2.1. Flash Flood Modelling Approaches Using Radar Data

There are three different approaches for rainfall-runoff modelling, including flood forecasting, that have explored the usefulness of radar rainfall estimates. Those are process-based, machine learning-based, and data-based mechanistic models.

Process-based models can represent the hydrological processes with different degrees of detail, from small detail in lumped models (e.g., reservoir or tank models) to highly detailed, physically based, distributed models. When radar data became available, lumped models were preferred due to the low computational cost^[13]. However, semi-distributed and distributed models have become more attractive due to the enormous increase in high computer power. Additionally, it is clear that the distributed nature of radar rainfall can be better exploited with a distributed model^[14]. Nevertheless, distributed models are complex and have a large number of parameters that need to be calibrated in each model cell, which produces a large uncertainty in modelling estimates (i.e., the equifinality problem). Since all hydrological processes are represented in detail, distributed models demand large amounts of distributed data sets: vegetation, topography, soils, land use, and geology, to name a few. These data are seldom available at the scale of interest, which limits the applicability of these models.

Another source of uncertainty comes from the selection of the initial conditions, mainly the soil moisture conditions (SMC). To account for correct SMC, the model needs to include a detailed soil map, the soils’ hydrological properties, and also distributed soil depths. Since soils and their properties are highly variable in mountain catchments, and very difficult and expensive to collect, the application of distributed models in mountain environments faces a big challenge. The problem of SMC initialization in the model is more complex for flash flood forecasting than for general rainfall-runoff modelling (as for hydrological design or post-event analyses), as the model needs to have good initial conditions for obtaining good results. Thus, each time the forecast is initialized (every few hours), the forecasting system has to update its SMC, which can be highly demanding and subject to uncertainty ^[15], although soil moisture assimilation strategies have proved successful in distributed models ^[16]. Using distributed models remains challenging, although they can benefit more from radar data. On the other hand, lumped models are used when there is scarce spatially-distributed data and/or computer power is limited. In this case, radar rainfall is aggregated at the basin scale (e.g., area-weighted mean of the overlaying radar grid cells), losing the details of the rainfall fields. This can be slightly avoided when applied in small catchments. Therefore, semi-distributed models are considered as a compromise between lumped and distributed models, where it is still possible to capture some details of the spatial variability while maintaining accessible data requirements. Here, the basin is divided into subbasins, and in each of them a lumped model is used^[17]. While there are difficulties in the application of distributed models, there are modelling objectives that can only be answered with them: hydrological impact of land use changes or discharge forecasting in rapidly evolving catchments^[18].

With the advent of artificial intelligence, the use of models based on machine learning (ML) models for rainfall-runoff mapping and discharge forecasting has dramatically increased. These models are known for their outstanding performance, but also for their complex training process and for being considered as black box models. Thus, model parameters lack physical interpretation regarding the runoff processes. A comprehensive review of several ML algorithms used for flood forecasting using radar rainfall data is provided by Mosavi et al. ^[19]. Besides the use of support vector machines, the authors highlighted the use of a variety of Artificial Neural Networks (ANN) derived models, such as neuro-fuzzy, adaptive neuro-fuzzy inference systems (ANFIS), wavelet neural networks (WNN), and multilayer perceptron (MLP), as the more frequent models in the literature. More sophisticated ML-based models such as genetic programming^[20] have also been explored with satisfactory results. Nonetheless, other ML-based models as those based on decision trees (DT) are less complex algorithms that have just recently been explored by using radar rainfall^[21]. Even though many ML algorithms serve as black box models, deep learning (DL) approaches have been demonstrated that are able to provide some insights about the relations of the inputs that fed the model towards the discharge. It should be of great advantage and interest to extract some knowledge of the rainfall-runoff process by using these techniques as a reverse engineering strategy. Kratzert et al. ^[22] performed a study using Long Short Term Memory (LSTM) ANN over 241 catchments and showed the ability of this DL approach to learn long-term dependencies between the inputs and the output of the model (e.g., those related to modelling storage effects) along with the possibility to transfer process understanding from the regional to the local scale. Recently, Xiang and Demir ^[23] proposed the use of DL for extending the forecast horizon until five days on an hourly basis with promising results. Because there is a very recent interest on the application of DL for discharge forecasting, it has been tested by using only spatially distributed rainfall derived from dense rain gauges. Therefore, the benefits of applying DL on radar rainfall for streamflow forecasting remain unknown.

Finally, data base mechanistic (DBM) models are another type of hydrological model that combines a statistical definition of the rainfall-runoff model with a supervised optimization of its parameters that ensures that the model parameters have a physical meaning. DBM models have been less explored for rainfall-runoff modelling, but have also proven to be efficient when using radar rainfall forecasts in small mountain catchments^[24]. In DBM models, radar data is aggregated as in a lumped model; thus, the distributed rainfall fields are lost. On the whole, there is a major need for research on developing smart model structures that are able to properly incorporate, as far as possible, the distributed nature of radar rainfall data. Thus, taking advantage of radar data comes from a combined strategy as a result of expert knowledge and the individual strengths of a hydrological model.

2.2. Uncertainty in Radar Estimates for Hydrological Modeling

Although radar-based precipitations estimates are known to provide significant spatially distributed rainfall information, they are still subject to errors, which can notoriously reduce hydrological model performances^[25]. Radar rainfall estimation is a necessary step for the use of spatially distributed rainfall on physically-based hydrological models. Thus, as weather radar provides an indirect measurement of rainfall (i.e., reflectivity), the transformation from reflectivity to rainfall implies many processes that add uncertainty to the estimations. Despite the nature of ML-based models that would allow the mapping of any input (independently of its physical meaning or interpretation) to an output, the vast majority of studies that applied ML-based models for streamflow modelling or forecasting also performed a radar rainfall retrieval process as a previous step to the modelling itself in order to guarantee a proper quantitative representation of rainfall^[19].

Quantification of uncertainty of radar estimates is of main importance, particularly when using physically-based models. It is because the quantitative estimation of the radar rainfall retrievals strongly influences model results. Studies with physically-based models have focused on two main sources of uncertainty: uncertainty in rainfall input^[26][27][28] originated from the systematic errors produced in the process of Z–R transformation, and uncertainty in model parameters^[29][30]. Investigations on radar hydrology are more frequently focused on rainfall input uncertainty.

In a trade-off between the added error of the radar rainfall derivation chain and the improvement on the radar rainfall estimates, the bias adjustment by means of rain gauge networks has been extensively accepted for applications on radar hydrology, while efforts have been made to reduce the negative effects of relative calibration on radar composites, as in Seo et al. ^[31]. For instance, uncertainty in radar rainfall estimates was evaluated by Seo et al.^[24] using different radar rainfall products that differ on the data composition (i.e., only radar-based product vs. rain gauge bias-adjusted radar product). The study demonstrated the need for bias-adjusted radar estimates related to the Iowa Flood Studies (IFloodS) experiment. Nonetheless, according to Paz et al.^[32], the heterogeneous distributions of rain gauge networks for radar bias adjustment strongly affect the quality of adjusted rainfall fields because of the fractality of the rain gauge network.

One strategy for evaluating the uncertainty of rainfall estimates is to use ensemble models. Here, some changes in the configuration of the model (input source, model parameters, or both) are carried out, and the corresponding model evaluation is performed, as in Pomeón et al. ^[32]. A radar rainfall ensemble is the result of the application of an error model, which may account for observed errors (i.e., as compared with rain gauges), spatial and temporal dependences, and their marginal distribution, that reflects several possible realizations on the rainfall field ^[27][28]. Thus, through the application of a hydrological model by using different radar rainfall ensembles, it is possible to evaluate the radar input uncertainty. Error models range from simple schemes that add a fixed Gaussian random error and evaluate the radar rainfall ensembles on different hydrological models^[33] to more refined but also complex error models that include geostatistical approaches for the generation of synthetic error fields ^[27] and non-Gaussian distributions^[28].

Another approach that has been explored for quantifying the precipitation data uncertainty when using spatial distributed rainfall is a Bayesian analysis that accounts for influence of the length of the rainfall time series. For instance, Sikorska and Seibert^[34] evaluated different rainfall data sources: only gauge station, interpolated gauge station, and radar-based precipitation in an alpine catchment by using different time series lengths for the model calibration process. The authors found the radar-based precipitation was more informative for the model, which derived in the higher accuracy. Thus, the evaluation of ensemble models towards several realizations of probability distributions allow uncertainty bands to be obtained, which exhibits the robustness of the model under induced errors on the input radar data. Therefore, this is a powerful tool not only for researchers, but also mainly for decision-makers using flood forecasting, which needs to be transferred to early-warning operational systems.

Even though the measurement error of weather radar retrievals cannot be avoided, the systematic error that comes from the Z–R transformation could be disregarded when using raw reflectivity records as inputs for ML-based models. Very recently, Orellana-Alvear et al. ^[21] demonstrated the suitability of using the native radar variable (reflectivity) as input for a random forest model for discharge forecasting. Performance of the model was comparable with the use of radar rainfall estimates, and therefore the authors concluded that differences should be overlooked. It opened a new alternative for performing discharge forecasting by using native radar data, which is extremely beneficial in regions with sparse and uneven distributed rain gauge networks, that would reduce the uncertainty of systematic errors.

2.3. Radar Spatial Resolution and Catchment Scale

^[35]). Results suggested that higher rainfall resolutions are relevant at smaller catchment scales and mainly when rainfall events of high variability occur. For instance, Thorndahl et al.

^[18], in their review, identified a reduced need of high resolution radar rainfall for bigger urban catchments. As illustration, a comparison of the use of C-band and X-band radar data as rainfall inputs for rainfall-runoff models was performed by Paz et al.^[36] in an urbanized catchment (3 km

²

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^[37]. A review paper of the effects of spatial and temporal variability on hydrological response in urban areas was performed by Cristiano et al.

^[38]. The authors concluded from the literature that physically-based models have become more specialized, and high-resolution spatial rainfall data is of utmost need to take advantage of the models.

^[39] introduced dimensionless scaling factors that reflect the interactions between rainfall, its input resolution, and catchment on the hydrological response in urban areas. The novelty of these scaling factors is that they allow the identification of the needed rainfall resolution in order to reach a given level of accuracy in model performance. Most studies (e.g., Anagnostou et al.

^[37]; Paz et al.

^[36]) in the literature have performed an evaluation of the impact of the radar rainfall resolution (i.e., spatial and temporal) in the hydrological response over a specific catchment, which impedes the generalization of their results. In this context, it is still difficult to assess if the findings in these studies respond to the size of the catchment, the variability of the rainfall event in time and space, the particularities of the terrain, etc. Nonetheless, those that have been able to reproduce their analysis on a wider scope have concluded that sensitivity of the hydrological models to different rainfall resolutions decreased when the size of the catchment increased. For instance, Ochoa-Rodriguez et al.

^[40] performed an analysis of the impact of different rainfall spatial (100–3000 m) and temporal (1–10 min) resolutions at seven urban catchments that differ on the geomorphological characteristics of their locations by using X-band polarimetric radar data. The authors found that a temporal resolution lower than 5 min is needed for performing an adequate hydrological modelling, whereas a spatial resolution of 3 km (cartesian grid size) does not properly work for urban catchments.

^[41]. Rather than focusing on the evaluation of a combination of spatial and temporal resolutions or radar data, this study used radar-based data with a fixed 1 km, 1-h resolution over a 10-year period in France as input for a lumped and a distributed model. Results were analyzed by considering catchment location and types of rainfall events (i.e., spatial variability of rainfall). The authors found that both models, lumped and distributed, performed similarly on the catchments in western France that are under oceanic climate conditions and thus exhibit fairly uniform precipitation fields. In contrast, the spatially distributed rainfall data was greatly beneficial to the model accuracy in southern France, where mountain catchments with highly variable precipitation in space are located. Interestingly, in certain regions, distributed models can outperform simpler models in certain periods of the year (e.g., when rainfall fields are complex), while in other periods they do not; thus, Loritz et. al. ^[14] propose the development of adaptive models as a way to exploit the information of distributed rainfall while reducing the computational costs of modelling.

2.4. Usefulness of Blending Data and Ancillary Data

2.5. Post-Event Flash Flood Analyses