Nat. Hazards Earth Syst. Sci., 6, 611–619, 2006 www.nat-hazards-earth-syst-sci.net/6/611/2006/ Natural Hazards © Author(s) 2006. This work is licensed and Earth under a Creative Commons License. System Sciences Rainfall downscaling and flood forecasting: a case study in the Mediterranean area N. Rebora1, L. Ferraris1,2, J. von Hardenberg3,1, and A. Provenzale3,1 1CIMA, University of Genoa and University of Basilicata, Savona, Italy 2DIST, University of Genoa, Genoa, Italy 3ISAC-CNR, Turin, Italy Received: 31 October 2005 – Revised: 29 May 2006 – Accepted: 29 May 2006 – Published: 12 July 2006 Abstract. The prediction of the small-scale spatial-temporal than 1000 km2, typical for the Mediterranean environment, pattern of intense rainfall events is crucial for flood risk as- have concentration times of less than 12 h; as this is less than sessment in small catchments and urban areas. In the ab- the time necessary for the population to react by following sence of a full deterministic modelling of small-scale rain- alert procedures (Siccardi et al., 2005), rainfall forecasts at fall, it is common practice to resort to the use of stochas- these scales, or smaller, become crucial. The use of limited- tic downscaling models to generate ensemble rainfall predic- area meteorological models (LAMs) that provide precipita- tions to be used as inputs to rainfall-runoff models. In this tion forecasts on scales of about 100 km2 and a few hours is work we present an application of a new spatial-temporal a common approach to this issue (Lin et al., 1985; Bacchi downscaling procedure, called RainFARM, to an intense pre- et al., 2003). However, obtaining reliable predictions from cipitation event predicted by the limited-area meteorological numerical models at these resolutions is still difficult. An model Lokal Model over north-west Italy. The uncertainty in alternate approach is to use statistical techniques to down- flood prediction associated with the small unresolved scales scale modeled precipitation to the fine resolutions needed for of forecasted precipitation fields is evaluated by using an hydrological applications (Droegemeier et al., 2000; Ferraris ensemble of downscaled fields to drive a semi-distributed et al., 2002; Siccardi et al., 2005). rainfall-runoff model. A downscaling procedure consists of a stochastic algo- rithm that allows for generating an ensemble of possible realizations of the small-scale rainfall field starting from a smoother field predicted on larger scales. The precipita- 1 Introduction tion fields generated by this approach are required to satisfy large-scale constraints imposed by the meteorological fore- In the Mediterranean region many cities are located in flood- cast (e.g., the total rainfall volume) and should be consistent prone areas and millions of people are exposed to inundation with the known statistical properties of the small-scale rain- risk. For this reason issuing early flood warning to the popu- fall distribution. lation is crucial to avoid loss of lives and to reduce property damage. Here we consider a simple hydrometeorological flood forecasting chain composed of three elements: (a) Lim- The solution to this problem relies on the knowledge of ited Area Model precipitation predictions, (b) ensembles of meteorological and hydrological processes that lead to flood high-resolution rainfall fields generated by a downscaling al- formation; depending on the characteristics of the watershed, gorithm and (c) ensembles of peak discharges obtained by many different approaches that use meteorological and hy- coupling the rainfall downscaling ensembles with a semi- drological models as well as observations have been pro- distributed rainfall-runoff model. The output of this proce- posed (Droegemeier et al., 2000). Very large basins, with ar- dure is a probabilistic distribution of peak discharges whose eas greater than 10 000 km2, have concentration times larger variability is generated by the small-scale fluctuations of the than 24 h; in this case flood forecasting based on precipita- precipitation input provided by the downscaling procedure. tion observations coupled with hydrological models suffices. However, small and medium catchments, with areas smaller The aim of this work is to show the performance of a downscaling algorithm, designed to generate small- Correspondence to: N. Rebora scale rain rate fluctuations, that preserves the spatial- ([email protected]) temporal evolution of rainfall patterns predicted by a LAM Published by Copernicus GmbH on behalf of the European Geosciences Union. Figures 0 10 −1 10 −2 10 −3 10 Power Spectrum −4 10 (a) (b) (c) −5 10 −2 −1 0 10 10 10 k [1/km] s Fig. 1. Example of the possible scales range of a power spectrum obtained from the spatial analysis of a LAM prediction: (a) reliable scales, (b) unreliable scales and (c) unresolved scales. 612 N. Rebora et al.: Rainfall downscaling and flood forecasting 0 10 −1 10 −2 10 −3 10 Power Spectrum −4 10 (a) (b) (c) −5 10 −2 −1 0 10 10 10 k [1/km] s Fig. 1. Example of the possible scales range of a power spectrum obtained from the spatial analysis of a LAM prediction: (a) reliable scales, (b) unreliable scales and (c) unresolved scales. Fig. 2. The downscaling domain over North-Western Italy and the (Rebora et al., 2005, 2006). Here we considerFig. 2. onlyThe the downscalingcatchments domain considered over North-Western in the work. Italy and the catchments considered in the ability of the downscaling procedure to generate,work. starting from a single meteorological forecast, an ensemble of high- resolution precipitation fields that in turn lead to an ensemble teorological models (Perica and Foufoula-Georgiou, 1996; of possible hydrographs. A comparison between observed Venugopal et al., 1999), but other information deriving from and forecasted hydrographs will be reported elsewhere. meteorological predictions is often not preserved. For exam- The work is organized as follows: a brief description of ple, the localization in space and in time of large scale struc- the downscaling procedure is given in the next section. In tures in the rainfall field, at scales reliably predicted by the the third section we discuss an example implementation of model, can be crucial for predicting sudden floods in small the hydrometeorological chain. We present an application of catchments and in urban areas (Droegemeier et al., 2000). the downscaling model and we generate an ensemble of pos- In this work a new downscaling16 procedure is used. This sible high-resolution rain fields. These fields are then used as approach is able to account for the reliable features of the inputs to a semi-distributed rainfall-runoff model. A discus- meteorological prediction and its parameters can be directly sion and conclusions are presented in Sect. 4. derived from the large-scale field with no need for calibra- tion. This procedure is called RainFARM, Rainfall Filtered AutoRegressive Model, and it was proposed by Rebora et al. 2 The RainFARM downscaling procedure (2006) to which we refer for a complete description and fur- ther details. RainFARM belongs to the family of algorithms A hydrometeorological forecasting chain designed for op- called metagaussian models (see, e.g. Guillot and Lebel erational purposes requires robust and computationally fast 1999) and it is based on a nonlinear transformation of a lin- downscaling models. Many procedures have been proposed early correlated process. This approach is closely related to for rainfall downscaling to this date. These algorithms can be the Turning Bands Method (Matheron, 1973) and has been grouped into three main families: (1) multifractal cascades, used both for satellite-based rainfall measurement validation (2) non-linearly transformed autoregressive models, and (3) and for stochastic rainfall modelling (Bell and Kundu, 2003; processes based on the superposition of many rainfall cells Bell, 1987; Lanza, 2000). The model is able to generate (cluster models). All these models have been proven to score small-scale rainfall fields that take into account not only the fairly well in reproducing the observed small-scale statisti- total amount of precipitation predicted by the meteorological cal properties of precipitation (Ferraris et al., 2003b). How- model but also its linear correlation structure and the position ever, linking these models with the features of the large scale of the main rainfall patterns. Due to the straightforward link fields is not immediate. Many downscaling procedures cur- between the model parameters and the large-scale field, this rently available for operational purposes account only for the model is suitable for operational downscaling procedures. total precipitation predicted by the LAM over a given spatial- RainFARM uses the spectral information of large-scale temporal domain; some other models are based on CAPE meteorological predictions and generates fine resolution pre- (Convective Available Potential Energy) predicted by me- cipitation fields by propagating this information to smaller Nat. Hazards Earth Syst. Sci., 6, 611–619, 2006 www.nat-hazards-earth-syst-sci.net/6/611/2006/ N. Rebora et al.: Rainfall downscaling and flood forecasting 613 80 0 10 LAM RainFARM 70 (a) −1 10 60 −2 50 10 40 −3 10 30 Power Spectrum −4 10 rainfall intensity [mm/h] 20 10 −5 10 −2 1 −1 0 10 10 10 L 0 k [1/km] 0 s 0 6 12 18 24 30 36 42 48 t [h] 4 Fig. 3. Spatial power spectrum of the original LAM field (dashed LAM line) compared to that obtained for a downscaled field (solid line). 3.5 RainFARM (b) 3 scales. The basic idea is to reconstruct the Fourier spectrum of the small-scale precipitation field by preserving the LAM 2.5 information at the scales where we are confident in the mete- 2 orological prediction. The rainfall field is seen as the super- position of a finite number of harmonics with amplitudes de- 1.5 creasing as spatial and temporal scales become smaller.