n_{s }

# L_{t }=

∑ i k ∑ D i =1 n_{s }k_{i }

i

# Equation 2.1

i =1

L_{t }is the average travel distance, n_{s }is the total number of cells in the subcatchment, D_{i }is the travel distance of cell i to the adjacent channel, and k_{i }is a weighting factor with a value of 1 for travel distances originating at subcatchment cells, and ½ for travel distances originating at channel cells. The weighting factor accounts for the fact that channel cells contain a channel and the cell area is evenly split between the right and left subcatchments adjacent to the channel. No adjustments are needed for subcatchment cells, so their weighting factor is 1 (Garbrecht et al., 1999b).

The second method, the average flow path length, shown in Equation 2.2, is different in that not all points in the subcatchment are considered in the length calculations. The flow path in this method is considered as the distance from a divide to the first adjacent downstream channel. Only the cells in the drainage divide are considered in this calculation. Drainage divides are not only located at the upstream boundary of the subcatchment, but also within the subcatchment as defined by local ridges in the topography. For this reason the flow path length is generally shorter than the average travel distance method to the drainage divide. (Garbrecht et al., 1999b)

# L_{f }=

1 n_{i }

## n_{i }

∑^{l }

i =1

f i

Equation 2.2

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