synth.peak.error: Generate synthetic peaks and peak errors

Description

These functions allow generation of synthetic hydrologic peaks generated from a combination of exponetial functions. Also, synthetic errors for the reproduction of a reference peak can be generated in order to subsequentially test the behaviour of performance measures with respect to these errors.

Usage

synth.peak(base = 0.07, base.time = 6, rise.time = 5, rise.factor,
recession.const = 0.2, length.out = 240, rez.time = length.out -
ceiling(base.time) - ceiling(rise.time))
synth.peak.error(base = 0.07, base.time = 6, rise.time = 5,
rise.factor, rise.factor2, recession.const = 0.2, length.out = 240,
rez.time = length.out - base.time - rise.time, err1.factor = c(1.2,
1.4, 1.6), err2.factor = c(0.01, 0.02, 0.04), err3.factor = c(2, 4,
8), err4.factor = c(9, 18, 27), err5.factor = c(0.1, 0.2, 0.4),
err6.factor = c(1.5, 2, 3), 
err9.factor = c(2, 3, 4.5))
p.synth.peak.error(peaks, y.max = (max(peaks, na.rm = TRUE)))

Arguments

base

level of the base flow component

base.time

number of time steps before the rise phase starts. May be negative, such that the peak starts outside the window.

rise.time

Number of time steps for the rise phase

rise.factor

The peak maximum is about rise.factor higher than the base flow.

rise.factor2

rise.factor for the "peaks" which only show a recession phase.

recession.const

Recession constant for the peak.

length.out

Total length of the time series to be returned.

rez.time

Length of the recession phase

err1.factor

Factors to use for the first error type: Over- and underestimation of the peak

err2.factor

Factors to use for the second error type: shifting of the entire time series

err3.factor

Factors to use for the third error type: Recession too fast/too slow

err4.factor

Factors to use for the fourth error type: Lag time

err5.factor

Factors to use for the fifth error type: Correct total volume, but peak over/underestimated

err6.factor

Factors to use for the sixth error type: Peak too wide/too narrow

err9.factor

Factors to use for the ninth error type: Shift during the recession phase

peaks

object returned from synth.peak.error()

y.max

upper limit for the y-axis

Value

synth.peak returns a vector with the synthetic peak according to the provided parameters synth.peak.error returns an array with dimension 3. The first dimension corresponds to the error type. The second dimension to the level of the corresponding error type. The third dimension corresponds to the time.

References

Reusser, D. E., Blume, T., Schaefli, B., and Zehe, E.: Analysing the temporal dynamics of model performance for hydrological models, Hydrol. Earth Syst. Sci. Discuss., 5, 3169-3211, 2008.

Examples

Run this code

ref.peak <- synth.peak(rise.factor=2, recession.const=0.02)
peaks <- synth.peak.error(rise.factor=2, recession.const=0.02, rise.factor2=1.5)
peaks2 <- synth.peak.error(rise.factor=2, recession.const=0.02,
     rise.factor2=1.5, err1.factor=c(1.3,1.5,2.0),
     err2.factor = c(0.02,0.03,0.06), 
     err3.factor=c(2,4,10), 
     err4.factor = c(9,22,40), 
     err5.factor = c(0.2,0.3,0.5),
     err6.factor =c(2,3,5),
     err9.factor=c(1.5,3,6)
   )

    p.synth.peak.error(peaks)
    p.synth.peak.error(peaks2)