Maraun (2013) criticizes quantile mapping (QM) on two counts regarding the downscaling of precipitation, stating that area-mean extremes are overestimated and that long-term trends are affected. I fully agree with Maraun’s criticism on extremes, but remark that this concern was first articulated more than a decade ago in the context of inflated regression (Bürger and Chen 2005). In this comment I am mainly concerned with the issue of long-term trends.
In his paper Maraun concludes: “Finally, as trends are affected, changes in future mean and extreme precipitation, as well as any related impacts, are likely to be misrepresented.” Because regional climate model (RCM) grids represent areal averages, the argument, by spelling it out, requires one to show that (i) a single station trend is representative of the areal average trend and (ii) the areal average differs from the RCM grid. Here I show that (i) is in fact invalid, that local trends can be different from the grid-scale average, a fact that is unrelated to downscaling.
While perhaps being appealing initially, evidence for the idea that long-term temporal features go hand in hand with large-scale spatial features has yet to been given. On the contrary, numerous studies indicate otherwise (Kambezidis et al. 2010; e.g., Ghosh et al. 2012; Philandras et al. 2011), namely, that observed long-term precipitation trends can be quite diverse spatially and may contain signals that are clearly of subgrid scale. The best example is given by Maraun (2013, his Fig. 5) himself, where grid size and local trends have partly opposite sign. This likewise applies to simulated projections. If, for example, the general flow over complex terrain were to change only slightly in the future, this could have drastic and quite different effects on the precipitation over the various slopes. It may be wise, hence, to recall that grid-scale features are nothing more than what they are in the numerics of climate models, namely an arithmetic average of their subgrid features. If anything, Maraun should have compared the downscaled station average against the RCM simulation [see (ii) above]. Whether or not this average is a representative sampling of the full areal mean, which is what the RCM simulates, is a different question though.
The argument that trends are affected as described in Maraun (2013) applies to QM only and not to inflated regression. However, Maraun goes on to relate that argument to an older controversy about the missing variance problem in regression-based downscaling [the perfect prognosis (“prog”) approach] and dismisses inflation in favor of randomization by following von Storch (1999). I will not delve much into this controversy as the various defects were discussed elsewhere. For example, as mentioned above, Bürger and Chen (2005) describe an overestimation of extremes by inflated regression [the same issue that Maraun (2013) reports for QM]. And just recently Bürger et al. (2012) have described how automated statistical downscaling, which is a relatively sophisticated, fully probabilistic version of randomization (Hessami et al. 2008), is of limited quality when compared to observed extremes. The likely reason is that under real-world conditions the model is difficult to calibrate. But a mathematically optimal solution does not exist anyway unless the character of the missing variance (its full multivariate spectrum) can be specified exactly, which is not very realistic. A more practical solution may depend on the area under study, or can perhaps be found by combining inflation and randomization techniques in some smart way. In a multivariate setting, local covariability must be factored in by all methods.
REFERENCES
Bürger, G., and Y. Chen, 2005: Regression-based downscaling of spatial variability for hydrologic applications. J. Hydrol., 311, 299–317.
Bürger, G., T. Q. Murdock, A. T. Werner, S. R. Sobie, and A. J. Cannon, 2012: Downscaling extremes—An intercomparison of multiple statistical methods for present climate. J. Climate, 25, 4366–4388, doi:10.1175/JCLI-D-11-00408.1.
Ghosh, S., D. Das, S.-C. Kao, and A. R. Ganguly, 2012: Lack of uniform trends but increasing spatial variability in observed Indian rainfall extremes. Nat. Climate Change, 2, 86–91, doi:10.1038/nclimate1327.
Hessami, M., P. Gachon, T. B. M. J. Ouarda, and A. St-Hilaire, 2008: Automated regression-based statistical downscaling tool. Environ. Modell. Software,23, 813–834.
Kambezidis, H., I. Larissi, P. Nastos, and A. Paliatsos, 2010: Spatial variability and trends of the rain intensity over Greece. Adv. Geosci., 26, 65–69.
Maraun, D., 2013: Bias correction, quantile mapping, and downscaling: Revisiting the inflation issue. J. Climate, 26, 2137–2143.
Philandras, C., P. Nastos, J. Kapsomenakis, K. Douvis, G. Tselioudis, and C. Zerefos, 2011: Long term precipitation trends and variability within the Mediterranean region. Nat. Hazards Earth Syst. Sci., 11, 3235–3250.
von Storch, H., 1999: On the use of “inflation” in statistical downscaling. J. Climate, 12, 3505–3506.
