HYDROLOGY IOF MIDSIZE CATCHMENTS

A midsize catchment is described by the following features: (1) rainfall intensity varies within the stonn duration; (2) stonn rainfall can be assumed to be unifonnly distributed in space; (3) runoff is by overland flow and stream channel flow; and (4) channel slopes are steep enough so that channel storage processes are small (see Chapter 9).

A catchment possessing some or all of the above properties is midsize in a hydrologic sense. Since rainfall intensity varies within the stonn duration, catchment response is described by methods that take explicit account of the temporal variation of rainfall intensity. The most widely used method to accomplish this is the unit hydro graph technique. In an nutshell, it consists of deriving a hydrograph for a unit stonn (the unit hydrograph) and using it as a building block to develop the hydro graph corresponding to the actual effective stonn hyetograph.

In unit hydrograph analysis, the duration of the unit hydrograph is usually a fraction of the time of concentration. The increase in time of concentration is due to the larger drainage area and the associated reduction in overall catchment gradient. The latter has the effect of increasing runoff diffusion

The assumption of uniform spatial distribution of rainfall is a characteristic of midsize catchment analysis. This assumption allows the use of a lumped method such as the unit hydrograph.

Unlike midsize catchments, for large catchments rainfall is likely to vary spatially, either as a general storm of concentric isohyetal distribution covering the entire catchment with moderate rainfall or as a highly intensive local storm (thunderstorm) covering only a portion of the catchment.

An important feature of large catchments that sets them apart from midsize catchments is their substantial capability for channel storage. Channel storage processes act to attenuate the flows while in transit in the river channels. Attenuation can be due either to longitudinal storage (for inbank flows) or to lateral storage (for overbank flows). In the first case, the storage amount is largely controlled by the slope of the main channel. For catchments with mild channel slopes, channel storage is substantial; conversely, for catchments with steep channel slopes, channel storage is negligible. Since large catchments are likely to have mild channel slopes, it follows that they have a substantial capability for channel storage.

In practice, this means that large catchments cannot be analyzed with spatially lumped methods such as the unit hydrograph , since these methods do not take explicit account of channel storage processes. Therefore, unlike for midsize catchments, for large catchments it is necessary to use channel routing (Chapter 9) to account for the expanded role of river flow in the overall runoff response.

As with the limit between small and midsize catchments, the limit between midsize and large catchments is not immediately apparent. For midsize catchments, runoff response is primarily a function of the characteristics of the storm hyetograph, with concentration time playing a sec~ndary role. Therefore, the latter is not well suited as a descriptor of catchment scale. Values ranging from 100 to 5000 km2 have been variously used to define the limit between midsize and large catchments. While there is no consensus to date, the current trend is toward the lower limit. In practice, it is likely that there would be a range of sizes within which both midsize and large catchment techniques are applicable. However, the larger the catchment area, the less likely it is that the lumped approach is able to provide the necessary spatial details.

It should be noted that the techniques for midsize and large catchments are indeed complementary. A large catchment can be viewed as a collection of midsize subcatchments. Unit hydrograph techniques can be used for subcatchment runoff generation, with channel routing used to connect streamflows in a typical dendritic network fashion (Fig. 5-1). Such a computationally intensive procedure is ideally suited to solution with the aid of a computer. Examples of hydrologic computer models using the network concept are HEC-1 of the U.S. Army Corps of Engineers and TR-20 of the USDA Natural Resources Conservation Service. These and other computer models are described in Chapter 13. '

In practice, channel-routing techniques are not necessarily restricted to large catchments. They can also be used for midsize catchments and even for small catchments. However, the routing approach is considerably more complicated than the unit hydrograph technique. The routing approach is applicable to cases where an increased level of detail is sought, above that which the unit hydrograph technique is able to provide-for instance, when the objective is to describe the temporal variation of streamflow at several points inside the catchment. In this case, the routing approach may well be the only way to accomplish the modeling objective.

The hydrologic description of midsize catchments consists of two processes: (1) rainfall abstraction and (2) hydrograph generation. This chapter focuses on a method of r~a~l abstraction that is widely used for hydrologic design in the United States: Natural Resources Conservation Service (NRCS) runoff curve number method. Other rainfall abstraction procedures used by e Isting computer models are discussed in Chapter 13.

With regard to hydrogra h generation, this chapter centers on the unit hydrograph technique, which is a efacto standard for midsize catchments, having been used extensively throughout the world. The NRCS TR-55 method, also included in this chapter, has peak flow and hydrograph generation capabilities and is applicable to small and midsize urban catchments with concentration time in the range 0.1-10.0 h. The ~R-SS meth~d is. ~ased on the runoff curve number method, unit hydrograph techmques, and sImplIfIed stream channel routing procedures.

This chapter is divided into three sections. Section 5.1 describes the runoff curve number method. Section 5.2 discusses unit hydrograph techniques, including unit hydrographs derived from measured data and synthetic unit hydrographs. Section 5.3 deals with the TR-SS graphical method for peak-discharge detenninations.

5.1 RUNOFF CURVE NUMBER METHOD

The runoff curve number method is a procedure for hydrologic abstraction of storm rainfall developed by the U.S. Natural Resources Conservation Service (formerly Soil Conservation Service) [21]. In this method, total storm runoff depth is a function of total storm rainfall depth and an abstraction parameter referred to as runoff curve number, curve number, or CN. The curve number varies in the range 0-100, being a function of the following runoff-producing catchment properties: (1) hydrologic soil type, (2) land use and treatment types, (3) hydrologic surface condition, and (4) antecedent moisture condition.

The runoff curve number method was developed based on daily rainfall P (in.) and its corresponding runoff Q (in.) for the annual floods at a given site. It limits itself to the calculation of runoff depth and does not explicitly account for temporal variations of rainfall intensity. In midsize catchment analysis, the temporal rainfall distribution is introduced at a later stage, during the generation of the flood hydrograph, by means of the convolution of the unit hydrograph with the effective storm hyetograph (Section 5.2).

Runoff Curve Number Equation

In the runoff curve number method, potential runoff (i.e., total rainfall) is referred to as P; actual runoff is referred to as Q. Potential retention (or, in NRCS's use, "potential maximum retention") is referred to as S; actual retention is defined as (P - Q), with (P - Q) ~ S.

The method assumes a proportionality between retention and runoff, such that the ratio of actual retention to potential retention is equal to the ratio of actual runoff to potential runoff:
(5-1)

This assumption underscores the conceptual basis of the runoff curve number method, namely the asymptotic behavior of actual retention toward potential retention for sufficiently large values of potential runoff.

For practical applications, Eq. 5-1 is improved by reducing the potential runoff by an amount equal to the initial abstraction I. The latter consists mainly of interception, surface storage, and some infiltrati~n, which take place before runoff begins.
(5-2)

Solving for Q from Eq. 5-2:
(5-3)
which is physically subject to the restriction that P ~ f a (i.e., the potential runoff minus the initial abstraction cannot be negative).

To simplify Eq. 5-3, initial abstraction is related to potential maximum retention as follows:
fa = 0.2S (5-4)

This relation was obtained based on rainfall-runoff data from small experimental   watersheds. The coefficient 0.2 has been subjected to wide scrutiny. For instance, Springer et al. [18] evaluated small humid and semiarid catchments and found that the coefficient in Eq. 5-4 varied in the range 0.0 to 0.26. Nevertheless, 0.2 is the standard initial abstraction coefficient recommended NRCS [21]. For research applications and particularly when warranted by field data, it is possible to consider the initial abstraction coefficient as an additional parameter in the runoff curve number method. In general:
I = a (5-5)
in which = initial abstraction parameter.

With Eq. 5-4, Eq. 5-3 reduces to:
(5-6)
which is subject to the restriction that P ~ 0.2S.

Since potential retention varies within a wide range (0-00), it has been conveniently mapped in terms of a runoff curve number, an integer varying in the range 0-100. The chosen mapping equation is:
(5-7)
in which CN is the runoff curve number (dimensionless), and S, 1000, and 10 are given in inches. To illustrate, for eN =100, S = 0; and for CN = 0, S = 00. Therefore, the catchment's capability for rainfall abstraction is inversely proportional to the runoff curve number. For eN = 100 no abstraction is possible, with runoff being equal to potential runoff, i.e., total rainfall. For eN = 0 the catchment's abstractive capability is infinite, and runoff is reduced to zero.

in which CN is the runoff curve number (dimensionless) and S, 1000 and 10 are given in inches. To illustrate, for CN = 100, S = 0; and for CN = 1, S = 990 in. Therefore, the catchment's capability for rainfall abstraction is inversely proportional to the runoff curve number. For CN = 100 no abstraction is possible, with runoff being equal to total rainfall. On the other hand, for CN = 1 practically all rainfall would be abstracted, with runoff being essentially equal to zero.

With Eq. 5-7, Eq. 5-6 can be expressed in terms of CN:
[CN(P + 2) - 200]2
Q = CN, [CN(P - 8) + 800] (5-8)
which is subject to the restriction that P ~ (2001 CN) - 2. In Eq. 5-8, P and Q are given in inches. In SI units, the equation is:
R[ CN(PI R + 2) - 200F
Q = CN [CN(PIR - 8) + 800]
(5-9)
which is subject to the restriction that P ~ R[(200I CN) - 2]. With R = 2.54 in Eq. 5-9, P and Q are given in centimeters. For a variable initial abstraction, Eq. 5-8 is expressed as follows:
[CN(P + 1~) - 100(¨ F
Q = CN{ CN [P - 10(1 - @)] + 1000(1 - @)} (5-10)
which is subject to the restriction that P ~ (100o@ICN) - 10@. An equivalent equation in SI units is:
R[CN(PIR + l eW> - 1Ooodi'F
Q = CN{CN[PIR - 10(1 - ~)] + 1000(1 - @)}
(5-11)
which is subject to the restriction that P ~ R[(1000@ICN) - lotl.

A graph of Eqs. 5-8 and 5-9 is shown in Fig. 5-2. This figure is applicable only for the standard initial abstraction value, Ia = 0.2S. If this condition is relaxed, as in Eqs. 5-10 and 5-11, Fig. 5-2 has to be modified appropriately.

Estimation of Runoff Curve Number From Tables

With rainfall P and runoff curve number CN. the runoff Q can be determined by either Eq. 5-8 or Eq. 5-9 or from Fig. 5-2.

For ungaged watersheds, estimates of runoff curve numbers are given in tables supplied by federal agencies (SCS, Forest Service) and local city and county departments. Tables of runoff curve numbers for various hydrologic soil-cover complexes are widely available. The hydrologic soil-cover complex describes a specific combination of hydrologic soil group, land use and treatment class, hydrologic surface condition, and antecedent moisture condition. All these have a direct bearing on the amount of runoff produced by a watershed. The hydrologic soil group describes the type of soil. The land use and treatmen class describes the type and condition of vegetative cover. The hydrologi surface condition refers to the ability of the watershed surface to enhance or impede direct runoff. The antecedent moisture condition accounts for the recent history of rainfall, and consequently it is a measure of the amount of moisture stored by the catchment.

Hydrologic Soil Groups. All soils are classified into four hydrologic soil groups of distinct runoff-producing properties. These groups are labeled A, B, C, and D.

Group A consists of soils of low runoff potential, having high infiltration rates even when wetted thoroughly. They are primarily deep, very well drained sands and gravels, with a characteristically high rate of water transmission.

Group B consists of soils with moderate infiltration rates when wetted thoroughly, primarily moderately deep to deep, moderately drained to well drained, with moderately fine to moderately coarse textures. These soils have a moderate rate of water transmission.

Group C consists of soils with slow infiltration rate when wetted thoroughly, primarily soils having a layer that impedes downward movement of water or soils of moderately fine to fine texture. These soils have a slow rate of water transmission.

Group D consists of soils of high runoff potential, having very slow infiltration rates when wetted thoroughly. They are primarily clay soils with a high swelling potential, soils with a permanent high water table, soils with a clay layer near the surface, and shallow soils overlying impervious material. These soils have a very slow rate of water transmission.

Maps showing the geographical distribution of hydrol~oil types for most areas in the United States are available either directly fro~r NRCS from pertinent local agencies. Additional detail on U.S. soils and their hydrologic soil groups can be found in NEH-4 [21].

Land Use and Treatment. The effect of the surface condition of a watershed is evaluated by means of land use and treatment classes. Land use pertains to the watershed cover, including every kind of vegetation, litter and mulch, fallow (bare soi!), as well as nonagricultural uses such as water surfaces (lakes, swamps, and so on), impervious surfaces (roads, roof!, and the like), and urban areas. Land treatment , applies mainly to agricultural land uses, and it includes mechanical practices such as contouring or terracing and management practices such as grazing control and crop rotation. A class of land use/treatment is a combination often found in a catchment.

The runoff curve number method distinguishes between cultivated land, grasslands, and woods and forests. For cultivated lands, it recognizes the following land uses and treatments: fallow, row crop, small grain, close-seed legumes, rotations (from poor to good), straight-row fields, contoured fields, and terraced fields. Additional detail on these land use and treatment classes can be found in NEH-4 [21].

Hydrologic Condition. Grasslands are evaluated by the hydrologic condition of native pasture. The percent of areal coverage by native pasture and the intensity of grazing are visually estimated. A poor hydrologic condition describes less than 50 percent areal coverage and heavy grazing. A fair hydrologic condition describes SO to 75 percent areal coverage and medium grazing. A good hydrologic condition describes more than 75 percent areal coverage and light grazing.

Woods are small isolated groves or trees being raised for farm or ranch use. The hydrologic condition of woods is visually estimated as follows: (1) poor-heavily grazed or regularly burned woods, with very little litter and few shrubs, (2) fairgrazed but not burned, with moderate litter and some shrubs, and (3) good-protected from grazing, with heavy litter and many shrubs covering the surface.

Runoff curve numbers for forest conditions are based on guidelines develope~ the U. S. Forest Service. The publication Forest and Range Hydrology Handbook [24] describes the determination of runoff curve numbers for national and commercial forests in the .eastern United States. The publication Handbook of Methods for Hydrologic Analysis [25] is used for curve number determinations in the forest-range regions in the western nited States.

Antecedent Moisture Condition. The runoff curve number method has three levels of antecedent moisture: AMC I, AMC II, and AMC ill. The dry antecedent moisture condition (AMC I) has the lowest runoff potential, with the soils being dry enough for satisfactory plowing or cultivation to take place. The average antecedent moisture condition (AMC II) has an average runoff potential. The wet antecedent moisture condition (AMC III) has the highest runoff potential, with the catchment being practically saturated by antecedent rainfalls. Prior to 1993, the appropriate AMC level was based on the total 5-d antecedent rainfall, for dormant or growing season, as shown in Table 5-1. The current version of Chapter 4, NEH-4, released in 1993 [23], no longer supports Table 5.1, which is in-  cluded here only for the sake of completeness. Applicable levels of AMC, including fractional values (see Table 5-4), have been developed on a regional basis.

TABLE 5á1 SEASONAL RAINFALL LIMITS FOR THREE LEVELS OF ANTECEDENT MOISTURE CONDITION (AMC) [21]

Note: This table was developed using data from the midwestern United States. Therefore. caution is recommended when using the values supplied in this table for AMC determinations in other geographic or climatic regions.

Tables of runoff curve numbers for various hydrologic soil-cover complexes are in current use. Table 5-2(a) shows runoff curve numbers for urban areas, Table 5-2(b) shows them for cultivated agricultural areas, Table 5-2(c) shows them for other agricultural lands, and-Table 5-2(d) shows them for arid and semiarid rangelands. Runoff
curve numbers shown in these tables are for the average AMC II condition. Corresponding runoff curve numbers for AMC I and AMC III conditions are shown in Table 5-3.

Using Eq. 5-7, Hawkins et al [8] have expressed the values in Table 5-3 in terms of potential maximum retention. They correlated the values of potential maximum retention for AMC I and III with those of AMC II and found the following ratios to be a good approximation:
(5-12)
This led to the following relationships:
(5-13)
(5-14)
which can be used in lieu of Table 5-3 to calculate runoff curve numbers for AMC l' and AMC III in terms of the AMC II value.



TABLE 5-2(a) RUNOFF CURVE NUMBERS FOR URBAN AREAS' [22]

Cover Description
Cover Type and Hydrologic Condition
Fully developed urban areas (vegetation established)
Open space (lawns. parks. golf courses. cemeteries. etc.)l:
Poor condition (grass cover less than 50"70 )
Fair condition (grass cover 50 to 750/0)
Good condition (grass cover greater than 750/0)
Impervious areas:
Paved parking lots. roofs. driveways. etc.
(excluding right-of-way)
Streets and roads:
Paved; curves and storm sewers (excluding right-ot-way)
Paved;, open ditches (including right-ot-way) ,
Gravel (including right-of-way)
Dirt (including right-of-way)
Western desert urban areas:
Natural desert landscaping (pervious areas only)'
Artificial desert landscaping (impervious weed barrier. desert
shrub with 1- to 2-in. sand or gravel mulch and
basin borders)
Urban districts:
Commercial and business
Industrial
Residential districts by average lot size:
i ac. or less (town houses)
I "4 ac.
I :3 ac.
I "2 ac.
1 ac.
2 ac.
Developing urban areas
Newly graded areas (pervious areas only. no vegetation)5
Idle lands (curve numbers (CNs) are determined using cover types
similar to those in Table 5-2(c)).
Notes:
'Average antecedent moisture condition and Iu = 0.25.
Average Percent
Impervious Area2
85
72
65
38
30
2S
20
12
Curve Numbers for
Hydrologic Soil Group:
A B C o
68 79 86 89
49 69 79 84
39 61 74 80
98 98 98 98
98 98 98 98
83 89 92 93
76 85 89 91
72 82 87 89
63 77 85 88
96 96 96 96
89 92 94 95
81 88 91 93
77 85 90 92
61 75 83 87
57 72 81 86
54 70 80 85
51 68 79 84
46 65 77 82
77 86 91 94
2
The average percent impervious area shown was used to develop the composite eNs.   Other assumptions are as follows: Impervious areas are directly connected to the drainage system; impervious areas have a eN = 98; and pervious areas are considered equivalent to open space in good hydrologic condition. eNs for other combinations of conditions may be computed using Fig. 5-16 or 5~-17. leNs shown are equivalent to those of pasture. Composite eNs may be computed for other combinations of open space COVer type. 'Composite CN' s for natural desert landscaping should be computed using Figs. 5-16 or  -17 based on the impervious ~rea percentage (eN = 98) and the pervious area eN. The pervious area eNs are assumed equivalent to desert shrub In poor hydrologic condition. I(:?mposite eNs to use for the design of temporary measures durjng grading and  onstruction should be computed IISlng Figs. 5-16 or 5-17. based on the degree of developmc;nt (impervious area percentage) and the CNs for the newly rraded pervious areas.



TABLE 5-2(b) RUNOFF CURVE NUMBERS FOR CULTIVATED AGRICULTURAL LANDS' [22]

Curve Numbers for
Cover Description Hydrologic Soil Group:
Hydrologic
Cover Type Treatment2 Conditionl A B C D
Fallow Bare soil 77 86 91 94
Crop residue cover (CR) Poor 76 85 90 93
Good 74 83 88 90
Row crops Straight row (SR) Poor 72 81 88 91
Good 67 78 85 89
SR + CR Poor 71 80 87 90
Good 64 75 82 8S
Contoured (C) Poor 70 79 84 88
Good 65 75 82 86
C + CR Poor 69 78 83 87
Good 64 74 81 8S
Contoured and terraced (C&T) Poor 66 74 80 82
Good 62 71 78 81
C&T + CR Poor 65 73 79 81
Good 61 70 77 80
Small grain .SB Poor 65 76 84 88
Good 63 75 83 87
SR + CR Poor 64 75 83 86
Good 60 72 80 84
C Poor 63 74 82 8S
Good 61 73 81 84
C + CR Poor 62 73 81 84
Good 60 72 80 83
C&T Poor 61 72 79 82
Good 59 70 78 81
C&T + CR Poor 60 71 78 81
Good 58 69 77 80
Close-seeded SR Poor 66 77 8S 89
or broadcast Good 58 72 81 8S
legumes or C Poor 64 75 83 8S
rotation Good 55 69 78 83
meadow C&T Poor 63 73 80 83
Good 51 67 76 80

Notes:
IAverage antecedent moisture condition and I. = 0.2S.
lCrop residue cover applies only if residue is on at least 5% of the surface throughout the year. lHydrologic condition is based on combination offactors that affect infiltration and runoff, including: (1) density and canopy of vegetated areas; (2) amount of year-round cover; (3) amount of grass or close-seeded legumes in rotation; (4) percent of residue cover on the land surface (good hydrologic condition is greater than or equal to 20"10); and (5) degree of surface roughness. Poor: Factors impair infiltration and tend to increase runoff. Good: Factors encourage average and better than average infiltration and tend to decrease runoff.


TABLE S-2(c) RUNOFF CURVE NUMBERS FOR OTHER AGRICULTURAL LANDS1 [22]

Curve Numbers for
Cover Description Hydrologic Soil Group:
Hydrologic
Cover Type Condition A
Pasture, grassland, or range-continuous Poor 68
forage for grazing2 Fair 49
Good 39
Meadow-continuous grass, protected from 30
grazing and generally mowed for hay
Brush-brush-weed grass mixture with brush Poor 48
being the major elementJ Fair 35
Good 3()4
Woods-grass combination (orchard or Poor 57
tree farm!' Fair 43
Good 32
Woods" Poor 45
Fair 36
Good 3()4
Farmsteads-buildings, lanes, driveways, 59
and surrounding lots.
Notes:
' Average antecedent moisture condition and I , = 0.25.
2Poor: less than 50% ground cover on heavily grazed with DO mulch.
Fair: 50 to 75% ground cover and not heavily grazed.
Good: more than 75% ground cover and lightly or only occasionally grazed.
JPoor: less than 50% ground cover.
Fair: 50 to 750/0 ground cover.
Good: more than 75% ground cover.
'Actual curve number is less than 30; use CN = 30 for runoff computations.
B C
79 86
69 79
61 74
58 71
67 77
56 70
48 65
73 82
65 76
58 72
66 77
60 73
55 70
74 82
D
89
84
80
78
83
77
73
86
82
79
83
79
77
86
5
CNs shown were computed for areas with 50% woods and 50% grass (pasture) cover.  Other combinations of conditions may be computed from the CNs for woods and pasture.
áPoor: Forest litter, small trees, and brush are destroyed by heavy grazing or regular  burning. Fair: Woods are grazed but not burned, and some forest litter covers the soil. Good: Woods are protected from grazing, and litter and brush adequately cover the soil.