This document explains the use of “distance” in the classification of of the hill slopes into Hydrological Response Units (HRUs). This is a key difference in the classification and model creation scheme used with dynatopGIS compared to previous model implementations (e.g. the dynatopmodel).

As with earlier versions of Dynamic TOPMODEL “physical” classification of the raster cells representing the hill slopes by characteristics such as topographic index, soil parameters and rainfall inputs forms etc. is the basis of determining HRUs. However having the performed a “physical” classification there is the need to determine the connectivity of the HRUs and (possibly) the computational sequence for their solution.

Consider the methods utilised in the dynatopmodel package which determined the connectivity based on the down slope contributions of each raster cell in the HRU. This resulted in a matrix \(\mathbf{M)\) of flow fractions such that if the vector of outflows from the HRUs was \(\mathbf{l}_{o}\) the inflows \(\mathbf{l}_{i}\) are given by \[ \mathbf{l}_{i} = \mathbf{M} \mathbf{l}_{o} \] Determining the down slope contributions in such as fashion enables a high degree of spatial averaging of the inflow. For example an area at the bottom of the hillslope near a channel may fall into the same class as the low gradient area higher up the hillslope, where it might be reasonable to presume the inflow from adjacent HRUs was much lower. While such averaging may prove adequate for the hydrological simulation of the outflow it limits the ability of the model to represent interventions on a smaller scale (e.g. reforestation of a low fraction of raster cells; leaky dams limiting slowing the transfer of surface water)

To address this a “banding” is used to ensure an order to the HRUs. Currently the compute_band method computes a strict sequencing such that all the hillslope cells (or channel lengths) that flow into a cell (or channel length) in band \(n\) are in bands \(n+1\) and greater.

In handling the flow contributions this way we ensure a computational sequence for the HRUs is established (that is \(\mathbf{M}\) is triangular) which is required for the computational scheme used within the associated dynatop package.

In principle it possible to consider other means of sequencing. For example bands could be generated by partitioning the flow length calculated using the compute_flow_length method. These are

  • Shortest length. The minimum length to a river channel through any flow path.

  • Dominant length. The length to a river channel following the flow direction with the highest fraction for each pixel on the path.

  • Expected length. The length to a river channel based on the sum of down slope flow weighted by the fraction of flow to each cell.

Alternatively contour based banding could be used to define the sequences. The addition of such options will be considered in future versions of dynatopGIS.