Due to inherent bias and relatively coarse resolution, the climate model simulated precipitation and temperature cannot be used to drive a hydrological model without pre-processing - statistical downscaling. This often consists of reducing the bias in climate model simulations (bias correction) and/or transformation of the observed data in order to match the projected changes (change factor methods). Numerous methods have herefore been recently proposed. These methods range from simple scaling, considering mean, through nonlinear transformations affecting mean and variability, to more sophisticated methods transforming the whole distribution of variables of interest, spatial or inter-variable dependence, etc. An overview of bias correction methods has been provided by Maraun et al. (2010), various aspects of change factor methods are discussed e.g. by Anandhi et al. (2011). Despite their wide use in climate change impact assessment, some serious concerns about common approaches as well as their fundamental assumptions have been raised in the literature in recent years. These relate especially to stationarity of bias (Chen et al., 2015), potential alteration of climate change signal (Hagemann et al., 2011; Muerth et al., 2013) as well as inter-variable (Ehret et al., 2012; Teng et al., 2015) and spatial (Hnilica et al., 2016) dependence.
Simulations of regional and global climate models are usually provided at daily time step, and this is also the temporal scale at which the simulated variables are downscaled and statistical downscaling methods are evaluated, although many applications (e.g. reservoir storage-yield assessment or drought analysis) often consider monthly data (see e.g. Hanel et al., 2013; Turner and Galelli, 2016) or integrate data on different scales. Example for the latter is the river basin management under climate change conditions with typical scales ranging from daily (e.g. weather and climate) and monthly (water demand and use, reservoir management) to annual (land-use, crop choice) or longer (Van Delden et al., 2007; Efstratiadis et al., 2014). The state-of-the-art bias correction methods are able to transform the simulated data such that the corrected distribution perfectly matches that of observed data and also so that the dependence structure between variables can be reasonably considered. The correspondence of the distribution of corrected and observed variables at daily time scale does not, however, imply correspondence at longer (or shorter) temporal scales. This is due to the temporal structure of the simulated variable, which is typically unaffected by the correction. This has already been recognized by, for example, Haerter et al. (2011), Johnson and Sharma (2012), Ehret et al. (2012) or Mehrotra and Sharma (2016). Similarly, daily change factors applied to observed data do not necessarily result in the same monthly, seasonal and annual changes as expected from the climate model simulation used for the derivation of (daily) change factors.
In addition, the evaluation of bias correction methods is often limited to those variables simulated by the climate model (e.g., precipitation and temperature) and does not consider the output variables of an impact model. In combination with uncorrected bias at multi-day and longer time scales, this may have serious consequences for assessing long-term hydrological balance of a catchment as well as of extreme hydrological events, because catchment dynamics is to a large extent related to temporal distribution of rainfall. Indeed Teng et al. (2015) demonstrated that some widely used bias correction methods cannot overcome the limitations of the climate models in simulating all important precipitation characteristics that influence runoff, in particular, daily precipitation sequence. While the scale dependence and alteration of bias through the impact model has already been described in the literature (see references above) together with complex statistical downscaling methods, the vast majority of climate change impact assessment studies still relies on standard approaches, without recognizing potential magnitude of the introduced errors. We argue, that this is, at least partly, due to the lack of ready-to-use tools for multiscale assessment of statistical downscaling methods, which is in general simple, yet might be technically unappealing.
This was a motivation for development of the R package ”musica”. The main purpose of the package is to make the performance assessment of the statistical downscaling methods at multiple time scales comfortable in order to become standard part of climate change impact assessment. The focus is not only on driving variables of the impact model (typically precipitation and temperature) but also on the output of the impact model (e.g. runoff). For demonstration purposes and assessment of uncertainty due to statistical downscaling methods the package also includes several methods allowing for standard and multiscale bias correction and delta
change transformation implementing the time-scale nesting procedure suggested by Pegram et al. (2009). Currently we do not implement any method for correction of the dependence between variables since the published methods, though in principle universal, often lead to spurious results when applied to different variables than those that were used for the development of the method. For instance the application of the method proposed by Hnilica et al. (2016) or Efstratiadis et al. (2014) for multi-site precipitation leads to negative precipitation amounts when used for correction of the dependence between precipitation and temperature at single site. The capabilities of the package are described in the paper.