## 2 Methods
### Statistical Analyses  
All analyses were performed in the R statistical environment [58]. As the relationship between cover crop biomass and VIs is often non-linear [14], we fit three regression models to estimate cover crop biomass from optical data: (1) log-transformed, (2) polynomial, and (3) segmented regression. Regression models were evaluated using various measures: goodness-of-fit statistic (adjusted R\({}^{2}\)), error measures such as the root mean square error (RMSE) and the mean absolute error (MAE), and model fit using Akaike's Information Criterion for small sample sizes (AICc) [74]. We opted to use AICc over the traditional AIC to avoid overfitting our data, as the number of observations increases AICc and AIC \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Sentinel-1 Synthetic Aperture Radar Metrics** & \\ \hline VV & Vertical Transmit—Vertical Return Backscatter Intensity & \(\sigma^{\circ}\)VV \\ VH & Vertical transmit—horizontal return backscatter intensity & \(\sigma^{\circ}\)VH \\ VHVV & Ratio of VH to VV & \(\sigma^{\circ}\)VH \\ RVI & Radar vegetation index & \(\left(\frac{\sigma^{\circ}\text{VH}}{\sigma^{\circ}\text{VH}}\right)\) \\ \(H\) & Entropy & \(-\sum\limits_{i=1}^{n-3}P_{i}log(P_{i})\) \\ \(A\) & Anisotropy & \(\frac{\lambda_{2}+\lambda_{3}}{\lambda_{3}-\lambda_{3}}\) \\ \(\alpha\) & Alpha & \(\frac{i\sum\limits_{i=1}^{n}}{\sum\limits_{i=1}^{n}}\) \\ InSar coherence & Interferometric synthetic aperture radar coherence & \(\frac{\{\{\{\{\{\}}}_{1}+\{\}_{1}}\}}{\sqrt{(|\textbf{s}_{1}|)^{2}(|\textbf{ s}_{2}|)^{2}}}\) & [44] \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Sentinel-1 synthetic aperture radar (SAR) backscatter, polarimetric, and phase parameters where \(\sigma^{\circ}\) indicates backscatter intensity per unit area, \(Pi\) represent the probabilities from the eigenvalues in the polarimetric decomposition, \(\lambda\) is the non-negative real eigenvalues of the diagonal matrix, alpha is the alpha angle, entropy (\(H\)) and anisotropy (\(A\)) are additional output parameters from the polarimetric decomposition, and InSAR coherence from an analysis in which the first and second scene are denoted as \(S_{1}\) and \(S_{2}\), respectively. converge, whereas, for smaller sample sizes, AICc are penalized more heavily. AICc were calculated using the following equation:  
\[\text{AICc}=2k-2 ln\big{(}\hat{L}\big{)}+\frac{2k^{2}+2k}{n-k-1} \tag{1}\]  
where \(k\) denotes the number of predictors in a model, \(\hat{L}\) represents the maximum likelihood, and \(n\) is the sample size. Finally, we calculated AIC weights (AICw) for the log-linear and polynomial models. AICw quantifies the probability that a given model was the best model in the set of compared models--in our case, the best model among the 27 VIs compared for a given model type (e.g., log-linear). Note that AICc and AICw cannot be used to compare different model sets (i.e., log-linear vs. polynomial). We also checked for the normality and homoscedasticity of the residuals for each model. After identifying the best-performing optical index using the above steps (objective 1), we assessed whether there were seasonal- or species-level differences using analysis of variance (ANOVA) and slope and intercept contrasts in the R 'emmeans' package [75]. To assess whether the integration of optical and SAR data could improve our estimations of cover crop biomass (objective 2), we paired the best-performing optical index with each SAR metric (\(n=8\)) individually. As with objective 1, these models were then evaluated using adjusted R\({}^{2}\), RMSE, MAE, AICc, and AICw. If more than one SAR metric improved model fit (i.e., \(\Delta\text{AICc}<-2\)) and these metrics were not collinear (i.e., r < 0.7), we evaluated combined models with the optical index identified in objective 1 and multiple SAR variables. We used ANOVAs to assess whether models containing both optical and SAR data were significantly better than models with only optical predictors.