The image processing software system (Erdas Imagine 9.3) was used for the geometric correction; calibration and processing of raw satellite data [8] .

For Landsat images that are not in the original United States Geological Survey (USGS) “GeoTIFF with Metatdata” format, it was needed to manually convert these data to radiance values. There are two formulas that can

METADATA; SPACECRAFT_ID = “Landsat7”; SENSOR_ID = “ETM+”; ACQUISITION_DATE = 2000-08-24 and 2000-06-21; WRS_PATH = 167; WRS_ROW = 046 and 047; REFERENCE_DATUM = “WGS8”; REFERENCE_ELLIPSOID = “WGS84”; MAP_PROJECTION = “UTM (Universal Transverse Mercator)”; ZONE_NUMBER = +38.

be used to convert DN’s to radiance; the method depends on the scene calibration data available in the header file ([9] and [10] . One method uses the Gain and Bias (or Offset) values from the header file. The longer method uses the LMin and LMax spectral radiance scaling factors. The following formulas have been adapted from the USGS Landsat Users handbook [11] .

A. Gain and Bias Method:

The formula to convert DN to radiance using gain and bias values is:

where:

CV_R is the cell value as radiance,

CV_DN is the cell value digital number,

G is the gain value for a specific band,

B is the bias value for a specific band,

B. L_Min and L_Max Method:

The formula to convert DN to radiance using L_min and L_max values is:

where:

L = Spectral radiance,

LMIN = (Spectral radiance of DN value 1),

LMAX = (Spectral radiance of DN value 255),

DN = Digital Number.

Table 2 lists these values for ETM band 6 for the two images

Using these values in Table 2 absolute radiance values can calculate for each pixel in the two images. It should be noticed that the radiance values are real numbers, while the DN values in Band 6 are integers.

Once the DN’s values for the thermal bands have been converted to radiance values, it is simply a matter of applying the inverse of the Planck function to derive temperature values.

The formula to convert radiance to temperature is:

where:

T = Effective at-satellite temperature in Kelvin,

K₂ = Calibration constant 2 from Table 3,

K₁ = Calibration constant 1 from Table 3,

CV_R1 = is the cell value as radiance,

ε = is emissivity (typically 0.95).

The temperature values are estimated in degrees Kelvin, and are then converted to degree Celsius.

A vegetative index is a value that is derived from sets of remotely-sensed data that is used to quantify the vegetative cover on the Earth’s surface. The NDVI is calculated as a ratio between measured reflectivity in the red and near infrared portions of the electromagnetic spectrum. These two spectral bands are chosen because they are most affected by the absorption of chlorophyll in leafy green vegetation and by the density of green vegetation on the surface. Also, in red and near-infrared bands, the contrast between vegetation and soil is at a maximum.

The Thematic Mapper bands 3 and 4 provide red and near-infrared measurements respectively and therefore can be used to generate NDVI data sets with the following formula.

Software (ArcGIS-ArcInfo 10.0) were used to prepare maps that represent the relationship between vegetation cover and (LST) in addition to the preparation of all study result maps.

The relationship, between Vegetation Cover (VC) and (LST) of the Four Parts of Wadi Bisha, are presented in the following Figures, Tables, and graphs. Regarding the first part, Figure 4 & Figure 5 and Table 4 demonstrate the distribution of LST and VC respectively. Table 4 demonstrates the relationship between the two parameters. It is found that LST values range between 30˚C to 48˚C while NDVI values between 0.19 and 0.34. Figure 6 shows a negative correlation coefficient of −0.96 between the two parameters.

The first part is characterized as follow: LST (Kelvin) = (303.1976768 - 320.5987138). LST (Celsius) = (30˚C - 48˚C). NDVI Value (0.19 - 0.34). R = −0.98322. R² = 0.966 (Figure 6).

In regard with part 2 of Wadi Bisha, the distribution of LST and NDVI values are shown in Figure 7 and Figure 8 respectively. Table 5 demonstrates the values of the two parameters in different locations. It is found that LST ranges between 30˚C to 49˚C, while NDVI between 0.20 and 0.48. Table 5 and Figure 9 show that a negative correlation coefficient of 0.98 cauterizes the relation between the two parameters.

The second part is characterized as follow: (Figure 7 and Figure 8) (Table 5). LST (Kelvin) = (302.633713 - 322.3257189). LST (Celsius) = (30˚C - 49˚C). NDVI Value (0.2 - 0.48). R = −0.96896. R² = 0.938 (Figure 9).

Distribution of LST and NDVI, at the third part 3 of Wadi Bisha, is shown in Figure 10 and Figure 11 respectively. Table 6 demonstrates the values of the two parameters in different locations. It is found that LST ranges between 31˚C to 46˚C, while NDVI ranged between 0.21 and 0.29. A negative correlation coefficient of 0.98 characterizes the relation between the two parameters.

The third part is characterized as follow: LST (Kelvin) = (304.3182571 - 319.3527926). LST (Celsius) = (31˚C - 46˚C). NDVI Value (0.21 - 0.29). R = −0.97987. R² = 0.960 (Figure 12).

Regarding the Forth part of Wadi Bisha, the distribution of LST and NDVI is shown in Figure 13 and Figure 14 respectively. It is found that LST ranges between 28˚C to 47˚C, while NDVI lies between −0.30 and 0.42. A negative correlation coefficient 0.98 (Table 7 and Figure 15) is found between the two parameters.

The forth part is characterized as follow: (Figure 13 and Figure 14) (Table 7). LST (Kelvin) = (300.6399705 - 319.8524179). LST (Celsius) = (28˚C - 47˚C). NDVI value (0.303 - 0.42). R = - 0.99245. R² = 0.985 (Figure 15).

Finally, a number of 10 geographic locations were chosen randomly to represent the study area, for measuring both LST and NDVI. The measurements show that LST ranges between 33˚C to 49˚C, while NDVI values range

is 0.16 to 0.23. Table 8 and Figure 16 show that a negative correlation coefficient of 0.94 characterizes the relation between the two parameters.

LST and NDVI measurement at several locations). LST (Kelvin) = (306.2563744 - 321.5880036). LST (Celsius) = (33˚C - 49˚C). NDVI value (0.169 - 0.229). R = −0.942713. R² = 0.888.

Table 9 and Table 10 summaries the overall obtained results related to SLT and NDVI values found in different study portions. It can be outlined that the abundance of vegetation cover is one of the most influential in controlling (LST) in Wadi Bisha. As per the (NDVI values) the data indicates that areas having lowest surface temperatures were rich in vegetation (dense vegetation). A clear example may be highlighted at the part 4 of Wadi Pisha, where the Lowest LST was (28˚C) and highest NDVI (0.41) are recorded. Also, part 2 includes the bar land area of highest LST (49˚C) characterized by the lowest NDVI value (−0.20).

The statistical test of the obtained data identified the relationship between vegetation cover and the land surface temperature. The correlation between the (VC) and the (LST) over (50) locations in the study area is quite significant. This means that the increased vegetation cover (VC) indicates decrease in (LST), and the decreased vegetation cover (VC) indicates increased (LST).