Reanalysis data are being increasingly used as gridded weather data sources for assessing crop-reference evapotranspiration (ET₀) in irrigation water-budget analyses at regional scales. This study assesses the performances of ET₀ estimates based on weather data, respectively produced by two high-resolution reanalysis datasets: UERRA MESCAN-SURFEX (UMS) and ERA5-Land (E5L). The study is conducted in Campania Region (Southern Italy), with reference to the irrigation seasons (April–September) of years 2008–2018. Temperature, wind speed, vapor pressure deficit, solar radiation and ET₀ derived from reanalysis datasets, were compared with the corresponding estimates obtained by spatially interpolating data observed by a network of 18 automatic weather stations (AWSs). Statistical performances of the spatial interpolations were evaluated with a cross-validation procedure, by recursively applying universal kriging or ordinary kriging to the observed weather data. ERA5-Land outperformed UMS both in weather data and ET₀ estimates. Averaging over all 18 AWSs sites in the region, the normalized BIAS (nBIAS) was found less than 5% for all the databases. The normalized RMSE (nRMSE) for ET₀ computed with E5L data was 17%, while it was 22% with UMS data. Both performances were not far from those obtained by kriging interpolation, which presented an average nRMSE of 14%. Overall, this study confirms that reanalysis can successfully surrogate the unavailability of observed weather data for the regional assessment of ET₀.

Tracer pebbles are often used to study bed load transport processes in gravel bed rivers. Models have been proposed for their downstream dispersion, and also for vertical dispersion, but not for the combined effects of downstream and vertical movement. Here we use the Exner‐Based Master Equation to characterize the transient coevolution of streamwise and vertical advection‐diffusion of tracer pebbles under equilibrium transport conditions (no net aggradation or degradation). The coevolution of streamwise and vertical dispersion gives rise to behavior that can differ markedly from that associated with purely streamwise processes with no vertical exchange. One example is streamwise advective slowdown. Particles that are advected downward into zones where the probability of reentrainment becomes asymptotically small are essentially trapped and can no longer participate in streamwise advection. As a result, the mean streamwise velocity of the tracer plume declines in time. Qualitative and quantitative comparisons with two field experiments show encouraging agreement despite the simplified boundary conditions in the model.

Ideas deriving from the standard formulation for continuous time random walk (CTRW) based on the Montroll‐Weiss Master Equation (ME) have been recently applied to transport and diffusion of river tracer pebbles. CTRW, accompanied by appropriate probability density functions (PDFs) for walker step length and waiting time, yields asymptotically the standard advection‐diffusion equation (ADE) for thin‐tailed PDFs and the fractional advection‐diffusion equation (fADE) for heavy‐tailed PDFs, the latter allowing the possibilities of subdiffusion or superdiffusion. Here we show that the CTRW ME is inappropriate for river pebbles moving as bed load: a deposited particle raises local bed elevation, and an entrained particle lowers it so that particles interact with the “lattice” of the sediment‐water interface. We use the Parker‐Paola‐Leclair framework, which is a probabilistic formulation of the Exner equation of sediment conservation, to develop a new ME for tracer transport and dispersion for alluvial morphodynamics. The formulation is based on the existence of a mean bed elevation averaged over fluctuations. The new ME yields asymptotic forms for ADE and fADE that differ significantly from CTRW. It allows vertical as well as streamwise advection‐diffusion. Vertical dispersion is nonlocal but cannot be expressed with fractional derivatives. In order to illustrate the new model, we apply it to the restricted case of vertical dispersion only, with both thin and heavy tails for relevant PDFs. Vertical dispersion shows a subdiffusive behavior.