This study investigates the spatial distribution of direct solar irradiation on rugged terrain over Pakistan. Digital elevation model (DEM), observational data of solar radiation from 6 meteorological observatories located in Pakistan and 5 meteorological observatories located in China were used in the present study. This conjunction is based on the same climatic conditions. MODIS Level-2 (L2) cloud fraction products and observational data of cloud cover from 21 meteorological observatories in Pakistan were incorporated to quantify the cloud cover influences on solar radiation amount and spatial distribution. The emerging field of remote sensing and GIS makes it possible to calculate solar radiation with finer spatial resolution and better understanding of terrain and cloud effects. ArcGIS with RS platform were used to simulate the model for direct solar radiation for the first time over Pakistan region. The results show clear quantitative influences of local topography and cloud cover on the DSR. Similarly, the area (east of Indus river) affected by monsoon receives less solar radiation during summer compared to the west of the Indus River.

We use a distributed modeling approach to investigate the spatial and quantitative distribution of incoming global solar radiation (GSR) falling over the complex terrain using remote sensing (R S) and geographical information system (GIS). To apply distributed model, we use SRTM digital elevation models (DEM) for impact assessment of slope, aspect orientation and correcting possible sunshine duration over the inclined surface. Similarly, to evaluate the impact of cloud cover on incoming global solar radiation amount and spatial distribution, we use MODIS Level-2 (L2) cloud fraction products and observational data of cloud cover from 21 meteorological observatories in Pakistan. As an input for incoming GSR model, the direct, diffused, and terrain reflected components ofGSR were employed. The model results show clear quantitative influences of local topography based on slope angles and cloud cover variations on the distribution ofGSR in the North and Northwest of Pakistan. Similarly, slope and aspect influences are evident over the mountainous areas in Himalaya, Karakorum and Hindukush Ranges in North and Suleiman Ranges in Northwest. Furthermore, terrain effect for eastern and western slopes is not significant; the slopes receive almost the same radiation due to the orientation of topography and latitudinal consistency, but inter-shielding effect in eastern-western oreintation is more prominent compared to the one in northern southern.

In this work, the predator-prey model with the ratio-dependent functional response is considered,  where the randomness enters into the equations only through their initial conditions. It is done by assuming normal distribution as the initial states of the model to treat the randomness. The passage from the deterministic situation to the random one for these equations is also the most transparent. In addition, a numerical simulation will be offered using the modified approach founded on the fifth-order improved Runge-Kutta method. Furthermore, the stability of the equilibrium points, and certain statistical properties related to the random behaviour of predators and their prey, will be analyzed and discussed.