Contaminants can be rapidly transported at the soil surface by runoff to surface water bodies. Physically-based models (PBMs), which are based on the mathematical description of main hydrological processes, are key tools for predicting surface water impairment. Along with PBMs, data-driven models are becoming increasingly popular for describing the behavior of hydrological and water resources systems since these models can be used to complement or even replace physically based-models. Here we propose a new data-driven model as an alternative to a physically-based overland flow and transport model. First, we have developed a physically-based numerical model to simulate overland flow and contaminant transport. A large number of numerical simulations was then carried out to develop a database containing information about the impact of various relevant factors on surface runoff quantity and quality, such as different weather patterns, surface topography, vegetation, soil conditions, contaminants, and best management practices. Finally, the resulting database was used to train data-driven models. Several Machine Learning techniques were explored to find input-output functional relations. The results indicate that the Neural Network model with two hidden layers performed the best among selected data-driven models, accurately predicting runoff water quantity and quality over a wide range of parameters.

The North China District (NCD) is one of the main grain production regions in China. The double cropping system of irrigation has been leading to the groundwater table decline at the speed of 1–2 m per year. Climate change leads to uncertainty surrounding the future of the NCD agricultural system, which will have great effects on crop yields and crop water demands. In this research, the Meteorological dataset from 54 weather station sites over the period 1960–2015 were collected to quantify the long-term spatial and temporal trends of meteorological data, including daily minimum temperature (T_min), maximum temperature (T_max), precipitation, solar radiation, reference evapotranspiration (ET₀), and aridity index (AI). The results show that the long-term wheat and maize growing season and annual average air temperatures (T_min and T_max) showed strong north to south increasing trends throughout the NCD. The average annual precipitation was 632.9 mm across the NCD, more than 70% of which was concentrated in the maize growing season. The regional average annual ET₀ was 1026.1 mm, which was 531.2 and 497.4 mm for the wheat and maize growing season, respectively. The regional precipitation decreased from northwest to southeast in each growing season and annual timescale. The funnel areas have lower precipitation and higher ET₀ than the regional average, which may lead to the mining of the groundwater funnel area. The regional average annual AI is 0.63, which lies in the humid class. For temporal analysis, the regional average trends in annual T_min, T_max, solar radiation, ET₀, precipitation, and AI were 0.37 °C/10a, 0.15 °C/10a, −0.28 MJ/day/m²/10a, −2.98 mm/10a, −12.04 mm/10a, and 0.005/10a, respectively. The increasing trend of temperature and the decreasing trend of solar radiation may have a negative effect on the regional food security. The funnel area AI showed a significant increasing trend for the winter wheat growing season and a decreasing trend for maize, which indicated that more irrigation will be needed for the maize growing season and the winter fallow policy may lead to the increasing trend precipitation being wasted. Analyzing the growing season and the annual meteorological elements of the spatiotemporal trends can help us better understand the influence of climate change on the natural resources and agricultural development in both the past and the future, and will provide us with invaluable information for the modification of cropping patterns to protect the regional and national water and food security.

Core Ideas: HYDRUS‐1D code was adapted to solve the diffusion wave equation for overland flow. The modified code can simulate transport and fate of many different kinds of solute. The model can simulate physically nonequilibrium overland flow and transport processes. Surface runoff is commonly described in numerical models using either the diffusion wave or kinematic wave equations, which assume that surface runoff occurs as sheet flow with a uniform depth and velocity across the slope. In reality, overland water flow and transport processes are rarely uniform. Local soil topography, vegetation, and spatial soil heterogeneity control directions and magnitudes of water fluxes. These spatially varying surface characteristics can generate deviations from sheet flow such as physical nonequilibrium flow and transport processes that occur only on a limited fraction of the soil surface. In this study, we first adapted the HYDRUS‐1D model to solve the diffusion wave equation for overland flow at the soil surface. The numerical results obtained by the new model produced an excellent agreement with an analytical solution for the kinematic wave equation. Additional model tests further demonstrated the applicability of the adapted model to simulate the transport and fate of many different solutes (non‐adsorbing tracers, nutrients, pesticides, and microbes) that undergo equilibrium and/or kinetic sorption and desorption and first‐ or zero‐order reactions. HYDRUS‐1D includes a hierarchical series of models of increasing complexity to account for both uniform and physical nonequilibrium flow and transport, e.g., dual‐porosity and dual‐permeability models, up to a dual‐permeability model with immobile water. This same conceptualization was adapted to simulate physical nonequilibrium overland flow and transport at the soil surface. The developed model improves our ability to describe nonequilibrium overland flow and transport processes and our understanding of factors that cause this behavior.