Investigation of digital elevation model uncertainty in GIS-based solar radiation models using Markov Chain Monte Carlo simulation

Ismaila, Abdur-Rahman Belel
In this study, a Markov chain Monte Carlo (MCMC) simulation approach that incorporates digital elevation model's (DEM) spatial autocorrelation is developed with the aim of assessing the impact of DEM uncertainty in GIS-based solar radiation models. The method utilized the error probability distribution function (pdf) of Shuttle Radar Topography Mission (SRTM) DEM, and variogram model parameters of the study area's SRTM DEM as a priori information for the formulation of Metropolis-Hasting algorithm. Statistical analysis of the data extracted from the literature revealed that SRTM DEM error exhibit lognormal distribution with a mean of 4.209 m and standard deviation of 0.054 m. An exponential variogram model with sill of 125.74, range of 1,556.85) and nugget of 0 represent the spatial autocorrelation of the study area DEM. A total of 1,080 simulations is executed using chains and the initial burn-in period of 80, representing 7.41% of the simulation is discarded. Multivariate potential scale reduction factor (MPSRF) of 0.99 is obtained after executing 1,080 MCMC simulations which indicates that the MCMC sampler has converged to a stationary distribution, being less than 1.1. Thus, the results are assumed to be drawn from lognormal pdf. Whereas, the check for variogram reproduction based on 95% confidence level indicate that the variogram simulation remains valid since T2=1.751 is less than the corresponding F-statistic of 23.19.The proposed methodology is coded and executed in MaTLAB Environment. Based on the simulation results, it is observed that the proposed framework allows better representation of the DEM data. The realized DEMs together with other inputs were used to run the Solar Analyst and r.sun models. The results of both models showed a better performanceusing the realized DEMs than the original SRTM DEM. For Solar Analyst, DEM uncertainty has greater effect on diffuse radiation and direct duration, while, direct and global radiations are less affected. For r.sun, the DEM uncertainty has less influence on solar radiation outputs. Comparison of the two models shows that Solar Analyst is more sensitive to uncertainty than r. sun. Interestingly, the study reveals that relatively flat terrains where DEM uncertainty seems to be low also exhibit high uncertainty in solar radiation estimates. This indicates that DEM may not be the only input associated with uncertainty.