CIVE 445 - ENGINEERING HYDROLOGY
CHAPTER 5C: HYDROLOGY OF MIDSIZE CATCHMENTS, TR-55 METHOD

5.3 TR-55 METHOD

TR-55 is a collection of simplified procedures developed by the NRCS (ex SCS).
It consists of two main procedures:
graphical,
tabular.

The graphical method calculates peak flows, for catchments with time of concentration in the range 0.1-10 hr.
The tabular method calculates flood hydrographs, for catchments with time of concentration in the range 0.1-2 hr.
The graphical method is described here.
TR-55 storm, catchment, and runoff parameters

Rainfall in TR-55 is described in terms of total rainfall depth and one of four type rainfall distributions: I, IA, II, and III.
These type distributions are shown in Page 189.
The location for these type distributions is shown in Page 189.
The duration is 24 hr.
This constant duration was selected because most rainfall data is reported on a 24-hr basis.
Rainfall intensities corresponding to durations shorter than 24 hr are contained within the SCS distributions.
For instance, if a 10-yr 24-hr rainfall is used, the 1-hr period with the most intense rainfall corresponds to the 10-yr 1-hr rainfall depth.
TR-55 uses the CN method to abstract total rainfall.
TR-55 is intended to be used for midsize basins, greater than 2.5 km², with time of concentration up to 10 hours.
Therefore, TR-55 includes procedures to determine the time of concentration for the following three types of surface flow:
overland flow,
shallow concentrated flow, and
channel flow.

Selection of runoff curve number CN

TR-55 defines two types of areas in urban catchments:
pervious,
impervious

Runoff curve numbers are calculated by area weighing.
Impervious areas are of two types:
connected
unconnected

Connected impervious areas are those in which runoff flows directly into the drainage system, or where runoff (from the impervious area) flows over a pervious area as shallow concentrated flow as in a grass-lined swale.
Unconnected impervious areas are those in which runoff (from the impervious area) flows over a pervious area (as overland flow) before it enters the drainage system.

Table 5-2(a) shows urban runoff curve numbers for different classes of pervious areas and connected impervious areas.
Table 5-2(b), Table 5-2(c), and Table 5-2(d) show runof curve numbers for agricultural lands, forest, and semiarid rangelands, respectively.
Figure 5-16 is used in lieu of Table 2 if the impervious area percentages or the pervious area classes are other than those shown in the table (table shows only typical values).
When the impervious areas are unconnected, Fig. 5-16 is used in cases where the total impervious area exceeds 30% of the catchment.
Fig. 5-16 gives a composite CN as a function of percent imperviousness and pervious area CN.
Figure 5-17 is used to determine the composite CN when all or portions of the impervious areas are unconnected and the total impervious area is less than 30%.
Fig. 5-17 gives a composite CN as a function of percent imperviousness, ratio of unconnected impervious area to total impervious area, and pervious area CN.

Travel time and time of concentration

For any reach or subreach, travel time is defined as the ratio of flow length to average flow velocity.
At any given point in the catchment, the time of concentration is the sum of travel times through the upstream reaches.
For overland flow, TR-55 uses the following formula for travel time:

t_t = [0.007 (nL)^0.8] / [P₂^0.5 S^0.4]

in which t_t = travel time in hours, n = Manning's n, L = flow length in ft, P₂ = 2-yr 24-hr rainfall in inches, and S = average land slope, in ft/ft.
In SI units, the travel time is:

t_t = [0.0288 (nL)^0.8] / [P₂^0.5 S^0.4]

in which L = flow length in m, P₂ = 2-yr 24-hr rainfall in cm, and S = average land slope, in m/m.
Table 5-11 shows values of Manning's n applicable to overland flow.

Overland flow lengths more than 300 ft lead to a form of surface flow referred to as shallow concentrated flow.
For shallow concentrated flow, the average flow velocity is determined from Figure 5-18.

TR-55 graphical method

The TR-55 graphical method calculates peak discharge based on the concept of unit peak flow.
The unit peak flow is the peak flow per unit area per unit runoff depth.
Unit peak flow is a function of
time of concentration,
ratio of initial abstraction to total rainfall, and
storm type.

Peak discharge is calculated by the following formula:

Q_p = q_u A Q F

in which:

Q_p = peak discharge (L³T^-1)
q_u = unit peak flow (T^-1)
A = area, (L²)
Q = runoff depth (L)
F = surface storage correction factor (dimensionless).

It is first necessary to evaluate the catchment flow type (overland flow, shallow concentrated flow, or channel flow).
The time time of concentration is evaluated with formulas or graphs.
The runoff curve number CN is determined from tables or figures.
A flood frequency is selected.
The rainfall depth P for the 24-hr duration and chosen frequency is determined from depth-duration-frequency maps.
With P and CN, the runoff Q is determined by the curve number method.
The initial abstraction I_a is estimated as 20% of the potential maximum retention S (standard value of NRCS initial abstraction):

I_a = 0.2 S

S is mapped to CN by the Mockus mapping equation:

S = (1000/CN) - 10

from which the initial abstraction in inches, is:

I_a = (200/CN) - 2

The initial abstraction in cm, is:

I_a = (508/CN) - 5.08

The surface storage correction factor F is obtained from Table 5-12.

With time of concentration t_c, initial abstraction ratio I_a/P, and storm type (I, IA, II, or III), the unit peak flow is determined from the TR-55 graphical charts.

Type I
Type IA
Type II
Type III

Interpolation can be used for values of I_a/P other than those shown.
For values out or range, the maximum or minimum value shown should be used.
To obtain unit peak flow in SI units (m³s^-1km^-2cm^-1), the values of the graphs are multiplied by the conversion factor 0.0043.
Peak discharge is calculated by the following formula:

Q_p = q_u A Q F

TR-55 method is limited to:
CN greater than 40,
time of concentration between 0.1 and 10 hours, and
surface storage areas throughout the catchment and covering at most 5% of it.

Assessment of TR-55 graphical method

Time of concentration accounts for btoh runoff concentration and diffusion.
The unit-peak-flow graphs show that unit peak flow decreases with time of concentration.
This implies that diffusion increases with catchment size and time of concentration.
This is the same finding than Creager's (See Creager curves)
The parameter I_a/P is related to the catchment's abstractive properties.
The factor F reduces the peak discharge to account for additional runoff diffusion caused by surface storage features typical of low-relief catchments (ponds and swamps).
The climate and geographical location is accounted for by the storm type distributions.
Thus, the TR-55 methos accounts for hydrologic abstraction, runoff concentration and diffusion, climate and geographical location, and depression storage.
The TR-55 method is an extension of the rational method to midsize catchments.
The unit peak flow q_u (peak discharge per unit area per unit runoff depth) is similar to the runoff coefficient C (peak discharge per unit drainage area per unit rainfall intensity).
Unlike the rational method, the TR-55 method is applicable to midsize catchments.

Comparison with the rational method

Assume A = 1 mi², t_c= 1 hr, C = 0.95 (high).
A calculation with the rational method gives: Q_p = C I A = 613 cfs.
A calculation with the TR-55 method, using the lowest possible value of abstraction (I_a/P = 0.10, roughly equivalent to C = 0.95), gives the following results:

For storm type I: Q_p = 200 cfs.
For storm type IA: Q_p = 108 cfs.
For storm type II: Q_p = 360 cfs.
For storm type III: Q_p = 295 cfs.

This example shows the effect of the storm type on the calculated peak discharge by the TR-55 method.
The type II storm is the most intense, while the type IA storm is the least intense.
This example shows that th TR-55 method gives generally lower values than the rational method.
This is to be expected, since the TR-55 method is accounting for runoff diffusion in a better way thatn the rational method.
The graphs were developed by running the TR-20 computer model many times.
Conclusion: Use TR-55 method to develop peak discharges for midsize catchments.

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