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/s D 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.

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There is an urgent need for countries to transition their national food and land-use systems toward food and nutritional security, climate stability, and environmental integrity. How can countries satisfy their demands while jointly delivering the required transformative change to achieve global sustainability targets? Here, we present a collaborative approach developed with the FABLE—Food, Agriculture, Biodiversity, Land, and Energy—Consortium to reconcile both global and national elements for developing national food and land-use system pathways. This approach includes three key features: (1) global targets, (2) country-driven multi-objective pathways, and (3) multiple iterations of pathway refinement informed by both national and international impacts. This approach strengthens policy coherence and highlights where greater national and international ambition is needed to achieve global goals (e.g., the SDGs). We discuss how this could be used to support future climate and biodiversity negotiations and what further developments would be needed.

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.