perfect prognosis
The so called perfect prognosis approach (aka perfect prog) is based on the use of observational data for both predictors and predictands in the training (calibration) stage. In the latter case, "observational" data is taken from different reanalysis projects, which assimilate day by day the available observations into the model space. Since different global models are used in the training and downscaled phases, large-scale circulation variables well represented by the global models are typically chosen as predictors in this approach. Variables directly influenced by the models' parameterizations and orography (e.g. precipitation, instability indices, etc.) are not considered suitable predictors in this approach. Therefore, one of the most time-consuming tasks for these methods is the screening of appropriate combinations of predictors for each particular predictand and region of study. This task is typically undertaken by cross-validating the performance of the different configurations using standard validation scores: accuracy measures, distributional similarity scores, inter-annual variability, trend matching scores, etc. As general recommendations, a number of aspects need to be carefully addressed when looking for suitable predictors for the perfect approach approach:
- The predictors should account for a major part of the variability in the predictands
- The links between predictors and predictands should be temporally stable/stationary and
- The large–scale predictors must be realistically reproduced by the global climate model. For instance, predictors generally fulfilling these conditions for downscaling precipitation are sea–level pressure, humidity and geopotential.
The analog method was introduced in the field of atmospheric science by Lorenz (1969). It is a simple and powerful downscaling technique which assumes that similar (or analog) atmospheric patterns X over a given region lead to similar local meteorological outcomes Ys for a particular location or set of locations s. In this example, Y = {tasmin} (i.e. minimum -daily- surface temperature); note that boldface is used for vectors.
This assumption provides a simple algorithm to downscale the local occurrence of the variables of interest Ysi from a given atmospheric pattern Xi (e.g. from the i-th daily projection of a GCM). The local occurrence is estimated from the historical daily occurrences Ysa(i) in a set of "analog dates" a(i) within a calibration period (1991–2000 in this example). Under the perfect prognosis approach, the atmospheric patterns in the calibration period are built using a reanalysis dataset and, hence, the analog dates correspond to those historical days with atmospheric reanalysis patterns closest to Xi.
In particular, in this demo we apply the deterministic nearest neighbor method (e.g. Cubasch et al. 1996; Gutiérrez et al. 2013; Bedia et al. 2013), by which only the closest analog (in the sense of the Euclidean distance) is considered. Then, Ysi = Ysa(i) and, hence, both the spatial and inter-variable (or physical) dependence structure of the observational data is preserved in the downscaled series. However, other approaches are possible, as for instance the random selection of one neighbour from the k-nearest, where k is a user-defined number of closest neighbours to be retained, or the assignation of their mean value (see the function's help for more details).
- Bedia, J., Herrera, S., Martín, D.S., Koutsias, N., Gutiérrez, J.M. (2013). Robust projections of Fire Weather Index in the Mediterranean using statistical downscaling. Clim. Change 120, 229–247.
- Benestad, R.E. (2001). A comparison between two empirical downscaling strategies, Int J Climatol, 21, 16451668.
- Benestad RE, Hanssen-Bauer I, Chen D (2008) Empirical-Statistical Downscaling, 1st edn. World Scientific Publishing, Singapore
- Cubasch U, von Storch H, Waszkewitz J, Zorita E (1996) Estimates of climate change in Southern Europe derived from dynamical climate model output. Clim. Res. 7:129–149
- Gutiérrez J., San-Martín D., Brands S., Manzanas R., Herrera S. (2012). Reassessing statistical downscaling techniques for their robust application under climate change conditions. J Clim 26, 171–188.
- Gutiérrez, J.M., Cofiño, A.S., Cano, R. and Rodríguez, M.A. (2004). Clustering Methods for Statistical Downscaling in Short-Range Weather Forecasts, Monthly Weather Review, 132, 2169–2183
- Johansson, K.E., Barnston, A., Saha, S. and van den Dool, H. (1998). On the Level and Origin of Seasonal Forecast Skill in Northern Europe, J Atmos Sci, 55, 103–127
- Lorenz E (1969) Atmospheric predictability as revealed by naturally occurring analogues. J. Atmos. Sci. 26:636–646
