Bayesian analysis and particle filter application in rainfall-runoff models and quantification of uncertainty

Applying hydrologic models and forecast is a necessity in different studies in water resources. There should be multiple assumptions in forecasting the outflow of watersheds due to different complex relations in hydrologic cycle. Because of assumptions and simplifications those applied in the structure of models and developed relations, forecasts made by rainfall runoff models are always subject to uncertainties. Different sources of uncertainty are categorized into three parts: first, the uncertainty attributed to the applied data, second, the structure of model and third, and the parameters. It is also necessary to address uncertainties and improve the precision of the forecasts. Therefore, there are multiple methods developed to analyze uncertainties. For this aim, data assimilation is a recommended approach and particle filter method is one of the developed models in this regard. The main goal of this research is to apply particle filter to update and improve the HYMOD rainfall runoff model forecasts based on observed stream flow. In addition, by the use of this approach, quantification and decreasing the uncertainty is evaluated based on different sources of error.
In this study, improving the forecasts is implemented by data assimilation approach. To this aim, particle filter method, successive Bayesian estimation and posterior probability density function are applied for obtaining the soil moisture and Hymod parameters in daily scale in Kassilian river basin with approximately 67 square kilometers area. Particle filter is based on Bayes equation and maximum likelihood function of errors for the given time period. Moreover, this method should be combined with statistical resampling that prevents divergence of the analysis, and corrects degeneracy, sample impoverishment of particles and tendency of the state variables particle weights to unit value (1).
Applying particle filter method makes it possible to use the intended model parameters for simulating and forecasting by random ensemble parameters generation and calculating prior probability density function. This method is also effective for precising forecasts and simultaneous application of parameters and soil moisture variable in analysis. Also this method helps to modify the forecasts using Baysian theory and definition of primary errors maximum likelihood function. In addition, this method also represents the posterior probability density function and corrects the prior density function.
The results show applicability of particle filter method in combination with statistical resampling for hydrological data assimilation and improvement of the precision of forecasts of outflow from Kassilian river basin. It is shown that, the applied method improved the Nash-Sutcliffe statistic in comparison with open loop procedure. As the Nash-Sutcliffe statistic improved by 22%, rising from 0.55 to 0.67.