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1. Scope of the document 1. Scope of the document

Scope of the document

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• Each time series (𝑇_𝑚𝑜𝑑(𝑖), 𝑃_𝑚𝑜𝑑(𝑖)) (for model (mod) and observation (obs) equivalently) are separated into two new time series
  1. a time series of daily time steps subjected to a 30-day running mean, indicated with an overbar

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       \overline{T_{mod}(i)} = \sum_{k=1i}^{i+29}T_{mod}(k)/30

       
       

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       \overline{P_{mod}(i)} = \sum_{k=1i}^{i+29}P_{mod}(k)/30

       
       

  2. a daily time series of the anomalies of the original data to the 30-day running The anomalies are multiplicative for precipitation and additive for temperature.

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       T_{mod}(i)' = T_{mod}(i) - \overline{T_{obs}(i)}

       
       

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       P_{mod}(i)' = P_{mod}(i) / \overline{P_{obs}(i)}

       
       

• For each day-of-year, 𝑗, (i.e. not on calendar months as in most bias adjustment procedures, to avoid introducing “steps” at calendar month changes in the time series), empirical distribution functions for temperature, 𝐹𝑇, and precipitation, 𝐹𝑃, are calculated for each of the four-time series based on the 30 days surrounding the selected day-of-year and for the full time period:

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      FT_{obs,j}(\overline{T_{obs}(j-15,...,j+15)})

      
      

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      FT'_{obs,j}(\overline{T'_{obs}(j-15,...,j+15)})

      
      

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      FT_{mod,j}(\overline{T_{mod}(j-15,...,j+15)})

      
      

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      FT'_{mod,j}(\overline{T'_{mod}(j-15,...,j+15)})

      
      

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      FP_{obs,j}(\overline{P_{obs}(j-15,...,j+15)})

      
      

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      FP'_{obs,j}(\overline{P'_{obs}(j-15,...,j+15)})

      
      

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      FP_{mod,j}(\overline{P_{mod}(j-15,...,j+15)})

      
      

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      FP'_{mod,j}(\overline{P'_{mod}(j-15,...,j+15)})

      
      

• Each of the two model time series are then bias adjusted based on a transfer function for temperature,𝑇𝑇𝑗, and for precipitation, 𝑇𝑃𝑗, which transfers the model to the reference distribution. The bias adjusted time series have the sub-script “adj” for adjusted.

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      \overline{T_{adj}(i)} = TT_{j} \left(\overline{T_{mod}(i)} \right) = F_{obs,j}^{-1}(F_{mod,j}(\overline{T_{mod}}))

      
      

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      \overline{T'_{adj}(i)} = TT_{j} \left(\overline{T'_{mod}(i)} \right) = F'_{obs,j}^{-1}(F'_{mod,j}(\overline{T'_{mod}}))

      
      

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      \overline{P_{adj}(i)} = TP_{j} \left(\overline{P_{mod}(i)} \right) = F_{obs,j}^{-1}(F_{mod,j}(\overline{P_{mod}}))

      
      

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      \overline{P'_{adj}(i)} = TP_{j} \left(\overline{P'_{mod}(i)} \right) = F'_{obs,j}^{-1}(F'_{mod,j}(\overline{P'_{mod}}))

      
      

• The final adjusted model time series is constructed by (additively or multiplicatively) merging the 30-day mean and anomaly time series.

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      T_{adj}(i) = \overline{T_{adj}(i)} + T'_{adj}(i)

      
      

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      P_{adj}(i) = \overline{P_{adj}(i)} \ast P'_{adj}(i)

      
      

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Ntegeka, V., P. Salamon, G. Gomes, H. Sint, V. Lorini, M. Zambrano-Bigiarini, and J. Thielen (2013) EFAS-Meteo: A European daily high-resolution gridded meteorological data set for 1990 – 2011, JRC Tech. Report, doi: 10.2788/51262.

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