A collaboration between: Dr Renaud Hostache, Luxembourg Institute of Science and Technology (LIST); Professors Nancy K Nichols and Peter Jan vanLeeuwen, University of Reading; Ms Concetta di Mauro, Luxembourg Institute of Science and Technology (LIST)
The objective of this DARE pilot project is to investigate the application of advanced filters to assimilate high-resolution flood extent information derived from SAR images (75m spatial resolution) for the purposes of improving near real-time flood forecasts. The forecasting system is composed of a hydrological model loosely coupled to a hydraulic model with uncertain rainfall forcing (from ERA interim). The ensemble of model outputs is compared to satellite-derived flood probability maps taking into account satellite image classification uncertainty. Standard ensemble Kalman filter (EnKF) methods that assume a normal distribution of the observation errors cannot be applied and therefore new filters need to be developed for the assimilation. From experiments already carried out at LIST, three challenges arise: (i) to prevent ensemble members/particles being given a weight of zero solely due to local mismatch at a few pixels; (ii) to reduce biases due to over-prediction of flood extent (false positive) being penalized more strongly than under-prediction; and (iii) to reduce the risk of particle degeneration, where weights for all but a few particles go to zero. The aim of the project will be to assess how these challenges can be met using new advanced filters that are being developed at the University of Reading, such as equal-weight particle filters and variational mapping particle filters.
Flood forecasting chains have been set up to enable the evaluation of the proposed data assimilation filters in controlled environments using synthetic (twin) experiments. Two studies have been carried out using these systems.
- We first use a variant of a Particle Filter (PF), namely a PF with Sequential Importance Sampling (PF-SIS), to assimilate flood extent in near real-time into a hydrological hydraulic-model cascade. To reduce the risk of particle degeneration, a “tempering” power factor is applied to the conditional probability of the observation given the model prediction (also called likelihood in a PF). This allows inflation of the model posterior distribution variance. Various values of the “tempering coefficient”, leading to different Effective Ensemble Size (EES) are evaluated. The experiment shows that the assimilation framework yields correct results in the sense that the assimilation updates the particle weights so that the updated predictions move towards the synthetic truth. It also shows that the proposed tempering factor helps in reducing degeneracy while inflating posterior distribution variance. Fig. 1 shows the synthetic truth together with the ensemble expectations (ensemble weighted means) for the open loop (no assimilation) and the assimilation (using various tempering factor values) runs. As shown in this figure, the experiment also demonstrates that the reduction of degeneracy is at the cost of a slight degradation of the overall performance as the higher the EES, the lower the performance of the assimilation run. This is shown by the black and blue lines moving closer to the synthetic truth (compared to orange and light blue line Figure 1).
- We also investigated how innovative satellite earth observations of soil moisture and flood extents can help in reducing errors and uncertainties in conceptual hydro-meteorological modelling, especially in ungauged areas where potentially no, or limited, runoff records are available. A spatially distributed conceptual hydrological model was developed to allow for the prediction of soil moisture and flood extents. Using rainfall and potential evapotranspiration time series derived from the globally and freely available ERA5 database as forcing of this model, long-term simulations of soil moisture, discharge and flood extents were carried out. Time series of soil moisture and flood extent observations derived from freely available satellite image databases were then jointly assimilated into the hydrological model in order to retrieve optimal parameter sets. The performance of the calibrated model was evaluated using the tempered PF in twin experiments. This synthetic experiment shows that the assimilation of long time series (~10 years) of observations of flood extents and soil moisture maps acquired every three days enable a satisfactory calibration of the hydrological model. The Nash Sutcliffe Efficiency, computed based on the comparison of simulated and synthetic discharge time series, reach high values (above 0.95) both during the calibration period and a 10-year validation period.
Figure 1: Water surface elevation time series at Saxons Lode: synthetic truth (red), open-loop (green) and assimilation experiments using the standard PF-SIS (black), and using various tempering factor values (blue, light blue and orange) enabling various effective ensemble sizes to be reached (indicated between parentheses as percentage of the ensemble size). The vertical dashed lines indicate the assimilation time steps. PF-SIS=Particle Filter with Sequential Importance Sampling. EES=Effective Ensemble Size.