Contributors: Peter Berg (SMHI), Riejanne Mook (SMHI), Thomas Bosshard (SMHI), Christiana Photiadou (SMHI), Lisanne Nauta (WUR)
1. Scope of the document
This document describes the applied bias adjustment method as well as the reference data set used in the dataset entitled Climate indicators and essential climate variables from EURO-CORDEX EUR11 projections. The dataset was used as forcing to calculate the data set entitled Water Indicators for the European water sector using EURO-CORDEX.
2. What is bias adjustment?
Bias adjustment is the collective term for the process of reducing biases in climate models in a post processing step. It is often a necessary step when meteorological data from climate models are to be employed as driving data for impact models. To this end, we here define bias as systematic deviations from the reference data used for the impact modeling, including deviations due to discrepancy in the spatial resolution. The latter is commonly called statistical downscaling, but can as a first approximation be treated as a "bias".
3. Reference dataset: EFAS-Meteo
The reference data set for the bias adjustment is the EFAS-Meteo data set (Ntegeka et al., 2013). The dataset records start in year 1990, and the reference period is therefore set to 1990-2018 for both the reference and models. Since the RCP scenario experiments start in 2006 for all CORDEX/CMIP5 experiments, we perform the bias adjustment separately for each RCP, to compare with the simpler setup when calibrating the correction parameters on the historical period only. The EFAS-Meteo dataset is on a 5 km grid across Europe. It is also the target grid for the bias adjustment, which therefore also constitutes a statistical downscaling process.
4. Bias adjustment method
4.1.1.1. Quantile mapping of two timescales
The employed method consists of a separation of two time-scales (following Haerter et al. (2011)), which are separately bias adjusted using an empirical quantile mapping. The quantile mapping is essentially constructing a transfer function, which transforms the distribution of the model data to that of the reference. The transfer function is calibrated on the historical period (1990-2018), and the same function is then applied to the complete time series of the models (1971-2100).
The method was implemented with the following main steps, for each grid point separately and independently for temperature, π(π), and precipitation, π(π). i indicates the time step.
- Each time series (ππππ(π), ππππ(π)) (for model (mod) and observation (obs) equivalently) are separated into two new time series
- a time series of daily time steps subjected to a 30-day running mean, indicated with an overbar
\( \overline{T_{mod}(i)} = \sum_{k=i}^{i+29}T_{mod}(k)/30 \)
\( \overline{P_{mod}(i)} = \sum_{k=i}^{i+29}P_{mod}(k)/30 \)
- 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.
\( T_{mod}(i)' = T_{mod}(i) - \overline{T_{obs}(i)} \)
\( P_{mod}(i)' = P_{mod}(i) / \overline{P_{obs}(i)} \)
- a time series of daily time steps subjected to a 30-day running mean, indicated with an overbar
- For each day-of-year, π, (i.e. not on calendar months as in most bias adjustment procedures, to avoid introducing βstepsβ at calendar month changes in the time series), empirical distribution functions for temperature, πΉπ, and precipitation, πΉπ, 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:
\( FT_{obs,j}(\overline{T_{obs}(j-15,...,j+15)}) \)
\( FT'_{obs,j}(\overline{T'_{obs}(j-15,...,j+15)}) \)
\( FT_{mod,j}(\overline{T_{mod}(j-15,...,j+15)}) \)
\( FT'_{mod,j}(\overline{T'_{mod}(j-15,...,j+15)}) \)
\( FP_{obs,j}(\overline{P_{obs}(j-15,...,j+15)}) \)
\( FP'_{obs,j}(\overline{P'_{obs}(j-15,...,j+15)}) \)
\( FP_{mod,j}(\overline{P_{mod}(j-15,...,j+15)}) \)
\( FP'_{mod,j}(\overline{P'_{mod}(j-15,...,j+15)}) \)
- Each of the two model time series are then bias adjusted based on a transfer function for temperature,πππ, and for precipitation, πππ, which transfers the model to the reference distribution. The bias adjusted time series have the sub-script βadjβ for adjusted.
\( \overline{T_{adj}(i)} = TT_{j} \left(\overline{T_{mod}(i)} \right) = F_{obs,j}^{-1}(F_{mod,j}(\overline{T_{mod}})) \)
\( \overline{T'_{adj}(i)} = TT_{j} \left(\overline{T'_{mod}(i)} \right) = F'_{obs,j}^{-1}(F'_{mod,j}(\overline{T'_{mod}})) \)
\( \overline{P_{adj}(i)} = TP_{j} \left(\overline{P_{mod}(i)} \right) = F_{obs,j}^{-1}(F_{mod,j}(\overline{P_{mod}})) \)
\( \overline{P'_{adj}(i)} = TP_{j} \left(\overline{P'_{mod}(i)} \right) = F'_{obs,j}^{-1}(F'_{mod,j}(\overline{P'_{mod}})) \)
- The final adjusted model time series is constructed by (additively or multiplicatively) merging the 30-day mean and anomaly time series.
\( T_{adj}(i) = \overline{T_{adj}(i)} + T'_{adj}(i) \)
\( P_{adj}(i) = \overline{P_{adj}(i)} \ast P'_{adj}(i) \)
This more complex method, compared to directly applying the empirical quantile mapping to daily data, was chosen to avoid potentially affecting the climate change signals by statistical artifacts of inflated variance. As shown by e.g. Haerter et al. (2011) and Berg et al. (2012), a model with a variance bias is likely to have an amplified climate change signal compared to the original model. Since we are also performing a downscaling step from 12.5 km to 5 km, the models are likely to underestimate the variance, and therefore to exaggerate climate change signals when adjusted with standard methods. The applied method is therefore conservative of the climate change signals. Note that the use of empirical transfer functions automatically adjusts low precipitation values in the models to zero, as all the models suffer from a drizzle bias compared to the reference data for most parts of Europe. Some occasions of too few precipitation days occur in the drier Mediterranean parts, but the effect is negligible on the final result.
Transfer to standard calendar
The HadGEM-ES driven RCM simulations have a non-standard 360-day calendar. This is generally not compatible with impact models, such as the HYPE and VIC hydrological models. Therefore, the calendar is in a pre-processing step changed into a standard calendar by adding dates through duplication of days spread out across each year. The following days (in a standard calendar) are repeated for non-leap years: Feb-6, Mar-18, Jun-30, Aug-12, Oct-24; with the addition of Feb-28 for leap years. The days are determined in the 360-day calendar by counting days from the 1st of January.
Transfering bias adjustment to sub-daily timesteps
One of the target impact models, the VIC model, has been setup with sub-daily forcing data, hence temporal downscaling needs to be applied on the daily bias adjusted model timeseries.
For precipitation, this is performed by evenly distributing the daily precipitation value equally over the sub-daily time intervals. Even though this is not a realistic diurnal distribution, but most importantly the water budget is conserved. The simplification is expected to have minor impact on the results of daily output frequency.
For temperature, a diurnal cycle is important in order to correctly calculate the energy balance at the model time step, and therefore needs a different approach. There are several difficulties with bias adjustment of daily minimum and maximum temperature: observations across Europe uses different observational practices such as time of day and time interval of measurement, and separate bias adjustment of each variable may introduce inconsistencies between them, such as minimum being larger than maximum. Therefore, we employ a simplified and robust method with the main assumption that the model bias at daily mean temperature is equally valid for sub-daily time steps. First, the original daily minimum and maximum temperature (πππππ and ππ₯πππ, respectively) are used to generate sub-daily temperature data (ππππ (π, π‘)) at sub-daily timestep π‘ following the principles of Bohn et al. (2013).
\( T_{mod}(i,t) = f(Tx_{mod} (i), Tn_{mod}(i)) \)
Then a daily bias adjustment factor, ππππ(π), is calculated from adjusted and original temperature data.
\( T_{baf}(i) = T_{adj}(i) - T_{mod}(i) \)
Finally, both values are added to construct sub-daily bias adjusted temperature:
\( T_{adj}(i) = T_{mod}(i,t) - T_{bcf}(i) \)
5. Quality assurance
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.
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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.
6. References
Berg, P., Feldmann, H., & Panitz, H. J. (2012). Bias correction of high resolution regional climate model data. Journal of Hydrology, 448, 80-92.
Bohn, T. J., B. Livneh, J. W. Oyler, S. W. Running, B. Nijssen, and D. P. Lettenmaier (2013). Global evaluation of MTCLIM and related algorithms for forcing of ecological and hydrological models, Agricultural and Forest Meteorology, 176:38-49, doi:10.1016/j.agrformet.2013.03.003.
Haerter, J., Hagemann, S., Moseley, C., & Piani, C. (2011). Climate model bias correction and the role of timescales. Hydrology and Earth System Sciences, 15, 1065-1073.
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 β 2011, JRC Tech. Report, doi: 10.2788/51262.
