HFB {hydroGOF}

High-flows bias

Description

High flow bias between sim and obs, with treatment of missing values.

This function is designed to identify differences in high values. See Details.

Usage

HFB(sim, obs, ...)

## Default S3 method:
HFB(sim, obs, na.rm=TRUE, 
             hQ.thr=0.1, start.month=1, out.PerYear=FALSE,
             fun=NULL, ...,
             epsilon.type=c("none", "Pushpalatha2012", "otherFactor", "otherValue"), 
             epsilon.value=NA)

## S3 method for class 'data.frame'
HFB(sim, obs, na.rm=TRUE, 
             hQ.thr=0.1, start.month=1, out.PerYear=FALSE,
             fun=NULL, ...,
             epsilon.type=c("none", "Pushpalatha2012", "otherFactor", "otherValue"), 
             epsilon.value=NA)

## S3 method for class 'matrix'
HFB(sim, obs, na.rm=TRUE, 
             hQ.thr=0.1, start.month=1, out.PerYear=FALSE,
             fun=NULL, ...,
             epsilon.type=c("none", "Pushpalatha2012", "otherFactor", "otherValue"), 
             epsilon.value=NA)
             
## S3 method for class 'zoo'
HFB(sim, obs, na.rm=TRUE, 
             hQ.thr=0.1, start.month=1, out.PerYear=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

na.rm

a logical value indicating whether 'NA' should be stripped before the computation proceeds.
When an 'NA' value is found at the i-th position in obs OR sim, the i-th value of obs AND sim are removed before the computation.

hQ.thr

numeric, representing the exceedence probabiliy used to identify high flows in obs. All values in obs that are equal or higher than quantile(obs, probs=(1-hQ.thr)) are considered as high flows. By default hQ.thr=0.1.
On the other hand, the high values in sim are those located at the same i-th position than the i-th value of the obs deemed as high flows.

start.month

[OPTIONAL]. Only used when the (hydrological) year of interest is different from the calendar year.

numeric in [1:12] indicating the starting month of the (hydrological) year. Numeric values in [1, 12] represent months in [January, December]. By default start.month=1.

out.PerYear

logical, indicating whether the output of this function has to include the median annual high-flows bias obtained for the individual years in sim and obs or not.

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.

Details

The median annual high flow bias (HFB) is designed to drive the calibration of hydrological models focused in the reproduction of high-flow events.

The high flow bias (HFB) ranges from 0 to Inf, with an optimal value of 0. Higher values of HFB indicate stronger differences between the high values of sim and obs. Essentially, the closer to 0, the more similar the high values of sim and obs are.

The HFB function is inspired in the annual peak-flow bias (APFB) objective function proposed by Mizukami et al. (2019). However, it has four important diferences:

1) instead of considering only the observed annual peak flow in each year, it considers all the high flows in each year, where "high flows" are all the values above a user-defined quantile of the observed values, by default 0.9 (hQ.thr=0.1).

2) insted of considering only the simulated high flows for each year, which might occur in a date/time different from the date in which occurs the observed annual peak flow, it considers as many high simulated flows as the number of high observed flows for each year, each one in the exact same date/time in which the corresponding observed high flow occurred.

3) for each year, instead of using a single bias value (i.e., the bias in the single annual peak flow), it uses the median of all the bias in the user-defined high flows

4) when computing the final value of this metric, instead o using the mean of the annual values, it uses the median, in order to take a stronger representation of the bias when its distribution is not symetric.

Value

If out.PerYear=FALSE: numeric with the median high flow bias between sim and obs. If sim and obs are matrices, the output value is a vector, with the high flow bias between each column of sim and obs.

If out.PerYear=TRUE: a list of two elements:

HFB.value

numeric with the median annual high flow bias between sim and obs. If sim and obs are matrices, the output value is a vector, with the median annual high flow bias between each column of sim and obs.

HFB.PerYear

-) If sim and obs are not data.frame/matrix, the output is numeric, with the median high flow bias obtained for the individual years between sim and obs.

-) If sim and obs are data.frame/matrix, this output is a data.frame, with the median high flow bias obtained for the individual years between sim and obs.

Note

obs and sim has to have the same length/dimension

The missing values in obs and sim are removed before the computation proceeds, and only those positions with non-missing values in obs and sim are considered in the computation

Author(s)

Mauricio Zambrano-Bigiarini <[e-mail]>

References

Mizukami, N.; Rakovec, O.; Newman, A.J.; Clark, M.P.; Wood, A.W.; Gupta, H.V.; Kumar, R.: (2019). On the choice of calibration metrics for "high-flow" estimation using hydrologic models, Hydrology Earth System Sciences 23, 2601-2614, doi:10.5194/hess-23-2601-2019.

See Also

APFB, NSE, wNSE, , wsNSE, gof, ggof

Examples

##################
# Example 1: Looking at the difference between 'NSE', 'wNSE', and 'HFB'
# Loading daily streamflows of the Ega River (Spain), from 1961 to 1970
data(EgaEnEstellaQts)
obs <- EgaEnEstellaQts

# Simulated daily time series, created equal to the observed values and then 
# random noise is added only to high flows, i.e., those equal or higher than 
# the quantile 0.9 of the observed values.
sim      <- obs
hQ.thr   <- quantile(obs, probs=0.9, na.rm=TRUE)
hQ.index <- which(obs >= hQ.thr)
hQ.n     <- length(hQ.index)
sim[hQ.index] <- sim[hQ.index] + rnorm(hQ.n, mean=mean(sim[hQ.index], na.rm=TRUE))

# Traditional Nash-Sutcliffe eficiency
NSE(sim=sim, obs=obs)

# Weighted Nash-Sutcliffe efficiency (Hundecha and Bardossy, 2004)
wNSE(sim=sim, obs=obs)

# HFB (Garcia et al., 2017):
HFB(sim=sim, obs=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 'HFB' for the "best" (unattainable) case
HFB(sim=sim, obs=obs)

##################
# Example 3: HFB for simulated values created equal to the observed values and then 
#            random noise is added only to high flows, i.e., those equal or higher than 
#            the quantile 0.9 of the observed values.

sim           <- obs
hQ.thr        <- quantile(obs, hQ.thr=0.9, na.rm=TRUE)
hQ.index      <- which(obs >= hQ.thr)
hQ.n          <- length(hQ.index)
sim[hQ.index] <- sim[hQ.index] + rnorm(hQ.n, mean=mean(sim[hQ.index], na.rm=TRUE))
ggof(sim, obs)

HFB(sim=sim, obs=obs)

##################
# Example 4: HFB for simulated values created equal to the observed values and then 
#            random noise is added only to high flows, i.e., those equal or higher than 
#            the quantile 0.9 of the observed values and applying (natural) 
#            logarithm to 'sim' and 'obs' during computations.

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

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


##################
# Example 5: HFB for simulated values created equal to the observed values and then 
#            random noise is added only to high flows, i.e., those equal or higher than 
#            the quantile 0.9 of the observed values and applying a 
#            user-defined function to 'sim' and 'obs' during computations

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

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

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