique. degrees of freedom (for our model setup about Each of the ensemble members uses identical 5 £ 107), the ensemble strategy can only partly lateral boundary conditions but slightly modified represent the full spectrum of uncertainty. The initial conditions realised by shifting the initialisa- choice of the initial conditions of the individual tion time of six simulations. Member 1 is initialised ensemble members is thus of key importance. To this at 2100 UTC, member 2 at 2000 UTC, etc. and end, a large number of techniques have been finally member 6 at 1600 UTC. This procedure is developed (Section 1). The aim of these is to find shown in Fig. 2. Within this framework, differences initial perturbations that (i) grow quickly in time, and between ensemble members essentially derive from (ii) to realistically represent typical observational and model differences between the driving low-resol- analysis uncertainties. For systems with an approxi- ution simulation (MC2 14 km) and the target high- mately linear behaviour, rapidly growing pertur- resolution simulations (MC2 3 km). As all ensem- bations may be derived using singular vector ble members entail the same observational data (as analysis. This analysis delivers linear structures that contained in the driving model simulation), it is not exhibit a maximum linear growth over some surprising that the generated perturbations have specified time period, and the initial amplitude of small amplitudes (Walser et al., 2004), and this will these perturbations is specified such as to match require amplification after some initial integration typical analysis uncertainties. Singular vector tech- time, such as to represent initial analysis uncer- niques have been highly successful in global NWP tainty. Such a procedure is straightforward, pro- (Buizza and Palmer, 1995) to identify large-scale vided that the amplitude of the perturbations is in baroclinic perturbations that may grow into forecast- the range of validity of linear theory. ing errors. However, on the small scales considered In order to amplify the initial perturbations, the in the present study, alternative growth mechanisms deviations from the ensemble mean of each need to be addressed, such as moist dynamical member are amplified at 0000 UTC by some factor processes and convective instabilities. In addition, a: This is performed uniformly for temperature, due to the large growth rates of small-scale humidity, horizontal wind and pressure with a ¼ 3; perturbations (which often possess doubling times leading to six atmospheric states for 0000 UTC

Fig. 2. Model chain and setup for the ensemble simulations. The MC2 ensemble members (horizontal thin arrows) utilise a high-resolution grid (3 km grid spacing, 50 vertical levels) and are generated using a shifted initialisation strategy followed by an amplification of the perturbations and a change of the perturbations’ sign at 0000 UTC (see text). A. Walser, C. Scha¨r / Journal of Hydrology 288 (2004) 57–73 61 with enlarged perturbations. Six additional atmospheric states are obtained by setting a ¼ 23; that is, by inverting the sign of the amplified perturbations. Together, the 12 different atmospheric states are used as initial conditions to perform 12 members with a 24-h integration period from 0000 to 2400 UTC. Since the perturbations are comparatively small, the integrations are continued without using an additional initialisation procedure after the amplification/inversion of the perturbations with the a-factor. Negative values for humidity resulting from the amplification are set to zero. Super- saturation is not corrected but is removed in the first few time steps of the model integration. The proposed ensemble strategy is not meant as a setup for an operational forecasting system. However, Fig. 3. Catchment definitions used for the analysis: extended Po catchment (blue line), Po catchment upstream of Piacenza (red), it allows isolating predictability issues related to Lago Maggiore (black), Toce (green), Maggia (violet), Verzasca meso-b scale, since the identical lateral boundary (white), and Ticino (gold). The background field shows the MC2 conditions for the ensemble members prevent synop- model topography of the innermost computational domain. tic-scale perturbations. The method thus reveals the inherent uncertainty in high-resolution weather fore- Alpine crest: the river catchments Verzasca, Maggia, casts due to nonlinear error growth of small-scale Ticino, Toce, Lago Maggiore as well as the Po errors in the initial conditions. With the proposed catchment upstream of Piacenza (see Fig. 3 and ensemble strategy, the initial perturbations are Table 1). In order to include the entire eastern flat part generated by design choices of the driving NWP of the Po Valley (from which a large fraction does not model chain. Such small-scale perturbations have a belong to the Po river basin), a hypothetical extended tendency to grow within the forecasting system Po catchment is defined which encompasses the whole (Walser et al., 2004), such that presumably fewer Po plain between Venezia in the North and Ravenna members are needed for a representation of the in the South. The main idea behind selecting these uncertainty as compared to randomly generated catchments is to span a wide range of scales from 2 2 perturbations. However, our EPS strategy is ad hoc 186 km (Verzasca) to 120,000 km (extended Po). in many regards and does hardly produce those perturbations that would grow faster. In this respect, 2.4. Convection in a cloud-resolving model our ensemble simulations may suggest rather too optimistic (i.e. low) uncertainty levels. In this section, we present some background information on the process of deep convection in 2.3. Analysis strategy our simulations. The mesh size of 3 km allows Table 1 Ensemble simulations are performed for four case Catchments used for the analysis of the ensemble simulations studies. These were chosen from the year 1999 and 2 include a strong convective summer day, two heavy Catchment Gauge/gorge Area (km ) precipitation events with embedded convection in Extended Po ,120,000 September, and a late autumn frontal passage. An Po Piacenza 42,030 overview of these cases is presented together with the Lago Maggiore Miorina 6599 discussion of the results in Section 3. Toce Candoglia 1531 For the analysis of the ensemble simulations Ticino Bellinzona 1515 attention is given to precipitation in six sub-catch- Maggia Locarno–Solduno 926 Verzasca Lavertezzo 186 ments of the Po basin, located to the south of the main 62 A. Walser, C. Scha¨r / Journal of Hydrology 288 (2004) 57–73 an explicit simulation of deep convection, i.e. the vertical motions and condensation/evaporation in up- and downdrafts are explicitly represented. The cloud physics is treated with an advanced version of Kong and Yau (1997) explicit cloud microphysics scheme. It includes a bulk representation of the five water species water vapour, cloud water, rain water, ice crystals and graupel (Misra et al., 2000). Ice microphysics is of particular importance for the simulation of Alpine heavy precipitation (Richard et al., 2003; Yuter and Houze, 2003). At present, it is still somewhat unclear whether a horizontal grid spacing of 3 km resolves convection sufficiently, despite the promising experience from the MAP experiment with the same setup as used in our study (Benoit et al., 2002). Moist deep convection requires three ingredients: instability, moisture, and some vertical lifting. In a dry Fig. 4. MC2 simulated 12 min accumulated precipitation (grey- atmosphere, the criteria for static instability can be scales) in millimetre per hour for 2000 UTC 20 Sep 1999, deduced from the first law of thermodynamics superimposed by wind vectors at 700 hPa and by vertical velocity at (Holton, 1992) and requires that the potential 500 hPa (contours 1 m/s, with zero-contour omitted) showing updrafts (solid contours) and downdrafts (dashed contours) in a temperature strong southerly flow. The diagram zooms into the Swiss/Italian = Lago Maggiore area. The black line indicates the vertical section = R cp u ¼ Tðps pÞ ð1Þ used in Fig. 5. Wind arrows are shown at every second grid point. decreases with height, i.e. ð›u=›zÞ , 0: Here, T is the Fig. 4 shows an example of modeled convective temperature; R; the gas constant for dry air activity due to a potentially unstable lower tropo- (287 J K21 kg21); c is the specific heat of dry air at p sphere in the Lago Maggiore area. In the evening of constant pressure (1004 J K21 kg21). In a moist 20 September 1999 (for a case description see later in atmosphere the situation is more complicated since Section 3.1) a strong southerly flow impinges upon the the release of condensational energy has to be taken Alps and the orographically forced lifting releases the into account. This leads to the equivalent potential instability. Two convective cells produce strong temperature, u ; defined as the potential temperature e updrafts and precipitation rates exceeding 25 mm/h. that an air parcel would have if all its moisture is The characteristic time-scale of such convective cells condensed and the resulting latent heat is used to is typically only a few hours, for the two cells shown warm the parcel. For a saturated parcel, u is defined e in Fig. 4 even less. as (Holton, 1992, p. 289) The temporal evolution of the convective cell to = the north is shown in the vertical section in Fig. 5. The ue < u expðLcqs cpTÞð2Þ baseline of this section is represented by the black line where Lc is the latent heat of condensation in Fig. 4. The main flow is almost along the cross- 6 21 (2.5 £ 10 Jkg at 0 8C), and qs the saturation section with a strong vertical wind shear (the mixing ratio (mass of vapour per unit mass of dry horizontal wind increases from 10 m/s in the bound- air in a saturated parcel). If ue decreases with height, ary layer to about 40 m/s at 300 hPa). Panel (a) shows the atmosphere is referred to as potentially unstable. the updraft roughly 1 h after the initial triggering of The term potential here signals that the unstable layer the cell, while it is still growing. must first undergo some finite vertical displacement The extent of the convective cloud centred at a and reach saturation in order to release the instability height of 6 km is represented by the cloud water (Schultz and Schumacher, 1999; Houze, 1993). concentration (liquid and solid phases). Panel (b) A. Walser, C. Scha¨r / Journal of Hydrology 288 (2004) 57–73 63

Fig. 5. Time series of cloud water concentration (condensed water and ice crystals) (g/kg) of a convective cell along the south–north vertical section indicated by the black line in Fig. 4. The vertical velocity (contours 1 m/s, with zero-contour omitted) is overlaid and shows the strong updraft (solid contours) and weak downdrafts (dashed contours). The time interval between the panels is 12 min, and the first panel is at 1948 UTC 20 Sep 1999. The axes are labeled in kilometres. shows the cell 12 min later at the time of maximum under different atmospheric stratifications and differ- updraft (9 m/s) and with a vertical extension up to the ent synoptic conditions. Three of these cases are in the tropopause. In panel (c), again 12 min later, the MAP SOP. All cases have already been discussed in updraft becomes weaker and a secondary updraft Walser et al. (2004). evolves upstream. The horizontal displacement of the The 29 July 1999 was characterised by a flat primary deep cell is about 21 km in 24 min, pressure distribution over Central Europe and thus by corresponding to a propagation speed of 15 m/s. In a weak synoptic forcing (Fig. 6a). In the entire Alpine comparison, the horizontal wind velocity amounts to area strong thermal convection developed in the 25 m/s at the level of the maximum updraft. potentially unstable stratified atmosphere, producing Although state-of-the-art NWP models are capable locally heavy precipitation. Daily accumulated pre- to resolve large-scale convective clouds quite realis- cipitation exceeding 100 mm are simulated by the tically, one cannot expect a skilful prediction of the ensemble simulations over some Alpine peaks (see spatial and temporal occurrence of convective cells. later in Fig. 8b). Convection is an intrinsically chaotic process which The 20 September 1999 belongs to the MAP implies that the evolution of convection depends upon intensive observing period (IOP) 2b. It represents the the initial conditions in a highly nonlinear way. strongest precipitation event during the whole MAP SOP and is the subject of several recent studies (Medina and Houze, 2003; Rotunno and Ferretti, 3. Results 2003). A trough was approaching the Alps from west, leading to a strong persistent low-level moist flow In this section, we first present a brief overview of from the Mediterranean Sea towards the south side of the weather conditions for the four case studies. In the the Alpine barrier (Fig. 6b). The flow, strong at all following, we then analyse the model’s ability to levels, was warm, moist and potentially unstable in simulate precipitation by intercomparison against the lower troposphere. Hence, the air rose easily over radar data, and assess the potential predictability of the rising terrain, releasing the instability and precipitation in Alpine river catchments. favouring the development of convective cells. Radar observations show moderate convection during 3.1. Description of the case studies the day and deep convection in the afternoon (Rotunno and Ferretti, 2003). Our simulations suggest The four day–long case studies are chosen from sporadic deep convection in the afternoon after the the year 1999 such as to involve heavy precipitation passage of the cold front (as discussed in Section 2.4). 64 A. Walser, C. Scha¨r / Journal of Hydrology 288 (2004) 57–73

Fig. 6. Overviews of the synoptic situation in the four case studies in terms of geopotential height (m) at 850 hPa (contour interval is 40 m) at 1200 UTC from ECMWF analysis for (a) 29 Jul 1999, (b) 20 Sep 1999, (c) 25 Sep 1999, and (d) 6 Nov 1999.

According to the dataset of Frei and Ha¨ller (2001), the On 6 November 1999 (MAP IOP 15), a cutoff heavy rainfall intensity led to more than 100 mm low originating from the British Isles moved accumulated daily precipitation in the Lago Maggiore quickly towards the Alps, advecting very cold air (LM) area and on the Alpine slopes of the Friuli- towards the Mediterranean Sea (Fig. 6d). This Veneto region. evolution was followed by a fast lee cyclogenesis The 25 September 1999 was part of MAP IOP 3, event centred over the Gulf of Genova. In the LM which is characterised by a similar synoptic area, this led to a southerly, later south-easterly situation as IOP 2b. A trough extending from the flow towards the Alpine barrier, before a northerly British Isles to Spain propagated slowly eastwards, flow established. The maximum rainfall amounts leading to a persistent south-westerly flow over the were observed in the eastern Po Valley, where the Alpine region (Fig. 6c). South of the Alps, this daily sum exceeded 60 mm (dataset of Frei and moist potentially unstable flow impinges on the Ha¨ller, 2001). Alpine slopes, leading to heavy prefrontal precipitation enhanced by embedded convection in the LM 3.2. Comparison with radar observations area. In contrast to the 20 September, the heavy rainfall is confined to the LM area and to south- An objective validation of the MC2’s simulation of eastern France where strong frontal precipitation precipitation was performed by Jasper and Kaufmann occurred. (2003) for the Ticino–Verzasca–Maggia basin. They A. Walser, C. Scha¨r / Journal of Hydrology 288 (2004) 57–73 65 compared the operational real-time MC2 forecasts precipitation amounts. However, radar scans provide during the MAP SOP (Benoit et al., 2002) with an high spatially and temporally resolved observations. extensive surface observation network. They reported These allow evaluating how well the model performs that the temporal variability of the predicted precipi- in reproducing the spatiotemporal occurrence of tation sequences was generally in good agreement precipitation. Due to a lack of radar scans in the with the observations, while the MC2 precipitation eastern Po Valley, the comparison does focus on the amounts were substantially and persistently under- western part of the valley, in particular on the LM estimated by as much as 43%. Similarly, Benoit et al. area, and on Switzerland. (2002) reported a systematic underestimation for the Subsequently, the radar derived precipitation and entire model domain evaluating also the MAP SOP the simulated precipitation of member 2 of the forecasts. ensembles are compared at the time of the strongest In this section a comparison of radar derived and intensity in the LM area (Fig. 7). The choice of modeled precipitation is presented. During the MAP ensemble member 2 is arbitrary. Since the ensemble SOP a radar composite combining the data of spread is small for 20 September and 6 November operational radar networks from France, Germany, (see later), the comparison depends not on the chosen Switzerland and Austria has routinely been generated member in these cases. The spread is larger, in quasi-real time (Hagen, 1999). Unfortunately, such however, for the 25 September and thus the choice a product is not available for the 29 July. Thus, the of the member does somewhat influence the comparison is restricted to the three MAP cases comparison. considered in this study. Radar derived precipitation On 20 September 1999, precipitation was persist- is clearly less accurate than rain gauge measurements ently strong in the LM area until 1500 UTC with (Joss et al., 1998; Germann and Joss, 2002), and a reenhancement in the evening. The model simu- thus less suited for a validation of accumulated lates this evolution quite accurately (Fig. 7a and b).

Fig. 7. Comparison of modeled and radar derived precipitation intensity (mm/h). The panels show the MC2 3-km simulation of ensemble member 2 (top) and the MAP Alpine composite (bottom) for (a,b) 0800 UTC 20 Sep 1999, (c,d) 1930 UTC 25 Sep 1999, and (e,f) 1330 UTC 6 Nov 1999, zoomed into Switzerland and the northwestern Po Valley. 66 A. Walser, C. Scha¨r / Journal of Hydrology 288 (2004) 57–73

At 0800 UTC when the strongest intensity occurred, 3.3. Modeled precipitation the model captures well the precipitation pattern in the western Po Valley including the heavy precipi- In this section, the potential predictability of tation in the LM area and the shielded region to the precipitation in the four case studies is investigated. southeast. The model appears to capture the squall A measure for predictability is the spread of an line extending from south-western Switzerland to the ensemble, which can be determined, for example, by French Vosges, but its amplitude is considerably the standard deviation of the ensemble members with underestimated. respect to the ensemble mean. In order to evaluate the On 25 September 1999, the prefrontal precipitation potential predictability of accumulated daily precipi- in the LM area started at around 0400 UTC, enhancing tation p from our ensemble simulations, a normalised slowly and reaching the maximum only at 1930 UTC. spread is defined as This maximum as well as the evolution is quite well vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u captured by the model (Fig. 7c and d). However, north u XM 1 t 1 of the Alps the precipitation pattern of the approach- S ¼ ðp 2 pÞ2; ð3Þ p p M 2 1 m ing cold front is very poorly simulated, showing a m¼1 serious underestimation of the extension of the rainfall area at this time. where pm denotes the daily precipitation of member On 6 November 1999, the prefrontal precipitation m; p; the ensemble mean daily precipitation; M is the in the LM area, which started on the previous evening, ensemble size (equals to 12). Because of the normal- persisted until about 1700 UTC. It reached its isation by p; the analysis is restricted to areas with maximum at 1330 UTC. The model simulates the p $ 1 mm. Fig. 8 provides normalised spread Sp and precipitation related to the passing cold front well in ensemble mean accumulated daily precipitation, this case (Fig. 7e and f). The simulation misses, respectively, for the four case studies. The panels however, the latest 3 h of the precipitation in the LM reveal large differences in Sp among the case studies, area. In addition, the model represents the postfrontal but also in the spatial distribution. These aspects are cellular precipitation in the west near the French/ discussed below. Swiss borderline quite realistically. For 29 July the highest Sp values exceed 2 in Overall, the model simulates the evolution of the some regions, implying that the standard deviation precipitation in the western Po Valley qualitatively of the daily precipitation amounts to more than remarkably well, even though it underestimates the twice the ensemble mean (Fig. 8a). Such high persistency of the rainfall in the LM area in one of values occur in particular over sea and over the flat the cases. The model has also demonstrated its ability eastern Po region, while in the Alps and Appen- to simulate small-scale shower-like cellular precipi- nines the values are smaller. tation behind the cold front. The systematic under- In contrast, the heavy precipitation event on 20 estimation of precipitation by the MC2 is evident September is characterised by a small normalised from this comparison, despite the rather uncertain spread (Fig. 8c), similar as the late autumn case on accuracy of the radar-derived precipitation amounts. 6 November (Fig. 8g). In the Po basin, where the At least in the cases considered, the model bias can highest precipitation amounts occurred in both these be related to a misrepresentation of the spatial cases, the Sp values for the 20 September amount to extension of the precipitation bands, while the less than 0.1 in a large part of that region, while simulated precipitation intensities appear realistic. they are substantially larger for 6 November in the In addition, the model shows a distinct shortage of eastern Po Valley and over the Ligurian Sea. precipitation near the in flow boundary, affecting up The ensemble for 25 September shows a higher to 100 km in the flow direction (see later in Fig. 8). normalised spread in the LM area and north of the This feature must be associated with the treatment in Alps, as compared to the other two MAP cases the lateral relaxation zone. In particular, the con- (Fig. 8e). The large spread in the western part of the densed and frozen water is not nested from the model domain is likely associated with convective driving simulation. activity at the leading edge of the cold front, while A. Walser, C. Scha¨r / Journal of Hydrology 288 (2004) 57–73 67

Fig. 8. Spatial distribution of (left) normalised ensemble spread S p of accumulated daily precipitation (see text), and (right) ensemble mean of accumulated daily precipitation (mm) for (a,b) 29 Jul 1999, (c,d) 20 Sep 1999, (e,f) 25 Sep 1999, (g,h) 6 Nov 1999. The panels show the MC2 3 km model domain without the relaxation zone. 68 A. Walser, C. Scha¨r / Journal of Hydrology 288 (2004) 57–73 the high values to the north occur with ensemble the accumulated daily precipitation of the 12 members mean precipitation of only a few millimetres. for the four case studies. It should be noted that the Overall, the four case studies considered reveal mean precipitation amounts in the smaller catchments remarkable differences in the normalised ensemble differ by up to an order of magnitude between the case spread of daily precipitation Sp: Convective activity, studies. above all thermal convection, enhances Sp and hence For 29 July, the members show notable differences reduces the potential predictability. However, as will at all catchments considered, even in the extended Po be seen below the predictability is not a mere function basin. In the Po Piacenza basin, member 1 suggests of convective activity. more than twice the value of member 8. In the other, smaller catchments the differences are similar. In 3.4. Predictability in typical Alpine river catchments contrast, for 20 September the members yield very similar amounts in all catchments, despite the presence The simulated precipitation of the four ensembles of convective activity in this case. On 25 September, are evaluated for the seven river catchments Verzasca, even though the synoptic conditions and the intensity Maggia, Ticino, Toce, LM, Po Piacenza and extended of the convection are qualitatively similar as on 20 Po, deﬁned in Section 2.3. Fig. 9 provides September, the LM catchment, and in particular its

Fig. 9. Accumulated daily precipitation (mm) in seven river catchments (Section 2.3) from four case studies. Shown are catchment-mean amounts from ensemble simulations with 12 members. Note the different ordinate in the four panels. A. Walser, C. Scha¨r / Journal of Hydrology 288 (2004) 57–73 69 sub-catchments Verzasca, Maggia and Ticino, show information is shown in Fig. 11 as a function of substantial differences between the members. On catchment area (see symbols). 6 November, the differences between the members In addition, a location-independent background are small, except in the Verzasca catchment. normalised spread SpðAÞ is evaluated as a function of In the following, attention is given to the temporal the area A: SpðAÞ is derived from the simulation evolution of the accumulated precipitation in the river output in a 768 £ 768 km2 box centred in the 3 km catchments. Fig. 10 displays the evolution in the model domain (equals to almost the entire 3 km model Verzasca, Maggia, Toce, Po Piacenza and extended domain). To this end, SpðAÞ was calculated according ; Po catchment. As expected, the 20 September and the to Eq. (3) with pm and p representing averages for all 6 November do show little spread (except in the possible subdomains with the areas Verzasca catchment on 6 November) pointing out that x 2 2 not only the daily precipitation sum of the members A ¼ð3 £ 2 Þ km ; x ¼ 0; …; 8 ð4Þ are close to each other, but also the temporal evolution of precipitation. within this box (see Walser et al., 2004 for details). On 29 July, the precipitation intensities averaged The results are summarised in terms of the solid lines over the different catchments are rather small, and in Fig. 11, quantifying the predictability of precipitation amounts for the four case studies and for areas precipitation is mostly due to scattered convective 2 6 2 cells. The evolution of the precipitation intensity between 10 km (grid point scale) and 10 km .In ð Þ varies remarkably within the members, even in the Po essence, the background spread Sp A represents a Piacenza catchment (first column in Fig. 10). This mean location-independent estimate of normalised spread as a function of area A: behaviour is very pronounced in the Toce catchment A general trend towards high predictability with where some members show higher precipitation increasing area is obvious in both the catchments and intensities in the earlier hours of the day, while others background values. For 29 July, the background have maximum precipitation in the afternoon or are S ðAÞ exceeds 1 for the smallest areas considered. characterised by relatively constant intensities during p Even for larger areas, S ðAÞ does not appear to most of the day. However, the comparatively high p converge to 0, in contrast to the other three cases. For precipitation intensity in the first few hours in some most of the smaller catchments and in all the cases, the members, in particular in the Verzasca and Maggia Sp values are substantially lower than the back- catchment, appears to be related to model spinup ground values. In the larger catchments, however, the caused by the amplification of the perturbations. Sp values are mostly higher than the background Nevertheless, even when disregarding the first few values, in particular in the Po Piacenza catchment. hours, the remaining period is clearly unpredictable. The transition between the two characteristics occurs The differences highlight the unpredictable spatial in the LM catchment, which is the largest of the and temporal occurrence of convective cells and the catchments with entirely mountainous character, respective impact upon accumulated precipitation located directly to the south of the main Alpine within a typical Alpine river catchment. ridge. Hence, complex topography seems to increase On 25 September, when precipitation was much the predictability of quantitative precipitation. This is stronger, the ensemble reveals also remarkably also indicated, at grid point scale, in Fig. 8a. It is likely varying precipitation intensities between the members that this property is related to the topographic control in the small Verzasca catchment. In this case, some of both the convection triggering mechanism and the members suggest a notable increase in precipitation larger-scale uplift on the Alpine slopes. intensity at 1600 UTC, whereas other members show Additionally, the Sp values for the river catch- it later and weaker. ments exhibit a large case-to-case variability. As an In order to calculate the normalised spread of daily extreme example, consider the Maggia catchment. It precipitation Sp for the seven river catchments, Eq. shows values between 0.015 (20 September) and 0.33 (3) is used with pm and p representing averages over (29 July) indicating excellent and poor predictability, the catchments instead of grid point values. This respectively. Note also the large differences among 70 A. Walser, C. Scha¨r / Journal of Hydrology 288 (2004) 57–73

Fig. 10. Evolution of accumulated precipitation (mm) from ensemble simulations for four cases studies in the river catchments Verzasca, Maggia, Toce, Po Piacenza, and extended Po. The x-axis in the panels indicates time in UTC. A. Walser, C. Scha¨r / Journal of Hydrology 288 (2004) 57–73 71

in this study is thus not meant as an operational limited-area EPS. The study is based on four case studies and includes a summer day with strong thermal convection, two early autumn day with embedded convection, and a late autumn frontal passage with stable stratiﬁcation. The results were analysed with respect to the potential predictability of precipitation in selected Alpine river catchments spanning a wide range of scales from 200 to 120,000 km2. The key results are:

† The potential predictability strongly depends upon the weather conditions. In particular during episodes of thermal convection, precipitation forecasts can be critically affected by predictability limitations, even in intermediate-scale river catch- Fig. 11. Scale dependence of predictability of precipitation in ments (,50,000 km2). doubly logarithmic display. Normalised spread Sp for 29 Jul 1999 † (red), 20 Sep 1999 (green), 25 Sep 1999 (brown), 6 Nov 1999 (blue) However, the presence of convection alone does is shown. Symbols and solid lines refers to the seven river not necessarily limit predictability, at least in catchments and to background values for the model domain, mountainous regions. More speciﬁcally, in one respectively (see text). case with moderate convection, we found the ensemble members to be virtually identical. The the catchments within a single case. For instance on dynamical and physical reason for this peculiar behaviour is beyond the scope of the present study, 29 July, the Po Piacenza catchment reveals a Sp value of 0.29, while for the smaller LM catchment it is only but it clearly deserves further investigation. 0.15. For a single event, a simple dependence of † The potential predictability of precipitation shows predictability upon the size of a speciﬁc catchment is large case-to-case and catchment-to-catchment thus not generally deducible. variability. A relationship between catchment area and predictability can be noted in the mean, but is not deducible in a single case. 4. Summary and conclusions † Precipitation amounts in mountainous catchments appear to be more predictable than in the The predictability of quantitative precipitation in foreland. This is most likely due to the typical Alpine river catchments has been investigated topographic control of precipitation, both through using ensembles of numerical weather simulations. the triggering of convection and the larger-scale These simulations were performed with the Canadian uplift due to the underlying topography. NWP model MC2 in a convection-resolving setup. The applied variant of the ensemble methodology The present study has some notable limitations. assumes perfectly predictable synoptic conditions and The initial perturbations are generated using an ad hoc a prefect model. Since the uncertainty arises only from technique that does at best qualitatively match the small-scale perturbations in the initial conditions, this observational uncertainties. Furthermore, only four setup allows to isolate predictability limitations cases were considered, and each of them investigated related to the meso-b scale, e.g. related to convection with only 12 ensemble members. In addition, the MC2 and gravity-wave propagation. In reality, uncertainties is characterised by a systematic underestimation of due to synoptic-scale atmospheric evolution as well as the precipitation. Nevertheless, we believe that model errors would contribute towards further redu- the main conclusion are not affected by these model cing the predictability. The ensemble strategy applied and setup shortcomings. 72 A. Walser, C. Scha¨r / Journal of Hydrology 288 (2004) 57–73

In particular, our results suggest that short-range Buizza, R., Miller, M., Palmer, T.N., 1999. Stochastic represen- quantitative precipitation forecasting may at least on tation of model uncertainties in the ECMWF ensemble occasion be seriously affected by intrinsic predict- prediction system. Q. J. R. Meteorol. Soc. 125, 2887–2908. Droegemeier, K.K., Smith, J.D., Businger, S., Doswell III, C., ability limitations, even with a perfect model and a Doyle, J., Duffy, C., et al., 2000. Hydrological aspects of perfect synoptic forcing. This result underlines the weather prediction and flood warnings: report of the ninth practical importance of probabilistic forecasting prospectus development team of the US weather research strategies. The trend in NWP towards finer meshes program. Bull. Am. Meteorol. Soc. 81, 2665–2680. will unquestionably continue, favouring further the Du, J., Mullen, S.L., Sanders, F., 1997. Short range ensemble one-way coupling of atmospheric and hydrologic forecasting of quantitative precipitation. Mon. Wea. Rev. 125, 2427–2459. models. Hence, the combination of an atmospheric Ehrendorfer, M., 1997. Predicting the uncertainty of numerical short-range high-resolution EPS with a hydrologic weather forecasts: a review. Meteorol. Zeitschrift, N.F. 6, model and uncertainty processor seems to be an 147–183. attractive strategy towards flood forecasting and Ehrendorfer, M., Errico, R.M., Raeder, K.D., 1999. Singular-vector warning systems. perturbation growth in a primitive equation model with moist physics. J. Atmos. Sci. 56, 1627–1648. Frei, C., Ha¨ller, E., 2001. Mesoscale precipitation analysis from MAP SOP rain-gauge data, MAP Newsletter No. 15, MeteoS- Acknowledgements wiss, Zurich, pp. 257–260. Frei, C., Davies, H.C., Gurtz, J., Scha¨r, C., 2000. Climate dynamics and extreme precipitation and flood events in Central Europe. We are indebted to Robert Benoit and his research Integrated Assessment 1, 281–299. group at Recherche en Pre´vision Nume´rique (RPN), Fritsch, J.M., Houze Jr., R.A., Adler, R., Bluestein, H., Bosart, Canada, for providing access to and support of the L., Brown, J., et al., 1998. Quantitative precipitation MC2 model. The authors acknowledge the support of forecasting: report of the eight prospectus development Karsten Jasper and Massimiliano Zappa for providing team, US weather research program. Bull. Am. Meteorol. Soc. 79, 285–299. the coordinates of the river catchments. The numeri- Forgner, I.-L., Iversen, T., 2002. High-resolution limited-area cal simulations have been conducted on the NEC SX- ensemble predictions based on low-resolution targeted singular 5 at the Swiss Center for Scientific Computing (SCSC, vectors. Q. J. R. Meteorol. Soc. 128, 1321–1341. Manno). The research has been funded by ETH Zu¨rich Gal-Chen, T., Somerville, R., 1975. On the use of a coordinate under research contract TH02134. transformation for the solution of the Navier–Stokes equations. J. Comput. Phys. 17, 209–228. Germann, U., Joss, J., 2002. Mesobeta profiles to extrapolate radar precipitation measurements above the Alps to the ground-level. References J. Appl. Meteorol. 41, 542–557. Grimit, E.P., Mass, C.F., 2002. Initial results of a mesoscale short- range ensemble forecasting system over the Pacific northwest. Benoit, R., Desgagne´, M., Pellerin, P., Chartier, Y., Desjardins, Wea. Forecast. 17, 192–205. S., 1997. The Canadian MC2: a semi-Lagrangian, semi- Hagen, M., 1999. The Alpine radar composite, MAP Newsletter No. implicit wideband atmospheric model suited for finescale process studies and simulations. Mon. Wea. Rev. 125, 11, MeteoSwiss, Zurich, pp. 20–21. 2382–2415. Holton, J.R., 1992. An Introduction to Dynamic Meteorology. Benoit, R., Pellerin, P., Kouwen, N., Ritchie, H., Soulis, E.D., 2000. Academic Press, New York, 511 pp. Toward the use of coupled atmospheric and hydrologic models Houtekamer, P.L., Lefaivre, L., Derome, J., Ritchie, J., Houteka- at regional scale. Mon. Wea. Rev. 128, 1681–1706. mer, H.L., 1996. A system simulation approach to ensemble Benoit, R., Scha¨r, C., Binder, P., Chamberland, S., Davies, H.C., prediction. Mon. Wea. Rev. 124, 1225–1242. Desgagné¯, eM., et. al., 2002. The real-time ultrafinescale forecast Houze, R.A., 1993. Cloud Dynamics. Academic Press, New York, support during the special observing period of the MAP. Bull. 573 pp. Am. Meteorol. Soc. 83, 85–109. Jasper, K., Kaufmann, P., 2003. Coupled runoff simulations as Bougeault, P., Binder, P., Buzzi, A., Dirks, R., Houze, R., Kuettner, validation tools for atmospheric models at the regional scale. J., et al., 2001. The MAP special observing period. Bull. Am. Q. J. R. Meteorol. Soc. 129, 673–692. Meteorol. Soc. 82, 433–462. Joss, J., Scha¨dler, B., Galli, G., Cavalli, R., Boscacci, M., Held, E., Buizza, R., Palmer, T.N., 1995. The singular-vector structure et al., 1998. Operational Use of Radar for Precipitation of the atmospheric general circulation. J. Atmos. Sci. 52, Measurements in Switzerland. VDF Hochschulverlag AG an 1434–1456. der ETH, Zurich, 108 pp; ISBN 3 7281 2501 6. A. Walser, C. Scha¨r / Journal of Hydrology 288 (2004) 57–73 73

Kelly, K.S., Krzysztofowicz, R., 2000. Precipitation uncertainty observed in the Lago Maggiore area on 17 September 1999 processor for probabilistic river stage forecasting. Water (MAP IOP2a). Q. J. R. Meteorol. Soc. 129, 543–563. Resour. Res. 36, 2643–2653. Rotunno, R., Ferretti, R., 2003. Comparative analysis of rainfall in Kong, F., Yau, M.K., 1997. An explicit approach to microphysics in MAP cases IOP2b and IOP8. Q. J. R. Meteorol. Soc. 129, MC2. Atmos. Ocean 35, 257–291. 373–390. Krzysztofowicz, R., 1998. Probabilistic hydrometeorological fore- Scha¨r, C., Sprenger, M., Lu¨thi, D., Jiang, Q., Smith, R.B., Benoit, casts: toward a new area in operational forecasting. Bull. Am. R., 2003. Structure and dynamics of an Alpine potential Meteorol. Soc. 79, 243–251. vorticity banner. Q. J. R. Meteorol. Soc. 129, 825–855. Krzysztofowicz, R., Herr, H.D., 2001. Hydrologic uncertainty Schultz, D.M., Schumacher, P.N., 1999. The use and misuse of processor for probabilistic river stage forecasting: precipitation- conditional symmetric instability. Mon. Wea. Rev. 127, dependent model. J. Hydrol. 249, 46–68. 2709–2732. Lorenz, E.N., 1963. Deterministic nonperiodic flow. J. Atmos. Sci. Stensrud, D.J., Brooks, H.E., Du, J., Tracton, M.S., Rogers, E., 20, 130–141. 1999. Using ensembles for short-range forecasting. Mon. Wea. Rev. 127, 433–466. Marsigli, C., Montani, A., Nerozzi, F., Paccagnella, T., Tibaldi, S., Stensrud, D.J., Bao, J.W., Warner, T.T., 2000. Using initial Molteni, F., Buizza, R., 2001. A strategy for high-resolution conditions and model physics in short-range ensemble simu- ensemble prediction. Part II: Limited-area experiments in lations of mesoscale convective systems. Mon. Wea. Rev. 128, four Alpine flood events. Q. J. R. Meteorol. Soc. 127, 2095–2115. 2077–2107. Medina, S., Houze, R.A., 2003. Air motions and precipitation Tanguay, M., Robert, A., Laprise, R., 1990. A semi-implicit semi- growth in Alpine storms. Q. J. R. Meteorol. Soc. 129, 345–371. Lagrangian fully compressible regional forecast model. Mon. Miller, N.L., Kim, J., 1996. Numerical prediction of precipitation Wea. Rev. 118, 1970–1980. and river flow over the Russian river watershed during the Toth, Z., Kalnay, E., 1997. Ensemble forecasting at NCEP and the January 1995 California storms. Bull. Am. Meteorol. Soc. 77, breeding method. Mon. Wea. Rev. 125, 3297–3319. 101–105. Walser, A., Lu¨thi, D., Scha¨r, C., 2004. Predictability of precipitation Misra, V., Yau, M.K., Badrinath, N., 2000. Atmospheric water in a cloud-resolving model. Mon. Wea. Rev. 132, 560–577. species budget in mesoscale simulations of lee cyclones over the Yu, Z., Lakhtakia, M.N., Yarnal, B., White, R.A., Miller, D.A., Mackenzie river basin. Tellus 52A, 140–161. Frakes, B., Barron, E.J., Duffy, C., Schwartz, F.W., 1999. Molteni, F., Buizza, R., Palmer, T.N., Petroliagis, T., 1996. The Simulating the river-basin response to atmospheric forcing by ECMWF ensemble prediction system: methodology and linking a mesoscale meteorological model and hydrologic validation. Q. J. R. Meteorol. Soc. 122, 73–119. model system. J. Hydrol. 218, 72–91. Palmer, T.N., 2000. Predicting uncertainty in forecasts of weather Yuter, S.E., Houze, R.A., 2003. Microphysical modes of precipi- and climate. Rep. Prog. Phys. 63, 71–116. tation growth determined by vertically pointing radar at Richard, E., Cosma, S., Tabary, P., Pinty, J.-P., Hagen, M., 2003. Locarno–Monti during MAP. Q. J. R. Meteorol. Soc. 129, High-resolution numerical simulations of the convective system 455–476.