Loss Methods

Overview

Loss methods compute the portion of rainfall that does not become direct runoff. These "losses" include interception by vegetation, depression storage, and infiltration into the soil. HydraLink supports two loss methods: SCS Curve Number and Green-Ampt.

SCS Curve Number Method

Theory

The SCS (now NRCS) Curve Number method is an empirical method that estimates cumulative runoff from cumulative rainfall using a single parameter — the Curve Number (CN).

Equations

Cumulative runoff:

Where:

• Q = cumulative runoff depth (inches)
• P = cumulative rainfall depth (inches)
• S = potential maximum retention = (1000 / CN) − 10 (inches)
• I_a = initial abstraction = 0.2 × S (inches)

The initial abstraction I_a represents all losses before runoff begins (interception, depression storage, initial infiltration).

Incremental Excess Rainfall

For hydrograph computation, HydraLink computes incremental excess rainfall at each time step:

1. At each time step, compute cumulative rainfall P(t)
2. Compute cumulative runoff Q(t) from the SCS equation
3. Incremental excess = Q(t) − Q(t−1)

Curve Number Selection

CN depends on land cover, treatment, hydrologic condition, and hydrologic soil group (HSG).

Hydrologic Soil Groups

Group	Infiltration Rate	Soil Textures
A	High (> 0.30 in/hr)	Sand, loamy sand
B	Moderate (0.15–0.30 in/hr)	Sandy loam, loam
C	Low (0.05–0.15 in/hr)	Sandy clay loam
D	Very Low (< 0.05 in/hr)	Clay loam, silty clay, clay

Example CN Values (AMC-II)

Cover Description	A	B	C	D
Open space (good condition)	39	61	74	80
Impervious areas	98	98	98	98
Residential (1/4 acre)	51	68	79	84
Residential (1 acre)	46	65	77	82
Commercial (85% imp)	89	92	94	95
Woods (good condition)	30	55	70	77
Pasture (good condition)	39	61	74	80

Green-Ampt Method

Theory

The Green-Ampt method is a physically-based infiltration model that represents the wetting front as a sharp boundary moving downward through the soil. It provides a more detailed representation of infiltration than the CN method, especially for long-duration storms.

Equations

Infiltration rate:

Cumulative infiltration:

Where:

• f(t) = infiltration rate at time t (in/hr)
• K = saturated hydraulic conductivity (in/hr)
• ψ = wetting front suction head (in)
• Δθ = initial moisture deficit (dimensionless, 0–1)
• F(t) = cumulative infiltration at time t (in)

The cumulative infiltration equation is implicit in F and is solved iteratively.

Parameters

Parameter	Units	Description
K	in/hr	Saturated hydraulic conductivity — rate at which water moves through saturated soil
ψ (Psi)	inches	Wetting front suction head — capillary pressure pulling water into dry soil
Δθ (Delta Theta)	dimensionless	Initial moisture deficit — difference between porosity and initial moisture content (0–1)

Typical Values by USDA Soil Texture Class

Texture Class	K (in/hr)	ψ (in)	Porosity
Sand	4.74	1.95	0.437
Loamy Sand	1.18	2.41	0.437
Sandy Loam	0.43	4.33	0.453
Loam	0.13	3.50	0.463
Silt Loam	0.26	6.69	0.501
Sandy Clay Loam	0.06	8.66	0.398
Clay Loam	0.04	8.27	0.464
Silty Clay Loam	0.04	10.63	0.471
Sandy Clay	0.02	9.45	0.430
Silty Clay	0.02	11.42	0.479
Clay	0.01	12.45	0.475

Choosing a Loss Method

Criterion	SCS CN	Green-Ampt
Simplicity	Single parameter (CN)	Three parameters (K, ψ, Δθ)
Physical basis	Empirical	Physically-based
Best for	Standard practice, most applications	Detailed analysis, known soil properties
Long storms	May underestimate infiltration	Better representation of infiltration recovery
Data needs	Land cover + soil group	Soil hydraulic properties

References

• NRCS (2004). National Engineering Handbook, Part 630, Chapter 10 — Estimation of Direct Runoff from Storm Rainfall.
• Green, W.H. and Ampt, G. (1911). "Studies of Soil Physics, Part I." Journal of Agricultural Science.
• Rawls, W.J. et al. (1983). "Green-Ampt Infiltration Parameters from Soils Data." ASCE Journal of Hydraulic Engineering.