## Data and Methods
### Wetland Probability Mapping Algorithm
#### 2.3.4 Logistic Regression Model for Probability Mapping  
The logistic regression model describes how predictor variables relate to the binary dependent responses of wetland or non-wetland. In this case, the predictor variables are the indices described above. The Bernoulli response is modeled as:  
\[Log_{e}\bigg{(}\frac{P(X)}{1-P(X)}\bigg{)}=\omega_{0}+\omega_{1}x_{1}+\cdots+ \omega_{n}x_{n}=\omega^{T}X,\,P(X)\in(0,\,1), \tag{4}\]  
where \(P(X)=\exp\big{(}\omega^{T}X\big{)}/\big{(}1+\exp\big{(}\omega^{T}X\big{)} \big{)}\) and describes the probability of wetland presence within a given pixel based on the predictors \(X\). The regression coefficients \(\omega_{i}\) serve as weights for each of the predictor variables that describe their relative contribution to the outcome probability. The nonlinear probability is transformed to a generalized linear model with a binomial distribution and logit-link function (Equation (4)). The logit transformation maps the probability from (0, 1) to (\(-\infty\), \(+\infty\)) and allows for explicit calculation of the probability of event success.  
The weights for the logistic regression model were determined from a training period comprised of three consecutive hydrologic wet years (2010 to 2012). First, a stationary land cover map was generated by removing pixels that varied in land cover type over the three-year period (Figure 3a). This stationary map was used to determine the fixed Bernoulli response values (i.e., wetland pixel = 1 and non-wetland pixel = 0). The resulting training pixels are summarized in Table 2. In the training data, the predictor variables (i.e., indices calculated from MODIS NBAR) were selected from the rainy seasons only (21 March-6 April) for training pixels randomly sampled from within the UZRB study region. Several models were trained using different combinations of indices. Once the weights were determined from the training data, the logistic regression model was applied to generate independent probability maps of wetlands every 8 days.  
Figure 3: Stationary land cover map and histograms for unitless remote sensing indices using only the pixels representing wetland and non-wetland in the training data. Stationary land cover data and indices were derived from the MODIS MCD12Q1 and MCD43B4, respectively. (**a**) Stationary land cover map derived from MODIS MCD12Q1 data for 2010–2012. (**b–g**) Histograms for wetland and non-wetland pixels using NIR (**b**), NDVI (**c**), NDWI (**d**), TC Brightness (**e**), TC Greenness (**f**) and TC Wetness (**g**).  
The best predictors for the linear regression model are those where there are clear differences in index values for wetland and non-wetland pixels. This can be observed in histograms of the indices that show isolated peaks for wetland and non-wetland pixels (Figure 3). The histograms represent moist conditions because the training data were obtained from only the rainy season. Thus, for a dry period the resulting histograms could be drastically different. Individually, NIR, NDWI, TC Brightness and TC Wetness show the clearest separations between wetland and non-wetland pixels. Using combinations of these indices in the logistic regression model will help remove the overlapping effects observed in the individual histograms.