Loss Methods: Deficit and Constant Method

Loss Methods (Infiltration and Abstractions)

While a subbasin element conceptually represents infiltration, surface runoff, and subsurface processes interacting together, the actual infiltration calculations are performed by a Loss Method contained within the subbasin.

A total of twelve different Loss Methods are provided. Some of the methods are designed primarily for simulating events while others are intended for continuous simulation. All of the methods conserve mass. That is, the sum of infiltration and precipitation left on the surface will always be equal to total incoming precipitation. The suitability of the various methods for event and continuous simulation is shown in the following table.

The Loss Method for a subbasin is selected on the Component Editor for the subbasin element as shown in the following figure. 

1) Deficit and Constant Loss

With this method, an initial volume must be satisfied and any additional precipitation is lost at a constant rate. Anything that is not infiltrated becomes excess precipitation. However this method is capable of continuous simulation by accounting for the subbasin moisture state. To do this, a maximum moisture deficit and evapotranspiration data are also required. Evapotranspiration increases the subbasin moisture deficit during periods of no precipitation. In other words, evapotranspiration acts to dry out the soil. 

The infiltration start at an initially high rate and decrease exponentially towards an asymptotic limit called the saturated hydraulic connectivity. 
When using the Deficit and Constant Loss Method there's only an initial loss volume which is the green rectangle in the image below and a constant rate which is the top of the red rectangle on the image. To recreate this exponential curve as such just like with the initial and constant method you'll typically overestimate infiltration rates at some times and underestimate them at other times in order to provide a good fit throughout the entire simulation time window.

Parameters estimation

Initial Deficit - When estimating the initial deficit, it's important to consider the weather conditions before the simulation starts. For example, did it rain a week ago, or has it been dry for months? However, when using this method, it is suggested to start the simulations well before the period you are interested in. This way, the initial conditions don’t matter much, as long as the evaporation rate is reasonable and the maximum deficit is set sensibly.

Maximum Deficit - This parameter represents how dry the soil can get after losing water through gravity drainage, evaporation, and plant transpiration. This value is measured as an effective depth in inches or millimeters. Typically, it’s estimated by finding the difference between saturation storage (the maximum water the soil can hold when fully saturated) and wilting point storage (the water so tightly bound to soil particles that plants can’t use it). To estimate this, we can assume an active soil layer depth of 24 to 36 inches. A good way to estimate saturation storage is by using the soil’s effective porosity. Wilting point storage, on the other hand, is usually defined as the water left in a fully saturated soil column after being exposed to a pressure of -15 bar (or 217.5 psi). You can estimate these values based on soil texture data from a soil database and compare them to values found in scientific literature.

Constant Loss Rate - you can first determine soil texture from a database and relate it to published values of saturated hydraulic conductivity. For example, if more than half of a subbasin consists of silt loam, a good starting point is using a known hydraulic conductivity value for that soil type and then adjusting as needed.

Impervious areas (like pavement or buildings) - GIS tools like the National Land Cover Database can help estimate them. Also, be sure to include large water bodies, like lakes and reservoirs, because rain falling on them does not infiltrate into the soil.

An example of surficial texture from soil database is show in the figure below:

Calibration Techniques

When calibrating the Deficit and Constant method, first you have to adjust the initial parameter estimates until the start of runoff in my model matches the observed data. Specifically, you have to focus on getting the timing right for when runoff begins to rise. After that, you adjust the model to match the total runoff volume.

For example, in this case, the observed flow is shown in black, and the computed flow is in blue. While I’ve matched the timing of runoff, my peak flow on September 10th is too high, so I’ll need to reduce my constant loss rate. When calibrating, always use multiple statistical metrics, like Nash-Sutcliffe Efficiency, Root Mean Square Error and Percent Bias, instead of relying only on visual comparison. These metrics provide more objective ways to evaluate model performance.

Advantages & Disadvantages

The Deficit and Constant method has similar advantages to the Initial and Constant method:
✅ It’s simple and widely used.
✅ Its parameters can be estimated from observed data.
✅ It’s efficient and easy to calibrate.

However, one key advantage of this method is that it accounts for evapotranspiration, meaning infiltrated water can later be removed from the system.

The Deficit Constant Loss Method uses a single soil layer to account for continuous changes in moisture (humidity) content. Using the Deficit Constant Loss Method allows for continuous simulation. It should be used in combination with a Canopy Method that will extract water from the soil in response to potential evapo-transpiration computed in the Meteorologic Model. The soil layer will dry out between precipitation events as the canopy extracts soil water. There will be no soil water extraction unless a Canopy Method is selected. It may also be used in combination with a Surface Method that will hold water on the land surface. The water in surface storage infiltrates to the soil layer. 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.

2) Initial and Constant Loss

With the Initial and Constant method, all rainfall is lost (soaked into the ground) until a certain initial loss amount is reached. After that, any extra rain is lost at a constant rate. Any rain that is not lost becomes runoff.

One important thing: this method does not allow for water to be removed from the ground once it infiltrates. If you need to simulate water leaving the soil (through processes like evaporation), you should use a more advanced infiltration method in HEC-HMS. Here are a few options:

1️⃣ Deficit and Constant Loss Method

• Similar to the Initial and Constant method but allows for water to be removed from the soil over time.
• Includes a deficit term, which represents how much water the soil can still absorb before it reaches full capacity.
• Can simulate water loss due to evapotranspiration, making it more realistic for long-term simulations.

2️⃣ Green & Ampt Method

• Based on soil physics, providing a more detailed representation of infiltration.
• Uses parameters like soil porosity and suction head to model how water moves into the soil.
• Can be used for storm events where infiltration changes dynamically over time.

3️⃣ SCS Curve Number (CN) Method

• Often used for watershed-scale hydrology.
• Accounts for antecedent moisture conditions (how wet the soil was before the rainfall event).
• While it doesn’t directly simulate evapotranspiration, it provides a more flexible way to estimate runoff in different conditions.

4️⃣ Gridded Deficit and Constant Method

• A spatially distributed version of the Deficit and Constant method.
• Can be used for models that require a more detailed, grid-based approach to infiltration and soil moisture changes.

Which Method Should You Use?

• If you want a simple improvement over Initial and Constant, go with Deficit and Constant.
• If you need a more physically based model, Green & Ampt is a good choice.
• If you’re modeling large watersheds and need a simpler empirical approach, SCS Curve Number is widely used.
• If you’re working with gridded models, Gridded Deficit and Constant might be best.

Infiltration typically starts at a high rate and then gradually decreases over time, approaching a limit known as saturated hydraulic conductivity. However, when using the Initial and Constant loss method, infiltration is simplified:

• Initial loss volume (represented by the green rectangle in the image).
• Constant infiltration rate (shown as the top of the rectangle).

Because this method does not follow the natural exponential decline of infiltration, it often overestimates infiltration at some points and underestimates it at others to balance the overall simulation.
(Instead, the Deficit and Constant Method allows infiltrated water to be extracted over time through evapotranspiration).

To use this method, you need to provide two main parameters:
1️⃣ Initial loss (the amount of rain that must be absorbed before runoff begins).
2️⃣ Constant infiltration rate (the fixed rate at which water continues to infiltrate after initial loss is satisfied).

There is also an optional parameter: the directly connected impervious area.

• If you set this value to zero, infiltration is calculated for the entire sub-basin.
• If you specify a non-zero value, infiltration will not be calculated for that portion, and all rainfall on that area will turn directly into runoff.

If you're modeling a completely asphalted area (so 100% impermeable), you should set the Directly Connected Impervious Area (DCA) = 100% or 1.0 (depending on the unit used in the software).

What happens when Impervious = 100%?

✅ All rainfall becomes immediate runoff.
❌ Infiltration is not calculated because there is no permeable soil.

This is typical for surfaces such as:

• Asphalt roads
• Building rooftops
• Sidewalks that are fully paved and connected to a drainage system

If you're modeling a partially impervious area (e.g., a gravel parking lot or a road with gaps between tiles), you should use a lower value, like DCA = 60-80%, to indicate that a small portion of the rain can still infiltrate the soil.

💡 Note: If you want to simulate the difference between asphalt with and without drainage, you might:

• DCA = 100% → Asphalt connected to the drainage system (all rain becomes runoff).
• DCA = 0% and a very low infiltration rate → Asphalt without drainage (water stagnates and infiltrates very slowly).

Example

This example shows how excess precipitation is calculated using the Initial and Constant method. In the first time step, half an inch of rain is lost to initial losses. After that, precipitation is lost at a constant rate of 0.25 inches per hour.

Parameters estimation

Initial Loss - When estimating the initial loss volume, you need to consider the conditions before the start of your simulation. For example, did it rain recently, like a week before the start, or has it been dry for a long time? You also need to think about how long it usually takes for the rainwater to be removed from the system by drainage or evaporation.

Constant Rate - When estimating the constant loss rate for your watershed, I recommend that you don’t use actual parameter values from a soil database. Instead, check the soil type and texture from the database, then look up the saturated hydraulic conductivity values for the main soil types. For example, in this case, more than half of the sub-basin is covered by silty loam, so you can start by using the saturated hydraulic conductivity estimate for silty loam and then calibrate as needed.

Impervious Area - When estimating the percent impervious area, you can use GIS data like the National Land Cover Database. Also, don’t forget to include large bodies of water like lakes or reservoirs in your estimates, because rain falling directly onto these areas doesn’t infiltrate into the ground.

Calibration Techniques

When calibrating the Initial and Constant method, first, it's suggested to adjust the initial parameter estimates until you get the timing of the runoff correct. Specifically, you have to try to match the time when the computed runoff starts to rise, as compared to the observed runoff.

Next, you focus on matching the total runoff volume. In the example shown, the observed flow is represented by the black line, and the computed flow is shown in blue.
In the case shown in the picture below, the timing of runoff initiation is matched pretty well, but the initial runoff is too high, so you need to increase the initial loss and/or the constant rate.

When calibrating, it’s important not to just rely on a simple visual check ("eyeball test") to see if your model is accurate. You should also use statistical metrics, like the Nash-Sutcliffe Efficiency (NSE), which is available in HEC-HMS for locations with observed data. Use these metrics to measure the model’s performance from different angles and make sure the results are as accurate as possible.