XPRafts uses Laurenson's (1964) method to generate its hydrographs. Laurenson's model was directed at single catchments, or more particularly, the derivation of a single hydrograph at the outlet of a catchment. However, in the case of XPRafts the sub-catchments are divided into ten sub-areas.
Sub-areas are established by dividing each of the sub-catchments into ten areas defined between lines of equal travel time or isochrones.
XPRafts uses Laurenson's model to derive separate sub-catchment inlet hydrographs. These hydrographs are then manipulated through the link system to the outlet of the total catchment via the channel routing module.
Sub-areas are established by constructing lines of equal travel time from the sub-catchment boundary to its outlet. These are referred to as isochrones.
The model storage delay parameters have been calibrated based on 10 isochronal areas making up a sub-catchment. In many instances the simple division of a sub-catchment into ten equal sub-areas provides very similar results. This is particularly true in urban areas where isochrones vary with storm frequency and can sometimes be difficult to determine due to the complexity of the pipe and overflow network.
The ten equal sub-areas are calculated automatically by XPRafts. However if a user wishes to define ten isochronal areas, these must be inputted as data.
Within the workbench environment the facility for including a single sub-area, rather than the ten in XPRafts, has been added.
The procedure for computing the isochrones is based on the assumption that travel for any element of area is proportional to:
tt= travel time
L= length along a reach of the major flow path
S= average slope of the reach
The summation is carried out for each selected point in the sub-catchment along the flow path to the outlet. Laurenson’s (1964) procedure for estimating isochrones is summarized as follows:
A large number of points uniformly distributed over a sub-catchment are marked on a contour map of the sub-catchment.
For each point, the distances between adjacent contours along the flow path to the outlet are tabulated.
These individual distances are raised to the 1.5 power since time of flow through any reach is assumed proportional to:i.e.
Where: H = contour interval
Since H is constant, the time of flow is proportional to L1.5 (A correction has to be made for the lowest reach since the outlet of the catchment is not, in general, on a contour. This correction involves multiplying the length of the lowest reach by (H/H1)0.5 where H1is the fall through the lowest reach). The lengths to the power of 1.5 are then summed for each point.
- The sums obtained in (3) are each divided by the greatest sum to give relative travel times for all points.
- Isochrones are then drawn through the points of relative travel time to give the lines of equal travel times to the outlet. These are designated as the 1, 2, 3….10 isochrones. The areas between adjacent isochrones are referred to as the subareas.
It is recommended, unless very large sub-catchments are being considered, or flow paths and times through sub-catchments are particularly variable, that 10 equal subareas be considered to save data preparation. XPRafts provides a default for this treatment if required.