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Description and validation of a two-step analogue/regression downscaling method

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Abstract

This study describes a two-step analogue statistical downscaling method for daily temperature and precipitation. The first step is an analogue approach: the “n” days most similar to the day to be downscaled are selected. In the second step, a multiple regression analysis using the “n” most analogous days is performed for temperature, whereas for precipitation, the probability distribution of the “n” analogous days is used to define the amount of precipitation. Verification of this method has been carried out for the Spanish Iberian Peninsula and the Balearic Islands. Results show good performance for temperature (BIAS close to 0.1 °C and mean absolute errors around 1.9 °C) and an acceptable skill for precipitation (reasonably low BIAS except in autumn with a mean of −18 %, mean absolute error lower than for a reference simulation, i.e. persistence and a well-simulated probability distribution according to two non-parametric tests of similarity).

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Acknowledgments

This study was partly supported by the Ministry of Science and Innovation funding under the GENCEI project (contract no. CGL2005-06600-C03-03, 2006–2008). The authors thank the Spanish Meteorology Agency (Agencia Estatal de Meteorología – AEMET) for providing the observed data set and the European Centre for Medium-Range Weather Forecasts (ECMWF) for offering the ERA-40 reanalysis data (http://data-portal.ecmwf.int/data/d/era40_daily). We also thank Clare Goodess (Climate Research Unit, East Anglia University) for her help.

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Authors and Affiliations

  1. Fundación para la Investigación del Clima, C/ Tremps 11, Madrid, 28040, Spain

    J. Ribalaygua, L. Torres, J. Pórtoles, R. Monjo & E. Gaitán

  2. Instituto de Medio Ambiente, Facultad de Ciencias de la Salud, Universidad de San Jorge, Zaragoza, Spain

    M. R. Pino

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  1. J. Ribalaygua
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Correspondence to J. Ribalaygua.

Appendix

Appendix

An example will help to understand the proposed method and its justification (see Section 3.3.2). To simplify, in this example, m = 4, n = 4, and all the analogous days will have the same probability, π ij  = 1/4. Table 1 shows the supposed observed precipitation (ρ ij ) of each analogous day (a ij ) and the preliminary precipitation estimate (Eq. 4).

Table 1 Preliminary precipitation estimates (Eq. 4) using m = 4 problem days and n = 4 analogous days
Full size table

Within these four problem days together, there would be a probability of 1 day with precipitation over 50 mm of 25 % (for x 1) + 25 % (for x 2) + 50 % (for x 4), so it is expected that 1 day of those four has a precipitation over 50 mm. However, no preliminary precipitation estimate reaches that amount, due to smoothing in the average. Likewise, the probability of no rain would be 50 % (for x 1) + 50 % (for x 2) + 100 % (for x 3), so it is expected that two of those 4 days are dry, while the preliminary precipitation estimate suggested only one, again due to averaging and smoothing.

To solve this problem, we pooled all n · m analogues (n analogues for each of all m days in the month) to construct a sample distribution, and obtained the final precipitation amount estimation from this joint probability distribution (Eq. 5). Sorting the m · n observed precipitation amounts (ρ ij ), the m final precipitation amounts are obtained by averaging each of the m groups of n sorted analogues. This way, 1 day over 50 mm and two dry days are obtained, and these final precipitation amounts are assigned to each of the problem days according to their preliminary precipitation amount estimates (see Table 2).

Table 2 Final precipitation estimates (Eq. 5) using the n × m analogues of Table 1, sorted by analogue precipitation (ρ ij )
Full size table

The final precipitation distribution is much more similar to the m · n analogue observed precipitation distribution than the preliminary precipitation distribution was. In addition, the extremes (high values and dry days) of that m · n analogue distribution are much better represented.

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Ribalaygua, J., Torres, L., Pórtoles, J. et al. Description and validation of a two-step analogue/regression downscaling method. Theor Appl Climatol 114, 253–269 (2013). https://doi.org/10.1007/s00704-013-0836-x

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