# Chapter 5 Tabular Hydrograph Method Tabular Hydrograph Method

## Transcript Of Chapter 5 Tabular Hydrograph Method Tabular Hydrograph Method

CChahptear 5pter 5

Tabular Hydrograph Method Tabular Hydrograph Method

Technical Release 55 Urban Hydrology for Small Watersheds

This chapter presents the Tabular Hydrograph method of computing peak discharges from rural and urban areas, using time of concentration (Tc) and travel time (Tt) from a subarea as inputs. This method approximates TR-20, a more detailed hydrograph procedure (SCS 1983).

The Tabular method can develop partial composite flood hydrographs at any point in a watershed by dividing the watershed into homogeneous subareas. In this manner, the method can estimate runoff from nonhomogeneous watersheds. The method is especially applicable for estimating the effects of land use change in a portion of a watershed. It can also be used to estimate the effects of proposed structures.

Input data needed to develop a partial composite flood hydrograph include (1) 24-hour rainfall (in), (2) appropriate rainfall distribution (I, IA, II, or III), (3) CN, (4) Tc (hr), (5) Tt (hr), and (6) drainage area (mi2).

Tabular Hydrograph method exhibits

Exhibit 5 (5-I, 5-IA, 5-II, and 5-III) shows tabular discharge values for the various rainfall distributions. Tabular discharges expressed in csm/in (cubic feet of discharge per second per square mile of watershed per inch of runoff) are given for a range of subarea Tc’s from 0.1 to 2 hours and reach Tt’s from 0 to 3 hours.

The exhibit was developed by computing hydrographs for 1 square mile of drainage area for selected Tc’s and routing them through stream reaches with the range of Tt’s indicated. The Modified Att-Kin method for reach routing, formulated by SCS in the late 1970’s, was used to compute the tabular hydrographs (Comer et al., 1981). A CN of 75 and rainfall amounts generating appropriate Ia/P ratios were used. The resulting runoff estimate was used to convert the hydrographs in exhibits 5-I through 5-III to cubic feet of discharge per second per square mile of watershed per inch of runoff.

An assumption in development of the tabular hydrographs is that all discharges for a stream reach flow at the same velocity. By this assumption, the subarea flood hydrographs may be routed separately and added at the reference point. The tabular hydrographs in exhibit 5 are prerouted hydrographs.

For Tt’s other than zero, the tabular discharge values represent the contribution from a single subarea to the composite hydrograph at Tt downstream.

Information required for Tabular Hydrograph method

The following information is required for the Tabular method:

1. Subdivision of the watershed into areas that are relatively homogeneous and have convenient routing reaches.

2. Drainage area of each subarea in square miles.

3. Tc for each subarea in hours. The procedure for estimating Tc is outlined in chapter 3. Worksheet 3 (appendix D) can be used to calculate Tc.

4. Tt for each routing reach in hours. The procedure for estimating Tt is outlined in chapter 3. Worksheet 3 can be used to calculate Tt through a subarea for shallow concentrated and open channel flow.

5. Weighted CN for each subarea. Table 2-2 shows CN’s for individual hydrologic soil cover combinations. Worksheet 2 can be used to calculate the weighted runoff curve number.

6. Appropriate rainfall distribution according to figure B-2 (appendix B).

7. The 24-hour rainfall for the selected frequency. Appendix B contains rainfall maps for various frequencies (figures B-3 to B-8).

8. Total runoff (Q) in inches computed from CN and rainfall.

9. Ia for each subarea from table 5-1, which is the same as table 4-1.

10. Ratio of Ia/P for each subarea. If the ratio for the rainfall distribution of interest is outside the range shown in exhibit 5, use the limiting value.

(210-VI-TR-55, Second Ed., June 1986)

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Chapter 5

Tabular Hydrograph Method

Technical Release 55 Urban Hydrology for Small Watersheds

Development of composite flood hydrograph

This section describes the procedure for developing the peak discharge and selected discharge values of a composite flood hydrograph.

Selecting Tc and Tt

First, use worksheet 5a to develop a summary of basic watershed data by subarea. Then use worksheet 5b to develop a tabular hydrograph discharge summary; this summary displays the effect of individual subarea hydrographs as routed to the watershed point of

Table 5-1

Curve number

40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69

Ia values for runoff curve numbers

Ia (in)

3.000 2.878 2.762 2.651 2.545 2.444 2.348 2.255 2.167 2.082 2.000 1.922 1.846 1.774 1.704 1.636 1.571 1.509 1.448 1.390 1.333 1.279 1.226 1.175 1.125 1.077 1.030 0.985 0.941 0.899

Curve number

70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98

Ia (in)

0.857 0.817 0.778 0.740 0.703 0.667 0.632 0.597 0.564 0.532 0.500 0.469 0.439 0.410 0.381 0.353 0.326 0.299 0.273 0.247 0.222 0.198 0.174 0.151 0.128 0.105 0.083 0.062 0.041

interest. Use ∑ Tt for each subarea as the total reach travel time from that subarea through the watershed to

the point of interest. Compute the hydrograph coordinates for selected ∑ Tt’s using the appropriate sheets in exhibit 5. The flow at any time is:

q = qtAmQ where:

[eq. 5-1]

q = hydrograph coordinate (cfs) at hydrograph time t

qt = tabular hydrograph unit discharge from exhibit 5 (csm/in)

Am = drainage area of individual subarea (mi2) Q = runoff (in)

Since the timing of peak discharge changes with Tc and Tt, interpolation of peak discharge for Tc and Tt values for use in exhibit 5 is not recommended. Interpolation may result in an estimate of peak discharge that would be invalid because it would be lower than either of the hydrographs. Therefore, round the actual values of Tc and Tt to values presented in exhibit 5. Perform this rounding so that the sum of the selected table values is close to the sum of actual Tc and Tt. An acceptable procedure is to select the results of one of three rounding operations:

1. Round Tc and Tt separately to the nearest table value and sum,

2. Round Tc down and Tt up to nearest table value and sum,

3. Round Tc up and Tt down to nearest table value and sum.

From these three alternatives, choose the pair of

rounded Tc and Tt values whose sum is closest to the sum of the actual Tc and Tt. If two rounding methods produce sums equally close to the actual sum, use the

combination in which rounded Tc is closest to actual Tc. An illustration of the rounding procedure is as follows:

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(210-VI-TR-55, Second Ed., June 1986)

Chapter 5

Tabular Hydrograph Method

Technical Release 55 Urban Hydrology for Small Watersheds

Actual values

Tc

1.1

Tt

1.7

Sum

2.8

Table values by rounding method

1

2

3

1.0

1.0

1.25

1.5

2.0

1.5

2.5

3.0

2.75

In this instance, the results from method 3 would be selected because the sum 2.75 is closest to the actual sum of 2.8.

Selecting Ia / P

The computed Ia / P value can be rounded to the nearest Ia / P value in exhibits 5-I through 5-III, or the hydrograph values (csm/in) can be linearly interpolated because Ia / P interpolation generally involves peaks that occur at the same time.

Summing for the composite hydrograph

The composite hydrograph is the summation of prerouted individual subarea hydrographs at each time shown on worksheet 5b. Only the times encompassing the expected maximum composite discharge are summed to define a portion of the composite hydrograph.

If desired, the entire composite hydrograph can be approximated by linear extrapolation as follows:

1. Set up a table similar to worksheet 5b. Include on this table the full range of hydrograph times displayed in exhibit 5.

2. Compute the subarea discharge values for those times and insert them in the table.

3. Sum the values to obtain the composite hydrograph.

4. Apply linear extrapolation to the first two points and the last two points of the composite hydrograph. The volume under this approximation of the entire composite hydrograph may differ from the computed runoff volume.

Limitations

The Tabular method is used to determine peak flows and hydrographs within a watershed. However, its

accuracy decreases as the complexity of the watershed increases. If you want to compare present and developed conditions of a watershed, use the same procedure for estimating Tc for both conditions.

Use the TR-20 computer program (SCS 1983) instead of the Tabular method if any of the following conditions applies:

• Tt is greater than 3 hours (largest Tt in exhibit 5). • Tc is greater than 2 hours (largest Tc in exhibit 5). • Drainage areas of individual subareas differ by a

factor of 5 or more. • The entire composite flood hydrograph or entire

runoff volume is required for detailed flood routings. The hydrograph based on extrapolation is only an approximation of the entire hydrograph. • The time of peak discharge must be more accurate than that obtained through the Tabular method.

The composite flood hydrograph should be compared with actual stream gage data where possible. The instantaneous peak flow value from the composite flood hydrograph can be compared with data from USGS curves of peak flow versus drainage area.

(210-VI-TR-55, Second Ed., June 1986)

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Chapter 5

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Technical Release 55 Urban Hydrology for Small Watersheds

Examples

A developer proposes to put a subdivision, Fallswood, in subareas 5, 6, and 7 of a watershed in Dyer County, northwestern Tennessee (see sketch below). Before approving the developer’s proposal, the planning board wants to know how the development would affect the 25-year peak discharge at the downstream end of subarea 7. The rainfall distribution is type II (figure B-2), and the 24-hour rainfall (P) is 6.0 inches (figure B-6).

Example 5-1

Compute the 25-year frequency peak discharge at the downstream end of subarea 7 for present conditions, using worksheets 5a and 5b. To do this, first calculate the present condition CN, Tc, and Tt for each subarea, using the procedures in chapters 2 and 3. Enter the values on worksheet 5a (figure 5-1).

Next, compute the prerouted hydrograph points for each subarea hydrograph over a range of time near the peak discharge using worksheet 5b (figure 5-2) and the appropriate exhibit 5. For example, for subarea 4, in which Tc= 0.75 hr, refer to sheet 6 of exhibit 5-II. With ΣTt of 2.00 hr (the sum of downstream travel time through subareas 5 and 7 to the outlet) and Ia / P of 0.1, the routed peak discharge of subarea 4 at the outlet of subarea 7 occurs at 14.6 hr and is 274 csm/in.

2

1

4 3

6 5

7

1 Subarea

Stream

Watershed boundary Subarea boundary

Solving equation 5-1 with appropriate values provides the peak discharge (q) for subarea 4 at 14.6 hr:

q = qt(AmQ) = (274)(0.70) = 192 cfs.

Once all the prerouted subarea hydrographs have been tabulated on worksheet 5b, sum each of the time columns to obtain the composite hydrograph. The resulting 25-year frequency peak discharge is 720 cfs at 14.3 hr (figure 5-2).

Example 5-2

Compute the 25-year frequency peak discharge at the downstream end of subarea 7 for the developed conditions, using worksheets 5a and 5b.

First, calculate the developed condition CN, Tc, and Tt for each subarea, using the procedures in chapters 2 and 3. Enter the values on worksheet 5a (figure 5-3).

Next, compute the prerouted hydrograph points for each subarea hydrograph over a range of time near the peak discharge using worksheet 5b (figure 5-4) and the appropriate exhibit 5. For example, for subarea 6, in which Tc= 1.0 hr, refer to sheet 7 of exhibit 5-II. With ΣTt of 0.5 hr (downstream travel time through subarea 7 to the outlet) and Ia / P of 0.1, the peak discharge of subarea 6 at the outlet of the watershed occurs at 13.2 hr and is 311 csm/in. Solving equation 5-1 provides the peak discharge (q):

q = q t (AmQ) = (311)(1.31) = 407 cfs

Once all the prerouted subarea hydrographs have been tabulated on worksheet 5b, sum each of the time columns to obtain the composite hydrograph. The resulting 25-year frequency peak discharge is 872 cfs

Comparison

According to the results of the two examples, the proposed subdivision at the downstream end of subarea 7 is expected to increase peak discharge from 720 to 872 cfs and to decrease the time to peak from 14.3 to 13.6 hr.

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(210-VI-TR-55, Second Ed., June 1986)

Tabular Hydrograph Method Tabular Hydrograph Method

Technical Release 55 Urban Hydrology for Small Watersheds

This chapter presents the Tabular Hydrograph method of computing peak discharges from rural and urban areas, using time of concentration (Tc) and travel time (Tt) from a subarea as inputs. This method approximates TR-20, a more detailed hydrograph procedure (SCS 1983).

The Tabular method can develop partial composite flood hydrographs at any point in a watershed by dividing the watershed into homogeneous subareas. In this manner, the method can estimate runoff from nonhomogeneous watersheds. The method is especially applicable for estimating the effects of land use change in a portion of a watershed. It can also be used to estimate the effects of proposed structures.

Input data needed to develop a partial composite flood hydrograph include (1) 24-hour rainfall (in), (2) appropriate rainfall distribution (I, IA, II, or III), (3) CN, (4) Tc (hr), (5) Tt (hr), and (6) drainage area (mi2).

Tabular Hydrograph method exhibits

Exhibit 5 (5-I, 5-IA, 5-II, and 5-III) shows tabular discharge values for the various rainfall distributions. Tabular discharges expressed in csm/in (cubic feet of discharge per second per square mile of watershed per inch of runoff) are given for a range of subarea Tc’s from 0.1 to 2 hours and reach Tt’s from 0 to 3 hours.

The exhibit was developed by computing hydrographs for 1 square mile of drainage area for selected Tc’s and routing them through stream reaches with the range of Tt’s indicated. The Modified Att-Kin method for reach routing, formulated by SCS in the late 1970’s, was used to compute the tabular hydrographs (Comer et al., 1981). A CN of 75 and rainfall amounts generating appropriate Ia/P ratios were used. The resulting runoff estimate was used to convert the hydrographs in exhibits 5-I through 5-III to cubic feet of discharge per second per square mile of watershed per inch of runoff.

An assumption in development of the tabular hydrographs is that all discharges for a stream reach flow at the same velocity. By this assumption, the subarea flood hydrographs may be routed separately and added at the reference point. The tabular hydrographs in exhibit 5 are prerouted hydrographs.

For Tt’s other than zero, the tabular discharge values represent the contribution from a single subarea to the composite hydrograph at Tt downstream.

Information required for Tabular Hydrograph method

The following information is required for the Tabular method:

1. Subdivision of the watershed into areas that are relatively homogeneous and have convenient routing reaches.

2. Drainage area of each subarea in square miles.

3. Tc for each subarea in hours. The procedure for estimating Tc is outlined in chapter 3. Worksheet 3 (appendix D) can be used to calculate Tc.

4. Tt for each routing reach in hours. The procedure for estimating Tt is outlined in chapter 3. Worksheet 3 can be used to calculate Tt through a subarea for shallow concentrated and open channel flow.

5. Weighted CN for each subarea. Table 2-2 shows CN’s for individual hydrologic soil cover combinations. Worksheet 2 can be used to calculate the weighted runoff curve number.

6. Appropriate rainfall distribution according to figure B-2 (appendix B).

7. The 24-hour rainfall for the selected frequency. Appendix B contains rainfall maps for various frequencies (figures B-3 to B-8).

8. Total runoff (Q) in inches computed from CN and rainfall.

9. Ia for each subarea from table 5-1, which is the same as table 4-1.

10. Ratio of Ia/P for each subarea. If the ratio for the rainfall distribution of interest is outside the range shown in exhibit 5, use the limiting value.

(210-VI-TR-55, Second Ed., June 1986)

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Chapter 5

Tabular Hydrograph Method

Technical Release 55 Urban Hydrology for Small Watersheds

Development of composite flood hydrograph

This section describes the procedure for developing the peak discharge and selected discharge values of a composite flood hydrograph.

Selecting Tc and Tt

First, use worksheet 5a to develop a summary of basic watershed data by subarea. Then use worksheet 5b to develop a tabular hydrograph discharge summary; this summary displays the effect of individual subarea hydrographs as routed to the watershed point of

Table 5-1

Curve number

40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69

Ia values for runoff curve numbers

Ia (in)

3.000 2.878 2.762 2.651 2.545 2.444 2.348 2.255 2.167 2.082 2.000 1.922 1.846 1.774 1.704 1.636 1.571 1.509 1.448 1.390 1.333 1.279 1.226 1.175 1.125 1.077 1.030 0.985 0.941 0.899

Curve number

70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98

Ia (in)

0.857 0.817 0.778 0.740 0.703 0.667 0.632 0.597 0.564 0.532 0.500 0.469 0.439 0.410 0.381 0.353 0.326 0.299 0.273 0.247 0.222 0.198 0.174 0.151 0.128 0.105 0.083 0.062 0.041

interest. Use ∑ Tt for each subarea as the total reach travel time from that subarea through the watershed to

the point of interest. Compute the hydrograph coordinates for selected ∑ Tt’s using the appropriate sheets in exhibit 5. The flow at any time is:

q = qtAmQ where:

[eq. 5-1]

q = hydrograph coordinate (cfs) at hydrograph time t

qt = tabular hydrograph unit discharge from exhibit 5 (csm/in)

Am = drainage area of individual subarea (mi2) Q = runoff (in)

Since the timing of peak discharge changes with Tc and Tt, interpolation of peak discharge for Tc and Tt values for use in exhibit 5 is not recommended. Interpolation may result in an estimate of peak discharge that would be invalid because it would be lower than either of the hydrographs. Therefore, round the actual values of Tc and Tt to values presented in exhibit 5. Perform this rounding so that the sum of the selected table values is close to the sum of actual Tc and Tt. An acceptable procedure is to select the results of one of three rounding operations:

1. Round Tc and Tt separately to the nearest table value and sum,

2. Round Tc down and Tt up to nearest table value and sum,

3. Round Tc up and Tt down to nearest table value and sum.

From these three alternatives, choose the pair of

rounded Tc and Tt values whose sum is closest to the sum of the actual Tc and Tt. If two rounding methods produce sums equally close to the actual sum, use the

combination in which rounded Tc is closest to actual Tc. An illustration of the rounding procedure is as follows:

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(210-VI-TR-55, Second Ed., June 1986)

Chapter 5

Tabular Hydrograph Method

Technical Release 55 Urban Hydrology for Small Watersheds

Actual values

Tc

1.1

Tt

1.7

Sum

2.8

Table values by rounding method

1

2

3

1.0

1.0

1.25

1.5

2.0

1.5

2.5

3.0

2.75

In this instance, the results from method 3 would be selected because the sum 2.75 is closest to the actual sum of 2.8.

Selecting Ia / P

The computed Ia / P value can be rounded to the nearest Ia / P value in exhibits 5-I through 5-III, or the hydrograph values (csm/in) can be linearly interpolated because Ia / P interpolation generally involves peaks that occur at the same time.

Summing for the composite hydrograph

The composite hydrograph is the summation of prerouted individual subarea hydrographs at each time shown on worksheet 5b. Only the times encompassing the expected maximum composite discharge are summed to define a portion of the composite hydrograph.

If desired, the entire composite hydrograph can be approximated by linear extrapolation as follows:

1. Set up a table similar to worksheet 5b. Include on this table the full range of hydrograph times displayed in exhibit 5.

2. Compute the subarea discharge values for those times and insert them in the table.

3. Sum the values to obtain the composite hydrograph.

4. Apply linear extrapolation to the first two points and the last two points of the composite hydrograph. The volume under this approximation of the entire composite hydrograph may differ from the computed runoff volume.

Limitations

The Tabular method is used to determine peak flows and hydrographs within a watershed. However, its

accuracy decreases as the complexity of the watershed increases. If you want to compare present and developed conditions of a watershed, use the same procedure for estimating Tc for both conditions.

Use the TR-20 computer program (SCS 1983) instead of the Tabular method if any of the following conditions applies:

• Tt is greater than 3 hours (largest Tt in exhibit 5). • Tc is greater than 2 hours (largest Tc in exhibit 5). • Drainage areas of individual subareas differ by a

factor of 5 or more. • The entire composite flood hydrograph or entire

runoff volume is required for detailed flood routings. The hydrograph based on extrapolation is only an approximation of the entire hydrograph. • The time of peak discharge must be more accurate than that obtained through the Tabular method.

The composite flood hydrograph should be compared with actual stream gage data where possible. The instantaneous peak flow value from the composite flood hydrograph can be compared with data from USGS curves of peak flow versus drainage area.

(210-VI-TR-55, Second Ed., June 1986)

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Chapter 5

Tabular Hydrograph Method

Technical Release 55 Urban Hydrology for Small Watersheds

Examples

A developer proposes to put a subdivision, Fallswood, in subareas 5, 6, and 7 of a watershed in Dyer County, northwestern Tennessee (see sketch below). Before approving the developer’s proposal, the planning board wants to know how the development would affect the 25-year peak discharge at the downstream end of subarea 7. The rainfall distribution is type II (figure B-2), and the 24-hour rainfall (P) is 6.0 inches (figure B-6).

Example 5-1

Compute the 25-year frequency peak discharge at the downstream end of subarea 7 for present conditions, using worksheets 5a and 5b. To do this, first calculate the present condition CN, Tc, and Tt for each subarea, using the procedures in chapters 2 and 3. Enter the values on worksheet 5a (figure 5-1).

Next, compute the prerouted hydrograph points for each subarea hydrograph over a range of time near the peak discharge using worksheet 5b (figure 5-2) and the appropriate exhibit 5. For example, for subarea 4, in which Tc= 0.75 hr, refer to sheet 6 of exhibit 5-II. With ΣTt of 2.00 hr (the sum of downstream travel time through subareas 5 and 7 to the outlet) and Ia / P of 0.1, the routed peak discharge of subarea 4 at the outlet of subarea 7 occurs at 14.6 hr and is 274 csm/in.

2

1

4 3

6 5

7

1 Subarea

Stream

Watershed boundary Subarea boundary

Solving equation 5-1 with appropriate values provides the peak discharge (q) for subarea 4 at 14.6 hr:

q = qt(AmQ) = (274)(0.70) = 192 cfs.

Once all the prerouted subarea hydrographs have been tabulated on worksheet 5b, sum each of the time columns to obtain the composite hydrograph. The resulting 25-year frequency peak discharge is 720 cfs at 14.3 hr (figure 5-2).

Example 5-2

Compute the 25-year frequency peak discharge at the downstream end of subarea 7 for the developed conditions, using worksheets 5a and 5b.

First, calculate the developed condition CN, Tc, and Tt for each subarea, using the procedures in chapters 2 and 3. Enter the values on worksheet 5a (figure 5-3).

Next, compute the prerouted hydrograph points for each subarea hydrograph over a range of time near the peak discharge using worksheet 5b (figure 5-4) and the appropriate exhibit 5. For example, for subarea 6, in which Tc= 1.0 hr, refer to sheet 7 of exhibit 5-II. With ΣTt of 0.5 hr (downstream travel time through subarea 7 to the outlet) and Ia / P of 0.1, the peak discharge of subarea 6 at the outlet of the watershed occurs at 13.2 hr and is 311 csm/in. Solving equation 5-1 provides the peak discharge (q):

q = q t (AmQ) = (311)(1.31) = 407 cfs

Once all the prerouted subarea hydrographs have been tabulated on worksheet 5b, sum each of the time columns to obtain the composite hydrograph. The resulting 25-year frequency peak discharge is 872 cfs

Comparison

According to the results of the two examples, the proposed subdivision at the downstream end of subarea 7 is expected to increase peak discharge from 720 to 872 cfs and to decrease the time to peak from 14.3 to 13.6 hr.

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(210-VI-TR-55, Second Ed., June 1986)