Compared to the growing number of utility-scale solar farms (USFs) sitting in hilly regions, knowledge of the hydrological behaviors in responding to the installation of USFs in these environments remains limited. We present herein a novel model (the Solar-Farm model) to understand the hydrological behaviors following the construction of a USF in the Loess Hilly Region of China, by combining it with an index of hydrological connectivity (HC). Scenarios were designed to estimate the effects of climate and terrain in controlling the effects of the USF on soil erosion, by altering the mean annual precipitation amount, the frequency of precipitation events, and the relief amplitude. Our results show that land use changes (e.g., vegetation removal) incurred a considerable increase in the accumulative soil erosion (22.45%-66.48%) during the installation period. During the 40-year deployment period, photovoltaic panels (PVs) incurred an average of 0.138 m deeper erosion in the USF compared with the background rate without PVs. A wetter climate induced the highest increase (88.25%) in erosion. However, the relief amplitude and precipitation frequency are also confirmed as important controlling factors for soil erosion (increased by 85.42% and 58%, respectively). The HC was increased during both the construction (0.005-0.12) and operation periods (0.149-0.314). Correlation analysis presented that the landscapes with higher HC were more likely to be exposed to the risks of soil erosion. USFs could increase soil erosion by increasing runoff and local HC, and higher background HC in turn could further aggravate the effects of USFs on soil erosion.

The arbitrary adoption of cell center to represent the whole cell is a compromise to the grid structure of the digital elevation models (DEMs), which greatly limits the accuracy of estimating flow distance and width functions. This study uses the triangulation with linear interpolation (TLI) method to approximate the missing flow distance values within a cell except for the cell center. A new flow distance algorithm (D∞-TLI) is proposed to improve the flow distance estimation by using a two-segment-distance strategy. The first segment distance from a cell center to a crossing point at the local 3 × 3 window boundary is modeled by the D∞ method. The second segment distance souring from the crossing point is estimated by the TLI using the flow distance values assigned for the two closest downstream cell centers, while these values have been assigned by iterating from lowest to highest cells. Then, using the continuous flow distance field approximated over a cell region, this cell can be divided into multiple equidistant belts (MEB) to estimate the width function. Four numerical terrains and two real-world terrains are used for assessments. The results demonstrate that D∞-TLI outperforms nine existing flow distance algorithms over any numerical terrains, and it is overall optimal for real-world terrains. Meanwhile, MEB extracts the width function which is less affected by unreasonable artificial fluctuation than the previous method. Hence, MEB combined with D∞-TLI can obtain a high-accuracy estimation of hydro-geomorphological attributes that may be conducive to the application of hydrologic modeling.