Terrain indices #

W-21 through W-28 added a full set of terrain-attribute indices to the DEM class. Every method returns a typed Dataset aligned with the DEM's geotransform and uses float32 storage with the DEM's no-data sentinel.

Focal-window stats (W-21 → W-24)#

These four indices share a private _focal_window_stats kernel — a no-data-aware scipy.ndimage.uniform_filter pass that divides by the per-window valid-neighbour count, so cells near the data envelope are computed only from the valid cells inside their window (not contaminated by no-data substitution).

Method	Formula	What it measures
`DEM.tpi(window)` (W-21)	`z - focal_mean(z)`	Topographic Position Index — ridges > 0, valleys < 0 (Guisan 1999)
`DEM.deviation_from_mean(window)` (W-22)	`(z - focal_mean) / focal_sd`	Standardised TPI; dimensionless
`DEM.elev_std(window)` (W-23)	`focal_sd(z)`	Local elevation SD; a roughness proxy
`DEM.ruggedness(window)` (W-24)	mean(\|z - z_neighbour\|)	Riley et al. 1999 terrain ruggedness index

Surface geometry (W-25, W-26)#

Curvature family (W-25)#

DEM.curvature(kind=...) fits a Zevenbergen-Thorne 1987 partial quartic polynomial to each cell's 3×3 neighbourhood and evaluates one of five variants from the coefficient grid:

`kind`	Formula	Geomorphological meaning
`"plan"`	`-2(D·H² + E·G² - F·G·H) / (G² + H²)`	Curvature perpendicular to slope direction
`"profile"`	`2(D·G² + E·H² + F·G·H) / (G² + H²)`	Curvature parallel to slope direction
`"total"`	`2(D + E)`	Total relief curvature (sign-independent)
`"mean"`	`D + E`	Average of the two principal curvatures
`"gaussian"`	`4·D·E - F²`	Product of the two principal curvatures

The polynomial coefficients are D = ∂²z/∂x²/2, E = ∂²z/∂y²/2, F = ∂²z/∂x∂y, G = ∂z/∂x, H = ∂z/∂y (Zevenbergen-Thorne notation).

Normal-vector angular deviation (W-26)#

DEM.normal_vector_deviation(window) computes each cell's outward-pointing surface normal from finite differences, focal-means the unit-normal components in a window, and returns the per-cell angle (in radians) between the local normal and the focal-mean normal. A roughness metric that grows with how strongly the surface bends inside the window.

Visibility (W-27, W-28)#

Both metrics share a numba-accelerated horizon_walk_kernel (in digitalrivers._numba) that walks outward from every cell along 8 azimuths up to search_radius cells, recording the maximum elevation angle (the "horizon") in each direction.

Topographic openness (W-27)#

DEM.openness(search_radius, kind="positive"/"negative") — Yokoyama 2002.

Positive openness = mean of (π/2 - horizon_angle) across the 8 azimuths. High values mark exposed / high-relief locations (the cell sees nothing higher than itself nearby).
Negative openness = same kernel applied to -z. High values mark deep depressions.

Sky-view factor (W-28)#

DEM.sky_view_factor(search_radius) — Zakšek et al. 2011. The fraction of the upper hemisphere visible from each cell:

SVF = mean over directions of (1 - sin(horizon_angle))

Range [0, 1]; 1 on flat terrain, < 1 wherever surrounding terrain occludes part of the sky.