Impact of Terrain and Cloud Cover on the Distribution of Incoming Direct Solar Radiation over Pakistan ()
Topography is one of the major factors determining the amount of incident solar energy radiation at a particular location [8]. The complexity of topography due to variations in altitude, slope, aspect and surface nature makes the radiation spatial distribution more complicated [9]. Pakistan’s north-south extension with complex and diversified terrain conditions and scarce network of observatories makes it difficult to measure the distribution of incoming solar radiation through an existing ground based network of observations.
So far, many domestic and international solar radiation estimation models based on flat surface observed data have been established [10]. There are many factors which make topographic solar radiation modeling more complex, such as complexity of physical based solar radiation formulation, insufficient observed data and lack of suitable modeling tools [8]. Since the late seventies of the last century, a series of distributed models for land surface have been developed rapidly, but the progress in the solar radiation estimation over the rugged terrain is not much significant [11-13]. Therefore, to explore new ways of estimating solar radiation over the undulating terrain and other space-time spatial and temporal distribution of volatile elements is of great theoretical significance and has wide application prospects. Till now, there is no published work on the distribution of DSR linked with terrain effect over Pakistan.
2. Study Area
Pakistan lies between latitudes 24˚N - 37˚N and longitudes 62˚E - 75˚E, covering a total land area of 796,096 km2 (www.gov.pk). The geography of Pakistan is a blend of landscapes varying from plains to deserts, forests, hills, and plateaus ranging from the coastal areas of the Arabian Sea in the south to the mountains of the HinduKush, Karakoram Himalaya range in the north. Pakistan is divided into three major geographic areas: the northern highlands; the Indus River plain, and the Baluchistan Plateau. The northern highlands of Pakistan contain the Karakoram, Hindu Kush and Pamir mountain ranges and some of the world’s highest peaks, including K2 (8611 m /28,251 ft) and Nanga Parbat (8126 m/26,660 ft). The Baluchistan Plateau lies to the west, and the Thar Desert in the east. An expanse of alluvial plains lies in Punjab and Sindh along the Indus River. The 1609 km (1000 mi) Indus River and its tributaries flow through the country from the Kashmir region to the Arabian Sea [14,15] Furthermore, 23.8% area of Pakistan is semi-arid, 56% is arid, 3.6% is mesodermal with dry winter and 16.1% is alpine [16] (Figure 1).
3. Data and Method
3.1. Meteorological Data
About 22 years data of daily global incoming solar radiation (1978-2000), 29 years data of monthly cloud cover and monthly sunshine duration (1979-2008) are provided by Pakistan Meteorological Department. The data for cloud cover and sunshine duration were processed for 21 stations, while for solar radiation, 6 meteorological observatories data from Pakistan (only Global Solar Radiation) and 5 meteorological stations from China (Direct and Global Solar Radiation) were processed. Data from Pakistan remain the pronounced concern of apprehension throughout the research period in terms of quality and availability. The continuity the data of solar radiation can be categorized into two groups, one from 1979 to 2000
Figure 1. Landform details for Pakistan.
and other from 2001 to 2008. The data in group one is used for simulation due to relatively better consistency in terms of availability, while the data from 2001 to 2008 is used to compare the results (only for Global Radiation).
3.2. Satellite and DEM Data
DEM over Pakistan is obtained from SRTM (Shuttle Radar Topography Mission at the website ftp://e0mss21u.ecs.nasa.gov/srtm. The data of 3 ArcSecond, which was obtained almost with 90m cell size, is employed in this paper. Moderate Resolution Imaging Spectroradiometer (MODIS) Level-2 cloud fraction product data were used to estimate cloud cover over Pakistan at a resolution of about
..
4. Methodology
To incorporate the cloud cover effect on DSR, MODIS cloud fraction data were processed and rectified using ground observed data of cloud cover on monthly mean basis using ArcGIS. Also, possible sunshine duration was corrected by DEM and used with rectified MODIS cloud fraction data to calculate the linear regression for obtaining fitted empirical coefficients for direct solar radiation.
According to the model given by [17] based on the theory of direct solar radiation over inclined surface [18], we have the following relation,
(1)
where
is the extraterrestrial solar radiation (ESR) quantity on slope, 
is incoming direct solar radiation (DSR) over rugged terrain, 
is ESR on flat surface and 
is direct incident solar radiation on flat surface. Given the values of
, 
and
, we get the distribution of direct solar radiation over rugged terrain.
Here, 
is calculated by using the methodology given by [19], i.e.,
where
is sun-earth distance correction factor, 
is solar declination, 
is solar hour angle at the beginning time of the possible sunshine duration (PSD), 
is solar hour angle at the ending time of the PSD, 
is ESR quantity falling on the slope from 
to
, and T is the total time length of one day, i.e. 1440 min. The physical meaning of this equation is that ESR on a slope is determined by geographic, topographic and astronomic factors. Using PSD as the range of integration
.
is calculated by theoretical formulae [20], i.e.,
where
is ESR amount on horizontal surface, 
is the time spac, 
is the solar constant and 
is calculated by meteorological data fitting statistical models [17], the detail of which is given below.
4.1. Horizontal Direct Incoming Radiation (Hb) Model
The model used for calculating direct solar radiation is given by [17].
(2)
where 
is global solar radiation quantity of flat surface, 
is relative sunshine duration, 
are empirical coefficients.
DSR observational data in Pakistan is not sufficient. Therefore, the compensatory method must be employed. Monthly DSRs of 5 stations of China were used for calculating DSR in Pakistan. Those 5 stations are located in China, having the semi-arid climatic conditions.
In Table 1, the statistical indices are square of correlation coefficient 
and empirical coefficients a, b and c are given. During the study it has been found that monthly models (observational data of all stations of the same month are used) have higher accuracy and stability as compared to unified model (observational data of all stations are used to fit the model).
4.2. Average Global Horizontal Radiation (H) Model
Various studies show that global solar radiation 
and relative sunshine duration 
are closely related [21,22] by using Angstrom-Prescott equation:
(3)
where 
are empirical coefficients.
Using the close-fitting empirical coefficients of the 5 meteorological stations from China as given in Table 1, we get 
(relative sunshine duration) of remote model and 
horizontal global solar radiation simulation.
By using Equations (2) and (3), we get the following relation.
(4)
This equation only needs relative sunshine duration.
4.3. Statistics for Different Model for Global Solar Radiation
Table 2 shows the statistics of different models to get the
Table 1. Empirical coefficients of monthly models for horizontal direct solar radiation; here n is the sample length.
Table 2. Statistics for different model for global solar radiation.
optimized values for empirical coefficients a, and b to fit global radiation model (Equation (3)). Model-1 is the synthetic model considering 6 stations from Pakistan and 3 stations from China. Models 6-8 are offered by other scholars. Considering all these factors (e.g. fitting precision, sample amount, and relativity), Model-4 has the most optimal values as compared to others. Therefore, Model-4 values are considered to solve the average global horizontal radiation model (Equation (3)).
5. Results & Discussion
By using Equation (1), we get the DSR for the years 2006 & 2007 (mean monthly values are considered here) with resolution of 
grid cell by incorporating DEM to analyze the terrain effect (Figure 2). The increasing trend from north to south, that is, latitudinal dependency is common in all resultsThe minimum annual values of DSR lies in Gilgit Baltistan and the surrounding areas, ranging from 727 to 1687 MJ×m‒2; while the maximum annual values are located in deserted areas of Baluchistan, Sindh and Punjab provinces, ranging from 5036 to 5720 MJ×m‒2
Figure 3 shows the distribution of DSR over the mountainous region of Pakistan in Indus upstream. There is a clear uneven distribution of DSR due to complex terrain, indicating the effect of local topography factors. The annual DSR quantity of sunny slope (or southern slope) of mountains is obviously larger than that of shady slope (or northern slope).
The observed data for DSR in Pakistan is only available for Quetta region. Therefore, results of simulation were being compared with high resolution solar maps produced by National Renewable Energy Laboratory [23] (Figure 4). The results with resolution of 4 km provided
Figure 2. Annual distribution of DSR (mean of 2006 & 2007) over rugged terrain of Pakistan.