The estimation of hydrological model parameters is a challenging task. With increasing capacity of computational power several complex optimization algorithms have emerged, but none of the algorithms gives a unique and very best parameter vector. The parameters of fitted hydrological models depend upon the input data. The quality of input data cannot be assured as there may be measurement errors for both input and state variables. In this study a methodology has been developed to find a set of robust parameter vectors for a hydrological model. To see the effect of observational error on parameters, stochastically generated synthetic measurement errors were applied to observed discharge and temperature data. With this modified data, the model was calibrated and the effect of measurement errors on parameters was analysed. It was found that the measurement errors have a significant effect on the best performing parameter vector. The erroneous data led to very different optimal parameter vectors. To overcome this problem and to find a set of robust parameter vectors, a geometrical approach based on Tukey's half space depth was used. The depth of the set of N randomly generated parameters was calculated with respect to the set with the best model performance (Nash-Sutclife efficiency was used for this study) for each parameter vector. Based on the depth of parameter vectors, one can find a set of robust parameter vectors. The results show that the parameters chosen according to the above criteria have low sensitivity and perform well when transfered to a different time period. The method is demonstrated on the upper Neckar catchment in Germany. The conceptual HBV model was used for this study.

This paper describes the design and use of a recursive ensemble Kalman filter (REnKF) to assimilate streamflow data in an operational flow forecasting system of seven catchments in New Zealand. The REnKF iteratively updates past and present model states (soil water, aquifer and surface storages), with lags up to the concentration time of the catchment, to improve model initial conditions and hence flow forecasts. We found the REnKF overcame instabilities in the standard EnKF, which were associated with the natural lag time between upstream catchment wetness and flow at the gauging locations. The forecast system performance was correspondingly improved in terms of Nash–Sutcliffe score, persistence index and bounding of the measured flow by the model ensemble. We present descriptions of filter design parameters and explanations and examples of filter behaviour, as an information source for other groups wishing to assimilate discharge observations for operational forecasting.

Reference Evapotranspiration (ET₀) is a complex hydrological variable defined by various climatic variables affecting water and energy balances and critical factors for crop water requirements and irrigation scheduling. Conventionally ET₀ is calculated by various empirical methods based on rigorous climatic data. However, there are many places where various climatic data may not available for ET₀ estimation. The objective of this study is to evaluate different machine learning (ML) techniques to estimate ET₀ with minimal climatic inputs. In this study, FAO-56 Penman-Monteith model was considered as the standard model and different ML models based on A Long short-term memory neural networks (LSTM), Gradient Boosting Regressor (GBR), Random Forest (RF) and Support Vector Regression (SVR) were developed to estimate ET₀ with climatic variables as input parameters. These models were evaluated in two different climatic regions, Hyderabad in India and Waipara in New Zealand. The results indicated that 99 % accuracy could be achieved with all climatic input, whereas accuracy drops to 86% with fewer data. LSTM model performed better than other ML models with all input combinations at both the stations, followed by SVR and RF. Both LSTM and SVR models have been noted as the most robust ML models for estimating ET₀ with minimal climate data. Even though the excellent performance can be achievable when all input variables are used, the study, however, found that even a three-parameter combination (Temperature, Wind Speed and Relative Humidity values) or two-parameter combination (Temperature and Relative Humidity, Temperature and Wind Speed) can also be promising in ET₀ estimation. The presented study will help to estimate ET₀ for data scare regions, which is vital for agricultural water management in semi-arid climates.