# Quantile mapping using a smoothing spline `fitQmapSSPLIN` fits a smoothing spline to the quantile-quantile plot of observed and modelled time series. `doQmapSSPLIN` uses the spline function to adjust the distribution of the modelled data to match the distribution of the observations. ```r fitQmapSSPLIN(obs, mod, ...) ## Default S3 method: fitQmapSSPLIN(obs,mod,wet.day=TRUE,qstep=0.01, spline.par,...) ## S3 method for class 'matrix' fitQmapSSPLIN(obs, mod, ...) ## S3 method for class 'data.frame' fitQmapSSPLIN(obs, mod, ...) doQmapSSPLIN(x,fobj,...) ## Default S3 method: doQmapSSPLIN(x,fobj,...) ## S3 method for class 'matrix' doQmapSSPLIN(x,fobj,...) ## S3 method for class 'data.frame' doQmapSSPLIN(x,fobj,...) ``` ## Arguments - `obs`: `numeric` vector, column `matrix` or `data.frame` with observed time series. - `mod`: `numeric` vector, column `matrix` or `data.frame` with modelled time series, corresponding to `obs`. - `wet.day`: `logical`, indicating whether to perform wet day correction or not. OR a `numeric` threshold below which all values are set to zero. See details. - `qstep`: `NULL` or a numeric value between 0 and 1. See Details. - `spline.par`: a named list with parameters passed to `smooth.spline`. - `x`: `numeric` vector or a column `matrix` of modelled time series - `fobj`: output from `fitQmapDIST` - ``...``: Further arguments passed to methods ## Details Before further computations the empirical cumulative distribution functions (CDF) of the observed (`obs`) and modelled (`mod`) are estimated. If `!is.null(qstep)` than `mod` and `obs` are aggregated to quantiles before model identification as: `quantile(x,probs=seq(0,1,by=qstep)`. If `!is.null(qstep)` than `mod` and `obs` are sorted to produce an estimate of the empirical CDF. In case of different length of `mod` and `obs` than `quantile(x,probs=seq(0,1,len=n)]` is used, where `n <- min(length(obs),length(mod))`. NOTE that large values of `qstep` effectively reduce the sample-size and can be used to speedup computations - but may render estimates less reliable. `wet.day` is intended for the use for precipitation data. Wet day correction attempts to equalise the fraction of days with precipitation between the observed and the modelled data. If `wet.day=TRUE` the empirical probability of nonzero observations is found (`obs>=0`) and the corresponding modelled value is selected as a threshold. All modelled values below this threshold are set to zero. If `wet.day` is `numeric` the same procedure is performed after setting all `obs. ## Author(s) Lukas Gudmundsson ## See Also `fitQmap`, `smooth.spline` ## Examples ```r data(obsprecip) data(modprecip) qm.a.fit <- fitQmapSSPLIN(obsprecip[,2],modprecip[,2], qstep=0.01,wet.day=TRUE) qm.a <- doQmapSSPLIN(modprecip[,2],qm.a.fit) ## example on how to use spline.par ## (this example has little effect) qm.b.fit <- fitQmapSSPLIN(obsprecip[,2],modprecip[,2], qstep=0.01,wet.day=TRUE, spline.par=list(cv=TRUE)) qm.b <- doQmapSSPLIN(modprecip[,2],qm.b.fit) sqrtquant <- function(x,qstep=0.01){ qq <- quantile(x,prob=seq(0,1,by=qstep)) sqrt(qq) } plot(sqrtquant(modprecip[,2]), sqrtquant(obsprecip[,2])) lines(sqrtquant(modprecip[,2]), sqrtquant(qm.a),col="red") lines(sqrtquant(modprecip[,2]), sqrtquant(qm.b),col="blue") legend("topleft",legend=c("cv=FALSE","cv=TRUE"), lty=1,col=c("red","blue")) qm2.fit <- fitQmapSSPLIN(obsprecip,modprecip, qstep=0.1,wet.day=TRUE) qm2 <- doQmapSSPLIN(modprecip,qm2.fit) op <- par(mfrow=c(1,3)) for(i in 1:3){ plot(sqrtquant(modprecip[,i]), sqrtquant(obsprecip[,i]), main=names(qm2)[i]) lines(sqrtquant(modprecip[,i]), sqrtquant(qm2[,i]),col="red") } par(op) ```

fitqmapssplin function