# Tropical Cyclone Winds from WindSat, AMSR2, and SMAP: Comparison with the HWRF Model
## Methods  
### Spatial Resampling  
One of the first and most important issues to address when comparing the satellite TC-winds to those of a high-resolution model such as HWRF is the differences in spatial scales between the two. The TC-winds measurements all have an approximate resolution of 40-50 km and are reported on a 0.25 \(\times\) 0.25 degree (\(\approx\)25 km) Earth grid. This is much coarser than the native resolution of the HWRF model used in this study. These differences in spatial scales can lead to large differences between wind intensities and the features that are resolved in the HWRF and satellite observations of the same storm. This is illustrated in Figure 2, which shows a side-by-side comparison of HWRF and SMAP TC-winds for Hurricane Florence on 12 September 2018 at 12:00 UTC and 10:50 UTC, respectively. It is apparent that, despite the images being within about an hour of one another, the features seen in the 2D wind fields at the two resolutions are quite different. For instance, the HWRF wind field shows the eye of the hurricane to have wind speeds near zero, while the SMAP observations show the eye winds to be closer to 35 m/s. It is also evident that the maximum wind speeds seen in the HWRF model at its original resolution are larger than the maximum wind speeds observed by the satellite. In order to account for the differences in spatial scales, the HWRF winds need to be resampled to the spatial resolution of the satellite observations. This is done by calculating the weighted average of the HWRF wind field at each satellite grid cell. The weight is defined by the gain pattern of the satellite antenna projected onto the Earth's surface. We employed a frequently used gain pattern approximation that takes the form of a radially symmetric Gaussian weighting function \(W(r)\) (Figure 3):  
\[W(r)=\exp\left(-\ln 2\cdot\left(r/r_{0}\right)^{2}\right) \tag{1}\]  
In (1), \(r\) denotes the distance (in km) between the HWRF wind measurement and the center of the 0.25 degree satellite product grid cell and \(r_{0}=D/2\), where \(D\) is the geometric average of the half-power footprint diameters. The values of \(D\) are approximately 40 km for SMAP, 48 km for AMSR2 and 52 km WindSat. This weighting function (1) provides a good approximation for the antenna gain over the main lobe and the near-side lobes of the antenna, and is sufficient for our purpose of approximately matching the spatial scales of HWRF winds to those seen by the satellite. Figure 4b shows the results of the resampled HWRF wind field compared to the SMAP wind field (Figure 4a). We see that this resampling method resulted in a wind field that captured the features seen in the satellite winds, and thus resembled the satellite observation well. Figure 2: Wind fields of Hurricane Florence on 12 September 2018 from the HWRF model at its original resolution of \(\sim\)1.5 km at 12:00 UTC (**a**) and from SMAP TC-winds at their native resolution of 40 km at 10:50 UTC (**b**). The maximum wind value for each field at these resolutions is shown in the bottom right of each panel. Figure 4: Various methods of resampling the HWRF data from its native resolution for a sample view of Hurricane Florence on 12 September 2018 at 12:00 UTC. (**a**) The SMAP pass over Hurricane Florence approximately 1 h before the HWRF time shown in (**b–d**), (**b**) HWRF resampled using a Gaussian weighting method with a 40 km half-power width, (**c**) resampling using a 25 km drop-in-the-bucket box average, and (**d**) resampling using a 40 km drop-in-the-bucket box average. Figure 3: A graphical illustration of the Gaussian weighting method applied to each 0.25 \(\times\) 0.25 degree grid point as described in Equation (1). The half-power footprint diameter was 40 km. For comparison, we also tested two other simple resampling schemes. Figure 4c shows the result for a 'drop-in-the-bucket' average for a 0.25 degree (~25 km) grid cell.