# Diurnal Cycle of Passive Microwave Brightness Temperatures over Land at a Global Scale
## 3 Computation of Diurnal Cycle of PMW TBs  
In order to characterize the diurnal cycle of intercalibrated TBs, data obtained from GMI, AMSR2, and SSMIS sensors were re-projected to an equal-area grid (equivalent to 0.25\({}^{\circ}\) at equator) and land-only pixels were extracted for computational efficiency. The goal is to harmonize these sensors' data in terms of channel and resolution, to construct diurnal cycle of TBs from their combination, and then to analyze TB variations across the globe. Figure 1: Percentage global land coverage of ten land cover types: namely, tropical/sub-tropical evergreen broad-leaved forest (LC01), deciduous forest (LC02), evergreen broad-leaved and needle-leaved forest (LC03), deciduous woodland (LC04), sclerophyllous woodland and forest (LC05), wooded and non-wooded grassland (LC06), tundra and mossy bog (LC07), boreal and xeromorphic shrubland (LC08), non-vegetated desert (LC09), and ice (LC10). As operating frequency channels in GMI, AMSR2, and SSMIS are not essentially the same, four frequency channels around 19 GHz, 23 GHz, 37 GHz, and 89 GHz were considered to construct diurnal cycles of TBs. For brevity, only one year of TB measurements for 2016 was considered in this study and results of arbitrarily any one (or two) frequency channel(s) are shown in most of the figures. Figure 2 shows the original records of available TBs from AMSR2, SSMIS, and GMI for October 2016 at frequency channels around 19 GHz (V) and 37 GHz (H) over a sample non-vegetated desert location (17.4\({}^{\circ}\)N and 28\({}^{\circ}\)E). TBs from all PMW sensors show a peak at afternoon as expected. Since the GMI sensor is onboard a non-sun-synchronous satellite, it provides TB measurements at several hours within a month. This makes the GMI data more suitable for diurnal analysis of TBs as well as for precipitation. In general, TBs at 19 GHz (V) are about 30K higher than TBs at 37 GHz (H) for all sensors. However, there are about 10K of TB variations at a specific time in AMSR2 and SSMIS sensors within a month. Computation of diurnal Cycle of Land TBs between Latitude 68\({}^{\circ}\)S and 68\({}^{\circ}\)N  
Taking advantage of the GMI sensor onboard a non-sun-synchronous satellite, the novel idea behind this study is to put TBs of all days of a month together to make a diurnal cycle shape for the month. Based on the previous study [7], it is reasonable to assume that general characteristics of TB diurnal variations such as amplitude do not change significantly in a month. Hence, half-hourly TB is constructed from a whole month with the GMI product by applying a mathematical method in the initial step. The mathematical fit utilized here is the least-squares approximation by cubic splines. Spline functions and, more generally, piecewise polynomial functions are some of the most successful approximating functions for such applications. The spline interpolation method has been successfully applied to study the diurnal variations of infrared land surface temperature  
Figure 2: Satellite-borne passive microwave brightness temperature (PMW TB) observations at a sample location (17.4\({}^{\circ}\)N and 28\({}^{\circ}\)E) with non-vegetated desert land cover for October 2016 using (**a**) SSMIS F16, F17, F18, and AMSR2 at 19.35 GHz vertical polarization; (**b**) GMI at 18.7 GHz vertical polarization; (**c**) SSMIS F16, F17, F18, and AMSR2 at 37 GHz horizontal polarization; (**d**) GMI at 36.5 GHz horizontal polarization. Time in each subplot is in local solar hours. (LST) and passive microwave TBs [6; 28; 29; 30]. They combine ease of computational handling with great flexibility; therefore, they are particularly appropriate for the approximation of experimental data or design curve measurements.