SCS Curve Number Method

Open Design Flood Estimation

Estimate runoff depth and flood hydrographs from rainfall using the SCS (Soil Conservation Service) Curve Number method — one of the most widely used rainfall-runoff models in hydrology. This guide covers the rainfall-runoff equation, curve number selection by soil group and land cover, antecedent runoff conditions, the South African (Schmidt-Schulze) adaptation, and worked examples.

Overview

The SCS Curve Number method — originally developed by the US Soil Conservation Service (now the NRCS) and documented in the National Engineering Handbook, Part 630, Chapter 10 — provides a simple, empirical relationship between storm rainfall and direct runoff for small ungauged agricultural watersheds. Since its formal publication in 1954 it has become arguably the most widely applied rainfall-runoff model in the world, embedded in the TR-55, HEC-HMS, SWMM and countless national design manuals including the SANRAL Drainage Manual (6th ed., 2013) and the South African HRU 1/72 method.

Its appeal rests on three qualities: it requires only one physically defensible parameter (the Curve Number, CN), tables of CN values are widely published for almost every combination of land use and soil type, and it works acceptably well for the design storms of engineering interest. The price of that simplicity is well known — the method is approximate, the initial abstraction ratio is fixed, and it can be misleading for small rainfall events or very wet antecedent conditions. These limitations are discussed later.

What is the SCS method?

The SCS method partitions a storm rainfall depth $P$ into three components: an initial abstraction $I_a$ (rainfall intercepted, stored on the surface, or infiltrated before runoff begins), a continuing retention $F$ (infiltration after runoff has started), and direct runoff $Q$. From an assumed relationship between the retention ratio $F/S$ and the runoff ratio $Q/(P-I_a)$, a closed-form rainfall-runoff equation is derived.

The maximum potential retention $S$ is replaced by a dimensionless Curve Number (CN) through the substitution $S = 25\,400/CN - 254$ (in mm). CN ranges from 0 (all rainfall retained, no runoff) to 100 (no retention, rainfall equals runoff). The CN for a catchment is selected from published tables based on hydrologic soil group (A, B, C, D), land cover and hydrologic condition, with area-weighting for mixed catchments.

What the method produces

The basic SCS equation yields only the runoff depth $Q$ (in mm) for a given rainfall depth $P$. To obtain a peak discharge or a flood hydrograph, the runoff depth is combined with a unit hydrograph (SCS dimensionless unit hydrograph or, in South African practice, the HRU 1/72 synthetic unit hydrograph) or a peak-rate equation such as the TR-55 graphical method.

The rainfall-runoff equation

The SCS rainfall-runoff equation follows directly from the assumption that, once runoff has started, the ratio of actual retention to potential retention equals the ratio of actual runoff to potential runoff:

$$\frac{F}{S} \;=\; \frac{Q}{P - I_a}$$

SCS retention assumption

Combining this with the continuity expression $P = I_a + F + Q$ and substituting $I_a = \lambda S$ (with $\lambda = 0.2$ in the standard formulation) yields the familiar runoff equation:

$$Q \;=\; \frac{(P - 0.2\,S)^2}{P + 0.8\,S} \qquad \text{for } P > 0.2\,S$$

SCS runoff equation (metric units)

For $P \le 0.2\,S$, all rainfall is absorbed and $Q = 0$. $P$ and $Q$ are in mm; $S$ is the maximum potential retention in mm.

The maximum potential retention $S$ is linked to the Curve Number through:

$$S \;=\; \frac{25\,400}{CN} \;-\; 254$$

Potential retention from Curve Number (mm)

In US customary units (inches), the equivalent expression is $S = 1000/CN - 10$.

Dimensional sanity check

For $CN = 75$, $S = 25\,400/75 - 254 = 85$ mm. The threshold rainfall for runoff to start is $I_a = 0.2 \times 85 = 17$ mm — a useful number to keep in mind when interpreting small storms.

Curve Number concept

The Curve Number is a dimensionless index that reflects the combined effect of soil infiltration capacity, land cover and hydrologic condition on the runoff response of a catchment. It is the only parameter a user selects, and the method is highly sensitive to it — a CN change from 75 to 85 more than doubles the runoff for a 100 mm storm.

Hydrologic soil groups

Soils are classified into four hydrologic soil groups (HSGs) based on minimum infiltration capacity after prolonged wetting:

Group	Infiltration rate	Typical soils	Runoff potential
A	> 7.6 mm/hr	Deep sands, loamy sands, well-drained sandy loams	Low
B	3.8 – 7.6 mm/hr	Shallow loess, sandy loam, silty loam	Moderately low
C	1.3 – 3.8 mm/hr	Clay loams, shallow sandy loams low in organic content	Moderately high
D	< 1.3 mm/hr	Swelling clays, shallow soils over nearly impervious layers	High

In South Africa, soil hydrological classification is commonly mapped via the Schulze & Schmidt (1987) soil texture to HSG translation of the 1:250 000 Land Type Survey, or — for HydroDesign — from the AfSIS / SoilGrids global texture layers.

Hydrologic condition

For vegetation-covered surfaces, CN additionally depends on hydrologic condition, which describes density and health of vegetation, residue cover, and surface roughness:

• Good — dense cover, > 75% ground cover, minimal compaction
• Fair — moderate cover, 50 – 75% ground cover
• Poor — sparse cover, < 50% ground cover, compacted or grazed

CN reference table

The following CN values are for average antecedent runoff condition II (ARC II), which represents average soil moisture at the start of the design storm. Values are drawn from NRCS NEH-4 Chapter 9 Table 9-1 and, for South African conditions, SANRAL Drainage Manual Table 3.9.

Land cover / land use	A	B	C	D
Urban / developed
Fully paved (parking, roads, roofs)	98	98	98	98
Commercial / business (85% impervious)	89	92	94	95
Industrial (72% impervious)	81	88	91	93
Residential 500 m² (65% impervious)	77	85	90	92
Residential 1000 m² (38% impervious)	61	75	83	87
Residential 2000 m² (25% impervious)	54	70	80	85
Open space — good condition (> 75% grass)	39	61	74	80
Open space — fair condition (50 – 75% grass)	49	69	79	84
Open space — poor condition (< 50% grass)	68	79	86	89
Agricultural
Row crops, straight row, good condition	67	78	85	89
Row crops, contoured, good condition	65	75	82	86
Small grain, straight row, good condition	63	75	83	87
Pasture, good condition	39	61	74	80
Pasture, fair condition	49	69	79	84
Pasture, poor condition	68	79	86	89
Meadow — continuous grass, protected	30	58	71	78
Forest and brush
Woods — good condition	30	55	70	77
Woods — fair condition	36	60	73	79
Woods — poor condition (grazed, burned)	45	66	77	83
Brush — good condition	30	48	65	73
South African veld types (SANRAL)
Grassveld (good condition)	49	69	79	84
Bushveld / thornveld	57	73	82	86
Karoo / semi-desert	63	77	85	88

For a catchment with mixed land cover, the composite CN is calculated as the area-weighted average:

$$CN \;=\; \frac{\sum_i CN_i \cdot A_i}{\sum_i A_i}$$

Area-weighted composite CN

Area-weight CN, not runoff

It is common practice (and the SANRAL recommendation) to area-weight the Curve Number itself. For highly heterogeneous catchments — especially those with very impervious sub-areas — computing runoff for each sub-area and then area-weighting the runoff depths gives a larger, more conservative answer. HydroDesign’s SCS implementation uses the CN-weighting approach for consistency with SANRAL.

Antecedent Runoff Condition

The Antecedent Runoff Condition (ARC, formerly AMC — Antecedent Moisture Condition) adjusts CN to account for the soil wetness at the onset of the storm. Three classes are defined based on the 5-day antecedent rainfall:

Condition	Description	5-day antecedent rainfall (growing season)	5-day antecedent rainfall (dormant season)
ARC I	Dry	< 35 mm	< 13 mm
ARC II	Average	35 – 53 mm	13 – 28 mm
ARC III	Wet (near sat.)	> 53 mm	> 28 mm

Tabulated CN values are for ARC II. Conversions to ARC I and ARC III are given by:

$$CN_I \;=\; \frac{4.2 \cdot CN_{II}}{10 - 0.058 \cdot CN_{II}} \qquad\qquad CN_{III} \;=\; \frac{23 \cdot CN_{II}}{10 + 0.13 \cdot CN_{II}}$$

ARC conversions (Hawkins et al., 1985)

For design flood estimation the standard practice is to use ARC II with a design rainfall depth that already embeds a chosen return period. Explicit use of ARC I or III is uncommon in SA practice, but may be justified for modelling a specific recorded event or for a short-duration, high-intensity design storm on wet soils.

Initial abstraction (Ia = 0.2 S) and its critique

The assumption $I_a = 0.2\,S$ underpins the standard SCS equation. It was fitted to a large dataset of small agricultural watersheds in the US, but subsequent studies have shown it is often too high — particularly for semi-arid and arid environments. Hawkins, Ward, Woodward & Van Mullem (2009, NRCS Technical Note) reviewed several hundred storm-runoff datasets and recommended $\lambda \approx 0.05$ as a better central value.

In South African practice the SANRAL Drainage Manual and the HRU 1/72 method historically use $\lambda = 0.1$ rather than the US default of 0.2, because South African design storms tend to yield too little runoff when $\lambda = 0.2$ is applied. HydroDesign defaults to $\lambda = 0.1$ for SA calculations and exposes the value as a configurable parameter.

With $\lambda = 0.1$, the equation becomes:

$$Q \;=\; \frac{(P - 0.1\,S)^2}{P + 0.9\,S} \qquad \text{for } P > 0.1\,S$$

SCS runoff equation with λ = 0.1 (SA practice)

Choice of λ matters

The choice between $\lambda = 0.2$ (US default) and $\lambda = 0.1$ (SA practice) can change the runoff depth for small storms by a factor of two or more. Always state the $\lambda$ value in the design report, and be consistent with the CN source — CN values calibrated against a $\lambda = 0.2$ model should not be reused with $\lambda = 0.1$ without adjustment.

South African adaptation

South African engineering hydrology adapted the SCS method in three principal ways, documented in HRU Report 1/72 (Schmidt & Schulze, 1984) and the SANRAL Drainage Manual:

1. Lag equation (Schmidt-Schulze). Rather than the NRCS lag equation that embeds CN and slope in US units, the SA version uses a catchment-specific lag time derived from the hydraulic length, median catchment slope, mean annual precipitation (MAP) and a regional parameter. The Schmidt-Schulze lag equation is:

$$T_L \;=\; \frac{L^{0.35} \cdot MAP^{1.10}}{41.67 \cdot S^{0.30} \cdot I_{30}^{0.87}}$$

Schmidt-Schulze lag equation (HRU 1/72)

Where $L$ = hydraulic length (km), $MAP$ = mean annual precipitation (mm), $S$ = catchment slope (m/m) and $I_{30}$ = 2-year 30-minute rainfall intensity (mm/hr). $T_L$ is in hours.

2. Peak rate factor (PRF). The SCS dimensionless unit hydrograph has a fixed peak rate factor of 484 (US customary) or 2.08 (SI, m³/s per mm per km² per hour). For flat or well-vegetated catchments this often overestimates the peak. SA practice allows the PRF to vary from roughly 1.30 (very flat, marshy catchments) through 2.08 (standard rolling terrain) to 2.60 (steep, highly responsive catchments). HydroDesign assigns a default PRF based on catchment slope bands.

3. λ = 0.1 initial abstraction ratio. As discussed above.

Worked example

A 12 km² catchment in KwaZulu-Natal with the following characteristics is designed for a 1:50 year, 6-hour storm of 135 mm:

Given information

• Catchment area: 12 km²
• Land cover: 60% pasture in good condition (CN = 61, HSG B); 25% cultivated row crops, contoured (CN = 75, HSG B); 15% low-density residential with 25% impervious (CN = 70, HSG B)
• Design rainfall: $P = 135$ mm (1:50 year, 6-hour)
• ARC: II (average)
• Initial abstraction ratio: $\lambda = 0.1$ (SA practice)

Step 1 — Composite CN

$$CN \;=\; 0.60 \times 61 + 0.25 \times 75 + 0.15 \times 70 \;=\; 36.6 + 18.75 + 10.5 \;=\; 65.85 \;\approx\; 66$$

Step 2 — Potential retention

$$S \;=\; \frac{25\,400}{66} - 254 \;=\; 384.8 - 254 \;=\; 130.8 \text{ mm}$$

Step 3 — Initial abstraction

$$I_a \;=\; \lambda\,S \;=\; 0.1 \times 130.8 \;=\; 13.1 \text{ mm}$$

Since $P = 135 > I_a = 13.1$, runoff will occur.

Step 4 — Runoff depth

$$\begin{aligned} Q &= \frac{(P - 0.1\,S)^2}{P + 0.9\,S} \\[6pt] &= \frac{(135 - 13.1)^2}{135 + 0.9 \times 130.8} \\[6pt] &= \frac{(121.9)^2}{135 + 117.7} \\[6pt] &= \frac{14\,860}{252.7} \\[6pt] &= \boxed{58.8 \text{ mm}} \end{aligned}$$

Step 5 — Runoff volume

$$V \;=\; Q \times A \;=\; 0.0588 \text{ m} \times 12 \times 10^6 \text{ m}^2 \;=\; 705\,000 \text{ m}^3$$

Step 6 — Peak flow (SCS triangular UH)

With a computed lag time $T_L = 2.0$ h and PRF = 2.08:

$$Q_p \;=\; \frac{2.08 \times Q \times A}{T_p} \;=\; \frac{2.08 \times 58.8 \times 12}{1.0 + 2.0} \;\approx\; 489 \text{ m}^3/\text{s}$$

Where $T_p = D/2 + T_L$ (unit hydrograph time to peak) assuming a unit storm of 1 hr.

The peak discharge of approximately 489 m³/s corresponds to the 1:50 year design flood for the catchment. As a cross-check, the result should be compared with the Rational Method and, where applicable, the SDF method — see Design Flood Estimation.

Sensitivity check

Increase CN from 66 to 71 (reflecting somewhat poorer pasture condition). $S$ drops to 103.7 mm, $Q$ increases to 73.4 mm, a 25% increase in runoff — which propagates directly to a 25% increase in peak. The SCS method is highly sensitive to CN, so always bracket the estimate with a reasonable CN range.

Limitations

• No direct time distribution. The basic SCS equation yields only a storm-total runoff depth; a unit hydrograph (SCS or synthetic UH) or peak-rate equation is needed to distribute runoff in time.
• Fixed $\lambda$ assumption. The $I_a = 0.2\,S$ assumption is empirically derived from a specific dataset and has been shown to overestimate $I_a$ for many regions. Sensitivity to $\lambda$ is large for small storms.
• No true infiltration modelling. The method is a storm-total budget, not a time-varying infiltration model. Use Green-Ampt or Richards-equation-based methods if infiltration dynamics matter.
• High sensitivity to CN. CN is often estimated with considerable uncertainty; a 10-point error in CN can double or halve the runoff for a mid-range design storm.
• Unsuited to very small storms. For $P$ only slightly larger than $I_a$, small errors in $I_a$ produce very large relative errors in $Q$.
• Soil-saturation effects. The method does not account for saturation-excess runoff on variable source areas, which dominates some humid catchments.
• Originally agricultural. CN tables were developed for small agricultural watersheds; extension to urban or forested catchments relies on later CN-table additions that are less well validated.

Related tools and guides

• Rational Method — simpler peak-only method for small catchments
• Unit Hydrograph — convert rainfall excess to a full hydrograph
• DRH Method — Direct Runoff Hydrograph with convolution
• SDF Method — Standard Design Flood for South African SANRAL projects
• TR-55 Calculator — SCS-based urban hydrology with graphical peak discharge
• Tc Calculator — time of concentration methods including NRCS lag
• Design Rainfall — design storm depth for the chosen return period
• Design Storm — temporal distribution of design rainfall

References

• USDA-NRCS. (2004). National Engineering Handbook, Part 630 Hydrology, Chapter 9 — Hydrologic Soil-Cover Complexes, Chapter 10 — Estimation of Direct Runoff from Storm Rainfall. United States Department of Agriculture.
• USDA-SCS. (1986). Urban Hydrology for Small Watersheds, Technical Release 55 (2nd ed.). Soil Conservation Service, Washington DC.
• SANRAL. (2013). Drainage Manual (6th ed.). South African National Roads Agency, Pretoria. Chapter 3 — Hydrology; Section 3.5: SCS Method.
• Schmidt, E.J. & Schulze, R.E. (1984). Improved estimates of peak flow rates using modified SCS lag equations. ACRU Report 17, University of Natal, Pietermaritzburg.
• Schulze, R.E., Schmidt, E.J. & Smithers, J.C. (2004). Visual SCS-SA User Manual Version 1.0. ACRU Report, School of Bioresources Engineering and Environmental Hydrology, University of KwaZulu-Natal.
• Hawkins, R.H., Ward, T.J., Woodward, D.E. & Van Mullem, J.A. (2009). Curve Number Hydrology: State of the Practice. ASCE, Reston, VA.
• Hawkins, R.H., Hjelmfelt, A.T. & Zevenbergen, A.W. (1985). Runoff probability, storm depth, and curve numbers. ASCE Journal of Irrigation and Drainage Engineering, 111(4), 330 – 340.

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Open Design Flood Estimation