714 JOURNAL OF HYDROMETEOROLOGY VOLUME 3

The Uncertainty in the Prediction of Flash Floods in the Northern Mediterranean Environment

LUCA FERRARIS,ROBERTO RUDARI, AND FRANCO SICCARDI Centro di Ricerca Interuniversitario in Monitoraggio Ambientale, UniversitaÁ di Genova e della Basilicata, Savona, and Dipartimento di Ingegneria Ambientale, UniversitaÁ di Genova, Genova,

(Manuscript received 10 August 2001, in ®nal form 9 May 2002)

ABSTRACT Development of an operational ¯ood forecasting system and assessment of forecast uncertainty are the principal topics of this paper. Flood forecasting procedures are developed for a Mediterranean environment. A procedure that uses the Ensemble Prediction System as input for a semidistributed hydrologic model is presented. A rainfall downscaling model is used to bridge the scale gap between numerical weather prediction model output and hydrologic modeling input. The results are illustrated for the November 1994 ¯ood.

1. Introduction hydrologic domain have been treated separately. In hy- drology the discussion about the uncertainty dates back The orography of the northern Mediterranean coast- to a few decades ago, but traditionally it was based on line is very rough. The hydrologic timescale of most a given rainfall ®eld (Beven 1993). The uncertainty was watersheds is on the order of a few hours. Flash ¯oods not addressed quantitatively with respect to the whole develop rapidly during the rainy season and suddenly operational chain (Ferraris et al. 2000). inundate the terminal ¯ood plains. Historical cities de- The meteorological uncertainty has a larger scale veloped on such ¯ood plains in the past. Therefore, town when compared with the time and space scales of the centers are, nowadays, exposed to a high risk of inun- dation. Civil protection procedures require that popu- concerned watersheds. Hydrologists refer to it as ``ex- lations undertake precautionary measures when a ¯ood ternal-scale'' uncertainty, meaning that it cannot be re- warning is issued. However, the timescale of the social duced by improving the observational network at the system to put ef®cient measures into action is on the basin scale. This uncertainty increases as the forecast order of a day. focuses on smaller scales typical of hydrology. About Traditional warning systems based on rainfall obser- a decade ago limited area models (LAMs) were devel- vations and rainfall±runoff modeling do not provide the oped in order to downscale global circulation model timely predictions required to implement the required (GCM) outputs, using a better representation of the me- precautionary civil protection measures (Siccardi 1996). soscale processes (Mesinger et al. 1988), for example, Social safety demands that hydrologists reliably predict atmosphere±ground interactions. Nesting an LAM into ground effects 24 h in advance. In order to accomplish the GCM deterministic boundary conditions, however, this task they have to use rainfall predictions as input did notÐand still does notÐimprove the forecasts as to rainfall±runoff models. required by hydrologists, because the ``external-scale'' Two major sources of uncertainty are present in cou- uncertainty is not addressed. A technique was intro- pling meteorological with hydrologic models: the un- duced by Molteni et al. (2001), in which the Ensemble certainty at the meteorological scale per se and the un- Prediction System (EPS), which gives a measure of the certainty at the interface between meteorology and hy- external-scale uncertainty, was downscaled through the drology (Castelli 1995). use of a LAM. A summary of this technique is given The uncertainty issue has been extensively debated in section 2. in the literature, but usually the meteorological domain The second source of uncertainty is due to the lack (Buizza et al. 1999; Toth et al. 1998, 2001) and the of coherence among the time and space scales of me- teorological and hydrologic models. Even in the event that the external uncertainty is negligible, the meteo- Corresponding author address: Dr. Luca Ferraris, Centro di Ri- rologically predicted rainfall intensities are not enough cerca Interuniversitario in Monitoraggio Ambientale, Via Cadorna, 7, 17100 Savona, Italy. to produce saturation excess in the time intervals in E-mail: [email protected] which ¯oods develop, because of the scales' inconsis-

᭧ 2002 American Meteorological Society

Unauthenticated | Downloaded 09/28/21 01:26 AM UTC DECEMBER 2002 FERRARIS ET AL. 715 tency. In order to make rainfall ®elds coherent with Centers for Environmental Prediction (NCEP) have im- hydrologic scales, hydrologists have to disaggregate the plemented the EPS forecast system, capable of gener- large-scale meteorological predictions by preserving the ating different possible future scenarios, throughout the expected value of the ®eld at the large scale and by perturbation of initial conditions (Buizza et al. 1999; introducing appropriate second- and upper-order mo- Molteni et al. 1996; Toth et al. 2001). ments of the probability distribution (Deidda et al. At ECMWF the initial perturbations are based on 1999). singular vectors, which represent the most sensible re- In order to bridge the space and time gap between gions for error growth over the Northern Hemisphere. the meteorological models' outputs and the inputs con- As a result, EPS is optimized for this area (Molteni et sistent with the distributed hydrologic model (in this al. 1996). work), a multifractal disaggregation model, as proposed Until 1999, in order to improve EPS in the short to in Deidda (2000), is utilized. This is basically a prob- early-medium range over Europe, ensembles, whose abilistic tool that contributes information about the ``in- members concentrate on maximal error growth above ternal-scale'' uncertainty of the hydrologic processes in- the European area only, were integrated (Hersbach et volved. al. 2000). This Targeted Ensemble Prediction System Two approaches have been used to address statistical (TEPS) proved capable of presenting a more compre- modeling of precipitation ®elds within mesoscale areas: hensive description of the temporal evolution of the re- cluster-based models and fractal/multifractal models. liability of the forecast for Europe. The situation in Rainfall processes in cluster-based models are com- which a complete ensemble misses the occurrence of monly organized in a preferred hierarchy of scales in an extreme event had a much lower frequency for TEPS space and time. This hierarchy of scales describes the than for EPS. Consequently, in a case of hazardous process of rainband arrival, the cluster organization of events, TEPS was accepted as capable of giving more cells within a rainband, and the life cycle of cells be- precise information as to when to take preventive ac- longing to each cluster. A hierarchical description was tions. Such a procedure should result, on average, in ®rst designed by LeCam (1961), while a large diffusion lower economic losses. For operational purposes, in or- of cluster-based models was determined after Waymire, der to save computational time, the Meteorological Ser- Gupta, and Rodriguez-Iturbe proposed the well-known vice of Emilia±Romagna Region (SMR) developed a WGR model (Waymire et al. 1984). A disadvantage of hierarchical clustering technique to group TEPS mem- this kind of models is certainly the large number of bers into classes (Molteni et al. 2001). One member parameters that need tuning (Marsan et al. 1996; Ferraris from each class is extracted. Such a member is called et al. 2002, manuscript submitted to Water Resour. the ``representative member'' of that speci®c cluster and Res.). A more parsimonious approach uses multifractal is tagged with a probability measure representing the models based on random cascades (Gupta and Waymire relative size of the cluster. This procedure is then in- 1993; Kumar and Foufoula-Georgiou 1993a,b; Deidda tegrated by nesting the LAM, used by SMR, into each 2000). representative member in order to downscale the TEPS The same parsimonious criterion guided the choice outputs. The procedure is named Limited Area Model of the hydrologic model. The state-of-the-art procedure on Targeted Ensemble Prediction System (LAM±TEPS) uses distributed models (Beven 1989), which results in (Molteni et al. 2001; Marsigli et al. 2001). a better description of the heterogeneity of the physics This system is used in this work within the operational of the soil response and of the rainfall input. However, chain instead of the original EPS members in order to these models are overparameterized and it is dif®cult to reduce the extremely high computational load and to use them in an operational context, especially in mul- take into account the additional information introduced ticatchment systems. In the present work we use a sem- by the LAM. Such information could be crucial in a idistributed model, synthetically described in section 4, region with complex orography. which exploits the advantages of distributed modeling A scienti®c debate exists on the possibility of tagging in a more ef®cient framework for peak discharge eval- the different clusters with a probability measure that can uation (Giannoni et al. 2000; Giannoni et al. 2001, man- be used quantitatively in a forecast procedure. The ®rst uscript submitted to Water Resour. Res.). concern is about the poor sample produced if compared The three previously described components are linked with the complexity of the system. The computational into an operational ¯ood forecasting procedure, able to load is in this case a constraint, which also leads to use give results that are usable in terms of probability with of a less re®ned model. This brings about another debate reference to the simulation of the November 1994 ¯ood- issue on the utilization of the EPS for operational pur- ing event in northwest Italy. poses involving warning decisions. The second concern is about the possible dependency and bias of the initial perturbations set, which might not provide a ®nal result 2. The LAM±TEPS procedure able to represent a ``base'' of events as used in the theory Since 1992, the European Centre for Medium-Range of probability. Though aware of its limits, we have used Weather Forecasts (ECMWF) and the U.S. National this tool because we consider it the only way to produce

Unauthenticated | Downloaded 09/28/21 01:26 AM UTC 716 JOURNAL OF HYDROMETEOROLOGY VOLUME 3 a measure of the probability of each LAM±TEPS mem- (Venugopal et al. 1999; Ferraris 2000). Analyzing the ber and of the relative importance of external and in- observed ®elds, Deidda (2000) showed how the sto- ternal uncertainty in the hydrologic forecasts. chastic cascade parameters are related to the volume of rainfall to be disaggregated. In a forecast framework we obtain this volume from the forecasts of the meteoro- 3. Multifractal rainfall disaggregation logical model. The multifractal theory can be considered the most The advection velocity, U, is computed using the fore- powerful approach to nonlinear and intermittent pro- cast ®elds as observations. An example of a three-di- cesses like precipitation (Gupta and Waymire 1993). mensional disaggregated rainfall ®eld is presented in Multifractal models, in fact, can capture any moment Fig. 1. of the observed signalÐespecially higher-order mo- mentsÐand permit direct space±time modeling, thus re- 4. The semidistributed rainfall±runoff model producing simultaneously the statistical properties of real rainfall in space and time. As the aim of the work is to test the bene®ts of the Regarding the problem of space±time simulation of probabilistic forecast against the deterministic ones in these models we need to make the time variable di- terms of ground effects, we need to transform reliably mensionally equivalent to space variables. Therefore, to the forecast rainfall ®elds into discharge values at the do that, two kinds of assumptions on the scaling be- appropriate scale. Therefore, we need a rainfall±runoff havior of rainfall should be essentially distinguished: model suitable for this goal. the ®rst one is that space±time rainfall displays self- In the last decade, research in rainfall±runoff mod- similarity, while the second one deals with a self-af®ne eling invested mostly in distributed, physically based process. The self-similarity assumption corresponds to models. Progress in distributed hydrologic modeling re- the Taylor hypothesis of ``frozen turbulence'' (Taylor sulted in a better understanding of both runoff formation 1938), widely applied in turbulence to characterize the and propagation dynamic. The time and space scales velocity ¯uctuations in space from a time series of ve- involved are addressed in Wood et al. (1988, 1990). locity measurements taken at a ®xed point. The exten- Distributed modeling allows the description of the role sion of the Taylor hypothesis to the rainfall ®elds was played by soil and vegetation heterogeneity, topographic ®rst proposed by Zawadzki (1973). The temporal co- basin structure, and space±time distribution of the rain- ordinate is rescaled as ␭␶ Ϫ1 ϰ cost ϭ U at any scale ␭, fall input. Unfortunately, a detailed description of these where U is the advection velocity of the dynamic ®eld. aspects involves a large number of parameters with the In this manner a three-dimensional homogeneous iso- associated problem of their reliable estimation (Beven tropic process is obtained. 1989, 1993). In the present work, a semidistributed The self-af®ne assumption is a generalization of the modeling approach to the description of the hydrologic Taylor hypothesis whereby a scale-dependent velocity response is used. This approach, somewhere in the mid- H parameter, U␭ ϰ ␭ , is used to rescale the time variables. dle between the lumped and distributed ones, utilizes In this study a multifractal model, which is based on information and inputs (e.g., rainfall ®eld, elevation, and wavelets expansion with coef®cients extracted by a log± soil properties) distributed over the territory, while it is Poisson distributed stochastic cascade, is used. This almost lumped in its parameters. The Discharge model is extensively presented in Deidda (2000). Forecast (DRiFt) was developed by the Centro di Ri- In order to apply the model to real rainfall ®elds the cerca Interuniversitario in Monitoraggio Ambientale event must be discriminated according to the self-sim- (CIMA) for hydrologic modeling in sites with signi®- ilarity or the self-af®ne hypothesis. If three-dimensional cant orography, as we ®nd in most of northwestern Italy. observations of rainfall (e.g., radar ®elds) are available, The model structure is shortly summarized here in re- it is possible to classify the event by comparing both lation to the advantages that this approach provides the one-dimensional temporal and spatial power spectra within the proposed framework. For a more detailed (Deidda 2000; Ferraris 2000). Then the velocity param- description see Giannoni et al. (2000). eter U is computed using the cross-correlation tech- Sometimes, the variety of shapes of natural environ- niques explained in detail in Johnson and Bras (1979). ments forces hydrologists to develop speci®c models. The two parameters of the model, which characterize The steepness and the relative limited sizes of the north- the log±Poisson distribution, are in this case estimated western Italian catchments suggest enhancing only some through the analysis of the structure functions of the characteristics of the ¯ood formation process. The low observed precipitation ®eld (Deidda 2000). soil depth combined with the features of potential ¯ood- In a forecast framework we discriminate the similar- ing storms (very high intensities and short-duration ity/af®nity structure and estimate the parameters from events) leads to describing runoff generation through a the meteorological predicted ®eld obtained from a GCM Hortonian scheme, focusing mainly on surface ¯ow or a LAM. The convective available potential energy rather than on the other processes involved. These sim- (CAPE) ®eld, computed by the model variables, is re- pli®cations are also possible because of the speci®c fo- lated to the self-af®ne properties of the precipitation cus of the model in reproducing the peak discharge value

Unauthenticated | Downloaded 09/28/21 01:26 AM UTC DECEMBER 2002 FERRARIS ET AL. 717 and the time at which this peak occurs. These last two many works as the leading factors in orographically aspects are of paramount importance for civil protection tormented basins (Rinaldo et al. 1991). As a conse- purposes. Thanks to its relatively simple and physically quence of this ef®cient representation, the model gives based formulation, the model presents bene®ts typical good results in geomorphologic homogeneous catch- of both distributed and lumped models. The model has ments with no variations in the parameters, regardless a distributed representation of soil characteristics (e.g., of the basin size and rainfall intensities. Therefore, it is in®ltration parameters and initial moisture conditions all possible to calibrate it ef®ciently and to use reliably the over the catchment) and of the rainfall input. Therefore, same set of parameters in nongauged sites, in those in- it allows different responses to different spatial distri- stances when direct calibration is impossible and in con- bution of the same temporal history as well as to a ditions clearly different from the ones encountered dur- different detail scale in the rainfall spatial and temporal ing the calibration phase. This robustness in respect to representation. Its ability to accept distributed infor- parameters makes it not only a good research tool but mation about the input rainfall ®elds allows us to dis- also a convenient link within an operational forecasting criminate the different possible rainfall histories and to chain. This point is important in this paper, as we want evaluate the bene®ts of the probabilistic framework. to describe a technology particularly valuable for op- However, the model preserves some important charac- erational practices. teristics of lumped models, which are not to be over- looked for operational use in multicatchment systems. The model, in fact, is described by ®ve parameters that 5. Experiment summarize ef®ciently most of the interesting character- istics of the basin from the hydrologic point of view. a. Case study application The ®rst two parameters describe the geomorphology The event chosen in this work as a case study took of the environment to which the model is applied (Roth place in the northwestern part of Italy from 4 to 6 No- et al. 1996). They allow the identi®cation of the drainage vember 1994 and it is considered one of the major ¯oods structure in its basic components, hillslopes and chan- observed in the Mediterranean area. nels, on the basis of the information contained in the The meteorological conditions were determined by digital elevation model of the basin. A physically based an intense meridional ¯ow advecting humid and unsta- calibration was successfully performed on these param- ble air mainly from the south. A meteorological block- eters in all the Ligurian basins as well as in the target ing situation due to the presence of a large anticyclonic area of this study (Giannoni et al. 2000, 2001). Two area over eastern Europe determined the persistence of kinematic parametersÐnamely, two characteristic ve- such a structure over western Europe considerably slow- locities, one for the hillslope links and the other for the channel pathsÐlink the geomorphic structure of the ba- ing down the eastward propagation of the cold front. sin to the hydrologic processes that take place on the The main meteorological feature of the event was there- different components of the drainage network. In this fore the persistent southwesterly ¯ow convergence at way, the scale de®nition of the Geomorphologic In- the lower levels of the atmosphere in the region of in- stantaneous Unit Hydrograph (GIUH), considered the terest, associated with intense vertical motions and a weak point of this kind of approach (Shamseldin and strong humidity convergence. The classical convective Nash 1998), is performed within a physically based instability was not the principal reason for the heavy framework directly linked to pluviometric and hydro- precipitation, but it contributed to enforce its intensity, metric records. The calibration of these velocities is particularly on 4 November. Local vertical velocities of performed by comparing computed hydrographs with dynamic source were the dominant factor during 5 and observed ones. The last parameter describes the mois- 6 November, when the most intense showers took place. ture condition in the different parts of the basin at the The ground effects considered in this work mainly beginning of the simulation. Obviously, it is an event- concerned the River basin, near the town of Al- sensitive parameter and is estimated from the rainfall essandria, and its major subcatchments. From the rain history of the previous days and the knowledge of the gauge records this event could be divided into three characteristics of the basin. different phases. In the ®rst phase, on 4 November, A large number of intense rainfall events in different heavy precipitation poured mainly on the southern part Ligurian basins of various sizes, ranging from 100 to of the basin at the Ligurian border with peaks of 50 mm 1000 km2, have been collected and used for parameter hϪ1 and a maximum depth of 150 mm in 5 h. In the calibration. A best-®t technique was applied to peak and second phase, on 5 November, the precipitation also time-to-peak values (Giannoni et al. 2000). The major extended northward, striking the Tanaro, , and advantage of this model is that it characterizes the hy- River basins. The precipitation intensities in- drologic response at the catchment scale, exploiting all creased in respect to the previous day, and the ®rst land- the available distributed information, especially that re- slides and ¯oods occurred during the ®rst hours of 5 garding the geomorphologic structure of the environ- November. The recorded precipitation depths over the ment. These pieces of information are recognized by 24 h ranged between 200 and 250 mm. In the third

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FIG. 2. Site of the Tanaro River basin (northwestern Italy) with rain gauges (dots) and select hydrometric sections (stars). phase, on 6 November, the phenomenon continued with Thus, we can better evaluate the improvements given lower precipitation rates. by the disaggregation scheme. In this environment, with very steep orography, the concentration times range from about 5 to about 20 h. b. Validation of the rainfall±runoff (R±R) model Twenty hours represents the limit of what can be con- Using recorded rainfall during the days from 4 to 5 sidered a ¯ash ¯ood. We use ``¯ash ¯ood'' as a term November from the rain gauges illustrated in Fig. 2 we describing an event, within a civil protection framework, simulated the discharge histories in four different hy- that can only be treated through meteorological fore- drometric sections, also shown in Fig. 2. casts. The areas drained by these sections range from about In Fig. 3c the simulation results in the hydrometric 400 to about 8000 km2. Four hundred square kilometers section of the city of Alba are shown together with the represents the lower limit for which a single site targeted observed hydrograph. The agreement between the peak forecast is reasonable. The decision of considering areas discharge and the time-to-peak values supports the suit- up to 8000 km2 is due to the necessity of having a ability of the hydrologic model for the environment and catchment we can directly couple with the meteorolog- civil protection purposes. It also shows how reliable the ical models, which allows a limited scale inconsistency. results are when the recorded rainfall is used as an input

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FIG. 1. Disaggregation output for one simulation: (a) the horizontal slices represent the disaggregated rainfall ®eld in space at two different temporal steps, while the vertical column represents a temporal evolution at a ®xed point in space; (b) an example of a spatial disaggregated ®eld; and (c) a typical rainfall history at a ®xed point in the x±y space.

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FIG. 3. The control run of the hydrologic model (recorded rainfall) against the simulation using the deterministic forecast of the LAMBO model. The vertical line represents the starting time of the prediction exercise. dataset. Unfortunately, the Alba hydrometric station was are cumulated at 6-h intervals on a 20 km ϫ 20 km the only section that recorded a reliable hydrograph. grid. This choice was made to test the quality of the 24- Other sections had the gauge washed out or the bridge h forecast before the heaviest precipitation took place. destroyed. In these cases the simulation obtained by the The ®rst panel in Fig. 4 represents the deterministic run recorded rainfall series is used as a control hydrograph of the LAMBO model used for the simulations of the to test the deterministic procedure against the proba- deterministic forecast. The Tanaro River basin is singled bilistic one. In order to be consistent throughout, we out by the white rectangle. The results (Fig. 3 curve shall refer to the recorded-rainfall simulated hydrograph marked as ``CTRL'') allow us to observe how the peak as the control hydrograph for all sections, Alba included. discharge, obtained with the deterministic forecast of In Figs. 3a±d they are shown in dotted curves. Herein the meteorological model, heavily underestimates the these control hydrographs will be referred to as ``rainfall actual peak in each section. Even in the sections, closing hydrographs.'' catchment areas above 1000 km2, where the scale gap between the meteorological and hydrologic model is consistently smoothed out, the underestimation is sys- c. Coupling the R±R model with the deterministic run tematic (Figs. 3a,b). The River basin is the only In this ®rst experiment the ``deterministic'' sequence case in which the run gives acceptable results, consid- of rainfall ®elds forecast by Limited Area Model Bo- ering the scale gap between the models. The results for logna (LAMBO), which is the same LAM as in the the Belbo River basin are particularly poor, as the sim- LAM±TEPS procedure, is used as input for DRiFt. The ulated peak value is 1/3 of the actual one. experiment is intended to function within a civil pro- Comparing the LAMBO rainfall forecast with the ob- tection framework. Therefore, the simulation is based served rainÐrain upscaled according to the scale of the on the LAMBO forecasts of 5 November 1994. We sim- meteorological model (Fig. 5)Ðwe observe that the ulated the hydrographs in the four above-mentioned hy- structure of the event on the whole is well captured. So drometric stations using the observed rainfall until 0600 we can say that the meteorological model gave a good UTC 5 November, while the following 24 h are simu- general meteorological description of the rainfall ®eld. lated with the LAMBO forecast rainfall ®elds, which However, the rainfall maxima are misplaced by LAM-

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FIG. 4. The Tanaro River basin (white rectangle) and the area where the rainfall volume used as input for the disaggregation algorithm is computed (dark rectangle).

BO, which gave the higher values on the French on the assumption that each TEPS is equally likely to and on the Ligurian Apennine, while the recorded rain- happen. The same is for RM2: Pr[RM2 | TEPS] ϭ 0.18; falls show the maxima more in the east, toward the RM3: Pr[RM3 | TEPS] ϭ 0.12; RM4: Pr[RM4 | TEPS] Tanaro River basin. This uncertainty in the position of ϭ 0.12; and RM5: Pr[RM5 | TEPS] ϭ 0.08. The study the heaviest precipitation clusters affects the ®nal results of the ®ve maps shows that a large part of the LAM± even in cases, like our case study, where the event is TEPS forecast areas does not indicate high rainfall daily forecast in a satisfactory way from the general meteo- depths in northwestern Italy, but more toward Western rological point of view. This uncertainty determines the Mediterranean areas. The actual rainfall peaks were ob- poor results on the Tanaro at Montecastello section served eastward in respect to the predicted ones (Fig. where, from the theoretical point of view, the scale in- 5). The effect of such a bias is evident in the following consistency with the meteorological model forecast paragraph. ®elds may not be relevant. On the basis of the observed rainfall until 0600 UTC 5 November, and the ®ve sequences of forecast rainfall of the ®ve LAM±TEPS representative members, we d. Coupling the R±R model with the LAM±TEPS run have simulated the hydrograph in the four hydrometric Figure 6 shows the precipitation ®elds forecast in 24 stations. The results are presented in Figs. 7a±d. It is h by the deterministic prediction and by the ®ve rep- clear that, despite the use of the LAM±TEPS, we do resentative members of the LAM±TEPS clusters given not have a real improvement in the peak discharge sim- at 0600 UTC on 5±6 November 1994. The ®rst panel ulation and we still underestimate the actual value sys- in the top-left corner is the deterministic run of LAM- tematically, even in sections where the scale inconsis- BO, which is the control run, while the remaining maps tency between the LAM±TEPS and the rainfall±runoff represent the TEPS clusters. The ®rst element, run mem- model should not be a critical issue any more. We must ber 1 (RM1), of the LAM±TEPS, in the top-right corner, then observe how some members, while correctly pre- coincides in this case with the control run. It is the dicting the order of magnitude of the rainfall intensities, representative member of a cluster containing 25 mem- show a wrong positioning of these heavy precipitation bers and, with the theoretical cautions referred to pre- clusters, as previously indicated in the deterministic run, viously (section 2), it should be tagged with a condi- thus affecting in a crucial way the hydrologic simula- tional probability Pr[RM1 | TEPS] ϭ 0.5, conditioned tion.

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FIG. 5. (a) The recorded precipitation ®eld and (b) the precipitation ®eld forecast by the LAMBO model cumulated in the 24 h from 0600 UTC 5 Nov to 0600 UTC 6 Nov 1994. e. The effect of rainfall ®eld disaggregation shown in the black rectangle in Fig. 4. Our choice is based on our con®dence in the reliability of the results To avoid introducing additional uncertainties we es- timated the downscaling model parameters from the 40 of meteorological models within the frame of such a h of rainfall intensity data, derived from the Doppler temporal and spatial aggregation scale. The temporal radar of the Swiss Meteorological Institute sited near dimension, once the spatial aggregation scale is ®xed, Monte Lema. Similar results would have been obtained is not arbitrary, because the consistency between time if we had proceeded within a strict forecast framework and space has to be maintained. The linking parameter where no observations are available as described in sec- is the advection velocity of the perturbation, here es- tion 3. The radar ®eld and the meteorological forecast timated to be around 12 km hϪ1, which gives for a 24- ®elds are consistent with the parameter estimation. h timescale a spatial dimension of L ഠ 300 km. The data spatial resolution is 1 km ϫ 1 km, while In Table 1 the forecast rainfall volumes contained in the temporal resolution is 10 min. From the analysis of this imaginary cube in the space±time dominium are the one-dimensional spectra in space and time we can shown for each LAM±TEPS member. consider valid the isotropy approximation between time For each member we simulated 100 possible equally and space, and the Taylor approximation holds true likely precipitation ®elds, independent of one another, (Marsan et al. 1996; Ferraris 2000; Deidda 2000). with a spatial resolution of about 3 km ϫ 3 km and From the LAM±TEPS outputs we took the integral temporal resolution of about 10 min. These rainfall of the 24-h forecast rainfall depths on the spatial domain ®elds were then the input for the rainfall±runoff model.

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FIG. 6. Forecast precipitation ®elds (mm) over 24 h obtained by the ®ve representative members of the LAM±TEPS at 0600 UTC 5±6 Nov 1994 (RM1±RM5). The ®rst panel in the top-left corner (CTRL) is the deterministic run of the LAMBO. In reality rainfall was observed more eastward than predicted. (Courtesy of the Servizio Meteorologico Regionale di Agenzia Regionale Prevenzione e Ambiente, Bologna, Italy.)

We are presenting the results for two chosen hydro- itation volume in the target area derived from the LAM± metric sections, representative of the small- and large- TEPS outputs. Each class of simulation (we have ®ve scale catchments of the Tanaro River basin. The ®rst is classes of 100 simulations, each class corresponding to the Belbo River basin in the Castelnuovo area, with a a different LAM±TEPS member) has a probability of drained area of 410 km2, and the second is the Tanaro occurrence equal to the one associated to its LAM±TEPS River basin in the Montecastello area, with a drained area member. Each peak discharge value of the 500 simula- of about 8000 km2. The results are summarized, for both tions has a probability of occurrence equal to 1/100 times, hydrometric sections, as the exceedence probability which is the probability of occurrence, within each class, curves of the peak discharge, conditioned to the precip- of each of the 100 independent simulations:

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FIG. 7. The control run of the hydrologic model (recorded rainfall) against the simulation using the deterministic forecast of the LAMBO model and the simulations using the LAM±TEPS members. The vertical line represents the starting time of the prediction exercise.

1 ability of being exceeded, Pr[Q Ͼ Q ] ϳ 0.8, in the Pr[Q ϭ q*] ϭ Pr[RM* | TEPS]. p md pp100 case of the Belbo River at Castelnuovo and even more so for the Tanaro River at Montecastello. The cumulative distribution functions (CDFs) for the It is also interesting to note that the peak ¯ow of the peak ¯ow of (a) the Tanaro River and (b) the Belbo recorded rainfall hydrograph, in fact, largely exceeds in River are plotted on a Gumbel chart in Fig. 8. The two both sites the meteorological deterministic prediction, vertical lines in each plot respectively denote the value and that, again in both sites, it is very near to the ex- of the peak ¯ow obtained by simulation using as input pected value of the probability distribution. If we can the nondisaggregated rainfall ®elds of the most probable compare the three proposed forecasting chains within a LAM±TEPS member, which happens to coincide with decision-making framework we can evaluate the ben- the ``deterministic'' LAMBO run in this case, and the e®ts of the complete forecasting chain. The civil pro- value of the peak ¯ow obtained by simulation using as tection issues a warning as long as the forecast peak input the recorded rainfalls over the catchment. discharge exceeds a predetermined threshold in the an- From the results summarized in Fig. 8 we can observe alyzed hydrometric section. The threshold peak ¯ow for how the peak ¯ow obtained with the meteorological the Belbo River is of about 200 m3 sϪ1, while for the deterministic run without disaggregation shows a prob- Tanaro River at Montecastello is of about 4000 m3 sϪ1. If the decision whether or not to issue a warning at 0600 TABLE 1. Forecasted rainfall volumes over the target area (about UTC 5 November 1994 had to be made only on the 300 km ϫ 300 km) in 24 h. basis of the information provided by the ``deterministic'' Forecast Volume (mm3) Depth (mm) LAMBO run, no warning would have been issued be- CTRL ϭ RM1 10 600 95 cause no peak ¯ow exceeded the threshold discharges RM2 9500 85 in the hydrometric sections analyzed. Using the addi- RM3 6470 60 tional information, provided by the LAM±TEPS out- RM4 7750 70 puts, gives the same result. On the other hand, the results RM5 2750 25 of the disaggregation procedure would have suggested

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FIG. 8. Peak discharge exceedence probability plotted on a Gumbel chart for (a) the Belbo River and (b) the Tanaro River. The ®rst vertical line shows the value of the peak ¯ow obtained by the nondisaggregated rainfall ®elds of the meteorological deterministic LAM±TEPS member; the second line shows the value of the peak ¯ow obtained by simulation using as input the recorded rainfalls over the catchment, i.e., the ``rainfall hydrograph.'' issuing a warning both for the Belbo River and the formal transferance of the information about uncertainty Tanaro River because the probability of exceedence of to the predicted hydrographs. the threshold peak ¯ow is, in both cases, more than 0.7. The results show how tackling the ¯ash ¯ood fore- casting problem within a deterministic approach, at least in the analyzed environments, is not to be considered 6. Conclusions particularly useful. It is, therefore, necessary to use a This work describes a procedure that uses LAM± probabilistic forecasting system able to address the un- TEPS predictions combined with a multifractal disag- certainty at the different scales involved. We believe gregation scheme of the large-scale predicted rainfall that the ``external-scale'' uncertainty is not suf®ciently volume on the area of interest: the procedure allows addressed by the ensemble system in our study case.

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