STATIC EVALUATION OF THE GLOBAL SOLAR POTENTIAL IN THE REGION OF KARA (TOGO) BY EMPIRICAL MODELS.

In this work, we propose different empirical models for the estimation of daily global solar radiation on a horizontal plane in the region of Kara in Togo. The performance of the models is evaluated on the basis of statistical indicators such as: the correlation coefficient (R) and the Root Mean Square Error (RMSE). It appears that the Angstrom-Prescott linear model is the most efficient for the site. For this model, the values of R and RMSE are 0.9256 and 0.046, respectively. It can therefore be used to estimate the solar potential of the region of Kara.


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logarithmic and exponential), which are the most adapted to the estimation of the daily global solar radiation on a horizontal plane on the site of Kara.

Materials and Methods:-
There is a relationship between the clarity index (ratio of daily global solar radiation to extraterrestrial daily global radiation measured on a horizontal plane) and a daily insolation fraction calculated from direct light measured by report to a normal plan. Thus, several models have been developed in this direction. In this article, Angstrom-Prescott linear (Angstrom, 1924), Ampratwum-Dorvlo logarithmic (Ampratwum and Dorvlo, 1999) and Almorox-Hontoria exponential (Almorox and Hontoria, 2004) models are considered. After a physical overview of the site, data and performance indicators selected for model validation are presented.

General Characteristics of the Site
Located in the northern part of Togo (400 km north of the capital Lomé), the regional area of Kara is made up of seven (07) districts covering an area of 11738km 2 , nearly 21% of the national territory. With a population of 769940 inhabitants at the last general census of population and housing in 2010, the Kara region is the fourth most populous region of the five administrative regions of Togo (see Figure 1).

Figure 1:-Location of the Study Area
The geographical coordinates are 9°40'0" N and 0°55'0" E in DMS (Degrees, Minutes and Seconds) or 9.66667 and 0.916667 (in decimal degrees). The altitude above sea level is 291m. It houses a unique meteorological station where average temperature, humidity, dew point, pressure and visibility are measured.

Collection of data
This study concerns the region of Kara in Togo. The radiation data used in this context are provided by MINES ParisTech/Armines (France). Those selected for the modeling range from January 1st to December 31st, 2005. The base includes: global solar radiation measured on a horizontal plane, global extraterrestrial solar radiation on the horizontal plane, duration of sunshine and the maximum duration of measured sunshine.

Presentation of models
Three models are used: the linear model (A. Angstrom, 1924), expressed by the relation (1) the logarithmic (Ampratwum and A. Dorvlo, 1999), expressed by relation (2) the exponential model (Almorox and C. Hontoria, 2004), expressed by the relation (3) where a and b are empirical coefficients to be estimated.
S is the duration of sunshine (h) and So is the maximum duration of measured sunshine (h), proportional to ω as following: G is the global solar radiation measured on the horizontal plane (Wh.m -2 .d -1 ) and G 0 is extraterrestrial global solar radiation on the horizontal plane (Wh.m -2 .d -1 ), given by equation (5 ω is the hour angle related to λ and δ trough equation (7)      tan tan cos 1    (7)

Model Performance Indicators
For the validation of the model, the recourse is made to two (02) popular and widely used statistical indicators which are: the correlation coefficient (R), given by formula (8) the Root Mean Square Error (RMSE), estimated by formula (9); it identifies the precision comparing the difference between the values obtained during the estimation and those of the measured data, it always has a positive value;    To validate the model, we compared the average values of the measured radiation with the estimated values by these models. Figure 7 shows the evolution of monthly average global solar radiation compared to those estimated by the three (03) models.

Conclusion:-
In this work, different models (linear, logarithmic and exponential) are simulated in order to choose the most efficient and this on the basis of performance indicators R and RMSE. The present work allowed us to compare the values measured and those estimated by the three (03) models. It follows that the most suitable model for estimating global solar radiation for the region Kara is the Angstrom-Prescott linear model. Indeed, the average global radiation found by applying the latter is 4.7303 kWh.m -2 .d -1 whereas that of the data measured by MINES ParisTech / Armines (France) [12] is 4.7366 kWh.m -2 .d -1 .