Radar-based rainfall information has been widely used in hydrological and meteorological applications, as it provides data with a high spatial and temporal resolution that improve rainfall representation. However, the broad diversity of studies makes it difficult to gather a condensed overview of the usefulness and limitations of radar technology and its application in particular situations.
Radar technology (an active instrument that operates in a microwave band) was intensively developed for military use in the period before and during World War II. During the war, radar operators noticed echoes on radar screens caused by weather phenomena. After the war, scientists studied how to use radars for detecting precipitation. Since then, weather radars have been used by national weather services and research institutions, since they enable the detection of precipitating clouds, as well as their structure and development. Considerable efforts have also been made to obtain more accurate quantitative precipitation information that can be used in hydrological modelling and numerical weather prediction.
The use of radar-based rainfall data for hydrological modelling was motivated by the need to accurately measure the spatial structure of precipitation fields and to exploit the potential of radar-based rainfall data to generate short-term and very short-term (near real-time) quantitative precipitation forecasts. One of the first uses of weather radar precipitation data in hydrological applications was as an input to rainfall-runoff models. Therefore, effective derivation of precipitation from radar retrievals has been a subject of interest from the beginning of radar meteorology and hydrology and still remains one of the most important areas of research.
In terms of the estimation of quantitative precipitation, the well-known Marshall–Palmer formula for converting radar reflectivity into precipitation intensity is still often used today. It is one of the most cited papers in the field of radar hydrology. The literature on this topic is extensive, and various reviews exist, e.g., Wilk and Kessler, Wilson and Brandes, Zawadzki, Joss and Waldvogel, and Krajewski and Smith.
Other areas of application of weather radar networks in operational hydrology include storm hazard assessment and flood forecasting, warning, and management. The current interest in land surface hydrological processes has stimulated research into the spatial and temporal variability of precipitation. A potential area for the application of weather radar in this context is in the validation and verification of sub-grid rainfall parameterizations for atmospheric mesoscale models and global circulation models .
Weather radar measurements are obviously connected with non-negligible and sometimes even large errors; hence, radar can be referred to as a semi-quantitative measurement device . The errors are due to measuring techniques and their extent depends on weather conditions, in particular on precipitation processes and the size distribution of precipitation particles. Nevertheless, radar provides very useful information, i.e., real-time coverage at high spatiotemporal resolution, with data being available after a very short time from being observed. Thus, the quality control procedures can be carried out simultaneously for a proper quantitative precipitation estimation.
The benefits of using rainfall radar data in hydrological applications were not reached effortlessly as one could have expected when this new spatially distributed data source became available. Berne and Krajewski  discussed several aspects of the challenges of using weather radar in hydrological modelling while arguing that the evidence pointed to contradicting results regarding the improvements achieved by using radar-based rainfall data on rainfall-runoff distributed models. Whereas many studies reported an added value of the high resolution of radar rainfall data on hydrological applications, some others did not find a significant improvement. Currently, many more investigations have come to light and an updated overview of the use of radar rainfall on hydrology can be provided. Hereafter, the major radar-related topics on rainfall-runoff modelling and streamflow forecasting will be covered to highlight the main approaches and concerns that have been tackled in relation to the use of radar rainfall estimates. This section does not entail an intensive documentation of all studies in the field of radar hydrology, but rather a comprehensive review of the main topics that are discussed in the literature while providing some relevant examples. Therefore, it aims to provide a general outline of current investigations and challenges when dealing with radar data for hydrological applications with a focus on rainfall-runoff modelling, particularly flash-flood forecasting.
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. 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. 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 , although soil moisture assimilation strategies have proved successful in distributed models . 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. 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.
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. . 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 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. 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.  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  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. 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.
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. 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.
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 originated from the systematic errors produced in the process of Z–R transformation, and uncertainty in model parameters. 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. . For instance, uncertainty in radar rainfall estimates was evaluated by Seo et al. 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., 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. . 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 . 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 to more refined but also complex error models that include geostatistical approaches for the generation of synthetic error fields  and non-Gaussian distributions.
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 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.  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.
). 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.
, 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. in an urbanized catchment (3 km
. A review paper of the effects of spatial and temporal variability on hydrological response in urban areas was performed by Cristiano et al.
. 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.
 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.
; Paz et al.
) 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.
 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.
. 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.  propose the development of adaptive models as a way to exploit the information of distributed rainfall while reducing the computational costs of modelling.
With the aim of improving the accuracy of rainfall-runoff modelling and discharge forecasting, ancillary data that relates to the physical runoff processes are usually included. Regularly, semi-distributed and distributed models already need additional geomorphological variables for an adequate model calibration. Nonetheless, additional information that comes from rainfall forecasts, NWP, and more sophisticated blending techniques of rainfall data have proven to enhance the performance of rainfall-runoff models and discharge forecasting by allowing the extension of the forecast horizon while using different modelling strategies. Ochoa-Rodriguez et al.  provided an in-depth review of radar–rain gauge merging techniques by proposing an application-oriented categorization. This classification accounted for radar bias adjustment methods, geostatistical methods such as kriging techniques, and finally integration methods where neither radar nor rain gauge data are considered as a primary data source, but a combination of both that extracts the best information from each instrument is produced as a final result. From those, mean field bias adjustment, kriging with external drift, and Bayesian merging were found the most relevant techniques. These methods were reviewed by considering their use in urban hydrology applications, and therefore they are a good starting point for evaluating their effectiveness on rainfall-runoff modelling. Likewise, McKee and Binns  performed a similar review but with a focus on near real-time application of gauge radar merging methods in operational systems. Moreover, the inclusion of satellite-based soil moisture estimations  or a related representation (e.g., a proxy based on rainfall accumulation) in addition to the radar-based rainfall information, has satisfactorily improved runoff modelling and discharge forecasting with distributed models.
Besides the blending of radar–rain gauge data, the inclusion of short-term radar rainfall forecasts is an important strategy that has improved streamflow forecasting. For instance, Heuvelink et al. demonstrated that the use of radar rainfall nowcasting improves the hydrological response, but also comes with the highest uncertainty in smaller catchments. It was an expected result, since rainfall forecasts were found to diminish its accuracy with increasing lead time. This effect also responded to other studies previously mentioned where smaller catchments are usually associated with higher spatial variability of rainfall. Heuvelink et al. found that the best scenario of discharge forecasting showed a gain of almost three hours more in advance than without rainfall nowcasting.
Finally, the use of Numerical Weather Predictions (NWP) as inputs for rainfall-runoff modelling has gained much attention on the last years. Radar rainfall data can be used for assimilation, thus forcing the generation of NWP, which would enhance its accuracy. As NWP provide longer-term rainfall forecast, its use as input for discharge forecasting has allowed not only the improvement the model performance, but also the increase of the lead time forecasts. More sophisticated techniques may involve blending data dynamically with changing weight functions. For instance, the combination of NWP and radar-based predictions with corrections for orographic rainfall whose weights are computed according to their expected skills can be found in Yu et al. . A relevant illustration of three operational early warning systems for flash flood forecasting in Europe that showed the advantage of using a combination of different data sources is documented in Alfieri et al..
Radar data has been extensively used in studies of flash flood processes understanding. Since heavy rainfall events—particularly in mountain areas—cannot be captured by conventional rain gauge networks, radar data opened a whole new dimension to the study of flash floods. Post-event analyses (e.g., Bouilloud et al.; Marchi et al.) or forensic hydrological (e.g., Bronstert et al. ; Borga et al. ) are studies that reconstruct (flash) floods in an attempt to understand the triggering mechanisms and the development of these extreme events; this new knowledge is then later used for developing forecasting models. Under this scheme, forecast models can be improved or developed further as to effectively simulate the flash flood processes given the detailed precipitation input, but hydrological models can also serve as test beds to identify adjustments to radar rainfall data (Borga et al. ; Seo et al. ). As an example, Javelle et al. analyzed the forecasting performance of a distributed model for different lead times in absence of quantitative precipitation forecasting. Radar data was able to improve simulations for short lead times; main limitations were attributed to both rainfall underestimation and the modelling uncertainty.
In summary, studying the combination of meteorological aspects, rainfall fields, hydrological processes, hydrological modelling, and human activities (e.g., land use change in floodplains) allows for an in-depth comprehension of flood events. This knowledge—together with social and infrastructure data—is crucial for flash flood risk management . Here, radar data has been key to understanding the impact of spatial distribution of rainfall and its evolution along the event.