Page History

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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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The input and bias adjusted data were subjected to a number of tests to assure high quality. Besides manual checks on the performance of the bias adjustment performance and scanning of log-files from the production, QA was performed regarding variable dependent valid ranges, distributions of the variables, that data are valid in all land grid points following the reference data set. The climatological means of all models are well adjusted to the reference data, and very little bias remains in the distributions.
Figure 1 shows an example of the "before and after" annual distributions of each of the climate simulations. The spread has been dramatically reduced for both variables, and lie essentially on top of the EFAS-Meteo reference distribution, as is expected from the method. The slight deviations between the distributions are due mainly to the running 30-day window applied in the bias adjustments, compared to the 'calendar' window-based evaluation. For the precipitation, the low and moderate intensities dominate the distribution, and are well adjusted by the method. However, the wet bias in the extremes is still present in most models, although reduced. The uncertainties are large at the tail of the precipitation distribution, and this is a common issue in bias adjustment methods, and does not cause concern for the subsequent hydrological modeling.

Figure 1: Example of original (top) and bias adjusted (bottom) distributions for temperature (left) and precipitation (right) for a domain in central Europe. The different colours mark the EFAS-Meteo reference and the different members of the model ensemble.

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