Basic Concepts and Equations

The Deficit and Constant loss method is very similar to the initial and constant loss method in that a hypothetical single soil layer is used to account for changes in moisture content.  However, the deficit and constant method allows for continuous simulation when used in combination with a canopy method that will extract water from the soil in response to potential ET computed in the meteorologic model.  Between precipitation events, the soil layer will lose moisture as the canopy extracts infiltrated water.  Unless a canopy method is selected, no soil water extraction will occur.  This method may also be used in combination with a surface method that will hold water on the land surface.  The water in surface storage can infiltrate into the soil layer and/or be removed through ET.  The infiltration rate is determined by the capacity of the soil layer to accept water.  When both a canopy and surface method are used in combination with the deficit constant loss method, the system can be conceptualized as shown in the following figure.

Conceptual Representation of the Deficit and Constant Loss Method

If the moisture deficit is greater than zero, water will infiltrate into the soil layer.  Until the moisture deficit has been satisfied, no percolation out of the bottom of the soil layer will occur.  After the moisture deficit has been satisfied, the rate of infiltration into the soil layer is defined by the constant rate.  The percolation rate out of the bottom of the soil layer is also defined by the constant rate while the soil layer remains saturated.  Percolation stops as soon as the soil layer drops below saturation (moisture deficit greater than zero).  Moisture deficit increases in response to the canopy extracting soil water to meet the potential ET demand. 

Since this method allows for the extraction of infiltrated water, this method can be used for both event and continuous simulations.

Infiltration

The soil layer used in the deficit and constant loss model has a maximum capacity to hold water. The soil is saturated when the soil layer is at the maximum storage capacity, and it is not saturated when the layer contains less than the maximum storage capacity. The deficit is the amount of water required at any point in time to bring the soil layer to saturation. If the deficit is zero then the layer is saturated. When the layer is not saturated, the deficit is the amount of water that must be added to bring it to saturation. The deficit is measured in millimeters or inches. The maximum capacity minus the deficit gives the amount of water currently in storage. The current deficit (or current storage) is assumed to be uniformly distributed throughout the soil layer. The soil within the layer is assumed to have homogeneous properties.

The soil layer will have a certain moisture deficit at the beginning of a storm event. This amount could be zero, indicating the soil is completely saturated. However, it is much more common for the layer to have a deficit greater than zero, indicating it is not saturated. The moisture deficit could equal the maximum capacity if there has been an extended period without rain, and evapotranspiration has extracted all water from the soil layer.

The soil layer has an infinite capacity for infiltration when the deficit is greater than zero. This means that when the layer is below the saturation level, that all precipitation will infiltrate until the soil is saturated. This is one of the simplifying assumptions in the model since in reality it is possible for the rainfall rate to exceed the infiltration rate of the soil and result in direct runoff when the soil is not saturated. Nevertheless, within this loss model, all precipitation will infiltrate until the soil layer is saturated. All infiltrated water remains in the soil layer and does not percolate out of the layer.

Percolation and Excess Precipitation

Water will percolate out of the bottom of the soil layer if there is precipitation and the deficit is equal to zero. This represents precipitation infiltrating from the soil surface into the soil layer, and then percolating through the soil layer. Percolation water passes out of the bottom of the layer. It is lost from the system, unless the linear reservoir baseflow method is used. In this case only, the percolation water becomes baseflow.

Percolation will continue as long as the soil layer is at maximum storage capacity, and precipitation continues. If the precipitation rate exceeds the percolation rate, then precipitation up to the percolation rate will infiltrate into the soil layer and percolate out of the bottom of the layer. Any precipitation above the percolation rate will become excess precipitation and subject to direct runoff. If the precipitation rate is less than the percolation rate, then all of the precipitation will infiltrate into the soil layer and percolate out of the bottom of the layer. When the precipitation rate is less than the percolation rate there will be no excess precipitation. Percolation can only happen as long as the soil layer remains at saturation.

Evapotranspiration

Evapotranspiration removes water from the soil layer between storm events. The potential evapotranspiration rate is taken from the meteorologic model, where a variety of methods are available for representing that process. The evapotranspiration rate is used as specified by the meteorologic model without any modification. Water is removed from the soil layer at the potential rate for every time interval when there is no precipitation. There is no further evapotranspiration after the water in the soil layer is reduced to zero. Evapotranspiration will start again as soon as water is present in the soil layer and there is no precipitation.

Required Parameters

Parameters that are required to utilize this method within HEC-HMS include the initial deficit [inches or millimeters], maximum deficit [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 Deficit 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 deficit defines the volume of water that is be required to fill the soil layer at the start of the simulation while the maximum deficit specifies the total amount of water the soil layer can hold.

The maximum deficit is typically defined using the product of the effective soil porosity and an assumed active layer depth, but it should be calibrated using observed data. 

The initial deficit must be less than or equal to the maximum deficit.  Both parameters are specified as effective depths (e.g., inches or millimeters). 

The constant rate defines the rate at which precipitation will be infiltrated into the soil layer after the initial deficit has been satisfied in addition to the rate at which percolation occurs once the soil layer is saturated.  Typically, this parameter is equated with the saturated hydraulic conductivity of the soil.

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.

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.