berryFunctions (version 1.22.5)

superPos: superposition of discharge, unit hydrograph

Description

superposition of precipitation along unit hydrograph (to simulate Q from P)

Usage

superPos(P, UH)

Value

Vector of streamflow values

Arguments

P

Vector with precipitation values

UH

Vector with discrete values of the Unit Hydrograph. This can be any UH summing to one, not just the storage cascade model.

Author

Berry Boessenkool, , July 2013

See Also

lsc where superPos is used, unitHydrograph

Examples

N <- c(9,5,2,14,1,3) # [mm/hour]
UH <- c(0, 0.1, 0.4, 0.3, 0.1, 0.1) # [1/h]
sum(UH) # sum must be 1

superPos(N, UH)
# If catchment area = 34 km^2 and precipitation is homogenous:
superPos(N/10^3, UH) * 34*10^6 / 3600  # m^3/s  # Add baseflow and you're done...

SP <- data.frame(Prec=c(N, 0,0,0,0,0),
          P1=c( UH*N[1], 0,0,0,0,0),
          P2=c(0, UH*N[2], 0,0,0,0),
          P3=c(0,0, UH*N[3], 0,0,0),
          P4=c(0,0,0, UH*N[4], 0,0),
          P5=c(0,0,0,0, UH*N[5], 0),
          P6=c(0,0,0,0,0, UH*N[6] ),
          runoff=superPos(N, UH))
SP # SuperPosition

SPcum <- t( apply(SP[2:7], 1, cumsum) )

plot(N, type="h", col=2:7, lwd=3, xlim=c(1, 10), ylim=c(30,0), lend=1)
par(new=TRUE)
plot(1, type="n", ylim=c(0, 15), xlim=c(1, 10), axes=FALSE, ann=FALSE)
axis(4, las=1)
polygon(x=c(1:11, 11:1), y=c(SPcum[,1], rep(0, 11)), col=2)
for(i in 2:6) polygon(x=c(1:11, 11:1), y=c(SPcum[,i], rev(SPcum[,i-1])), col=i+1)
text(3.5, 1, "Shape of UH")
lines( superPos(N, UH), lwd=3)

plot(UH, type="o", ylim=lim0(0.4), las=1)
lines(UH, type="h" )


# Effect of distribution of Prec:
P_a <- c(1,2,3,4,5,6,7,8)
P_b <- c(4,4,4,4,4,4,4,4,4)
P_c <- c(8,7,6,5,4,3,2,1)
sum(P_a) ; sum(P_b) ; sum(P_c)

UH_1 <- unitHydrograph(n=2, k=2.3, t=1:25)
UH_2 <- unitHydrograph(n=5.5, k=1.8, t=1:25)

par(mfrow=c(2,3), mar=c(2,3,2,1), las=1)
plot(P_a, type="h", col=3, lwd=3, ylim=c(0,8), main="Precipitation a")
plot(P_b, type="h", col=4, lwd=3, ylim=c(0,8), main="Precipitation b")
plot(P_c, type="h", col=5, lwd=3, ylim=c(0,8), main="Precipitation c")
#
plot(UH_1, type="l", main="unit hydrograph", ylab="",xlab="Zeit")
lines(UH_2, col=2)
text(c(7,14), c(0.12, 0.07), c("UH_1","UH_2"), col=1:2)
abline(h=0)
#
plot( superPos(P=P_a, UH=UH_1), col=3, ylim=c(0,5), type="l",
      main="Discharge", ylab="Q [m^3/s]")
lines(superPos(P=P_b, UH=UH_1), col=4)
lines(superPos(P=P_c, UH=UH_1), col=5)
legend("topright", c("P a","P b", "P c"), title="with UH_1", col=3:5, lty=1)
#
plot( superPos(P=P_a, UH=UH_2), col=3, ylim=c(0,5), type="l",
      main="Discharge", ylab="Q [m^3/s]")
lines(superPos(P=P_b, UH=UH_2), col=4)
lines(superPos(P=P_c, UH=UH_2), col=5)
legend("topright", c("P a","P b", "P c"), title="with UH_2", col=3:5, lty=1)