## 5 Comparison with MODIS Data  
To check the validity of the approach, AVHRR LST calculated with the Becker and Li 1990 algorithm combined with the Vegetation Cover Method (VCM) from [30] was compared with the MODIS V005 LST product (MOD11A1/MYD11A1) and the results of using the original Becker and Li 1990 coefficients and the NDVI approach of [40]. The comparison was done for the year 2001 and NOAA-16. For the calculation of the new AVHRR LST, preferably Case C (consideration of ranges for view angle, columnar water vapour and first guess LST) coefficients were used. In case where no coefficients were available due to missing coefficients in the database, case B or even case A might have been used. This could happen in rare extreme situations (e.g., very cold and humid), where the database would not provide enough profiles to calculate coefficients. The direct application of the coefficients provided for discrete ranges leads to discontinuities in the resulting LST images. To counteract this, actual LST values are weighted means from different parameter classes using trilinear interpolation. For the comparison, the data was filtered in several ways. Firstly, all pixels which were marked as cloud cover in either the AVHRR or the MODIS product were removed. Second, each cloud-free pixel was checked for its spatial homogeneity. If the standard deviation in a window of 3 \(\times\) 3 pixels would exceed 0.5 K, the middle pixel would be removed. This resulted in a 55% reduction of the data. This filtering was necessary to reduce noise effects due to inaccurate geometric alignment. The view angle difference between AVHRR and MODIS was allowed to be maximal 20\({}^{\circ}\); the difference between acquisition times was set to maximal 10 min. The minimum number of pixel per tile was set to 50. Statistical measures were then calculated for different geographical subsets as defined by the MODIS tiles. Such, overall MAD between these filtered AVHRR and MODIS is 1.8 K, overall standard deviation is 1.4 K. Using the same collection of pixels, the MAD between AVHRR and MODIS using the original approach [40] is 3.3 K.  
Figure 17 shows the MAD per MODIS tile and date in relation to mean total column water vapour, mean emissivity, and mean zenith view angle. The MAD values are given for the original (grey) and the newly calculated (black) coefficients. The figures do not reveal a relation between the MAD magnitudes with any of the other variables; the error seems to be distributed randomly. Figure 18 shows the same MADs as in Figure 17, but this time in relation to the difference of mean emissivities, mean absolute zenith angle and time difference, each between AVHRR and MODIS. To each MAD value its associated standard deviation is plotted. The  
Figure 16: Error in emissivity estimation resulting from misclassification of pixels. increasing MADs of emissivity and view zenith angle. Time differences (acquisition times around noon) hardly show an influence. Table 6 shows more statistical values in tabular form together with the number of available pixels per tile. In 13 out of 17 tiles, the MAD is below 2 K. In many cases, the AVHRR LST shows negative offset compared to the MODIS LST resulting in negative mean differences. It should be noted that the magnitude of the dataset should be enlarged for a more thorough validation. Nevertheless, the statistical values of this chapter may serve as indication of the validity the LST approach. Unfortunately, the data is, despite of application of the cloud masks and an additional cloud border buffer, not fully cleared of cloud contaminated pixels, which leads to higher MADs in some cases (e.g., Tile Nr. 16 in Table 6--data not shown). Figure 17: MAD per MODIS tile and date in relation to the (**a**) mean total column water vapour; (**b**) mean absolute emissivity difference; and (**c**) mean absolute zenith view angle difference between AVHRR and MODIS. The figures show the MAD resulting from applying the new coefficients (black circles) and the original approach (grey crosses).