The relationship between mean daily precipitation and elevation is often regarded as linear and positive, resulting in simple “precipitation lapse rate” equations frequently employed to extrapolate daily rainfall from a single weather station over a large area. We examine the precipitation-elevation relationship in the Swiss Alps using a combination of weather radar and rain gauge data to test this common assumption, challenging it by fitting a two-segment piecewise linear model with a mid-slope break-point as an alternative. By examining data stratified by catchment, season, and weather type, we assess the space–time variability of the precipitation-elevation relationship. We conclude that a non-linear and non-stationary model seems necessary to capture the variability of the observed precipitation-elevation relationship. Based on our findings, we suggest that the simplified precipitation lapse rate concept is misleading and should be reconsidered in hydrological applications, emphasizing the need for a more realistic representation of precipitation variability over time and space.
Explainable Artificial Intelligence (XAI) offers the promise of being able to provide additional insight into complex hydrological problems. As the “new kid on the block”, these methods are embraced enthusiastically and often viewed as offering something radically new and different. However, upon closer inspection, many XAI approaches are very similar to more “traditional” methods of “interrogating” existing models, such as sensitivity or break-even analysis. In fact, the approach of developing data-driven models to obtain a better understanding of hydrological processes to inform the development of more physics-based models is as old as hydrology itself. Consequently, rather than being considered a new approach, XAI should be viewed as part of a long-standing tradition, and XAI methods part of an ever-expanding hydrological modelling toolkit, rather than a silver bullet. Critically, there needs to be shift from focusing on how to best eXplain what AI models have learnt (i.e., the X component of XAI) to developing models that are able to capture relationships that are contained within the data in a robust and reliable fashion (i.e., the AI component of XAI), as there is little value in explaining AI-derived relationships if these do not reflect underlying hydrological processes. However, this is often not the case due to a focus on maximising the predictive ability of AI models “at all costs”, not uncommonly resulting in large models that often have thousands or even millions of parameters that are not well defined. Consequently, these models generally do not capture underlying hydrological processes in a robust and reliable fashion. Finally, there is also a need to stop thinking about XAI as a purely technical approach, but a socio-technical approach that views XAI as a process that can assist with solving problems that are situated within broader social and political contexts.
This study attempts to statistically characterize the Urban Heat Island Intensity (UHII) () for 55 cities under three climate regimes – arid, snow and temperate – across the US. The study uses remotely sensed data products, daily temperature from MODIS and daily evapotranspiration from SSEBop model, to calculate the urban–rural difference in daily-mean temperature and daily-mean evapotranspiration ( and respectively) for the selected cities. By developing a hierarchical model that explains UHII using temporally-varying and spatially-varying urban morphometric characteristics (total urban area and percentage impervious area) available for each city, we find that 89% of the spatio-temporal variability in annual can be explained. The relationship between and is found to be negative indicating increased difference in daily means of ET () result in increased difference in daily means of temperature () between urban and rural paracels The variation of per unit is found to be highest in arid and snowy environments and smallest in temperate environments in the south-southeast US. The relation between and is negative for most cities, except Madison (WI) and Sacramento (CA), across the US. Both the selected urban morphometric properties are found to be statistically significant in explaining the spatial variability in UHII, but the difference in urban–rural difference in evapotranspiration is the primary driver for UHII.