1. Downscaling and Error Correction

  2. Case Studies

      2.1  Estimating the Impact of Climate Change on the Energy Yield of a Hungarian Wind Farm
      2.2  Computation of snow water equivalent and snow height from regional climate model data
      2.3  Crop yield scenarios for Bulgaria and Romania
      2.4  Palmer Drought Severity Index
      2.5  Extremes

1. Downscaling and Error Correction

Due to the still occurring misrepresentation of local weather in state of the art regional climate models (RCM), statistical postprocessing is applied to overcome this problem leading to qualitatively enhanced climate information. Error correction methods compare and analyse the relation of atmospheric parameters from climate model simulations to meteorological observations.

Three error correction methods are implemented in STAT-CLIMATE

  • multiple linear regression (MLR) [Huth, 1999; Sailor and Li, 1999],
  • local scaling (LS) [Salathé, 2003; Schmidli et al., 2006] and
  • quantile mapping (QM) [Wood et al., 2004; Dettinger et al., 2004].

All three empirical statistical error correction methods are applied point-wise which implies a separate model for each grid cell of the RCM. In order to account for the effective RCM resolution and to avoid noise, the average of the 9 closest model grid cells is used instead of the single nearest cell.


MLR showed no significant improvement in the error mitigation of precipitation sums but notable problems with the method’s underlying assumptions, which are violated for daily precipitation sums [Helsel and Hirsch, 2002]. In order to mitigate these problems, various transformations of the predictors and/or the predictand have been applied, but no satisfying improvements could be achieved. Due to its unsatisfactory performance MLR results are not taken into account for further purposes.

Local scaling

This technique applies a spatially varying daily, scaling (correction) of the climate model output accounting for its bias relative to a reference (observation). A seperate correction for frequency and intensity is used in this context [Schmidli et al., 2006].

Quantile Mapping

Mean and variability of the simulated temperatures and precipitation amounts can be corrected using the anomaly of the modelled cumulative frequency distribution compared to the observed cumulative frequency distribution. Similar to LS the correction is preformed on the daily scale.

Evaluation of Error Correction Methods

A temporal cross validation is used to evaluate the skill of the EC methods. With cross validation the data sample is repeatedly divided into a calibration and independent validation period [Wilks, 1995].

Temporal and spatial refinement

For further applications the STAT-CLIMATE data are refined temporally and spatially. The temporal was based on applying the original 6 hours daily temporal distribution, from the raw regional climate model simulations, on the corrected 24 hours values. Since the STAT-CLIMATE-ECA dataset was only available in 0.25 degree resolution, a spatial downscaling procedure was performed in order to get a dataset in the needed resolution. This procedure based on the mean regional elevation functions of the variables. Distributions were defined on daily basis. Downscaling criteria are based on the preservation of grid areal mean precipitation and mean temperature values.


As shown especially QM systematically removes the median differences to zero. Additionally QM adopts the RCM variance characteristics to equal the observed one (not shown).

STAT-CLIMATE-ECA: Seasonal and annual error characteristics of daily precipitation amount(first image) and daily mean temperature(second image) in the CLAVIER region (area mean) of the REMO 5.7 (black) simulation and the local scaling (red) and quantile mapping (green) postprocessing methods. The median seasonal and annual differences between model and observation (ECA&D) are shown as lines in 25 and 75 quantile boxes. The “whiskers” represent the 5 and 95 quantiles.


    Dettinger, M.D., D.R. Cayan, M.K. Meyer, A.E. Jeton, Simulated hydrologic responses to
    climate variations and change in the Merced, Carson, and American river basins, Sierra Nevada, California, 1900-2099, Clim. Change, 62, 283-317, 2004.

    Huth, R., Statistical downscaling in central Europe: evaluation of methods and potential predictors, Clim Res., 13, 91-101, 1999.

    Sailor, D.J., X. Li, A semiempirical downscaling approach for predicting regional temperature impacts associated with climatic change, J. Climate, 12, 103-114, 1999.

    Schmidli, J., C. Frei, P.L. Vidale, Downscaling from GCM precipitation: A benchmark for dynamical and statistical downscaling methods, Int. J. Climatol., 26, 679-689, 2006.

    Wood, A.W., L.R. Leung, V. Sridhar, D.P. Lettenmaier, Hydrologic implications of
    dynamical and statistical approaches to downscale climate model outputs, Clim. Change, 62, 189-216, 2004.


2. Case Studies

2.1 Estimating the Impact of Climate Change on the Energy Yield of a Hungarian Wind Farm

The impact of climate change on the energy yield of a wind farm consisting of 12 turbines (2 MW) in the northwestern part of Hungary (close to Masonmagyaróvár) is estimated based on regional climate simulations from the Regional Model REMO. The climate change effects are based on the years 2007 and 2025. In order to avoid the influences of inter-annual variability the climate change signal of the mean annual energy yield is calculated as the difference between two 10 year periods, the scenario period 2021-2030 (centred around 2025) and the reference period 2003-2012 (centred around 2007). The annual energy yields are calculated based on statistical relations between modelled daily wind speeds and observed power outputs (10 minutes mean values) of the wind turbines taking into account annual turbine failure and wake-losses of the wind farm. Furthermore, the effects of climate change on air density and on wake-losses are discussed. Based on the available data, the concept for estimating the climate change effects on the annual energy yield by means of REMO’s climate simulations (REMO-A1B) splits up into three parts: a) deriving a transfer-function, which captures the relations between simulated wind speeds and the observed energy yields and, henceforth, bridges all spatial and temporal gaps, b) analysing trends of the simulated average air-density, and c) analysing shifts of simulated wind directions and quantifying their effects on the direction-depending wakelosses of the wind farm.


Concerning the periods of 2021-2030 and 2003-2012 the climate change effects of the mean annual error-corrected near surface wind speeds, the air density, and their impact on the energy yield are insignificantly small.

Impacts Significance*
mean annual wind speed -0.08% 0.97
air density -0.03% 0.80
mean annual energy yield -1.5% 0.68

*)Significant impacts are indicated by values Wake-losses depend on directions and velocities of the approaching air flows. The regional climate simulations (REMO-A1B) do not show a change effect on wind directions and since the expected changes of wind speeds are insignificantly small the impact on the energy yield is also supposed to be negligible within the investigated periods.


2.2 Computation of snow water equivalent and snow height from regional climate model data

The snow cover model applied in CLAVIER was developed by Wolfgang Schöner at the Austrian Central Institute for Meteorology and Geodynamics (ZAMG) for the estimation of the snow water equivalent (SWE) and snow height (SH) on a daily basis (W. Schöner, priv. communication) and adopted for CLAVIER by WegCenter. It is driven by daily mean air temperature and daily precipitation amount. Within CLAVIER it is applied to output from the regional climate simulations and interpreted with regard to the impact of climate change on snow cover in winter tourist areas in Romania and Bulgaria.

The computation of the snow water equivalent implies both, snow accumulation and snow melt. A degree day approach is applied for the estimation of snow melt. The cooling of the snow-cover on days with negative air temperature is accounted by the introduction of an accumulating freezing reservoir. Analogous to the snow melting a degree day factor is used. Snow height is a diagnostic output quantity, which is obtained by applying a seasonal varying snow density.
The general steps of the algorithm comprise the calculation of the snow temperature, the freezing reservoir, the snow melt, the snow water equivalent and the snow height.

Snowmodel: Sinaia 1984/85: Simulated (red) and observed (blue) snow height in the winter season 1984/1985 in Sinaia (Rumania)Snowmodel: Sinaia 1984/85: Simulated (red) and observed (blue) snow height in the winter season 1984/1985 in Sinaia (Rumania)


2.3 Crop Yield scenarios for Bulgaria and Romania

Meteorological conditions have an impact on crop yields (compare droughts, ...). This study assesses the importance of the impacts in the past, and provides future scenarios of various crop yields using a statistical climate-crop model. For this purpose, multiple linear regressions (MLR) are used with selected meteorological parameters as independent predictors and regional crop yields as dependent variable (Bulgaria – NUTS 3 regions Varna, Razgrad, Ruse, Silistra, Dobrich, Turgovishte and Shumen; Romania - all NUTS2 regions except Bucharest are taken into account separately). The most important crop yields for each region, chosen from the crop types wheat, maize, barley, sunflowers and potatoes are taken into account. As climate simulations the STAT-CLIMATE ECA-REMO57-era40 (training dataset) and STAT-CLIMATE-ECA-REMO57-a1b (control and scenario dataset) datasets have been used.
Climate-crop yield model evaluation is realised by using meteorological predictors from the “hindcast” simulation. A hindcast is considered to represent the oberserved local weather conditions in the past. Under the assumption that the estimated relationship between the predictors and the predictand remains unchanged over time, scenarios for Bulgaria and for Romanian regions are produced for the period 1951-2050. The scenarios are tested for significant linear trends. However, the interest of this report lies in the prediction of absolute values of crop yields, especially in yield anomalies and not in the prediction of growth rates in crop yields.

The applied meteorological predictors have been selected using expert knowledge and objective model selection criteria. Non-climatic influences like technological advancements, political changes, etc. are eliminated in advance, defining them as slowly developing trends.
Various model set ups have been tested against observations (black line)

Hindcast plot: for Maize in BulgariaHindcast plot: for Maize in Bulgaria

Hindcast plot: for Barley in Center RomaniaHindcast plot: for Barley in Center Romania

The thick black line represents observed yield anomalies and can be interpreted as the benchmark for all prediction results, which are drawn in the plot as lines in different colours. Light colours always represent models using a predictor pool without squared predictor terms, whereas dark colours symbolize models with potentially squared predictor terms. Model specifications can be taken from the header of the respective plot in the respective colour.

Model evaluation

Standard models (stand_basic, stand, stand_sq.; orange and red colour) show a very good performace, especially the standard MLR with squared predictors (stand_sq) outpeforms all the other models. Difference models (diff, diff_sq. diff(log) and diff(log)_sq.; green and blue colour) using month by month differences, generally capture the changes in the yield anomalies very well they possibly fail to predict the absolute level of yield anomalies. et0-models, which include potential evapotranspiration as drought indicator in the predictor set, have a very poor performance.


A brief analysis of crop yield scenarios and their trends based on the described model shows no homogeneous picture for the different crops and regions. A more detailed analysis, combined with an economic evaluation is performed within CLAVIER WP4.


2.4 Palmer Drought Severity Index

The Palmer Drought Severity Index (PDSI) was invented in 1965 by Wayne Palmer [Palmer, 1965] and belongs to the group of the agro-meteorological drought indices. The index is based on the calculation of a climatic soil water balance and requires long term temperature, precipitation data on a monthly time scale and the available water holding capacity (AWC) as a soil parameter, whereas the AWC is the amount of water which can be held in the root-zone between the wilting point of the plants and the field capacity.
The calculation of the soil water balance within the PDSI is strongly simplified and is based on a two layer soil model. It is assumed that the upper layer can hold one inch of water (25.4 mm) and the lower layer therefore AWC - 1 inches. The driving mechanism for the soil water balance is the difference between the monthly amounts of precipitation and potential evapotranspiration. The monthly potential evapotranspiration is estimated using the empirical relationship between monthly mean temperature and potential evapotranspiration sum suggested by Thornthwaite [1948].

The PDSI is arranged into 12 classes (from extremly wet to extremly dry). The Classification is mentioned in the table below.


≥4 extremely wet
3.00 to 3.99 very wet
2.00 to 2.99 moderatly wet
1.00 to 1.99 slightly wet
0.50 to 0.99 incipient wet spell
0.49 to -0.49 near normal
-0.50 to -0.99 incipient drought
-1.00 to -1.99 mild drought
-2.00 to -2.99 moderate drought
-3.00 to -3.99 severe drought
≤-4 extreme drought


The PDSI declines in all countries and all seasons by about 0.35 classes per decade. This would, e.g., shift present day mild droughts (class -1 to -1.99) to future severe droughts (class -3 to -3.99) within less than 60 years.
The annual cycle of the climate change signal for Hungary and Bulgaria seems to be at higher drought risk in future than Romania (shift of more that 3 classes towards drier conditions are expected) - future extreme droughts (class -4 and lower).

Seasonal as well as yearly time series and the respective trends are calculated nd evaluated for the PDSI between 1951 and 2050. The respective left panel shows seasonal and yearly maps of decadal trends of only significant grid cells in the entire domain. The trend direction and magnitude is colour-coded. The right panel of each plot shows seasonal and annual regional averages for the three CLAVIER countries Hungary, Romania and Bulgaria (thin line), the 1961-1990 mean value (dashed line), 10 year moving averages of the regional mean (bold line) and the linear trend of the unsmoothed regional mean represented by the thin line (bold straight line). The magnitude of the respective trend is indicated in the top left corner of each plot with significant trends being marked by an asterisk.


    Palmer, W., Meteorological drought, Research Paper 45, Office of Climatology, U.S. Weather Bureau, Washington D.C., USA, 1965.

    Thornthwaite, C.W., An approach towards a rational classification of climate, Geographical Review 38, 55-94, 1948.


2.5 Extremes

The eventual increase of weather and climate extremes due to a shift in mean climate (global warming) is a heavily discussed issue, as extremes present first-order menaces for the general public, the economy and the natural environment. According to IPCC [2001] an extreme weather event is an event that is rare within its statistical reference distribution at a particular place. Definitions of “rare” vary, but an extreme weather event would normally be as rare as or rarer than the 10th or 90th percentile. Beniston and Stephenson [2004] and the OcCC [2003] additionally characterize rare events by a certain frequency or return period. An extreme climate event is an average of a number of weather events over a certain period of time, an average which is itself extreme (e.g., rainfall over a season) [IPCC, 2001].

In this study, extreme parameters, which are listed in the table below, and their trends investigated for the CLAVIER study region between 1951 and 2050. The analysis is based on the empirical-statistical error corrected data from the STAT-CLIMATE-ECA-REMO57_a1b scenario (database link in the left bar).

Parameters for extremes

Name Shortcut Unit Description
mean temperature tas_dm K mean surface(2m) air temperature
90th percentile of maximum temperature txq10 °C 90th percentile of daily maximum temperature(tas_dx)
10th percentile of minimum temperature tnq10 °C 10th percentile of daily minimum temperature(tas_dn)
number of frost days tnfd days number of days with minimum temperature (tas_dn)
summer days txn25 days number of days where the maximum temperature (tas_dx) exceeds 25°C
tropical nights tnn20 days number of days where the minimum temperature (tas_dn) exceeds 20°C
90th percentile heat wave duration txhw90 days maximum number of days per year (at least 6) where the maximum temperature (tas_dx) exceeds its long term (30 years) 90th percentile calculated in 5-day windows
precipitation amount pr_24hc mm/day mean surface precipitation amount
precipitation intensity pint mm/day mean daily precipitation sum on rainy days (days where pr_24h exceeds 1mm/day)
90th percentile of wet day precipitation pq90 mm 90th percentile of daily precipitation sums (pr_24h)
90th percentile of wet day precipitation pdq90 mm 90th percentile of daily precipitation sums (pr_24h) on wet days (pr_24hc >= 1mm)
greatest 1-day rainfall px1d mm maximum precipitation sum in one day
greatest 5-day rainfall px5d mm maximum precipitation sum in 5 consecutive days
intense precipitation pn10 days number of days where the daily precipitation sum (pr_24hc) exceeds 10 mm/day
consecutive dry days pxcdd days maximum number of consecutive dry days

tnn20:Trend analysis for tropical nights

px5d:Trend analyses for the greates 5-day rainfall

Summary of the annual trends


Regarding the temperature-related indices for extremes, a throughout significant warming signal can be found in the entire CLAVIER domain with warming maxima in winter and autumn. Most drastically this can be seen in the summer months for tropical nights (tnn20, minimum temperature > 20°C) in Bulgaria. The duration of heat waves notably increases till the mid century. A comparison of the CLAVIER countries shows comparable trends in all three countries in most parameters, but on a higher level in Bulgaria..


Regarding precipitation-related indices for extremes, only few significant trends are found. In all three countries all parameters (mean precipitation and parameters for extremes) have the tendency to decline in summer and to increase in winter. Bulgaria again stands out with a strong increase in consecutive dry days (pxcdd) which is not featured in the Hungarian and Romanian time series.


    BENISTON, M., D.B. STEPHENSON, 2004: Extreme climatic events and their evolution under changing climate conditions, Global and Planetary Change, Vol. 44, pp. 1-9.

    IPCC, 2001: Climate Change 2001: The Scientific Basis. Contribution of Working Group I to the Third Assessment Report of the Intergovernmental Panel on Climate Change [Houghton, J.T., Y. Ding, D.J. Grigg, M.

    und Klimaänderung, 88 pp.