unitHydrograph: Unit Hydrograph In berryFunctions: Function Collection Related to Plotting and Hydrology

Description

Calculate continuous unit hydrograph with given n and k (in the framework of the linear storage cascade)

Usage

 `1` ```unitHydrograph(n, k, t, force = FALSE) ```

Arguments

 `n` Numeric. Number of storages in cascade. `k` Numeric. Storage coefficient [1/s] (resistance to let water run out). High damping = slowly reacting landscape = high soil water absorbtion = high k. `t` Numeric, possibly a vector. Time [s]. `force` Logical: Force the integral of the hydrograph to be 1? DEFAULT: FALSE

Value

Vector with the unit hydrograph along t

Note

The sum under the UH should always be 1 (if t is long enough). This needs yet to be checked...

Author(s)

Berry Boessenkool, [email protected], July 2013

`lsc` on how to estimate n and k for a given discharge dataset. `deconvolution.uh` in the package hydromad, http://hydromad.catchment.org
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36``` ```Time <- 0:100 plot(Time, unitHydrograph(n=2, k=3, t=Time), type="l", las=1, main="Unit Hydrograph - linear storage cascade") lines(Time, unitHydrograph(n=2, k=8, t=Time), col=2) lines(Time, unitHydrograph(n=5.5,k=8, t=Time), col=4) text(c(12, 20, 50), c(0.1, 0.04, 0.025), c("n=2, k=3","n=2, k=8","n=5.5, k=8"), col=c(1,2,4), adj=0) # try several parameters (e.g. in Monte Carlo Simulation to estimate # sensitivity of model towards slight differences/uncertainty in parameters): nreps <- 1e3 # 5e4 eg on faster computers n <- rnorm(nreps, mean=2, sd=0.8); n <- n[n>0] k <- rnorm(nreps, mean=8, sd=1.1); k <- k[k>0] UH <- sapply(1:nreps, function(i) unitHydrograph(n=n[i], k=k[i], t=Time)) UHquant <- apply(UH, 1, quantile, probs=0:10/10, na.rm=TRUE) if(interactive()) View(UHquant) plot(Time, unitHydrograph(n=2, k=8, t=Time), type="l", ylim=c(0, 0.06), las=1) # uncertainty intervals as semi-transparent bands: for(i in 1:5) polygon(x=c(Time, rev(Time)), y=c(UHquant[i,], rev(UHquant[12-i,])), col=rgb(0,0,1, alpha=0.3), lty=0) lines(Time, UHquant[6,], col=4) lines(Time, unitHydrograph(n=2, k=8, t=Time)) # Label a few bands for clarity: points(rep(24,3), UHquant[c(2,5,9),25], pch="+") for(i in 1:3) text(25, UHquant[c(2,5,9)[i],25], paste("Q", c(10,40,80)[i], sep=""), adj=-0.1, cex=0.7) # And explain what they mean: Explain <- "Q80: 80% of the 50000 simulations are smaller than this value" legend("topright", bty="n", legend=Explain) # Some n and k values are cut off at the left, that explains the shift from the # median of simulations relative to the n2k8 line. ```