# 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. 1.1 ```r 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`. ## Returns 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-baseddiagnostic approach to model evaluation: Application to the NWSdistributed hydrologic model, Water Resources Research, 44, W09417,doi:10.1029/2007WR006716. ## Author(s) Mauricio Zambrano Bigiarini ## Note The result is given in percentage (%). It requires the `hydroTSM` package. ## See Also fdc , `pbias`, `mae`, `mse`, `rmse`, `ubRMSE`, `nrmse`, `ssq`, `gof`, `ggof` ## Examples ```r ## Not run: ################## # 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) ## End(Not run) ```

pbiasfdc function