Spatiotemporal Non-Linear Dynamics Assessment (SNLDA) of ERA5-Land precipitation in the Magdalena River Basin

The study region is the Magdalena River basin in Colombia. The basin was divided into three distinct regions (Andean, Caribbean, and Pacific) and analyzed across different elevations. The study proposes a Spatiotemporal Non-Linear Dynamics Assessment (SNLDA) framework to compare ERA5-Land reanalysis data with in-situ rain gauge observations. It specifically examines the constraints imposed by nonlinear dynamical processes and their associated space-time complexities on the representation of precipitation, particularly in a tropical region. The SNLDA framework incorporates three main components: (i) standard performance metrics (e.g., correlations, RMSE, and dry spell duration), (ii) rainfall spatiotemporal objects (characterizing precipitation events through attributes such as volumes and start-end centroids), and (iii) non-linear dynamics complexity (reconstructing dynamical behavior from time series and evaluating attractors properties, including the Hurst and Lyapunov exponents). These elements were analyzed both individually and in combination. Daily ERA5-Land information (0.1°x0.1°) and in-situ rain gauge data comprising 558 stations from 1980 to 2020 were used, enriched by an Inverse Distance Weighting (IDW) interpolation (0.1°x0.1°) to facilitate comparison across spatial scales. Overall, ERA5-Land overestimates precipitation, producing shorter, more frequent events while poorly representing extreme wet and dry spells. Andean region: ERA5-Land overestimates rainfall, with largest errors at low elevations, driven by unresolved spatiotemporal object volumes displacements and nonlinear processes. Caribbean region: ERA5-Land shows the highest errors in nonlinear dynamics and extremes, despite lower annual bias and RMSE. Pacific region: ERA5-Land strongly overestimates precipitation volumes and RMSE, while nonlinear errors remain low; these biases are mainly driven by spatiotemporal objects displacement. • Assessment of ERA5-Land precipitation through a comprehensive methodology (SNLDA) • Incorporation of non-linear dynamics concepts to validate precipitation data • Characterize the spatiotemporal dynamics of precipitation objects • Identify regional disparities in the performance of ERA5-Land in a tropical region • Integration of multiple error metrics into a single plot for easier interpretation