## Luhanga and Andringa model

Linear regression analysis using the technique of least-squares has been performed on the global irradiation and the sunshine duration data recorded at Sebele Agricultural Research Station in Gaborone, Botswana, using the Angstrom-type relationships.

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Quoted from: Luhanga P ,  Andringa J . Characteristics of solar radiation at Sebele, Gaborone, Botswana[J]. Solar Energy, 1990, 44(2):77-81.

https://www.sci-hub.ren/10.1016/0038-092x(90)90069-o

Abstract

Linear regression analysis using the technique of least-squares has been performed on the global irradiation and the sunshine duration data recorded at Sebele Agricultural Research Station in Gaborone, Botswana, using the Angstrom-type relationships. The aim of the exercise was to check whether the scatter in the values of the regression parameters in Angstrom's equation can be reduced when we incorporate two effects mentioned by J. E. Hay, namely (i) multiple reflections of the radiation between the ground and the atmosphere and (ii) the performance characteristics of the sunshine recorder. The analysis shows that incorporation of Hay's effects does not reduce the scatter in the values of the regression parameters for Botswana data.

INTRODUCTION

In this paper we present an analysis of the monthly average of the daily global irradiation and the sunshine duration data recorded at the ARS Sebele station in Gaborone over a 7-year period using eqn (l), and also using a modification to this equation by incorporating the effects mentioned by Hay, and comparing the results.

METHODOLOGY

The global irradiation and sunshine duration data which is recorded at ARS Sebele station (latitude 24.57°S, longitude 25.95°E, altitude 994 m), were obtained in daily record form. The record length is from January 1976 to December 1982. The data was subjected to rigorous quality checks before being used in the analysis.

The initial check involved visually inspecting for obvious errors; e.g. where there is no record of irradiation and yet there exists a record of sunshine for the same day. Secondly, a computer test was conducted to check that the recorded global radiation was less than the extraterrestial radiation, and that the sunshine duration was not longer than the astronomical daylength, for each day. A whole day's data were omitted from the calculation of the monthly average if (i) the irradiation or the sunshine duration or both were missing, (ii) the irradiation or the sunshine duration or both were greater than their respective extraterrestial values. The whole month's data were omitted from the calculation of the yearly average if either the irradiation data or the sunshine duration or both were missing.

Luhanga and Andringa proposed model as follows:
$$𝐻/𝐻_0 = 0.241 + 0.488 𝑆/𝑆_0 .$$

SUMMARY AND CONCLUSIONS

The analysis of the global irradiation and sunshine duration data for the ARS Sebele station in Botswana using the least-squares linear regression technique shows that no improvement is obtained in the scatter of the values of the regression parameters in Angstrom's equation when we incorporate the effects of (i) multiple reflections between the ground and the atmosphere and (ii) the performance characteristics of the sunshine recorder, which fails to burn a trace on the card when the sun's elevation is less than 5 ° .

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P. V. C. LUHANG, J. ANDRINGA (2021). Luhanga and Andringa model, Model Item, OpenGMS, https://geomodeling.njnu.edu.cn/modelItem/dd32abc8-a39b-4bf3-95cc-06f6b981945e

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