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Document Type

Thesis - University Access Only

Award Date


Degree Name

Master of Science (MS)


Agricultural Engineering

First Advisor

Alan R. Bender


The principal source of energy for the earth-atmosphere system is solar radiation. Demand for solar radiation data has become very significant for modeling agricultural processes such as photosynthesis and evapotranspiration. Most historical climatic data sets do not include solar radiation, and those that do often have missing data values. Faulty radiation sensor output is a problem with radiation networks. Thus, a clear sky solar radiation reference is needed to remotely monitor radiation sensor integrity, to use in solar radiation estimation techniques, to use as a baseline for value comparisons over time and space, and to calculate estimation errors. Therefore, one objective of this study was to establish a reasonable clear sky solar radiation reference. The second objective of this study was to compare solar radiation estimation methods for usefulness and applicability to South Dakota data resources. A clear sky solar radiation model was developed independent of measured data based on extraterrestrial solar radiation and atmospheric attenuation calculated by the parameterized solar irradiance (PSI) model. The PSI model used clear sky estimates of precipitable water and turbidity. Two solar radiation estimation techniques were compared. One method, a slight modification of Richardson's model (Richardson, 1985), estimated daily solar radiation based on daily temperature range, clear sky solar radiation, and fitted parameters. Parameters were determined for 10 stations in South Dakota. A method involving the use of residuals at a known location to improve the estimate at an unknown location was investigated. A geostatistical method was the second approach used to estimate solar radiation. Investigations were made to define an appropriate semi-variogram for use in South Dakota. Kriging techniques were then applied to estimate solar radiation at 12 locations for 10 days. To better quantify estimation model error and normalize the data over time and space, estimation errors for both methods were calculated as a percent of the clear sky reference value. The developed clear sky solar irradiance model established a reasonable reference for comparison purposes. Hourly model estimates compared well with known clear days. Maximum daily measured values over a two year period also compared well with reference values. Pyranometer sensor calibration constant drift can be detected using the clear sky reference values. Parameters developed for Richardson's model had a definite east/west trend. Comparisons of daily measurements and estimates produced R2 values ranging from 0.56 to 0.72 and RMSE ranged from 3.3 to 4.5 MJ/m2. Applying model residuals from a known station increased R2 up to 0.85 but had little affect [sic] on RMSE for separation distances up to approximately 100 km. Geostatistical calculations were made with the program GEOEAS. An appropriate semi-variogram for use in South Dakota was defined using a linear model with a range of 322 km (200 miles) and a sill of 75 [MJ/(m2day)]2. Kriging estimates made for 12 locations and 10 days (120 total) resulted in R2 of 0.92 and RMSE of 1.77 MJ/m2. Comparison of the two solar radiation estimation methods was difficult due to incomplete data. Ogives of absolute error as a percent of the PSI value versus the cumulative percent of the estimates within the error were plotted. The kriging ogive was significantly above ogives for Richardson's model (both with and without residuals applied). Both solar radiation estimation methods may be applied in South Dakota, but they have varying degrees of usefulness and accuracy. Richardson's model can be applied to historical and current temperature measurements. Kriging requires an adequate network of measured solar radiation (which is recently available in South Dakota). When kriging can be properly applied, the results of this study show that it is the superior solar radiation estimation method for our data set.

Library of Congress Subject Headings

Solar radiation -- South Dakota -- Mathematical models




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