Exponential Loss Model

Basic Concepts and Equations

The exponential loss method models the reduction in infiltration rate as an exponentially decreasing function of accumulated infiltration. This method is highly empirical and, in general, should not be used without prior calibration. Before using this method, consideration should be given to the Green and Ampt method because it produces a similar exponential decrease in infiltration and uses parameters with better physical interpretation. Also, this method should only be used for event simulation.

The potential loss rate [in/hr or mm/hr] at time t, f_t, is computed using:

1)	$\begin{array}{l}\displaystyle f_t=(AK+DLTK)*p_t^{ERAIN}\end{array}$

2)	$\begin{array}{l}\displaystyle DLTK=0.2*DLTKR(1-\frac{CUML}{DLTKR}}))^{2}\end{array}$

3)	$\begin{array}{l}\displaystyle AK=\frac{STRKR}{RTIOL^{0.1*CUML}}\end{array}$

where p_t = precipitation rate [in/hr or mm/hr] at time t, ERAIN = precipitation exponent, AK = loss rate coefficient at the beginning of the time interval, DLTK = incremental increase in the loss rate coefficient during the first DLTKR [in or mm] of accumulated loss, F_t. When F_t is greater than DLTKR, DLTK = 0. Note that there is no direct conversion between metric and English units for the coefficients used by this method. Consequently, separate calibrations excesses are required to derive site-specific coefficient for both unit systems.

Required Parameters

Parameters that are required to utilize this method within HEC-HMS include the initial range DLTKR, [in or mm], the initial coefficient STRKR, the coefficient ratio, the precipitation exponent ERAIN, and directly connected impervious area [percent]. The initial range (DLTKR) is the amount of initial accumulated infiltration during which the loss rate is increased. This parameter is considered to be a function primarily of antecedent soil moisture deficiency and is usually storm dependent. The initial coefficient (STRKR) specifies the starting loss rate coefficient on the exponential infiltration curve. It is assumed to be a function of infiltration characteristics and consequently may be correlated with soil type, land use, vegetation cover, and other properties of a subbasin. The coefficient ratio indicates the rate at which the exponential decrease in infiltration capability proceeds. It may be considered a function of the ability of the surface of a subbasin to absorb precipitation and should be reasonably constant for large, homogeneous areas. The precipitation exponent reflects the influence of precipitation rate on subbasin-average loss characteristics. It reflects the manner in which storms occur within an area and may be considered a characteristic of a particular region; this parameter varies between 0.0 and 1.0.

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.