superPos {berryFunctions}

superposition of discharge, unit hydrograph

Description

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

Usage

superPos(P, UH)

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.

Value

Vector of streamflow values

Author(s)

Berry Boessenkool, [e-mail], 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)