Basic Hydrologic Science Course

Unit Hydrograph Theory

Application of unit hydrograph theory requires adapting the theory for real world factors.

For example, when using the Sacramento-Soil Moisture Accounting model, a different type of unit hydrograph is used. Also, it is typically necessary to account for excess precipitation amounts that are different than one depth unit, or that occur over various durations, or over multiple time periods.

Unit hydrograph theory can be applied to both rainfall and snowmelt events.

Finally, unit hydrographs may exist based on different units of measurement.

In this section you will learn to:

- Explain key issues for application of unit hydrograph theory
- Identify reasons that some rainfall events may not be accurately represented by a unit hydrograph
- Describe the process for application of unit hydrographs to storms covering multiple time durations
- Explain the impact of using English or metric units of measure

Topics in this section include:

Choose a section above by clicking on it, or scroll down to continue the module.

The majority of River Forecast Centers (RFCs) with the National Weather Service use the Sacramento Soil Moisture Accounting model (the Sacramento model). This model already accounts for the portion of quick-response runoff that occurs just below the surface, or interflow. Therefore, when using the Sacramento model, the unit hydrograph should not account for interflow again.

Thus, for RFCs that use the Sacramento model, the unit hydrograph has had both baseflow and interflow separated out in the derivation. This means that the unit hydrograph will only account for the surface runoff.

The primary difference when using the Sacramento model is that the unit hydrograph will peak faster and higher than the more traditional unit hydrograph. This is because the surface runoff will reach the stream faster than the subsurface runoff, or interflow.

Notice here that the areas under the two curves are equal because they both represent one unit of runoff.

How do we adapt a unit hydrograph for a storm with variations in rainfall magnitude over time?

Here we have a 6-hour unit hydrograph where 1 depth unit of excess rainfall results in a peak flow shown here in green. But we actually had 2 depth units of excess precipitation in that 6 hours.

So we apply a simple proportional adjustment so that 2 depth units result in a peak flow that is 2 times greater than with 1 depth unit.

Similarly, 0.5 depth units of excess precipitation would cause a flow magnitude only half of the magnitude that one depth unit of excess precipitation would cause.

Recall that a 6-hour unit hydrograph means that the excess precipitation occurred in 6 hours.

Now let’s consider a situation where the 1 depth unit of excess precipitation occurred in 1 hour instead of 6 hours, then the watershed would respond faster and thus, the peak would occur sooner. The peak would also be of greater magnitude because there would still be the same volume under the curve as there was with the 6-hour excess rainfall.

Similarly, if our period of excess was 12 hours instead of 6 hours, then the response would show a peak later and of lesser magnitude, but still with the same volume of runoff under the curve.

It is important to use the correct duration when applying a unit hydrograph. But the “correct” unit hydrograph duration may not exist.

For example, you may have a 6-hour unit hydrograph, but your current storm only produced 1 hour of excess precipitation. There are certain methodologies that can be applied to the available unit hydrograph to produce a unit hydrograph of either longer or shorter duration. The “Lagging” and “S-Curve” methods are two examples of these approaches.

Now let’s be more realistic and complicate things a bit. Consider a situation where the excess rainfall occurs over a 24-hour period. The hourly amounts vary from less than 0.1 depth unit to greater than 0.5 depth units of excess rainfall.

The only available unit hydrograph is for a 6-hour duration. Therefore, the available unit hydrograph does not match our excess rainfall duration of 24 hours.

First, we examine the bar graph more closely to see if the 24-hour period can be broken into 6-hour segments. It appears we can get four 6-hour periods with relatively consistent magnitudes as seen in the color segments.

Now that we have four periods of excess rainfall that each match the duration of the unit hydrograph, we can apply the unit hydrograph to each of the four 6-hour periods.

Notice the adjusted unit hydrographs for each period. Of course period 3, in red, is going to have a higher magnitude graph to match the higher magnitude excess rainfall.

Finally, we can take the sum of each of the four hydrographs and get one hydrograph as shown with the black line. In this way we used the 6-hour unit hydrograph to get a hydrograph for a 24-hour event. That is, we used multiple time periods to get a single hydrograph for the whole storm. This final hydrograph shows the quick-response runoff for that 24-hour excess rainfall event.

This process of combining hydrographs is sometimes referred to as convolution.

The input to runoff models can be either rainfall, snowmelt, or a combination of both. Unit hydrograph theory is applied within the runoff model.

Therefore, it does not matter if the excess precipitation used with the unit hydrograph was from rainfall or snowmelt. The runoff model, and thus unit hydrograph theory, will treat both inputs the same. However, forecasters should be aware of related issues such as frozen ground or river ice when dealing with snowmelt runoff.

How would a unit hydrograph be adjusted to convert from English, where the unit is 1 inch, to metric, where the unit for example may be 1 centimeter?

Choose the best response:

a) All data points on the metric graph must be multiplied by 2.54 for it
to work.

b) When applied, the two unit hydrographs will show the same thing.

c) The unit hydrograph must be re-derived with metric units for excess precipitation,
streamflow, and basin area.

Expert answer: The correct answer is b). Whether the unit hydrograph is in English or metric units, when applied to an actual precipitation event, it will arrive at the same timing and magnitude of streamflow response.

Let’s consider two unit hydrographs for the same basin. For the green line the unit is 1.00 inch. For the blue line the unit is 1.0 cm. Since 1 cm is only 39% of 1 inch, we can see that it is a curve with lower magnitudes, but the same timing.

Now let’s consider a storm that produces 0.75 inches, or 1.9 cm, of excess precipitation. The English unit hydrograph will now be adjusted downward by a factor of 0.75 since the excess precipitation is only 0.75 of a unit. The metric unit hydrograph will be adjusted upward by a factor of 1.9 since there were 1.9 units of excess. The resulting hydrograph will end up the same in either case as shown by the red curve.

(Choose the best response.)

a) 500

b) 1200

c) 2000

d) 5000

(Choose the best response.)

The correct answer is c), 2000.

If 1 inch produces 1000 cubic feet per second, then twice as much excess rainfall, or 2 inches, produces twice as much discharge, or 2000 cubic feet per second.

The correct answer is e).

The unit hydrograph will show only half of the peak magnitude if only 0.5 units of excess precipitation occurred. The timing and shape should not change.

The correct answer is a).

The 3-hour unit hydrograph will peak faster and higher than the 6-hour unit hydrograph, but the volume of water it represents should stay the same.

**End of Section Four: Application of Unit Hydrograph Theory**