Estimated Daily Global Radiation for Zhengzhou and Its Comparison With Observations

Three models relating daily global solar radiation to sunshine duration has been investigated in order to estimate daily global radiation for Zhengzhou, China. The data from January 1995 to December 2004 have been used in the models. Comparison of the estimated and measured values showed that the cubic model was able to estimate global radiation at high daily global solar radiation.


Introduction
The amount of solar energy reaching the surface of the earth is a primary source of renewable energy.A pre-requisite for the estimation of the daily global solar radiation on horizontal surface is the inclusion of the sky conditions in the computations at a locality for design purposes.Unfortunately, for many cases, solar radiation measurements are not easily available due to the cost and maintenance and calibration requirements of the measuring equipment.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

Methods of computation
In the present work, the following correlations were used to express the dependence of global radiation on various parameters: where g H is daily global solar radiation on a horizontal surface, 0 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.
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]), f is the eccentricity correction factor, O is the latitude of the site, G the solar declination and s Z the sunrise hour angle.The eccentricity correction factor, solar declination and sunrise hour angle can be respectively calculated as [11]: 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.( 1 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 Zhengzhou station during the period 1995-2004.From this table, the MBE values obtained from models (1, 2, 3) are negative, which shows that these models under estimate global radiation.The RMSE value, which is a measure of the accuracy of estimation, has been found to be smallest for model 3 (1.939MJ/m2), see Table 1.Also, MPE, MBE and RMSE are shown in Fig. 1-3, respectively.As a result, model 3 performs better than the other models.The MPE, MBE and RMSE of model 3 are 84.7%,-0.051 MJ/m2 and 1.939 MJ/m2.
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 Zhengzhou, and to find the most suitable model for global radiation estimation at Zhengzhou, China. 2 Data used and methods of computation 2.1 Database Zhengzhou meteorological station is chosen for the case study.Zhengzhou (34.7°N, 113.7°E) is located in the interior of China, at an altitude of 110.4 m.A database containing daily measured global solar radiation and sunshine duration of Zhengzhou station was obtained from China Meteorological administration.In this paper ten years' recorded daily solar radiation from 1995 to 2004 are used.

Figure 1
Fig.1 presents the plot of

2 DOI
where ie D is the ith estimated value, im D is the ith measured value and ȃ is the total number of 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.

Table 1 .
Prediction errors for daily global solar radiation of