Official reference number service contract: C3S2_410_Lot2
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Hydrological seasonal forecasts driven by dynamic meteorological forecasts are affected by bias from two main sources: (i) drift of the hydrological states when the forecast climate has bias relative to the historical initialization, and (ii) drift of the forecast model itself. The current operational C3S Water Service seasonal forecast system for Europe performs a bias adjustment of precipitation and temperature at the daily time scale, with separate bias adjustment factors for each initialization month and lead month combination. This efficiently addresses both the general offset with the reference data, as well as potential model drift for different lead months.
EFAS-Meteo data (Ntegeka et al., 2013) is used as reference data for the bias adjustment. It is a dataset built around gauge observations of precipitation, temperature, humidity, wind, etc., which have been gridded to the 5-km EFAS grid across Europe. Only the variables daily mean temperature and precipitation are used for the bias adjustment. The data is available from the Joint Research Centre (JRC, 2024).
ECMWF-s51, also known as SEAS5 (Johnson et al., 2019), consists of an ensemble forecast with 25 members for the reforecast period (1981-2016, here we use 1993 – 2016), and 51 members after that period. The forecasts have an initial date of the 1st of each month, and run for 7 calendar months. We consider forecasts for the first six months, i.e. to a maximum of 184 days. Data are extracted from the CDS archive at a 1.0-degree resolution. Note that the SEAS5.1 dataset at CDS is used (C3S, 2018), with documentation page here: Description of SEAS5-v20171101 C3S contribution.
CMCC-s35, also known as CMCC-SPS3.5 (Gualdi et al., 2020), consists of an ensemble forecast with 40 members for the reforecast period (here we use the first 25 members for the period 1993 – 2016), and 51 members after that period. We consider forecasts for the first six months, i.e. to a maximum of 184 days, and the C3S 1.0-degree resolution is used from the CDS dataset (C3S, 2018), with documentation page here: Description of CMCC-CM2-v20191201 C3S contribution.
The bias adjustment method is built upon methods developed in the MIdAS (MultI-scale bias AdjuStment) bias adjustment system (Berg et al., 2022) at SMHI, and has been simplified to more efficiently process seasonal forecast data in an operational environment. The core of the method is a quantile mapping bias adjustment that adjusts the complete distribution of a variable towards the reference data. The adjustments are performed separately for each grid point within the domain.
Bias adjustment of probabilistic forecasts needs to account for the spread between ensemble members and act to retain this spread as much as possible. Therefore, the basic approach to the bias adjustment is to read the 25 reforecast members, put all members in one large array of length (Ndays * Nyears) * 25 and sort them in ascending order. The array is then reshaped to [(Ndays * Nyears), 25] and averaged over the second dimension to arrive at an array of length Ndays * Nyears, which is the same length as the reference data. Now we have two arrays with equal size that can be used in the quantile mapping approach.
For precipitation, there is an initial step to bias adjust the number of wet days. This is performed following the SSR method (Singularity Stochastic Removal; Vrac et al., 2016), where first the lowest non-zero value in the datasets is saved, and then all data with zero values are replaced with random values between zero and the threshold from the first step. After the bias adjustment has taken place, a final step is setting all values below the threshold to zero. This method acts to both remove excessive wet days, and also promote new light precipitation wet days when the model lacks wet days.
The transfer function of the quantile mapping is calculated from the qq-plot of the two sorted time series, see Figure 1. A spline method is fitted to the data to avoid overfitting, and a smoothing function is applied to select the number of knots that the spline shall use. Special treatment is applied to the extreme tails of the distributions so that extrapolation to data beyond the range seen in the calibration period will act in a predictable manner. This is performed by excluding the five most extreme values (in the high-end tail for precipitation, and in both tails for temperature) from the calibration of the spline fitting. All values above the fifth most extreme value in the calibration period are then adjusted with the same constant factor, which is calculated from the mean difference between the most extreme five values from the model and the reference dataset. In data outside the calibration period, all values beyond the calibration periods’ fifth most extreme value will use that same adjustment (orange line in the Figure 1).
Figure 1: Example of the spline fit for precipitation in a data point in Sweden, and the replacement of the spline knots to a constant adjustment for the top five data points (orange line).
The bias adjustment is evaluated for the mean and the range (min to max) for all grid points, initialization and lead months for spatial averages of the domains presented in Figure 2.
Figure 2: Sub-domains of Europe used for the evaluation (1. BI = British Isles, 2. IP = Iberian Peninsula, 3. FR = France, 4. ME = Middle Europe, 5. SC = Scandinavia, 6. AL = Alpine, 7. MD = Mediterranean Domain, 8. EA = Eastern Europe, 9. IC = Iceland, 10. EMD = Eastern Mediterranean, 11. AS = Asia).
Figures 3 and 4 present a climatological assessment of the original and bias adjusted model data over the period 1993-2016 for temperature and precipitation, respectively. The figures show the original and bias adjusted data with statistics for the 1st percentile, the mean, and the 99th percentile for temperature and the mean, the 95th and the 99th percentile for precipitation, from bottom to top of the panels. All initialization months have been similarly assessed, but for brevity, only the January and July forecasts are presented in the plots in order to cover a complete year. The time of shift between forecasts is marked with a white section in all lines. There is some dependence on lead time, which is mostly apparent in the first weeks of the forecast, and is due some drift of the meteorological models from their initialized state to the models’ own climate state.
The bias in temperature (Figure 3) varies between the different regions, and is substantial (several degrees Celsius) in some regions. These larger deviations can, in mountainous regions, be due to large deviations in the elevation used in the originally coarser model, compared to the higher resolved observational dataset. The implicit downscaling step in the bias adjustment is also adjusting this lapse-rate related “bias”. After bias adjustment, the forecast temperatures are in high agreement with observations, and the spread between ensemble members is retained well.
Figure 3: Temperature statistics for the original (blue) and bias adjusted ECMWF-s51 forecasts compared to the EFAS-Meteo reference dataset. The presented statistics are from bottom to top of each panel: mean, P95, and P99.
Precipitation is generally underestimated for all statistics (mean, P95 and P99), especially in summertime in many of the regions, see Figure 4. The mean and P95 statistics are in good agreement with observations after bias adjustment, while the more extreme P99 statistic is improved but still somewhat underestimated in most regions.
Figure 4: Precipitation statistics for the original (blue) and bias adjusted ECMWF-s51 forecasts compared to the EFAS-Meteo reference data set. The presented statistics are from bottom to top of each panel: mean, P95, and P99.
Four different performance measures are calculated for each sub-basin or grid point, initialization month and lead time: The Fair Continuous Rank Probability Skill Score (fairCRPSS), the tercile fair Ranked Probability Skill Score (tercile fairRPSS), fair Brier Skill Score for lower and upper terciles (fairBSSbn and fairBSSan, respectively). All skill scores range between -infinity and 1, with 1 being the optimum. More details about the scores and how they were calculated can be found here: Hydrological model technical specifications, performance and forecast skill. The observational dataset EFAS-Meteo is used as reference for the skill score calculations on monthly mean values.
All calculated skill scores are available for download, and a few examples are presented below, again for the January and July forecasts, and only for the first lead month as there is very limited skill in the meteorological forecasts after that. The bias adjustment is significantly improving the skill scores for both precipitation (Figure 5) and temperature (Figure 6).
Figure 5: CRPSS of precipitation for the original ECMWF-s51 forecast (left), when bias adjusted (middle) and their absolute difference (adjusted minus original; right).
Figure 6: CRPSS of temperature for the original ECMWF-s51 forecast (left), when bias adjusted (middle) and their absolute difference (adjusted minus original; right).
Berg, P., Bosshard, T., Yang, W., & Zimmermann, K. (2022). MIdASv0. 2.1–MultI-scale bias AdjuStment. Geoscientific Model Development, 15(15), 6165-6180.
C3S (2018): Seasonal forecast daily and subdaily data on single levels. Copernicus Climate Change Service (C3S) Climate Data Store (CDS). DOI: 10.24381/cds.181d637e (Accessed on 06-03-2024)
Gualdi, S., A. Sanna, A. Borrelli, A. Cantelli, M. del Mar Chaves Montero, S. Tibaldi, 2020: The new CMCC Operational Seasonal Prediction System SPS3.5. Centro Euro-Mediterraneo sui Cambiamenti Climatici. CMCC Tech. Note RP0288, 26pp. DOI: https://doi.org/10.25424/CMCC/SPS3.5
Johnson, S. J., Stockdale, T. N., Ferranti, L., Balmaseda, M. A., Molteni, F., Magnusson, L., ... & Monge-Sanz, B. M. (2019). SEAS5: the new ECMWF seasonal forecast system. Geoscientific Model Development, 12(3), 1087-1117.
JRC (2024) EMO-5 (1990-2019) url: https://data.jrc.ec.europa.eu/dataset/0bd84be4-cec8-4180-97a6-8b3adaac4d26#description (Accessed on 06-03-2024).
Ntegeka V, Salamon P, Gomes G et al (2013) EFAS. weeks for a specific region. The Meteo: A European daily highblack dots are resolution gridded meteorological C3S_424_SMHI_2020SC2 data set for 19902011. Report EUR, 26408
Vrac, M., Noël, T., and Vautard, R.: Bias correction of precipitation through Singularity Stochastic Removal: Because occurrences matter, J. Geophys. Res.-Atmos., 121, 5237–5258, https://doi.org/10.1002/2015jd024511, 2016.
This document has been produced in the context of the Copernicus Climate Change Service (C3S). The activities leading to these results have been contracted by the European Centre for Medium-Range Weather Forecasts, operator of C3S on behalf of the European Union (Delegation Agreement signed on 11/11/2014 and Contribution Agreement signed on 22/07/2021). All information in this document is provided "as is" and no guarantee or warranty is given that the information is fit for any particular purpose. The users thereof use the information at their sole risk and liability. For the avoidance of all doubt , the European Commission and the European Centre for Medium - Range Weather Forecasts have no liability in respect of this document, which is merely representing the author's view. |