MetSim Precipitation

Basic Concepts and Equations

The MetSim Precipitation method, as implemented within HEC-HMS, follows that which is described in Bohn, et al (2019). This method interpolates a sub-daily precipitation depth from an input daily precipitation accumulation through the use of an isosceles triangle shaped temporal distribution. This method uses two parameters for disaggregation: a storm duration and a storm time to peak. The base width of the triangle is equivalent to the storm duration parameter while the triangle's time of peak is equivalent to the storm time to peak parameter.

The computations begin by calculating the peak intensity of the triangle, such that the area of the triangle equals the daily total P_daily. This value is calculated as:

1)	$\begin{array}{l}\displaystyle I(d,t)=P_{daily}(d)*k_{tri}(t)\end{array}$

where I(d, t) [in/hr or mm/hr] is the instantaneous intensity at time t within day d, P_daily(d) [in or mm] is the daily total precipitation on day d, and k_tri(t) (hours) is the kernel function (unit hyetograph) of the isosceles triangle. The kernel function is defined as:

2)

$\begin{array}{l}k_{\mathrm{tri}}(t)=\begin{cases} \frac{2}{D}+\frac{4}{D^2}\left(t-t_{\mathrm{pk}}\right), \quad t_{\mathrm{pk}}-0.5 D< t< t_{\mathrm{pk}} \\ \frac{2}{D}-\frac{4}{D^2}\left(t-t_{\mathrm{pk}}\right), \quad t_{\mathrm{pk}}< t< t_{\mathrm{pk}}+0.5 D \\ 0, \text { all other } t \end{cases}\right.\end{array}$

where t_pk is the storm time to peak [hours] and D is the storm duration [hours], which is allowed to range from 0.5 * Δt (where Δt is the computational time step) to 24 hours. A non-monotonic linear interpolation function, implemented using the Apache Commons Mathematics Library, is used to construct this kernal function. Once a kernal function has been constructed, a kernal value for the current computational interval, k(t), is extracted. This kernal value is then normalized as:

3)	$\begin{array}{l}\displaystyle k_{normalized}=k(t)*\frac{2}{D}\end{array}$

The normalized sum of all kernal values, k_{normalized sum}, within a day for the kernel function is then computed. Finally, the sub-daily precipitation depth, P_sub-daily, is computed as:

4)	$\begin{array}{l}\displaystyle P_{sub-daily}=P_{daily}/k_{normalized sum}*k_{normalized}\end{array}$

Required Parameters

Parameters that are required to utilize this method within HEC-HMS include a daily precipitation gridset, a Temporal Disaggregation method, a Storm Characteristics method, a Storm Duration [minutes], and a Storm Time to Peak [minutes]. An optional Time Shift method can be used to adjust the gridded precipitation data in time.

A tutorial describing an example application of this precipitation method can be found here: Using the New MetSim Precipitation and Temperature Methods.

The Temporal Disaggregation method dictates how precipitation will be disaggregated in time. Currently, only the Bohn el al. 2019 option is available for the Temporal Disaggregation method. Additional options will be added in the future.

There are currently three options for the Storm Characteristics method: Fixed Value, Annual Pattern, and Grid. When using the Annual Pattern method, Parameter Value Patterns must be used to specify both the Storm Duration and Storm Time to Peak. When using the Grid method, Storm Duration and Storm Time to Peak gridsets must be used to specify both parameters.

The Storm Duration defines the duration of precipitation in each day (i.e., base width of the isosceles triangle shaped temporal distribution). This parameter can vary between 1 and 1440 minutes.

The Storm Time to Peak defines the peak of the precipitation intensity in each day (i.e., peak of the isosceles triangle shaped temporal distribution). This parameter can vary between 0 and 1439 minutes.

Both the Storm Duration and Storm Time to Peak should be entered using the same time zone of the simulation (e.g., UTC).