## Data and Methods
### The SMAP FT Classification Algorithms  
#### 2.2.1 Normalized Polarization Ratio Based Seasonal Threshold Algorithm  
Unlike prior SMAP FT product releases, the latest R16 product uses two different classification algorithms preferentially applied to maximize the overall global FT accuracy and performance. The SMAP baseline FT algorithm uses a normalized polarization ratio (NPR) of vertically and horizontally polarized brightness temperatures (Tbv, Tbh) and examines the time series NPR evolution relative to signatures acquired during seasonal reference frozen and thawed states [7]. The NPR algorithm is consistent with previous SMAP FT product releases encompassing the northern polar domain. A frost factor index (\(FF_{\textit{rel}}\)) is defined as:  
\[FF_{\textit{rel}}=\frac{FF_{\textit{NPR}}-FF_{\textit{fr}}}{FF_{\textit{th}}-FF_{ \textit{fr}}} \tag{1}\]  
where \(FF_{\textit{fr}}\) and \(FF_{\textit{th}}\) are frozen and thawed reference states, respectively. The \(FF_{\textit{fr}}\) was derived as the average of the 20 lowest (January and February) \(FF_{\textit{NPR}}\) values over a three year operational record (2015-2018), \(FF_{\textit{th}}\) was derived as the \(FF_{\textit{NPR}}\) average over the summer months (July and August) from the same three year record. The \(FF_{\textit{NPR}}\) is the frost factor based on the normalized polarization ratio (NPR) derived for a given grid cell and time step as:  
\[FF_{\textit{NPR}}=\frac{Tbv-Tbh}{Tbv+Tbh} \tag{2}\]  
The SMAP global FT status is derived from the NPR frost factor time series on a per grid cell basis as:  
\[\text{FT status}=\left\{\begin{array}{c}thaw,\ if\ FF_{\textit{rel}}>\textit{ threshold}\\ frozen,\ if\ FF_{\textit{rel}}\leq\textit{threshold}\end{array}\right.) \tag{3}\]  
where a constant frost factor _threshold_ of 0.5 was used across the global FT domain.  
The temporal NPR decreases and increases are associated with respective landscape FT transitions representing changes in the predominant frozen or non-frozen status within a grid cell. The NPR decrease under frozen conditions results from a relatively small Tbv increase combined with a larger Tbh increase [6; 7; 24]. Several studies have shown the NPR to outperform other L-band Tb based FT algorithms while minimizing sensitivity to physical temperature [24; 25]. However, while the NPR is most effective in areas with relatively lower vegetation cover, the signal-to-noise is degraded over more densely vegetated areas due to the greater diffuse scattering of microwave emissions and reduced Tbv and Tbh differences [26; 27].  
There are two main limitations to the NPR algorithm. First, the algorithm relies on the derivation of proper FT references characteristic of winter frozen and summer non-frozen conditions. In the current scheme, the freezing references require at least 20 days of relatively stable frozen conditions for successful establishment. This requirement generally limits the boundary of a stable freezing reference to higher latitudes and altitudes with longer characteristic frozen seasons. Second, the NPR FT reference difference needs to be large enough to perform the algorithm (NPR \(>\) 0.1), which excludes relatively dry areas that undergo smaller dielectric changes during FT transitions.