Initial and Constant Loss Model

Basic Concepts and Equations

The Initial and Constant loss method uses a hypothetical single soil layer to account for changes in moisture content. While this method is very simple, it is widely used to model watersheds that lack detailed subsurface information.

Since no means for extracting infiltrated water is included, this method should only be used for event simulation.

The underlying concept of the initial and constant-rate loss model is that the maximum potential rate of precipitation loss, $\begin{array}{l}f_c\end{array}$ , is constant throughout an event. Thus, if $\begin{array}{l}p_t\end{array}$ is the MAP depth during a time interval t to t+ $\begin{array}{l}\Delta t\end{array}$ , the excess, $\begin{array}{l}pe_t\end{array}$ _, during the interval is given by:

1)	$\begin{array}{l}p e_{t}=\left\{\begin{array}{cc}p_{t}-f_{c} & \text { if } p_{t}>f_{c} \\ 0 & \text { otherwise }\end{array}\right\}\end{array}$

An initial loss, $\begin{array}{l}I_a\end{array}$ , is added to the model to represent interception and depression storage. Interception storage is a consequence of absorption of precipitation by surface cover, including plants in the watershed. Depression storage is a consequence of depressions in the watershed topography; water is stored in these and eventually infiltrates or evaporates. This loss occurs prior to the onset of runoff. Until the accumulated precipitation on the pervious area exceeds the initial loss volume, no runoff occurs. Thus, the excess is given by:

2)	$\begin{array}{l}p e_{t}=\left\{\begin{array}{cl}0 & \text { if } \sum p_{i}< I_{a} \\ p_{t}-f_{c} & \text { if } \sum p_{i}>I_{a} \text { and } p_{t}>f_{c} \\ 0 & \text { if } \sum p_{i}>I_{a} \text { and } p_{t}< f_{c}\end{array}\right\}\end{array}$

Required Parameters

Parameters that are required to utilize this method within HEC-HMS include the initial loss [inches or millimeters], constant rate [in/hr or mm/hr], and directly connected impervious area [percent].

A tutorial describing an example application of this loss method, including parameter estimation and calibration, can be found here: Applying the Initial and Constant Loss Method.

A tutorial describing how gSSURGO data can be formatted for use within HEC-HMS can be found here: Formatting gSSURGO Data for Use within HEC-HMS.

The initial loss defines the volume of water that is required to fill the soil layer at the start of the simulation. This parameter is typically defined using the product of the soil moisture state at the start of the simulation and an assumed active layer depth, but it should be calibrated using observed data. If the watershed is in a saturated condition, I_a will approach zero. If the watershed is dry, then I_a will increase to represent the maximum precipitation depth that can fall on the watershed with no runoff; this will depend on the watershed terrain, land use, soil types, and soil treatment. Table 6-1 of EM 1110-2-1417 suggests that this ranges from 10-20% of the total rainfall for forested areas to 0.1-0.2 inches for urban areas.

The constant rate defines the rate at which precipitation will be infiltrated into the soil layer after the initial loss volume has been satisfied. Typically, this parameter is equated with the saturated hydraulic conductivity of the soil. The SCS (1986) classified soils on the basis of this infiltration capacity, and Skaggs and Khaleel (1982) have published estimates of infiltration rates for those soils, as shown in the following table. These may be used in the absence of better information. Because the model parameter is not a measured parameter, it and the initial condition are best determined by calibration. Chapter 9 of this manual describes the program's calibration capability.

Finally, the percentage of the subbasin which is directly connected impervious area can be specified. Directly connected impervious areas are surfaces where runoff is conveyed directly to a waterway or stormwater collection system. These surfaces differ from disconnected impervious areas where runoff encounters permeable areas which may infiltrate some (or all) of the runoff prior to reaching a waterway or stormwater collection system. No loss calculations are carried out on the specified percentage of the subbasin; all precipitation that falls on that portion of the subbasin becomes excess precipitation and subject to direct runoff.

SCS soil groups and infiltration (loss) rates (SCS, 1986; Skaggs and Khaleel, 1982)

Soil Group	Description	Range of Loss Rates (in/hr)
A	Deep sand, deep loess, aggregated silts	0.30-0.45
B	Shallow loess, sandy loam	0.15-0.30
C	Clay loams, shallow sandy loam, soils low in organic content, and soils usually high in clay	0.05-0.15
D	Soils that swell significantly when wet, heavy plastic clays, and certain saline soils	0.00-0.05

A Note on Parameter Estimation

The values presented here are meant as initial estimates. This is the same for all sources of similar data including Engineer Manual 1110-2-1417 Flood-Runoff Analysis and the Introduction to Loss Rate Tutorials. Regardless of the source, these initial estimates must be calibrated and validated.