Modelling radar rainfall residual errors for hydrological applications

Weather radars are a key source of precipitation data in many hydrological applications, thanks to their wide coverage and high spatio-temporal resolution. Nevertheless, the complex nature of the radar systems makes them prone to different sources of errors. The propagation of the electromagnetic beams can be affected by the complexity of the atmospheric media, the presence of obstacles can limit the scan, the conversion of the backscattering signal into precipitation rate estimates carries some approximations, different phases of hydrometeors in the atmosphere can create artefacts or ambiguities, and so on. The list can be long and, although many of the errors can be partially corrected, a residual uncertainty is unavoidable in the radar-derived quantitative precipitation estimates (QPE). When it comes to hydrological applications, the estimation of QPE uncertainty is essential and assessing its propagation through different types of models is even more important. Radar rainfall ensembles are one of the best methods to model uncertainty in radar rainfall for model applications because they can be easily used to assess error propagation in hydrologic models. This approach consists in estimating the errors and their characteristics, usually by comparing radar QPE with point ground measurements like those obtained from rain gauges, as an approximation of true rainfall, and to produce a large number of possible, equiprobable realizations of the rainfall fields, constituting an ensemble. The error propagation estimation can be accomplished observing the result spread feeding a model with the different ensemble members. Methods to estimate errors and generate ensembles are various in literature, but many are based on the computation of the error covariance (See e.g. Germann et al. 2009). The radar error covariance approach for ensemble generation proposed by Germann et al. (2009) (REAL) works well with a medium number of point measurements, but is not very robust nor efficient when the number of rain gauges is too large. The critical passage is the calculation of the covariance matrix, which is computationally demanding, and its decomposition, which requires the covariance matrix to be positive definite. In addition, it generates error components for the ensemble only in ground measurement points, needing subsequent interpolation. This work proposes a different approach that sacrifices the directionality of the spatial dependency modelling, to improve robustness and speed of the algorithm. The estimation of the QPE errors is computed similarly to the REAL method, using quality checked rain gauge data as an approximation of true rainfall. The spatial correlation characteristics of the errors are modelled through their semivariogram, fitted with an exponential function. The error components are then generated filtering a random Gaussian field with a lowpass filter, designed to obtain the desired semivariogram of the residual radar errors. The errors are then scaled to obtain the target error variance. Finally, the error components and the radar QPE are combined. In this particular application the temporal dependency is not modelled, because it is negligible at hourly time steps. Nevertheless, a simple autoregressive model could easily be applied. This paper presents in detail a new approach to generate radar rainfall ensembles and compares it with the REAL method, both in terms of rainfall estimations and flow simulations using a hydrological model.