## 1. Introduction

Over the last few decades, much effort has been made in the field of flood prediction. The ground effects (e.g., floods, landslides) deriving from intense rainfall events can be devastating and very expensive in terms of the loss of human lives and damage to economic activities and assets.

In some regions the use of traditional alert systems based on rainfall observations, flood formation, and propagation modeling cannot be applied because of the very short watershed response times, which are often much shorter than what is necessary for starting up the “machine of civil protection” and its procedures. To overcome this problem, it is a common practice to resort to the use of numerical precipitation predictions issued by meteorological models as input for hydrological response models (e.g., Lin et al. 2002; Bacchi et al. 2002; Bartholomes and Todini 2005). Various works demonstrate that it is not possible to tackle the hydrological forecasting problem in a deterministic way (e.g., Krzysztofowicz 2001), and consequently they propose probabilistic approaches to properly account for the uncertainties in the hydrometeorological forecasting chain (Siccardi et al. 2005; Schaake et al. 2007; Verbunt et al. 2007; Cloke and Pappenberger 2009).

The two main sources of uncertainty associated with the meteorological input that have to be accounted for are 1) the uncertainties related to meteorological predictions and 2) the uncertainties due to the scale of inconsistencies between meteorological forecast input and hydrological response that arise when dealing with small- and medium-sized basins. In this last case, the different spatiotemporal scales between meteorological model outputs and hydrological model inputs can cause poor-quality streamflow predictions, even in cases where we have a perfect rainfall forecast for the spatiotemporal scales solved by a meteorological model (Ferraris et al. 2002). In this work, we do not consider the sources of uncertainty related to hydrologic modeling because they are at least one order of magnitude smaller than those associated with the meteorological forecast. We refer to Mascaro et al. (2010) and Zappa et al. (2011) for a complete description of this issue.

The literature that describes implementations of hydrometeorological prediction chains (e.g., Cloke and Pappenberger 2009) indicates that the most common option in accounting for the meteorological uncertainty is the use of precipitation predictions issued by ensemble prediction systems (EPSs). This framework cannot be the best option when dealing with predictions on very small catchments for two reasons. The first is that the output of an EPS needs a startup period of about 24 h to correctly reproduce the quantitative precipitation forecasts (QPF) uncertainty (Fundel et al. 2010; Marsigli et al. 2005); for this reason, we should use EPSs that are initialized at least one day before the forecasting time and that do not account for the latest atmospheric observations. The second is that, in order to cope with operational procedures and decision-making responsibility, hydrologists are allowed, in certain cases, to use “certified” predictions from (human) expert forecasters. These forecasters, on the basis of their knowledge, can analyze different meteorological models and estimate their reliability in different synoptic conditions and different local meteorological situations. This results in issuing a QPF that synthesizes a large quantity of information from synoptic to a very local scale.

In this work, we present the adaptation of a theoretical hydrometeorological forecasting system in an operational context designed for supporting decision makers in a civil protection system. The main goal is to quantitatively use the expert forecaster QPF as an input in the forecasting chain.

Two approaches are followed: the single-site approach for making predictions on medium-sized [*O*(*A*) ~ 10^{3} km^{2}] basins and the multicatchment approach for small basin [*O*(*A*) ~ 10^{1}–10^{2} km^{2}] forecasts. This procedure has been implemented in the Italian region of Liguria and is routinely used for civil protection purposes.

This paper is organized as follows: in sections 2 and 3, the general framework of the forecast chain and the territorial context are described. In section 4, the forecasting chain is contextualized within the framework adopted for the Liguria region. The application, the verification methodology, and the analysis of results are discussed in section 5, and discussions and conclusions are presented in section 6.

## 2. Probabilistic flood forecasting chain: General framework

The general framework of the probabilistic flood forecasting chain presented here is described in Siccardi et al. (2005). Because we are dealing with basins that have areas smaller than 10^{4} km^{2}, three elements for our forecasting chain are needed. This can be understood through Fig. 1 (derived from Siccardi et al. 2005), which shows the different methodological approaches to use when producing hydrometeorological ensembles.

The first ingredient in the chain is the meteorological input, usually a QPF issued by either a meteorological model or by EPS prediction. The use of different meteorological scenarios issued by EPSs may help in accounting for the uncertainty in a QPF but usually only after a spinup time of about 24 h.

The second ingredient is a rainfall downscaling procedure that allows for generating high-resolution (1 km–10 min) ensemble rainfall forecasts starting from the QPF issued by the first element in the chain (meteorological prediction). The downscaling algorithm usually preserves the statistical properties of the large-scale field, such as the average precipitation amount and the position of large-scale precipitation structures, and creates small-scale precipitation fields with statistical properties similar to those observed from meteorological observations at midlatitudes (Ferraris et al. 2003). The third ingredient is a rainfall–runoff model needed to simulate the streamflow caused by the predicted precipitation event.

Depending on the catchment dimension and the temporal scale of its response, there are two possible approaches for the probabilistic forecast: single site and multicatchment. Siccardi et al. (2005) show that different types of hydrological forecast chains should be used (see Fig. 1), depending on the two ratios *l*_{met}/*l*_{hydro} and *t _{c}*/

*t*.

_{s}The term *l*_{met} is the typical reliable meteorological scale (Siccardi et al. 2005), which can range from 10 to 100 km, and *l*_{hydro} is the hydrological scale considered as the square root of the catchment area. The term *t _{c}* is the time scale of basin response, and

*t*is the social response time to a civil protection warning that can be between 12 and 24 h.

_{s}For these reasons, when dealing with basins with an area of 10^{3}–10^{4} km^{2} (*l*_{met}/*l*_{hydro} ~ 10^{0} ÷ 10^{1}), it is necessary to downscale the rainfall forecast issued by meteorological models or by EPSs and use it as input in the rainfall–runoff model for generating a series of discharge scenarios with related peak flow probability distributions. With this approach, a probabilistic discharge forecast can be obtained for each single catchment. This type of procedure is what is called a single-site approach.

When the target is the forecast in very small basins (*A* ~ 10^{1}–10^{2} km^{2} that correspond to *l*_{met}/*l*_{hydro} ~ 10^{1}–10^{2} km^{2}), the single-site approach no longer represents the best option. The rainfall fields still need to be downscaled from the meteorological scale and used as input in a rainfall–runoff model. However, in this case it is impossible to evaluate which basins, belonging to a large region of *l*_{met} scale, will be affected by a flooding event. The forecasting procedure does not allow for any discrimination between one spatial localization and another, and therefore estimating the probability on a regional scale provides both useful and fundamental information for civil protection purposes. As a consequence, we cannot manage every single basin as an independent entity, so we must consider all the basins together inside the domain of *l*_{met} size. For this reason, we consider that the streamflow caused by a rainfall scenario on a particular catchment is representative of what could occur in one generic catchment inside the domain of size *l*_{met}. The results can be treated similarly to what is proposed by Boni (2000) in the regional analysis of peak discharge frequency for the Liguria region. The differences, which are due to morphological features of catchments of scale *l*_{hydro}, are overcome by introducing the flood index *Q*_{index} (Gabriele and Arnell 1991); the flows with return period *T*, indicated as *Q*(*T*); and the growth factors *k _{T}* =

*Q*(

*T*)/

*Q*

_{index}. These elements can be derived from the statistical analysis of peak flows.

To formalize the multicatchment approach, we estimate the probability that, in at least one basin inside the domain of size *l*_{met}, the flow with a certain *T* is exceeded and so a certain *k _{T}* is exceeded too. Following this approach, the fact that a rainfall scenario causes the exceedance of a certain

*k*in a particular basin is representative also of the other neighbor basins with similar hydrological response.

_{T}## 3. Territorial context

The Italian region of Liguria is a narrow strip of land about 250 km long and 20–30 km wide with a surface area of about 5421 km^{2}. It has very few flat areas and is covered mainly by forest. Most of the catchments have their outlet in the Mediterranean Sea and, because of the mountainous characteristics of the region, the main urban areas and towns have been established along the coast, often at the mouth of a river. This has elevated the risk of floods threatening lives and property. Another important fact that must be considered is that many basins have an area of less than 10^{2} km^{2}. Only a few catchments have a drainage area over 200 km^{2} with a response time to a rainfall event of just a few hours.

The Liguria region has a real-time meteorological network that provides a detailed set of meteorological variables. There are about 120 stations (each one provided with a rain gauge) with different sampling times ranging from 5 to 30 min.

The Hydro-Meteorological Monitoring Centre of Liguria Region (CMIRL) is the institution in charge of making hydrometeorological forecasts and it is responsible for the activities of nowcasting and the monitoring of rainfall events for civil protection purposes in the Liguria region. Liguria is divided in five alert subregions (Fig. 2) that correspond to five parts of the territory, and they are considered homogeneous from a meteorological point of view. They are divided into two groups: one group has three subregions with basins that have their outlets in the Tirrenic Sea (part of the Mediterranean Sea) and are called Tirreniche, and the other group has two subregions called Padane because their basins are in the mountainous part of the greater catchments that form the Padana Valley and the Po River.

## 4. The probabilistic flood forecasting chain in the Liguria region

### a. Meteorological input: The subjective forecast

The implementation of a hydrometeorological forecasting system on small- and medium-sized basins commonly uses the deterministic or probabilistic precipitation forecasts issued by meteorological models (e.g., Taramasso et al. 2005; Rebora et al. 2006a; Cloke and Pappenberger 2009). During recent years, a new need has arisen among operational flood forecasters and that is the quantitative usage of expert forecast. This is because the forecasters, in order to reduce meteorological uncertainty, use various meteorological models for obtaining the final forecast. Regional forecasters also base their predictions on their knowledge of the territory, of its climatic peculiarities, and on the particular meteorological situation. All this leads to QPFs, made by regional forecasters, to be expressed in terms of accumulated rainfall on predefined areas and durations. These quantities usually depend on the context and the features of the region for which the forecasts are made. We refer to such a prediction as the “subjective forecast.”

The CMIRL personnel use various meteorological models to make the subjective forecasts: the European Centre for Medium-Range Weather Forecasts (ECMWF) global circulation model, the limited area models Limited Area Model Italy (LAMI; Steppeler et al. 2003) and Bologna Limited Area Model (BOLAM; Buzzi et al. 1994), and a high-resolution limited area model called Modello Locale in *H* coordinates (MOLOCH; e.g., Diomede et al. 2008).

Statistical analysis of the extreme rainfall events in Liguria (Deidda et al. 1999; Boni et al. 2007) demonstrates that typical precipitation events associated with Mediterranean storms have durations of about 12–24 h. As already described, the regional catchments have a maximum dimension of about 10^{3} km^{2} that correspond to a concentration time (Maidment 1992) of about 10–12 h.

Based on these considerations, a meteorological precipitation subjective forecast is issued and provides three quantities (see the example in Table 1):

- The maximum average precipitation in a time window of 12 h for each homogeneous subregion (named Pf
_{12}): To define this quantity a certain number of meteorological models are analyzed during the 12-h time window where the maximum precipitation amount is expected. - Once the Pf
_{12}is defined, the meteorologist estimates the rainfall amount (Pb) that is expected between the reference starting time of the forecast (*t*_{0}) and the start of the 12-h window (*t*_{12}) associated with the maximum volume (*τ*b =*t*_{12}−*t*_{0}). This is done for each subregion. The reference start time is the time at which the meteorologist starts his forecast and this is usually 0000 UTC on the day he makes the prediction. - The third parameter of the event is the maximum precipitation amount forecasted in a time window of 3 h and on areas of about 10
^{2}km^{2}(named Pf_{3}). This number gives an idea of the local intensity of the forecasted event; high values means possible critical situations for basins with areas in the range 10^{1}–10^{2}km^{2}. It indicates how much the precipitation volume, defined by Pf_{12}, tends to be concentrated in localized areas. A single Pf_{3}is given for all the regional territory.

Example of a subjective forecast for the five alert subregions in Liguria, which are named A, B, C, D, and E. Here, Pf_{12}, the maximum rainfall cumulated in 12 h on the alert subregion, is furnished together with the time the 12-h time window began, with respect to the reference instant of forecast (usually at 0000 LT of the day of forecast); Pa is the rainfall forecasted between the reference instant of forecast and the beginning of the time window of Pf_{12} (12 h per subregion); and Pf_{3} (3 h per 100 km^{2}) is the maximum rainfall accumulated over 3 h on areas on the order of 10^{2} km^{2}.

As can be seen, the subjective forecast, albeit represented by only a few numbers, has a large information content for various reasons: 1) it is derived from different meteorological models, 2) it is influenced by the experience of forecasters and by their knowledge of climatology and territory characteristics, and 3) it is tailored to the type of precipitation event and its interactions with the involved catchments.

### b. Downscaling methodology: RainFARM

The downscaling procedure is crucial for generating an ensemble of precipitation fields that are consistent with large-scale predictions issued by meteorological models and/or by expert forecasters; it can reproduce the small-scale variability of precipitation needed to correctly force the rainfall–runoff model. The stochastic downscaling model accounts for the spatiotemporal variability of precipitation fields at scales smaller than those at which reliable quantitative precipitation forecasts are available.

In this part of the operational chain, Rainfall Filtered Autoregressive Model (RainFARM; Rebora et al. 2006a,b) has been used. This model is able to stochastically generate an ensemble of high-resolution precipitation fields by preserving the information at large scales derived from a quantitative precipitation prediction, and it is able to generate small-scale structures of precipitation that are consistent with radar observations of midlatitude precipitation events.

*α*and

*β*represent two parameters of the model that are estimated from the power spectrum of precipitation predicted by a meteorological model on the wavenumbers–frequencies that correspond to the spatiotemporal scales at which the meteorological model prediction is considered reliable.

The spectrum defined by (1) can be easily extended over larger wavenumbers–frequencies, thus allowing for the generation of a spatiotemporal field at a higher resolution (Rebora et al. 2006a,b). The choice of random Fourier phases associated with the power spectrum (1) and the backward transformation in real space allows for generating a stochastic ensemble of high-resolution fields that are consistent at large scale with the QPF issued by numerical models.

RainFARM has been conceived for stochastically downscaling predictions issued by a meteorological model on a regular grid. However, in the operational framework presented here, we need to apply it to a precipitation forecast issued as described in section 4a. To achieve this goal, we modify the original algorithm to allow for estimating the model parameters directly from the subjective forecast. In the next section, we explain how we adapted the original model in order to make it compliant with this new type of forecast output.

#### Application to subjective forecast

When dealing with the downscaling of the subjective forecast previously described, the estimation of spectral parameters is not as straightforward as when a meteorological model output is used. As in Rebora et al. (2006b), we assume a power-law shape for the power spectrum; however, instead of estimating the slopes from the analysis of the power spectrum of numerical model precipitation prediction, we derive the two values of the slopes of spatial and temporal spectra (*α* and *β*) by comparing, for each alert subregion, the average precipitation Pf_{12} and the maximum Pf_{3} as issued in the subjective forecast. The values of *α* and *β* observed for midlatitude precipitation events can range between −1.70 and −3.50 (i.e., between −0.70 and −2.50 if monodimensional average spatial spectra are considered).

We define a lookup table as one that, for each couple of possible values of Pf_{12} and Pf_{3} given by subjective forecast, returns a couple of spectral slopes that allow for generating an ensemble of high-resolution precipitation fields. These fields have an average value over the alert subregion equal to Pf_{12} and maxima over 3 h and 100 km^{2} that are, on average, equal to Pf_{3}.

To define the lookup table, we use a brute-force approach by generating *N* = 10 000 downscaled fields for each value of Pf_{12} in a range between 5 mm (12 h)^{−1} and 150 mm (12 h)^{−1} and for each couple of spectral slopes (*α* and *β*) in the monodimensional range between −0.7 and −2.50. For each field generated with the set of three parameters *α*, *β*, and Pf_{12}, the maximum value over 3 h and 100 km^{2} (Pf_{3i}, i = 1, … , *N*) has been calculated. The fourth parameter needed for operational downscaling, Pf_{3}, has been estimated as the mean of Pf_{3i}.

At this point, we have defined a correspondence between Pf_{12} and Pf_{3}, issued by the forecasters, and the two spectral slopes. Given the two values of the prediction, we can derive the two optimal spectral slopes that guarantee the generation of an ensemble of high-resolution precipitation fields that are consistent with the forecaster’s prediction both in terms of Pf_{12} and in terms of Pf_{3}.

Each final discharge scenario is composed of two parts. The first one has a constant intensity given by Pb/*τ*b (*τ*b defined as in section 4a) and is common to all the scenarios, whereas the second is one of the downscaled precipitation scenarios generated starting from Pf_{12} and Pf_{3}.

### c. Hydrological model: DRiFt

The hydrological model used in the system is a semidistributed (Giannoni et al. 2003) Discharge River Forecast (DRiFt) model (Giannoni et al. 2000, 2005). It has been designed for event-scale simulations and is based on a geomorphologic approach. It needs, as fundamental starting data, a digital elevation model by which the drainage network is individuated and every cell is classified as a channel or hill slope based on a filter that depends on drainage area and mean slope. Two different flow velocities are associated with channel cells and hill slope cells; as a consequence, the concentration time is defined for each point of the basin. The implemented infiltration scheme (Gabellani et al. 2008) allows the modeling of “multipeak” events making it possible to simulate quite long periods (5–8 days) during which different events can occur.

The runoff volume is routed to the outlet with a time variant T-hour Unit Hydrograph (TUH) technique, which, although representing the basin as a linear system, takes into account the spatial and temporal variability of the runoff production. Each cell that contributes to generate the basin response is considered separately from the others.

*B*is the drainage basin above the specified location,

*M*(

*t*,

*x*) is the runoff rate at time

*t*and location

*x*;

*d*

_{0}(

*x*) denotes the distances from

*x*to the closest stream channel,

*d*

_{1}(

*x*) denotes the distance from the stream channel closest to

*x*and the outlet, and

*υ*

_{0}and

*υ*

_{1}are the hill slope and channel velocities.

The hydrological model has been calibrated on the outlet sections where a hydrometric level gauge and reliable rating curve are available. The parameters on the other sections have been chosen on the basis of the calibration results and on both the authors’ and CMIRL personnel’s experiences (some examples in Gabellani et al. 2008; Giannoni et al. 2000, 2005). In Fig. 3 we report, by way of example, the simulation of the event occurred on 23 December 2009 in the calibrated outlet section Nasceto of Vara basin (202 km^{2}).

### d. Forecast chain output: Single-site and multicatchment approach

The basins in Liguria have drainage areas that vary between 10 and 10^{3} km^{2}. The applicable configurations of a probabilistic hydrological forecasting chain should be either the single-site approach with stochastic downscaling or the multicatchment approach with stochastic downscaling.

The civil protection rules define three different alert levels that depend on the criticality related to the forecasted event, level 0 (no alert), level 1, and level 2. From the point of view of the forecast system, the reference is to the return period of the peak flow. Two different return periods are related to the two alert levels, *T* = 2.9 yr (which is associated to the flood index) for alert level 1 and *T* = 10 yr for alert level 2. Otherwise, using detailed local knowledge, thresholds that are specific for certain outlet sections can be defined in order to have a forecast system that is not related to the return period but is based on the specific vulnerabilities of the catchment.

The statistical approach based on return period is useful because it permits the use of a homogenous system based on parameters that, when a frequency analysis of peak discharges is available, can be determined in all the basins of the region. In the case of Liguria, this analysis has been carried out by Boni (2000).

#### 1) Single site

The single-site approach is applied to catchments with a drainage area greater than 200 km^{2} (with *l*_{hydro} ≥ 15 km). Considering that the order of magnitude of homogeneous subregions areas is 10^{3} km^{2}, *l*_{met} is about 30–40 km and the ratio *l*_{met}/*l*_{hydro} is about 2. According to what is presented in Siccardi et al. (2005), the 200 km^{2} area can thus be considered as the lowest dimension for which the single-site approach is valid.

The results of the single-site approach are shown in plots like Fig. 4. Time is shown on the *x* axis, whereas the *y* axis reports the discharge. This plot shows the peak flows related to the rainfall scenarios as dots, whereas the 80% confidence intervals, estimated at each time step, are reported as gray-shaded areas (Ramos et al. 2010). On the same graph, the threshold corresponding to alert level 1 (discharge with *T* = 2.9 yr) and alert level 2 (discharge with *T* = 10 yr) are reported.

The peak flow for each discharge scenario represents crucial information for decision makers, in particular when they are dealing with small- and medium-sized basins where the peaks distribution can be positioned far from confidence intervals in *Q*-time domain. The two forecast products, confidence intervals and peak flows, furnish different kinds of information and in such a way they are complementary; by showing both of them, it provides all the information needed about the forecast.

#### 2) Multicatchment

The multicatchment approach is applied to basins with a drainage area smaller than 200 km^{2} grouped in the five subregions as indicated in section 3.

The forecast is carried out for each subregion following these steps:

- Rainfall scenarios are fed into the rainfall–runoff model and
*N*discharge scenarios are generated for each of the_{r}*N*catchments within the subregion._{b} - For each catchment, the peak flows of the discharge scenarios are extracted and divided by the catchment flood index (
*Q*_{index}) derived from Boni (2000). As a result,*N*×_{b}*N*forecasted dimensionless growth factors_{r}*k*are obtained._{T} - A value of return period
*T*can be associated to each value of*k*. An_{T}*N*×_{b}*N*matrix of return times_{r}*T*is available. - A return period
*T** is fixed, and the rainfall scenarios for which in at least one catchment an event with*T*>*T** is expected are counted up. This number is indicated as*N*(*T*>*T**). - The probability
*P*(*T**) that, in at least one catchment, an event with*T*>*T** is expected is defined as*P*(*T**) =*N*(*T*>*T**)/(*N*+ 1). Note that, according to this procedure, it does not matter if a rainfall scenario generates one or more exceedances of_{r}*T**. - The steps 3–5 are repeated for different values of
*T**.

The graphs in Fig. 5 show some examples of possible results of the multicatchment approach for a subregion; the *x* axis reports the return period *T* on a log scale, whereas the *y* axis indicates the probability *P*(*T*). If the probability associated to a certain return period *T* = *T*_{1} is *P* = *P*_{1}, it means that there is a probability *P*_{1} that at least in one of the basins within the considered subregion the peak flow will exceed the flow with return period *T*_{1} and a probability 1 − *P*_{1} that the peak flow will be lower than or equal to the flow with return period *T*_{1}.

The shape of this curve can give some information on the level of uncertainty associated with the forecast. When the curve has low slopes with a large range of *T* that correspond to nonnegligible probabilities, the uncertainty is high (dotted line in Fig. 5); if it tends to be step shaped, with a marked decrease after certain return periods, the forecast can be considered to be less uncertain (continuous line in Fig. 5).

### e. An index to evaluate the multicatchment forecast uncertainty

A problem that can come up when the result of the multicatchment approach is available is the evaluation of the degree of uncertainty associated with the forecast. The result of the forecast is a curve that is not exactly a probability of exceedance because it measures the probability that, in “at least one” basin, the flow with a certain *T* is exceeded. The curve can have more than one *T* with *P*(*T*) ~ 1: for example, we can have *P*(*T* = 2.9) ~ 1, *P*(*T* = 5) ~ 1, and *P*(*T* = 10) ~ 0.5 (see the black continuous line in Fig. 5).

The operational application of the multicatchment approach is quite new, and decision makers may need a synthetic measurement of the uncertainty associated with this probabilistic prediction. The shape of this curve may help to estimate the level of uncertainty of the forecast, and the goal is to try to formalize it while considering the practical difficulties related to the curve interpretation.

We therefore defined a synthetic index that accounts for the uncertainty related to the multicatchment prediction, and we explain it by referring to Fig. 6. In this case, we use a linear scale for *x* axis to understand it better. We plot an example of forecast results, (i) a curve with probability *P*(*T*) ~ 1 from *T* = 0 yr to *T* = 2.9 yr that drops to 0 for *T* = 50 yr and (ii) an ideal perfect reference forecast represented by a step-shaped curve because it has substantially no uncertainty: the probability is *P*(*T*) ~ 1 when *T* < *T _{s}* and then drops to 0. Here,

*T*is defined as the return period for which

_{s}*P*(

*T*) = 0.5 on the real forecast curve. Referring to Fig. 6, we state that the dashed area is a measure of how much the real forecast differs from a perfect forecast. If we divide this quantity for the area under the real forecast, we obtain a variable that we call

_{s}*U*and it varies from 0 (perfect and real forecasts coincide) to 1 (uncertainty tend to infinity). The discontinuity is positioned at

_{i}*T*, chosen as

_{s}*T*for which

*P*(

*T*) = 0.5, in order to minimize the dashed area for a given forecast. The choice of another

*P*(

*T*) as reference can be made without changing the index meaning.

_{s}*P*(

_{R}*T*) the function of a real forecast and with

*P*(

_{P}*T*) the perfect forecast, it is possible to mathematically formalize the index as follows:We had to use foresight because of the presence of events with very low severity: when as a result of the forecast

*P*(

*T*= 2 yr) ≤ 0.5 we set

*T*=

_{s}*T*(

*P*= 0.25), whereas, when

*P*(

*T*= 2 yr) < 0.25,

*U*is not calculated.

_{i}## 5. Case study

The hydrometeorological forecast chain presented in the previous sections has been running operationally at CMIRL since December 2008. Here it has been tested on a series of severe events that occurred between December 2008 and December 2009. The events for which both the maximum forecasted and observed accumulated rainfall in 12 h for all the alert subregions were less than 10 mm are not considered. A new statistical analysis should be performed once a larger number of events is available. Here, we consider eight severe events whose characteristics are reported in Table 2.

List of considered events with the main characteristics in terms of Po_{12}, the maximum observed cumulated rainfall over 12 h on an alert subregion, and of Po_{1}, the maximum observed hourly intensity.

For each event *N _{r}* rainfall downscaled scenarios have been generated by using RainFARM. We chose

*N*= 50 as a tradeoff between the computational performance of the system and the proper representativeness of the uncertainty due to the small-scale structure of the precipitation field. The discharge scenarios have been generated by feeding the RainFARM scenarios into the hydrological model DRiFt. There are

_{r}*N*= 83 modeled outlet sections homogeneously distributed on the five alert subregions. For each event, the forecast system produces

_{b}*N*×

_{b}*N*discharge scenarios throughout the Liguria territory.

_{r}The single-site–multicatchment approaches are applied depending on the drainage area and on the response time associated to the considered outlet section. We selected the outlet sections with drainage areas of more than 200 km^{2} and reliable discharge observations. For these pilot sites, the single-site approach has been tested. In addition, a comparison between observed and simulated discharge using precipitation observations has been made.

We then investigated the performances of a multicatchment approach. The forecast is made by building an exceeding probability curve for every event and for every alert subregion. To carry out the verification, we refer to the discharge simulations made with the hydrological model that uses observed rainfall as input; we consider them to be the “truth,” because discharge observations are available for only a few sections.

The scatterplot (Fig. 7) between observed (Po_{12}) and forecasted (Pf_{12}) precipitation amounts shows good performances of expert forecast. Although this is only one of the three ingredients in the meteorological subjective forecast, it is the most important because it defines the total volume of precipitation that is downscaled for obtaining the rainfall scenarios.

### a. Single site

As stated in the previous sections, we apply the single-site methodology to catchments with areas larger than 200 km^{2}. In the Liguria region system, there are only four outlet sections with drainage areas between 200 and 1600 km^{2} and with reliable and available observed discharge data. These sections are reported in Table 3 with their main characteristics and the section code that should be used as reference for the following figures.

Basins to which the single-site approach has been applied with the main characteristics and the corresponding codes have been used in the figures.

Table 4 shows the results of the single site approach. The observed peak flows and the simulated peak flows obtained forcing the model with observed rainfall (*Q*_{pobs} and *Q*_{psim}) are reported, allowing for the evaluation of the hydrological model performances. As a term of comparison, we reported the maximum and minimum peak flows of forecast scenarios (*Q*_{pfMax} and *Q*_{pfMin}) and the mean of the corresponding peak flows distribution (*Q*_{pfMean}). The relative error of the forecasted 12-h maximum rainfall (Pf_{12}) on the subregion with respect to the observation is also shown (rainfall percentage error). As can be noted, *Q*_{psim} and *Q*_{pobs} are often very similar with percentage errors in most of the cases in a range between 2% and 20%. This is quite a good result considering that the used rating curves have an associated error of about 15%. In the case of Magra–Ponte della Colombiera outlet section, events with observed discharges smaller than 300 m^{3} s^{−1} are very unreliable because the sea has far too much influence on the stream level and the corresponding observed flows are not realistic.

Single site forecasts and observations. The area is expressed in units of km^{2} and discharge is expressed in m^{3} s^{−1}. Only the basins hit by each event are considered. The terms *Q*_{pfMax}, *Q*_{pfMin}, and *Q*_{pfMean} are the maximum, minimum, and mean peak flows of the forecast discharge scenarios; *Q*_{pobs} and *Q*_{psim} are the observed and simulated peak flows; and the rainfall percentage error column is the percentage error of the forecasted maximum rainfall over 12 h on the subregion with respect to the observation.

Looking at the forecast performance, it can be noted that frequently both *Q*_{psim} and *Q*_{pobs} have values between *Q*_{pfMax} and *Q*_{pfMin}, and often they are quite close to *Q*_{pfMean}. There are only a few cases where the simulations and observations are different to the expected values derived from the forecast chain. Most of these cases depend on the large differences between observed and forecasted rainfall input.

To show the results at a glance, Fig. 8 reports the box plot for each basin and for each event. The four plots report the event number on the *x* axis (see Table 2) and the discharge peaks on the *y* axis. The box plot whiskers indicate the maximum and minimum peak flows, the horizontal line in the box indicates the mean value and the box indicates the 25% and 75% quantiles. The black dot represents the maximum observed peak flow, and the diamond represents the flow obtained by feeding the rainfall–runoff model with the observed precipitation. The sketched and dotted lines represent *Q*(*T* = 2.9 yr) and *Q*(*T* = 10 yr). The general good performance is also shown by this representation, the observed peak flows are often between the 25% and 75% quantiles and they are out of the range individuated by maximum and minimum peak flows in only a few cases.

A particular case is the event number 4 (9 October 2009); it was a very localized event that caused relevant ground effects on only two adjacent small basins with areas of 22 and 30 km^{2}, respectively. In this case, the observed and simulated peaks were almost 0 for all of the four sections, and for this reason we did not report the results in Table 4. The results of the multicatchment approach show that this was a very uncertain event (Fig. 10). It is evident, when looking at box plots in Fig. 8, that there was a great variance with peak flows in a range from 0 to relevant values. This is because Pf_3 was very high in respect to Pf_12 and, as a consequence, RainFARM concentrated the volume on very small areas (less than 1 km^{2}), causing high hourly intensities that generate high and very localized runoff amounts. This reflects what really happened during the event. It is nevertheless evident that both the 25% and 75% quantiles correspond to low flow values.

*Q*

_{index}) of the corresponding outlet section. We thus obtain a series of growth factors

*k*=

_{T}*Q*(

*T*)/

*Q*

_{index}. The probability of exceedance curve has been built using the plotting position,where

*n*is the dimension of the sample. Equation (4) represents the probability that the growth factor

*k*is greater than

_{T}The observed and forecasted series are reported in Fig. 9 along with the Kolmogorov–Smirnov 95% confidence interval. The forecast sample size is higher than the observed one because for each section there are *N _{r}* ×

*N*samples, where

_{e}*N*is the number of events. Figure 9 also shows that the observations belong to the population of forecasted peak flows. The observations always lay between the Kolmogorov–Smirnov confidence interval and, for

_{e}*k*> 0.7 (i.e.,

_{T}*T*> 2 yr), they are fitted very well by simulated peaks. This means that the forecast discharge scenarios describe the observations well, particularly when we refer to the peak flows.

### b. Multicatchment

The multicatchment approach is used for making streamflow predictions on catchments with areas smaller than 200 km^{2}. In the following we present the results for the eight severe events that were predicted and observed in Liguria during the considered period. The probability curves, similarly to those reported in Figs. 5 and 6, are represented, for one of the five subregions, in Fig. 10 (top) in a synthetic way. This gives the reader a prompt comparison between the predictive performances in different events. The *x* axis reports the reference number of the event, whereas the *y* axis reports the return period. A marker of a different shape for each probability level is set to the corresponding return period.

In the middle panel, a measure of prediction uncertainty is reported, which is called the uncertainty index *U _{i}*. As depicted in Fig. 6 and defined by (3), the larger the dashed area, the larger the uncertainty of the prediction compared to a “perfect” one (dashed line). According to (3), a value of

*U*= 1 means complete uncertainty, whereas

_{i}*U*= 0 means no uncertainty.

_{i}The operational use of this index is valuable because it gives a measure of the uncertainty associated with the lack of knowledge of the small-scale structure of precipitation as derived by a subjective forecast. The bottom panel shows the 12-h accumulated rainfall predicted over the area by the expert forecaster (Pf_{12}) compared to the 12-h rainfall observations for the event (Po_{12}).

In Fig. 10, we notice a good overall performance of the system. All the observed events fall inside the prediction interval (0.95 < Prob < 0.05), and there are no missed warnings. The exceeding probability curve in some cases is not very valuable because most of the observed events lay closer to a smaller return period than expected looking at intervals in the top panel. This is mainly due to the uncertainty in the prediction process. Consider, as an example, the prediction for event 4 (Fig. 10). The system predicts an event in this area that is potentially hazardous. In this case, *U _{i}* ~ 1 accounts for the low level of predictability of the event. It has to be noticed that, even for intense and well-predicted events, the values of

*U*are not lower than 0.4–0.6. This is due to the residual uncertainty and accounts for the effect associated to the impossibility of knowing the exact structure of the precipitation field at small scales (1 km–10 min).

## 6. Discussion and conclusions

In this work, a hydrometeorological probabilistic forecasting chain has been designed and implemented. It is composed of 1) an expert forecaster’s precipitation prediction as input, 2) a rainfall downscaling module (RainFARM), 3) a semidistributed hydrological model (DRiFt) and 4) a single-site–multicatchment postprocessing module. The forecast chain has been applied in the operational framework of the Liguria region civil protection system, using eight events as test cases. The characteristics of the territory and the dimension of the monitored basins does not allow for issuing discharge forecasts by using direct rainfall observations as input to an hydrological–hydraulic model for flow propagation nor does it allow for direct coupling of meteorological predictions (used instead of rainfall observations) and hydrological models. For these reasons, it is obligatory to use rainfall downscaling procedures.

We focused the analysis on the use of a subjective forecast, which is a QPF given by a meteorologist who uses different meteorological tools together with his personal experience contextualized in a well-defined territory. The good performance of the methodology depends on the reliability of each single component: the subjective forecast quality, the downscaling methodology, and the hydrological model.

Rabuffetti et al. (2008) evaluated how uncertainty on QPF affects the reliability of a hydrometeorological alert system. If the rainfall input is dramatically different from the real occurrence, the performance of the chain will be of low quality. The subjective forecast in particular is given as a deterministic meteorological forecast, which summarizes all the analysis carried out by the forecaster. A possible improvement in the forecasting procedure could be the introduction of a methodology that accounts for the residual external uncertainty by giving a subjective forecast ensemble prediction or by associating a percentage error to the forecasted quantities.

The chain has been implemented following the single-site and multicatchment approaches described in Siccardi et al. (2005), and in both cases the results have a probabilistic nature. If discharge thresholds based on the specific condition of a basin are available, they can be introduced as a term of comparison in a single site analysis in order to evaluate the real effects of the predicted rainfall event.

Investigating the operational application of a multicatchment approach and the quantitative use of expert forecasts are the two main novel ideas in this work. For the estimation of a forecast degree of uncertainty, a new uncertainty index *U _{i}* has been introduced. Although the multicatchment approach gives a probability of occurrence for any return period

*T*, the uncertainty index gives a measure of forecast uncertainty on a scale between 0 (certainty) and 1 (infinity uncertainty). For the analyzed events,

*U*values 0.4–0.6 are associated to the less uncertain forecasts, but further analysis needs to be carried out. The analysis of the curve and of the uncertainty index can help the decision maker in the interpretation of the forecast.

_{i}The multicatchment approach appears to be a useful way of dealing with flood forecasting in regions with very small basins. Moreover, it seems to be a suitable tool to satisfy the civil protection when they need to issue a warning on a regional scale rather than on single basins.

The presented system can be adapted to different contexts when a forecast chain on small- and medium-sized basins is needed. This specific chain uses DRiFt as the rainfall–runoff model, and it is suitable for orographically complex basins (see, e.g., Giannoni et al. 2000, 2005). The downscaling procedure also needs calibration based on the precipitation features in the given area.

The issue about the interpretation of the probabilistic chain results and the link with the final decision remains a matter for discussion. There is always a subjectivity factor that depends on the sensibility and experience of the hydrologist or the decision maker.

The probabilistic forecast gives, by definition, a number of possible scenarios and a probability that an event of a certain entity is likely to occur. Deciding whether to issue an alert depends on how much risk the decision maker is willing to take, and this in turn depends on the entity of damage and the danger to human lives.

The proposed approach allows the use of predictions issued by expert forecasters for an upcoming event and at the same time takes into account the uncertainties in ground effects due to small-scale spatiotemporal variability in the precipitation field. Many works have been devoted to the probabilistic approach in large-sized basins (e.g., Cloke and Pappenberger 2009, and references therein), whereas operational applications for small-sized basins are still not so common. As clearly demonstrated by Ramos et al. (2010), the probabilistic approach, albeit more powerful for characterizing the uncertainties in the prediction chain, is still not easily managed by an operational hydrological forecaster. Similar problems can be experienced when dealing with predictions on very small catchments.

## Acknowledgments

This work is supported by the Italian Civil Protection Department and by Regione Liguria. We acknowledge Regione Liguria for providing us with the data from the regional meteorological observation network. We are very grateful to the meteorologists and the hydrologists of the Meteo-Hydrologic Centre of the Liguria Region for many useful discussions. We are grateful to Thomas Pagano and two anonymous referees for their helpful reviews and to Mike Whalley for his suggestions in reviewing the quality of the writing.

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