6 SCS Curve number method

The SCS curve number (CN) is a method developed by the USDA in 1995, when is was formerly named Soil Conservation Service, hence the SCS in the name. ¹ CN helps with the estimation of runoff at basins where no runoff has been measured. The CN (curve number) ranges from 0 to 100 and is a dimensionless index representing the combined effect of LU/LC, Soil type and hydrological conditions. CN is used to calculate the potential maximum retention capacity \(S\)

\[ S = \dfrac{25400}{CN}-254 \] where the CN = 0 means complete infiltration, CN = 100 no infiltration at all.

The method estimates the precipitation excess \(P_e\) as a function of the cumulative precipitation depth, soil cover, land use, and antecedent soil moisture as

\[ P_e = \begin{cases} 0, \text{ for }\qquad P < I_a\\ \dfrac{(P-I_a)^2}{P - I_a + S}\qquad \text{otherwise } \end{cases} \]

where \(P_e\) is accumulated precipitation excess. \(P\) is the accummulated precipitation depth, \(I_a\) is the initial abstraction (loss) and \(S\) is the potential maximum retention

We have to start with some initial data.

\[ \dfrac{F}{S} = \dfrac{Q}{P-I_a} \]

\[ I_a = rS\approx0.2\cdot S \]

\[ S = \dfrac{1000}{\mathrm{CN}}-10\:\mathrm{[mm]} \] where \(S\) is a potential maximum retention after the initial runoff.

\[ Q = \dfrac{(P-I_a)^2}{(P-I_a)+S} \]

Code

LCLU_tbl <- data.frame(LCLU = c("Pasture", "Road", "Legumes"), 
                       AreaFrac = c(54, 20, 26))
LCLU_tbl

     LCLU AreaFrac
1 Pasture       54
2    Road       20
3 Legumes       26

Code

weather_db <- data.frame(
  dtm = seq(as.Date("2024-01-01"), as.Date("2024-11-30"), "1 day"), 
  P = sample(size = 335, c(0, 1), replace = TRUE)*rweibull(335, shape = 1))

head(weather_db)

         dtm         P
1 2024-01-01 0.0000000
2 2024-01-02 1.8577843
3 2024-01-03 0.6540523
4 2024-01-04 0.1640230
5 2024-01-05 0.8747414
6 2024-01-06 0.0000000

Code

# Function to calculate direct runoff using SCS CN method
scs_cn_method <- function(P, CN) {
  
  S <- (25400 / CN) - 254
  
  Ia <- 0.1 * S
  
  ifelse(P <= Ia, 0, ((P - Ia)^2) / (P - Ia + S))
}

1: Maximum potential retention (mm)
3: Calculate runoff

Code

precipitation <- seq(0, 200, by = 1)

curve_numbers <- seq(from = 40, to = 100, by = 5)

# Calculate runoff for each CN
runoff_results <- sapply(curve_numbers, function(CN) {
  sapply(precipitation, scs_cn_method, CN = CN)
})

# Plot results
plot(NULL, 
     xlim = c(0, max(precipitation)), 
     ylim = c(0, max(runoff_results)),
     xlab = "Precipitation (mm)", 
     ylab = "Runoff (mm)", 
     main = "SCS Curve Number Method: Runoff vs. Precipitation")

for (i in seq_along(curve_numbers)) {
  lines(precipitation, 
        runoff_results[, i], 
        col = "black", 
        lty = i, 
        lwd = 1)
}

# Add legend
legend("topright", 
       legend = paste("CN =", curve_numbers), 
       col = "black", 
       lty = i, 
       lwd = 1)

5: Add lines for each CN

Code

dat01138000 <- read.fwf("data/01138000.dly", 
                        widths = c(8, rep(10, 5))) |> 
  mutate(V1 = as.Date(gsub(V1, 
                           pattern = " ", 
                           replacement = "0"), 
                      format = "%Y%m%d")) 

names(dat01138000) <- c("dtm", "prec", "r", "pet", "tmax", "tmin")

dat01138000[which(dat01138000$prec == -99), "prec"] <- NA

head(dat01138000)

         dtm prec     r    pet    tmax     tmin
1 1948-01-01 0.00 0.080 0.2620 -2.9167 -11.2556
2 1948-01-02 4.44 0.081 0.2501 -2.9556 -11.8500
3 1948-01-03 4.74 0.081 0.2501 -0.1778  -5.6444
4 1948-01-04 0.00 0.081 0.2620 -1.8778  -4.2222
5 1948-01-05 0.00 0.083 0.2501  0.8778  -4.3389
6 1948-01-06 1.78 0.084 0.2620 -0.2889  -5.4833

Code

# Example measured precipitation time series (daily data in mm)
precipitation <- dat01138000$prec[100:1000]

# Define Curve Number
CN <- 75  # Example value for a watershed

# Calculate runoff for each day
runoff <- sapply(precipitation, scs_cn_method, CN = CN)

# Create a time vector for plotting
days <- seq_along(precipitation)

# Plot precipitation and runoff
plot(days, 
     precipitation, 
     type = "h", 
     col = "black", 
     lwd = 0.5, 
     ylim = c(0, max(c(precipitation, runoff), na.rm = TRUE)),
     xlab = "Day", 
     ylab = "Value (mm)", 
     main = "CN based Precipitation and Runoff", 
     lty = 3)
lines(x = days, 
      y = runoff, 
      type = "h", 
      col = "#0088BB", 
      lty = 1, 
      lwd = 1.5)
legend("topright", 
       legend = c("Precipitation", "Runoff"), 
       col = c("black", "#0088BB"), 
       lty = c(3, 1), 
       lwd = c(0.5, 1.5))

Exercise

In practice we would have more than one CN type in the watershed. Estimate the runoff from the watershed using the SCS CN method. Using the following data.

HRU	Area	CN\(_i\)
1	20	70
2	16	84
3	64	74

Compare two approaches to calculate runoff.

Weighted average of CN curves
Weighted contribution to discharge (separate contribution, first compute runoff and weight apply weights by fraction of area).

https://edepot.wur.nl/183157↩︎