Representing model uncertainty in ANN and HBV rainfall-runoff model pools, for use in real-time forecasting [Application to Iguatama Montante, sub-catchment of the São Francisco River, Brazil]

This paper investigates the benefits and applications of multiple models, both in general and in the specific area of reservoir forecasting. The purpose of the model pools is to represent the inherent model uncertainty present when estimating river streamflows from rainfall data, (rainfall-runoff modelling). The particular case study is a 5420km2 sub-catchment of a reservoir system in Brazil, Tres Marias, for which research has been previously carried out as to the flood control benefits of a model-predictive control, (MPC), tool developed by Schwanenberg, et al., 2015. Currently in this region, this control tool uses an input of 15-day streamflow forecasts of both reservoir inflows and downstream lateral inflows. These forecasts are generated by forcing a single model with a meteorological ensemble. This gives the motivation for this research, as it hypothesised that a representation of model uncertainty in the streamflow ensemble will eventually lead to improved results in the release decisions generated by the MPC tool model. 'Perfect forecast' data is used for the region, in the form of ten years of hourly catchment-averaged rainfall and streamflow measurements. Although input data uncertainty is still present in the resulting streamflows, it is significantly reduced in comparison to the use of meteorological forecast data. Three model pools are developed, a conceptual HBV model, a data-driven ANN model and a hybrid of the two. To represent the HBV model uncertainty, the 15-member model pool is formed based on the variation of model parameters. It can be argued that this model pool only represents parameter uncertainty, and this argument leads to the inclusion of the ANN model pools for comparison. The two ANN structures developed are also varied with the aim to represent model uncertainty through a pool of 15 members. The first uses the same catchment averaged rainfall as the HBV model, and the second can be seen to be a 'hybrid' as it uses state outputs from a HBV model run in parallel. As a fair comparison to the HBV model, observed flows are not used as inputs to the ANN models, as the hourly flows will be highly correlated. This also ensures the models are applicable to real-time forecasting. Variation is achieved in these models by adjusting the initial weights, the number of nodes, and the input data selection. These model pools are then examined for 1) how they represent model uncertainty, 2) how the individual members perform and 3) how the pool performs as a whole. The performances of the deterministic models are compared to the performances of the model pool as whole, as well as a comparison of the deterministic results made through averaging against the deterministic models. The metrics and graphs used in this analysis include rank histograms, CRPS, Kling-Gupta efficiency and bias, and are described in detail. While these analyses look at the model pools in general, other analyses are made that relate specifically to the forecasting applied in the case-study. The first is a comparison of the model pools in terms of peak volume and timing accuracies, each of which is considered to be important for the MPC tool forecast inputs. The second analysis is the comparison of the model pools for forecast use. Ordinarily, the models would be updated at forecast time through the use of data assimilation, applied to both the model inputs and the model states/weights. Due to time constraints data assimilation was not used in this study, and a simple output correction was applied to all models, to examine their performance in a scenario similar to that of forecasting. While data assimilation is technically possible for the ANN model pools, another method of including real-time information in Neural Networks is investigated in the form of two auto-regressive or recursive models. 'Auto-regressive' indicates that they use their own predictions as an input for the next timestep. This is relatable to forecasting as it means the models can use observed data up until the forecast begins. Again, two ANN models are examined here, the first only using the catchment averaged rainfall, and the second being a hybrid model, where ANN is used to correct the output from a HBV model. These auto-regressive models are also tested in the same 15 day forecasting scenarios as the model pools. The results from the model pools show that the model pools perform better than their deterministic equivalents when averaged, and as a whole when compared using CRPS. Of the different model pools, the hybrid is the most accurate, despite giving the largest spread of predictions around the observed values. The implication is therefore that the variation achieved in this model pool gives a better representation of model uncertainty than in the HBV, which has a much smaller spread of predictions. The volume and timing analyses proved inconclusive, and may require a different approach for further insight. When used in a forecasting scenario, again the output corrected hybrid model pool is seen to be the most accurate, despite the large spread of predictions. The auto-regressive hybrid model pool has similar results with an even larger spread, but needs to be compared against data-assimilated models if it is to be used in forecasting. In conclusion, the results suggest model uncertainty can be represented through model pools, but a 15-member HBV model pool in which only the parameters are varied may not be sufficient for this task. Adjusting the structure and parameters of ANN or ANN-Hybrid models represents more of their inherent model uncertainty, while maintaining, (and in some cases improving), accuracy in the streamflows. This holds true when the models are used in a forecasting scenario, where it is seen that recursive neural networks may have significant forecasting potential. Two fringe benefits are noted through different fusions of the model pool streamflows, 1) giving improved deterministic estimates through averaging, and 2) giving a visual representation of the model uncertainty when probability density functions are generated