Percent Bias in the Slope of the Midsegment of the Flow Duration Curve

Percent Bias in the slope of the midsegment of the flow duration curve (FDC) [%]. It is related to the vertical soil moisture redistribution.

Usage

pbiasfdc(sim, obs, ...)

# Default S3 method
pbiasfdc(sim, obs, lQ.thr=0.6, hQ.thr=0.1, na.rm=TRUE, 
       plot=TRUE, verbose=FALSE, fun=NULL, ..., 
       epsilon.type=c("none", "Pushpalatha2012", "otherFactor", "otherValue"), 
       epsilon.value=NA)

# S3 method for class 'data.frame'
pbiasfdc(sim, obs, lQ.thr=0.6, hQ.thr=0.1, na.rm=TRUE, 
        plot=TRUE, verbose=FALSE, fun=NULL, ..., 
        epsilon.type=c("none", "Pushpalatha2012", "otherFactor", "otherValue"), 
        epsilon.value=NA)

# S3 method for class 'matrix'
pbiasfdc(sim, obs, lQ.thr=0.6, hQ.thr=0.1, na.rm=TRUE, 
        plot=TRUE, verbose=FALSE, fun=NULL, ..., 
        epsilon.type=c("none", "Pushpalatha2012", "otherFactor", "otherValue"), 
        epsilon.value=NA)
       
# S3 method for class 'zoo'
pbiasfdc(sim, obs, lQ.thr=0.6, hQ.thr=0.1, na.rm=TRUE, 
        plot=TRUE, verbose=FALSE, fun=NULL, ..., 
        epsilon.type=c("none", "Pushpalatha2012", "otherFactor", "otherValue"), 
        epsilon.value=NA)

Arguments

sim

numeric, zoo, matrix or data.frame with simulated values

obs

numeric, zoo, matrix or data.frame with observed values

lQ.thr

numeric, used to classify low flows. All the streamflows with a probability of exceedence larger or equal to lQ.thr are classified as low flows

hQ.thr

numeric, used to classify high flows. All the streamflows with a probability of exceedence larger or equal to hQ.thr are classified as high flows

na.rm

a logical value indicating whether 'NA' values should be stripped before the computation proceeds.

plot

a logical value indicating if the flow duration curves corresponding to obs and sim have to be plotted or not.

verbose

logical; if TRUE, progress messages are printed

fun

function to be applied to sim and obs in order to obtain transformed values thereof before computing this goodness-of-fit index.

The first argument MUST BE a numeric vector with any name (e.g., x), and additional arguments are passed using ....

...

arguments passed to fun, in addition to the mandatory first numeric vector.

epsilon.type

argument used to define a numeric value to be added to both sim and obs before applying fun.

It is was designed to allow the use of logarithm and other similar functions that do not work with zero values.

Valid values of epsilon.type are:

1) "none": sim and obs are used by fun without the addition of any numeric value. This is the default option.

2) "Pushpalatha2012": one hundredth (1/100) of the mean observed values is added to both sim and obs before applying fun, as described in Pushpalatha et al. (2012).

3) "otherFactor": the numeric value defined in the epsilon.value argument is used to multiply the the mean observed values, instead of the one hundredth (1/100) described in Pushpalatha et al. (2012). The resulting value is then added to both sim and obs, before applying fun.

4) "otherValue": the numeric value defined in the epsilon.value argument is directly added to both sim and obs, before applying fun.

epsilon.value

-) when epsilon.type="otherValue" it represents the numeric value to be added to both sim and obs before applying fun.
-) when epsilon.type="otherFactor" it represents the numeric factor used to multiply the mean of the observed values, instead of the one hundredth (1/100) described in Pushpalatha et al. (2012). The resulting value is then added to both sim and obs before applying fun.

Value

Percent Bias in the slope of the midsegment of the flow duration curve, between sim and obs.

If sim and obs are matrixes, the returned value is a vector, with the Percent Bias in the slope of the midsegment of the flow duration curve, between each column of sim and obs.

References

Yilmaz, K.K., Gupta, H.V. ; Wagener, T. (2008), A process-based diagnostic approach to model evaluation: Application to the NWS distributed hydrologic model, Water Resources Research, 44, W09417, doi:10.1029/2007WR006716.

Author

Mauricio Zambrano Bigiarini <mzb.devel@gmail.com>

Note

The result is given in percentage (%).

It requires the hydroTSM package.

Examples

if (FALSE) { # \dontrun{
##################
# Example 1: basic ideal case
obs <- 1:10
sim <- 1:10
pbiasfdc(sim, obs)

obs <- 1:10
sim <- 2:11
pbiasfdc(sim, obs)

##################
# Example 2: 
# Loading daily streamflows of the Ega River (Spain), from 1961 to 1970
data(EgaEnEstellaQts)
obs <- EgaEnEstellaQts

# Generating a simulated daily time series, initially equal to the observed series
sim <- obs 

# Computing the 'pbiasfdc' for the "best" (unattainable) case
pbiasfdc(sim=sim, obs=obs)

##################
# Example 3: pbiasfdc for simulated values equal to observations plus random noise 
#            on the first half of the observed values. 
#            This random noise has more relative importance for ow flows than 
#            for medium and high flows.
  
# Randomly changing the first 1826 elements of 'sim', by using a normal distribution 
# with mean 10 and standard deviation equal to 1 (default of 'rnorm').
sim[1:1826] <- obs[1:1826] + rnorm(1826, mean=10)
ggof(sim, obs)

pbiasfdc(sim=sim, obs=obs)

##################
# Example 4: pbiasfdc for simulated values equal to observations plus random noise 
#            on the first half of the observed values and applying (natural) 
#            logarithm to 'sim' and 'obs' during computations.

pbiasfdc(sim=sim, obs=obs, fun=log)

# Verifying the previous value:
lsim <- log(sim)
lobs <- log(obs)
pbiasfdc(sim=lsim, obs=lobs)

##################
# Example 5: pbiasfdc for simulated values equal to observations plus random noise 
#            on the first half of the observed values and applying (natural) 
#            logarithm to 'sim' and 'obs' and adding the Pushpalatha2012 constant
#            during computations

pbiasfdc(sim=sim, obs=obs, fun=log, epsilon.type="Pushpalatha2012")

# Verifying the previous value, with the epsilon value following Pushpalatha2012
eps  <- mean(obs, na.rm=TRUE)/100
lsim <- log(sim+eps)
lobs <- log(obs+eps)
pbiasfdc(sim=lsim, obs=lobs)

##################
# Example 6: pbiasfdc for simulated values equal to observations plus random noise 
#            on the first half of the observed values and applying (natural) 
#            logarithm to 'sim' and 'obs' and adding a user-defined constant
#            during computations

eps <- 0.01
pbiasfdc(sim=sim, obs=obs, fun=log, epsilon.type="otherValue", epsilon.value=eps)

# Verifying the previous value:
lsim <- log(sim+eps)
lobs <- log(obs+eps)
pbiasfdc(sim=lsim, obs=lobs)

##################
# Example 7: pbiasfdc for simulated values equal to observations plus random noise 
#            on the first half of the observed values and applying (natural) 
#            logarithm to 'sim' and 'obs' and using a user-defined factor
#            to multiply the mean of the observed values to obtain the constant
#            to be added to 'sim' and 'obs' during computations

fact <- 1/50
pbiasfdc(sim=sim, obs=obs, fun=log, epsilon.type="otherFactor", epsilon.value=fact)

# Verifying the previous value:
eps  <- fact*mean(obs, na.rm=TRUE)
lsim <- log(sim+eps)
lobs <- log(obs+eps)
pbiasfdc(sim=lsim, obs=lobs)

##################
# Example 8: pbiasfdc for simulated values equal to observations plus random noise 
#            on the first half of the observed values and applying a 
#            user-defined function to 'sim' and 'obs' during computations

fun1 <- function(x) {sqrt(x+1)}

pbiasfdc(sim=sim, obs=obs, fun=fun1)

# Verifying the previous value, with the epsilon value following Pushpalatha2012
sim1 <- sqrt(sim+1)
obs1 <- sqrt(obs+1)
pbiasfdc(sim=sim1, obs=obs1)
} # }