In atmospheric modeling, sub-grid parameterization is an important method for studying the topographic effects of solar radiation using high-resolution Digital Elevation Model (DEM) data. For reducing the amount of computation, some approximate methods that can lead to errors are used in existing sub-grid parameterization schemes for clear-sky direct solar radiation (SPS-CSDSR). The lack of a high-precision fast terrain occlusion algorithm (HPFTOA) remains one of the biggest constraints in this field. This study proposed an HPFTOA. It mainly uses two kinds of acceleration algorithms. One method is to use a dynamic, lossless, and fast occlusion search radius. Another way is to use the rectangular grid for calculations within the accuracy of DEM data to avoid coordinate projection conversions. The test results indicate that the HPFTOA can carry out large-scale computation based on DEM data with a resolution of 90 m. Because it rarely uses approximation algorithms and considers the curvature of the Earth, SPS-CSDSR can achieve unprecedented precision. The HPFTOA can also be used in the fields of mountain solar energy assessment, remote sensing, and telemetry, including terrain-obscuring the probe. As computer performance improves and algorithms and execution code are optimized, the application prospects will be very broad.

Research shows that complex terrain can affect the spatial distribution of solar radiation and atmospheric physical processes. Based on the high-resolution topographic data, there are already several parameterization schemes available to couple the terrain effects on solar radiation with atmospheric models. However, to reduce the amount of calculation, some methods that can lead to errors are used in the sub-grid parameterization schemes for clear-sky direct solar radiation (SPS-CSDSR). In addition, the common finite difference slope algorithms and the assumption of consistent sub-grid atmospheric transparency can also result in errors. This renders existing SPS-CSDSRs unsuitable for complex terrain in middle and high latitudes and in turbid weather. In this study, these three problems have been effectively solved. The most accurate geometric algorithms for direct solar radiation so far, a high-precision and fast terrain occlusion algorithm and the triangulated sub-grid algorithm, are proposed. On Taiwan Island, the accuracy of the two methods is verified in the virtual vacuum atmosphere. Based on the fact that atmospheric transparency actually increases with altitude, a correction term based on sub-grid anomaly altitude is proposed for converting the sub-grid terrain effect factors into the atmospheric model. Overall improvements constitute a high-precision SPS-CSDSR in complex terrain. Eleven reduced calculation methods and common finite difference slope algorithms can no longer be used. In further study, atmospheric models need improvement in coupling the terrain effects on solar radiation to accurately describe vertical distributions. In this case, the high-precision scheme proposed in this study can play a key role.

Existing sub-grid parameterization schemes for clear-sky direct solar radiation (SPS-CSDSR) assume that the sub-grid cells have the same atmospheric transparency. This study shows that in undulating terrain, significant errors can occur when the sub-grid is in turbid weather or partly above the cloud top. A correction factor was proposed. It can effectively eliminate errors under a cloudless sky and can reduce some errors when part of the sub-grid is above the cloud or fog top. For atmospheric models with high horizontal resolution, example test verification shows that the cast shadowless coverage method can lead to large errors. It should no longer be used based on current computing power. These improvements and the high-precision fast terrain occlusion algorithm in Part I will allow SPS-CSDSR to achieve unprecedented high accuracy. Based on the proposed daily interpolation method, the high-precision SPS-CSDSR is also feasible for regional climate simulation. The analysis pointed out that the sub-grid terrain radiative effect (STRE) is distributed over inclined surfaces with larger areas and at different heights. Existing methods of coupling STRE on one flat surface have certain physical drawbacks. This paper suggests introducing parameterization of STRE at different altitudes and improving the coupling of land–air.