Comparison between Measurements and Models For Daily Global Solar Radiation of Urumuqi

In this study, daily global solar radiation data at Urumuqi in 1995-2004 were investigated. Sunshine based models were used to estimate the global radiation. Estimated values were compared with measured values in terms of statistical error tests such as mean percentage error (MPE), mean bias error (MBE), root mean square error (RMSE). The model performing best was selected. The global solar radiation estimated from the best model was compared with measured values. It was determined that the predicted values have good agreement with the measured values at high daily global solar radiation.


Introduction
Daily solar radiation is an important variable to any vegetative, biophysical and hydrological model that simulates mass, water and energy fluxes.An accurate knowledge of the global solar radiation data at a particular geographical location is of vital importance.However, there are many meteorological stations that do not measure solar radiation but do register other variables such as precipitation, pressure, sunshine hours and temperature.Thus, using models to estimate the global radiation has an excellent foreground.In order to achieve this, several empirical models have been developed to predict the solar radiation all over the world using various parameters.These parameters include extraterrestrial radiation, sunshine hours, mean temperature, maximum temperature, soil temperature, relative humidity, number of rainy days, altitude, latitude and cloudiness [1][2][3][4][5][6][7][8][9][10].The most commonly used parameter for estimating global solar radiation in the publications is sunshine duration.Sunshine duration can be easily and reliably measured and data are widely available.The most widely used method is that of Angström [1], who proposed a linear relationship between the ratio of average daily global radiation to the corresponding value on a completely clear day and the ratio of average daily sunshine duration to the maximum possible sunshine duration.The main objective of this paper is to estimate the daily global solar radiation with measured daily sunshine duration data from Urumuqi, and to find the most suitable model for global radiation estimation at Urumuqi, China.

2.
Data Used And Methods Of Computation

Methods of computation
In the present work, the following correlations were used to express the dependence of global radiation on various parameters: where The daily value of the extraterrestrial radiation on a horizontal surface was defined as [11]: ) sin sin 180 sin cos (cos 3600 24 where 0 I is the new solar constant (=1367 W/m2 [12]),  (7) where n is the number of day of year starting from first of January.
The maximum possible sunshine duration ( 0 S ) can be obtained as [11]:

Methods of comparison
In this study, three statistical tests, mean percentage error (MPE), mean bias error (MBE) and root mean square error (RMSE) were used to estimate the accuracy of the correlations described above.
The mean percentage error is defined as: The mean bias error is defined as: The root mean square error is defined as:

Results and discussion
The obtained empirical coefficients of the Eqs.

2. 1 .
Database Urumuqi meteorological station is chosen for the case study.Urumuqi (43.8°N, 87.7°E) is located in northwest China, at an altitude of 935 m.A database containing daily measured global solar radiation and sunshine duration of Urumuqi station was obtained from China Meteorological administration.In this paper ten years' recorded daily solar radiation from 1995 to 2004 are used.

H
is the daily value of the extraterrestrial radiation, S is sunshine duration, 0 S is the maximum possible sunshine duration, a are empirical coefficients.
Fig.1 presents the plot of

D
is the ith estimate value, im D is the ith measured value and N is the total number of observations.The mean bias error test provides information on the long term performance.A low MBE is desired.A positive value gives the average amount of over estimation of an individual observation, which will cancel an under-estimation in a separate observation.The root mean square error RMSE gives information on the short term performance of the correlations by allowing a term by term comparison of the actual deviation between the calculated and measured values.The smaller the value, the better the model's performance is.

Fig. 2 . 2 Fig. 3 . 2 Fig. 4 . 2 Fig. 5 .
Fig.2.MPE of the three models is the eccentricity correction factor, O is the latitude of the site, G the solar declination and s

Table 1 shows
MPE, MBE and RMSE errors for the three daily global radiation models (models (1-3) corresponding to Eqs.(12)-(14) respectively) of Urumuqi station during the period 1995-2004.From this table, the MBE values obtained from models (1, 2, 3) are positive, which shows that the models over estimate global radiation.The RMSE value, which is a measure of the accuracy of estimation, has been found to be smallest for model 3 (2.182MJ/m2), see Table 1.Also, MPE, MBE and RMSE are