This paper presents a Colombian-based study on hydrological modelling metrics, arguing that redundancies and overlap in statistical assessment can be resolved using principal component analysis. Numerous statistical scores for optimal operator water level models developed at 20 hydrological monitoring stations, producing daily, weekly and ten-day forecasts, are first reduced to a set of five composite orthogonal metrics that are not interdependent. Each orthogonal component is next replaced by a single surrogate measure, selected from a set of several original metrics that are strongly related to it, and that in overall terms delivered limited losses with regard to ‘explained variance’. The surrogates are thereafter amalgamated to construct a single measure of assessment based on Ideal Point Error. Depending on the forecast period, the use of three or four traditional metrics to deliver a combined evaluation vector, is the minimum recommended set of scores that is needed for analysis to establish the operational performance at a particular station in the gauging network under test.

Study regionThe Present work shows trend analysis results for temperature and precipitation around the world and for river discharges in the Americas, Australia and some European countries for a common time period with free access hydrometeorological information.Study focusHydrometeorological data sets for discharge, precipitation and temperature around the world were analysed for statistically significant trends both in average and extreme value data sets between 1970 and 2010. The data was analysed with the Mann–Kenndall trend test at annual, monthly and daily resolutions, to compare the results on a global scale and between the different time resolutions.New hydrological insights for the regionResults indicate that trends can be found for all variables and on all latitudes, with an increase of global temperature in the analysed time period. Fewer trends were observed in extreme value data. Trends in discharge data were predominantly negative, and precipitation trends were not very common. In some cases, an opposing pattern was observed in the northern and southern hemisphere. The highest number of trends was found at the annual and least on the daily resolution, nevertheless, trend patterns for discharges remained similar at different time scales. Some of the factors that might influence these results are discussed

This paper presents a finite difference, time-layer-weighted, bidirectional algorithm that solves the Fokker–Planck–Kolmogorov (FPK) equation in order to forecast the probability density curve (PDC) of the monthly affluences to the Betania hydropower reservoir in the upper part of the Magdalena River in Colombia. First, we introduce a deterministic kernel to describe the basic dynamics of the rainfall–runoff process and show its optimisation using the S/σΔ performance criterion as a goal function. Second, we introduce noisy parameters into this model, configuring a stochastic differential equation that leads to the corresponding FPK equation. We discuss the set-up of suitable initial and boundary conditions for the FPK equation and the introduction of an appropriate Courant–Friederich–Levi condition for the proposed numerical scheme that uses time-dependent drift and diffusion coefficients. A method is proposed to identify noise intensities. The suitability of the proposed numerical scheme is tested against an analytical solution and the general performance of the stochastic model is analysed using a combination of the Kolmogorov, Pearson and Smirnov statistical criteria.

This paper takes a stochastic approach to identify uncertainties in hydrological systems that can be applied to the study of hydrological extremes. The system to be identified is supposed to be governed by a stochastic differential equation of the Langevin type, whose parameters are found through the inverse solution of the equivalent Fokker–Planck–Kolmogorov equation. The study presents the algorithmic and numerical implementation for the inverse modelling process, along with the implementation of this approach in three study areas. Results showed a flexible method that made it possible to consider hydrological variability and seasonality during system identification. The identified system parameters rely on the internal–external driving factors of the analysed river basin and provide indications about the behaviour of extreme events in possible future climate scenarios or situations where internal system parameters are altered. While the study cases presented refer to non-stationary Markov processes that allow for one-dimensional systems identification only, the proposed methodological approach is a step in the right direction when it comes to identifying n-dimensional Markov processes/systems.