Unit Hydrograph Analysis• Unit Hydrographs (UH)

– Definition and Introduction of UH’s

– Assumptions of UH’s

– Limitations of UH’s

– Derivation of Measured UH

Unit Hydrograph (UH) - Introduction• Definition – It is the

hydrograph which would be generated from a unit depth (1 inch, 1 mm, 1 cm) of uniformly distributed over the watershed area and occurring within specified duration of time (i.e. duration of precipitation)

• Traditional method to evaluate watershed runoff response to rainfall input

• The concept of the unit hydrograph is based on the idea that similar storms will produce similar direct runoff hydrographs because the characteristics of the watershed remain relatively constant.

surface or direct runoff

effective rain

Unit Hydrograph - Introduction

• The UH is based on effective rain, that is the portion of rain remaining after all abstractions/losses (infiltration, detention storage, etc.) are accounted for.

• The UH is the surface or direct runoff, so the base flow must be abstracted from the total runoff hydrograph

• Generally the method is applicable to basins ranging from 100-2000 square miles (260 to 5200 km2)

Unit Hydrograph - Introduction• The UH is based on effective rainfall (ER)

occurring over a set period of time. The UNIT in Unit Hydrograph refers to the rainfall amount, not the duration of the ER

• As soon as rainfall duration changes, so does the UH. Therefore for the same watershed we can have as many UH as periods of ER. Can have any length of time of interest; 1 hour ER, 6 hour ER, 12 hour ER or 24 hour ER UH’s

• The period of time can be any finite duration up to the time of concentration.

• The concept is based on one unit depth of ER falls over the chosen period of time of ER (i.e. 1 cm ER over 1 hour (1 cm/hr), or 1 cm ER over 4 hour (0.25 cm/hour), etc.)

Unit Hydrograph –Introduction

• The ER may be any specified amount, measured as depth on the watershed area, usually 1 mm or 1 cm or 1 inch. A unit value is convenient for when determining effect of different depths of rain proportioning with a unit value is simpler.

• The unit ER then in turn transforms to surface runoff in the UH.

• As such the area under the curve defined by the UH (which is equal to the total volume of runoff) should be equal to the unit depth of ER over the area of the watershed.

• Remember… Area under a hydrograph is equal to volume and in the case of the UH which is direct runoff this will be equivalent to the depth of ER.

Unit Hydrograph - Introduction

• Overall objective in developing UH’s is that once developed the UH can be used to estimate storms of other proportions to determine runoff response.

Unit Hydrograph - Introduction• The UH for a watershed can be developed using a

number of methods. These methods depend on the type of data available.

• A UH can be developed from hydrometeorlogicaldata (runoff and rainfall) for gauged watersheds

• If data is not available it can be generated using synthetic UH’s based on watershed physiographic features (area, length, slope and shape).

• Today we will look at deriving UH based on guaged data. Next week we will look at synthetic UH’s

Unit Hydrograph – Assumption 1• The basis of the UH is based on 3 main

assumptions (Note that Assumptions 1 and 2 together make up the principle of proportionality and Assumption 3 is the principle of superposition):

1. For a given drainage basin, the duration of surface runoff is essentially constant for all uniform intensity storms of the same length, regardless of the differences in the total volume of surface runoff

What does this mean? The time base of the unit hydrograph is constant for a given ER duration. Therefore when you are using a UH (based on 1 cm ER over 2 hours) to determine the response of your watershed to a 5 cm ER over 2 hours, the time base remains the same for the response even though the volume of rainfall is increased.

Ø

Unit Hydrograph – Assumption 22. For a given drainage basin, if two uniform intensity

storms of the same length (but different intensities) produce different total volumes of surface runoff, then the rates of surface runoff at corresponding time, t, after the beginning of two storms, are in the same proportion to each other as the total volumes of surface runoff.

What does this mean? Since the time base of the unit hydrograph is constant for a given ER duration a proportionally larger volume of runoff must be generated for more intense storms. Therefore when you are using a UH (based on 1 cm ER over 2 hours) to determine the response of your watershed to a 5 cm ER over 2 hours, the runoff volume at a given time is proportionally higher. For this situation at each time interval the runoff hydrograph would be 5 times higher of a value than the UH.

Ø

Unit Hydrograph – Proportionality (Assumption 1 and 2)

Example 1

Unit Hydrograph –Proportionality

(Assumption 1 and 2)

Example 2

Unit Hydrograph – Assumption 3

3. The time distribution of surface runoff from a given storm period is independent of concurrent runoff from antecedent storm periods.

What does this mean? The resulting hydrograph from continuous and/or isolated periods of ER can be summed together by considering them individual hydrographs from each ER condition

Ø

Unit Hydrograph – Superposition (Assumption 3)

Example 1

Unit Hydrograph –Superposition

(Assumption 3)

Example 2

Unit Hydrograph

–Assumptions

UH – Derivation from Measured Data

• UH’s for a watershed are derived either from runoff (stream guage) and rainfall data for a gauged watershed OR by developing synthetic UH’s for ungauged watersheds.

• This week we will focus on deriving UH’sfrom gauged data, the following unit we will look at synthetic methods

• So how do we develop a unit hydrograph from gauged data?

• Step 1 – obtain effective rainfall amount

• Step 2 – obtain effective rainfall duration• Step 3 – separate total hydrograph into

direct runoff hydrograph and baseflowhydrograph

• Step 4 – divide the ordinates of surface runoff hydrograph by the amount of effective rainfall to obtain corresponding ordinates of the UH of the duration of the effective rainfall

UH – Derivation from Measure Data

1. Baseflowseparated to provide direct runoff hydrograph

2. Effective rainfall duration is provided and UH will be a 3 hour UH

3. Effective rainfall amount not provided – but can be solved from direct runoff values

4. Divide ordinates of runoff hydrograph by effective rainfall depth to obtain ordinates of 3 hour UH

3 hr UH Example

UH –Example Solution

Unit Hydrograph – Limitations• Limitations exist for UH’s and these should be

understood by those using the methods• Space Invariance of Effective Rainfall.

• Rainfall is assumed to be distributed in the same spatial (space) pattern for all rainfall storms occurring over the entire watershed

• ER of specified duration seldom occurs uniformly over a watershed of reasonable size.

• Therefore spatial invariance of ER is an assumption not a reality and becomes less ideal with larger watersheds

• One method to reduce the amount of errors due to non uniform rain across a watershed is by subdividing your watershed into smaller subwatersheds which are more likely to have more uniform conditions.

Unit Hydrograph – Limitations• Time Invariance of Effective Rainfall.

• Rainfall is assumed to be distributed in the same temporal (time) pattern for all rainfall storms occurring over the entire watershed

• ER usually does not occur uniformly WRT time and rainfall intensity can and typically does vary with time.

• However, the level of impact of variations or rainfall with time is dependant on the size of the watershed.

• Short duration high intensity rainfall may show significant variance on runoff from small watersheds but may not even be noticed in larger watersheds.

Unit Hydrograph – Limitations• Validity of Linearity

• In order for concepts of superposition and proportionality to work, systems must be linear. Watersheds are not linear.

• It is common for storms of same duration to have different time bases, and their ordinates are not in proportion to their volumes

• Watershed conditions can be variable and impact the response such as:

• Soil AMC or frost conditions• Forest growth active or dormant• Water levels within lakes and available watershed storage• Snow coverage

• Having different unit hydrographs for a range of conditions (such as intensity) is one method to assist in overcoming these limitations.

• Despite the assumptions of linearity and rainfall spatial and temporal distribution the UH method is still valuable.

• Given the limitations of the assumptions how do we manufacture a representative UH?

• The procedure to develop a UH of desired rainfall duration is to select a number of isolated rainfall storms of desired duration and assess their corresponding runoff hydrographs

• Each UH would have a unique form based on variations within the system and rainfall.

• Therefore an average UH is usually developed based on a number of storms and runoff responses.

Representative UH

• The procedure to compute an average peak flowand an average time to peak based on all the uniquely shaped UH’s available.

• The average UH can then be graphically sketched to conform to the shapes of other unit hydrographs such that it passes through the computed average peak flow at a location equal to the average time to peak.

• The unit hydrograph then must be constructed such that the area under the graph is equal to a unit volume of runoff over the watershed area (i.e. 1”, 1 cm, 1 mm, etc.).

Representative UH

• The average peak flow at a location equal to average time to peak is not calculated from an arithmetic averaging.

• Since the peaks may not exist at the same time the simple averaging procedure may reduce the overall peak.

Representative UH

• Storms should be restricted to:

1. Storms should be of approximately same duration within +/- 10%

2. Storms should be isolated and occur individually

3. Storms are approximately uniform during their duration of effective rainfall and spatially over the watershed.

Representative UH – Suitable Storms

• A screening process should be applied to selecting suitable rainfall storms to determine the most suitable UH

1. Duration of the selected rainfall storms should be 10 to 30% of the watershed lag time.

Representative UH – Suitable Storms

2. Storms should be flood producing storms such that surface runoff hydrographs for the selected rainfall storms in Step 1 should range from 1 to 5 cm.

3. A suitable number of rainfall storms and corresponding surface runoff hydrographs be analyzed to develop the most representative UH, 5 storms is sometimes suggested but if more is available, they should also be used.

4. Surface runoff ordinates of each rainfall storm hydrograph should be reduced (i.e. changed to UH ordinates) such that each event represents 1”or 1 cm or 1 mm of surface runoff.

5. The final UH is then obtained by averaging a number of UH’s for the specific time duration

Representative UH – Suitable Storms

• Often simple suitable storms are not available. It is then may be necessary to use complex storms

• This requires a separate procedure than that described previously

• If the storm pattern is such that it can be separated into isolated periods of rainfall, then UHs can be derived for all the periods using hydrograph separation

• These can be combined in a suitable manner to obtain a single average UH.

• However, complex storm often consists of consecutive periods of varying rainfall amounts

Representative UH – Complex Storms

• Methods exist for separating complex storms to derive unit hydrographs

• These methods are beyond the scope of this course.

Representative UH – Complex Storms

• Once a representative UH has been developed from streamflow data for a watershed, it can be used to estimate runoff from virtually any rain event.

• Methods are used to lag the hydrograph such that a UH can be adjusted for storms of any duration.

• These methods will be introduced in the next lecture.

Representative UH – Uses