Simulation of Soil Heating in Ridges partly covered with Plastic Mulch, Part I: Energy Balance Model

An energy balance model for a two-dimensional ridge surface partly covered by a plastic mulch is presented. Previous approaches are modified and extended to include: (1) the circumsolar part of diffuse radiation; and (2) the altered interception of diffuse short- and long-wave radiation due to horizon obstructions and surface slope. A simple solution was found for the interception problem under an uniform radiating sky, and an extensive numerical simulation study with broadly varying sky conditions and surface geometries revealed an error of about 10% using this approximation. Similarly simulations for long-wave sky radiation interception highlighted the good predictive quality of the uniform sky solution with errors of about 1%. Additionally, a thorough derivation of directional responses of transmissivity and reflectivity of different commonly used plastics is provided. Oblique direct radiation incidence angles due to ridged surfaces were taken into account using a Fresnel theory based approach adapted from window design research and extended to describe the effect of a liquid water film on the inside of the plastic. The validity of this proposed model to accurately predict the temperature dynamics for a two-dimensional ridge surface partly covered by a plastic mulch is presented in an accompanying paper.