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DIVISION 2 ME MORANDUM <br />2.6 Radiometric Correction <br />Pixel values in commercially available satellites are calibrated to fit a certain range of radiance values of <br />the earth's surface in the form of Digital Numbers (DN). Since each sensor has its own calibration <br />parameters used in recording the DN values, the DN values of two images taken by different sensors may <br />represent two different radiance values. In order to compare and analyze images taken by different <br />sensors (e.g., Landsat 5 TM versus Landsat 7 ETM) it is necessary to convert the DN values to absolute <br />radiance values. <br />In addition to instrument calibration, image pixel values must be normalized for differences in sun <br />illumination geometry and atmospheric effects. This improves the ability to mosaic adjacent imagery and <br />compare imagery over time (e.g., multi -date classification). Some normalizing procedures involve <br />collecting in -situ atmospheric measurements and radiometric transfer code (RTC) and are very difficult <br />and expensive to implement. However, the procedure described here is image -based and requires no <br />additional information other than that provided by the imagery. This procedure converts DN values to <br />reflectance and includes an image -based atmospheric correction procedure using the Chavez (1996) <br />COST method. The equation is as follows: <br />((DN * Gain + Bias — ( DO N * Gain + Bias * 7L * D <br />Where, <br />RN = <br />ESUN * (COS ((90 — 0) * 7d 180)) <br />R = <br />Reflectance for Band N <br />DNN = <br />Digital Number for Band N <br />DO = <br />Digital Number representing Dark Object for Band N <br />D = <br />Normalized Earth -Sun Distance <br />ESUN = <br />Solar Irradiance for Band N <br />9 = <br />Solar elevation angle <br />7C= <br />PI= 3.1416 <br />GainN + Bias = <br />Gain and bias values for Landsat 5 and Landsat 7 ETM described in <br />Markham and Barker (1986) and Huang et al. (2002) respectively, and <br />obtained from the image header file. <br />The digital numbers representing dark objects were obtained empirically by analyzing the histograms of <br />each spectral band. This was accomplished by calculating the image statistics using a skip factor of 1 and <br />then displaying and examining the histogram. The digital number selected for the dark object in each <br />band was the lowest value at the base of the slope of the histogram. If the slope of the histogram was <br />gradual and contained very few pixels, these pixels were ignored, and the digital number value was <br />selected where the slope of the histogram increased significantly. This information was included with the <br />other parameters of the equation described above and entered to atmospheric correction models <br />developed in ERDAS Imagine specifically for each Landsat scene (see Figure 6.0). An example of results <br />obtained with this method is shown in Figure 7.0. <br />Page 15 of 23 P Riverside Technology, inc. <br />Water Resources Engineering and Consulting <br />