# Melton Ratio

During landslide-triggering rainfall events, debris flows also commonly occur in steep, erosion-susceptible catchments. For this reason, we also need to show susceptibility to debris flows for each hillslope unit. The most commonly used measure of debris flow susceptibility is the Melton ratio (Melton-R), which measures a catchment's average steepness (Melton 1965) and gives an indication of the catchment’s ability to generate debris flows. Using the Melton-R, we can classify hillslope units into low (Melton-R < 0.3), medium (Melton-R = 0.3 - 0.6) or high (Melton-R > 0.6) susceptibility to debris flows. This provides an extra layer of information to assist us in managing landslide risks during the window of vulnerability.

Debris flow occurrence depends on three factors (Welsh and Davies 2010):

- steep channel slopes combined with
- availability of large volumes of sediment for mobilisation, either on slopes or in a stream channel
- rainfall and/or streamflow of sufficient intensity to mobilise the sediment.

These factors also contribute to the susceptibility as assessed by the Rainfall Induced Landslide (RIL) susceptibility model. The Melton-R focuses on the first factor (slope steepness), since steep channel slopes are far more likely to result in debris flows occurring.

The Melton-R is the ratio between catchment relief (difference between maximum and minimum elevations in the catchment) and the square root of watershed area (Melton 1965). The image below shows the most common method for estimating the Melton-R, where it is calculated for an entire catchment above the apex of the fan onto which a debris flow would discharge.

### Calculation of the Melton-R

```
Melton ratio = Relative Relief Ratio
Melton ratio (R) = Hb Ab^-0.5
Hb: basin relief (difference between maximum and minimum elevations in the basin)
Ab: total area of the basin
Example: Alpine Baldy, South Fork Skykomish
Top Elev.: 1,584 m
Bottom Elev.: 464 m
Area: 2,351,050 m²
R = (1584 - 464) * (2,351,050)^-0.5
= 0.73
```

Source: Melton, M. A. (1965).

To account for both landslides and debris flows, the FCP calculates the Melton-R for each HSU, then overlays these over the HSU’s Rainfall Induced Landslide (RIL) susceptibility, to provide an overall indication of where landslide sediments are more likely to mobilise as debris flows.