Phase 2 Methodology

Decision-Tree Snow Discrimination

A pixel is classified as snow when all the following predicates hold:

Predicate	Threshold	Source
NDSI	> 0.40	Hall et al. (1995)
NIR (B08)	> 0.11	suppresses ice-cloud confusion
TIR	< 280 K	rejects warm cloud tops
DEM elevation	> basin-floor	rejects valley-floor false positives
Cloud probability	< 0.30 (Fmask)	s2cloudless + Himalayan tuning
Temporal coherence	≥ 0.5	adjacent-pass agreement

Linear Spectral Mixture Analysis (LSMA)

For each pixel:

$$\rho_\text{obs}(\lambda) = \sum_{k=1}^{K} f_k \cdot E_k(\lambda) + \varepsilon$$

subject to non-negativity $f_k \ge 0$ and sum-to-one $\sum_k f_k = 1$.

Fractional snow cover is

$$\text{FSC} = f_\text{snow\_fresh} + f_\text{snow\_aged} + f_\text{ice}$$

clipped to $[0, 1]$.

Snowmelt Energy Balance

$$Q_m = Q_\text{sw,net} + Q_\text{lw,net} + Q_h + Q_l + Q_g + Q_p$$

with melt rate

$$M = \frac{\max(Q_m, 0)}{\rho_w \cdot L_f}, \quad L_f = 334{,}000 \,\text{J/kg}.$$

Validation Metric

$$R^2 = 1 - \frac{\sum_i (x_i - y_i)^2}{\sum_i (x_i - \bar{x})^2}$$

with $x$ = MOD10A1 NDSI snow cover and $y$ = SNOW IR FSC, resampled to the 500 m MODIS grid via area-weighted mean. Acceptance: $R^2 \ge 0.85$.