# Diurnal Cycle of Passive Microwave Brightness Temperatures over Land at a Global Scale
## 3 Computation of Diurnal Cycle of PMW TBs
In the next step, differences between daily SSMIS/AMSR2 measurements and constructed monthly GMI data on corresponding time points (\(\Delta_{i}\)) were calculated for each day and for all the pixels between latitude 68\({}^{\circ}\)S and 68\({}^{\circ}\)N. For instance, for each of the timing points with available observation data, \(\Delta_{i}\) would be the difference between the interpolated GMI fit and the corresponding AMSR2, SSMIS F16, SSMIS F17, and SSMIS F18 data. This difference is given by:  
\[\Delta_{i}=TB_{AMSR2/SSMIS}-TB_{GMI} \tag{1}\]  
The schematic estimation process of \(\Delta_{i}\) is depicted in Figure 3a for a sample location with non-vegetated land cover for 15 January 2016. The original GMI, AMSR2, SSMIS F16, SSMIS F17, and SSMIS F18 observations and the interpolated GMI fit for 18.7 GHz (V) are also shown in the figure. Finally, the diurnal cycle (\(TB_{final}\)) is computed by taking the average of (\(\Delta_{i}\)) s and then adding this value to the GMI initial fit, as follows:  
\[\Delta~{}=~{}\left(\sum_{i=1}^{8}\Delta_{i}/n\right) \tag{2}\]  
\[TB_{final}=TB_{GMI}+\Delta \tag{3}\]  
Figure 3b demonstrates the corrected TB diurnal cycle by adding \(\Delta\) to the GMI initial fit. Figure 4 illustrates the constructed TB diurnal variations at 37 GHz (V) at four different  
Figure 3: Schematic to compute diurnal cycle of PMW TBs for pixels between 68\({}^{\circ}\)S and 68\({}^{\circ}\)N, at a sample location (25.1\({}^{\circ}\)S and 138.6\({}^{\circ}\)E) with non-vegetated desert land cover for 15 January 2016 at 18.7 GHz vertical polarization (**a**) based on monthly GMI data, and (**b**) corrected by AMSR2 and SSMIS daily data. Time in each subplot is in local solar hours. dates and four sample locations (two in Northern and two in Southern Hemisphere) having distinct vegetation types. The original TBs from each sensor are also shown in the figure. Monthly mean differences between GMI and SSMIS/AMSR2 data for each land cover type in 2016 for channel 23 GHz (V) are shown in Table 1. The differences are generally between 1K and 3K. Only during a few months does the tundra and mossy bog land cover type (LC07) show higher values (above 10K) than the other land vegetation types. This particular land cover is only available in the Northern Hemisphere near Arctic regions. In recent years, it has gone under enormous changes due to a large number of disturbances and climate forcing such as wildfires. Considering 31-year satellite imagery, extensive shifts in the distribution of plant functional types and ecosystem productivity have been observed in response to the climate change [31]. It is worthwhile to mention that the spatial resolution of existing land cover datasets is not fine enough; small-scale land cover changes in this vegetation cover have been poorly characterized. Computation of Diurnal Cycle of Land TBs above Latitude 68\({}^{\circ}\)N and below Latitude 68\({}^{\circ}\)S  
Since there are no GMI data available for latitudes over 68\({}^{\circ}\)N and below 68\({}^{\circ}\)S, a new estimation method has to be developed for constructing TB diurnal cycles in those areas. Herein, the GMI data have been used as a point of reference to smooth the SSMIS and AMSR2 data in polar regions. For this reason, the TB diurnal cycle from GMI fit was normalized by taking the daily average away for each pixel. Then, for each of the ten land cover types, the average of the normalized graph was calculated. In the next step, the aforementioned normalized graph was applied to the SSMIS/AMSR2 data in the regions not covered by the GMI to obtain the smoothed data. Figure 5 represents the smoothing method step by step in details.