# D-Infinity Upslope Dependence

(c) 2010 by David G. Tarboton
The D-Infinity Upslope Dependence tool quantifies the amount each grid cell in the domain contributes to a destination set of grid cells. D-Infinity flow directions proportion flow from each grid cell between multiple downslope grid cells. Following this flow field downslope the amount of flow originating at each grid cell that reaches the destination zone is defined. Upslope influence is evaluated using a downslope recursion, examining grid cells downslope from each grid cell, so that the map produced identifies the area upslope where flow through the destination zone originates, or the area it depends on, for its flow.
The figures below illustrate the amount each source point in the domain `x` (blue) contributes to the destination point or zone `y` (red). If the indicator weighted contributing area function is denoted `I(y; x)` giving the weighted contribution using a unit value (1) from specific grid cells `y` to grid cells `x`, then the upslope dependence is: `D(x; y) = I(y; x)`.

This is useful for example to track where flow or a flow related substance or contaminant that enters a destination area may come from.

## Parameters

Number of Processes
Integer
  The number of stripes that the domain will be divided into and the number of MPI parallel processes that will be spawned to evaluate each of the stripes.
D-Infinity Flow Direction Grid
Raster Grid
  A grid giving flow direction by the D-Infinity method where the flow direction angle is determined as the direction of the steepest downward slope on the eight triangular facets formed in a 3 x 3 grid cell window centered on the grid cell of interest. This grid can be produced using the "D-Infinity Flow Direction" tool.
Destination Grid
Raster Grid
  A grid that encodes the destination zone that may receive flow from upslope. This grid must be 1 inside the zone y and 0 over the rest of the domain.

## Outputs

Upslope Dependence Grid
Raster Grid
  A grid quantifing the amount each source point in the domain contributes to the zone defined by the destination grid.