Estimation of satellite observations bias correction for limited area model

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1 Estimation of satellite observations bias correction for limited area model Roger Randriamampianina Hungarian Meteorological Service, Budapest, Hungary Abstract Assimilation of satellite radiances requires systematic bias correction. Biases are mainly from instrument characteristics, inaccuracies of the radiative transfer model and of the assimilating model and also in the observation preprocessing. Accurate bias correction methods have been worked out for the assimilation of satellite radiances in global models. Bias correction computed with global models comprises synoptic situations and different seasonal conditions (summer and winter hemispheres). Question arises when estimating the bias correction for a limited area model (LAM) regarding the period of computation to have the "most representative" bias characteristics. Our previous study showed that bias correction characteristics estimated using the global model could not guaranty stable positive impact in a LAM. This paper investigates the impact of different predictors and different periods in the computation of the bias correction characteristics for a LAM assimilation system. Introduction Direct assimilation of satellite measurements requires the correction of the biases computed as differences between the observed radiances and those simulated from the model first guess. These biases arise mainly from instrument characteristics, but inaccuracies in the radiative transfer model can be also significant. Harris and Kelly (2001) proposed an efficient scheme to remove this systematic error. This scheme is based on separation of the biases into scan-angle and state dependent components. The air-mass (state) dependent bias is expressed as a linear combination of a set of statedependent predictors. At the previous international TOVS conference (ITSC-14), we reported about the importance of the bias correction in the processing of satellite data in a limited area model (LAM) (Randriamampianina et al., 2005). We concluded that the air-mass bias correction must be included in the processing of satellite radiances in a limited area model. In the estimation of the air-mass bias, four predictors computed from the first-guess fields should be taken into account: p1 the hpa thickness, p2 the hpa thickness, p3 the skin temperature, and p4 the total column water. Atkinson et al. (2005) mentioned some problems related to the last two predictors (p3 and p4). During the NWP-SAF workshop on bias estimation and correction in data assimilation, in Reading, we had long discussion on the period and on the frequency of the computation and upgrade of the bias correction for LAMs assimilation system. First part of this paper discusses the reduction of the number of predictors in the estimation of the air-mass bias correction. The second part describes the results of the investigation of the appropriate period for the computation of the bias correction for a LAM. Our study is in progress so in this paper only preliminary conclusions are given. Section 2 describes the main characteristics of ALADIN/HU model and its assimilation system. Sections 3 discusses the preliminary results of the study on the number of the predictors in the estimation of the air-mass bias correction, and section 4 illustrates the results of the study on the period for the computation of the bias correction coefficients. Section 5 draws some preliminary conclusions of our studies. The ALADIN/HU models and the assimilation system used in the study At HMS, the ALADIN/HU model runs in its hydrostatic version. The cy28t3/al28 version of the ARPEGE/ALADIN codes were used in the investigations. The three-dimensional variational data assimilation system was applied to assimilate both conventional (surface, radiosonde and aircraft) and satellite (ATOVS) observations. As a consequence of the direct radiance assimilation, it is necessary

2 to simulate radiances from the model parameters. The RTTOV radiative transfer code, which has 43 vertical levels, was used to perform this transformation (Saunders et al., 1998) in the ARPEGE/ALADIN models. Above the top of the model, an extrapolation of the profiles is performed using a regression algorithm (Rabier et al., 2001). Below the top of the model, profiles are interpolated to RTTOV pressure levels. The background error covariance matrix was computed using the standard NMC method (Parrish and Derber, 1992; Berre, 2000; Široká et al., 2003). No surface analysis was applied, the ARPEGE (the coupling files) surface fields were interpolated to the ALADIN/HU grids. The 3D-Var is running in 6-hour assimilation cycle generating an analysis at 00, 06, 12 and 18 UTC. In this study, 48-hour forecasts were performed daily from 00 and 12 UTC. Investigation of different predictors in the estimation of the bias correction In this study, three experiments were performed. Each of them concerned a two-week period. The following settings were considered using Harris and Kelly scheme (HKS): SBF8- HKS using the following 4 predictors: - model first guess thickness ( hpa) - model first guess thickness ( hpa) - model first guess surface skin temperature - model first guess total column water vapour SB4P- HKS using the following 4 predictors: - model first guess thickness ( hpa) - model first guess thickness ( hpa) - model first guess surface skin temperature - model first guess total column water vapour SB3P- HKS using the following 3 predictors: - model first guess thickness ( hpa) - model first guess thickness ( hpa) - model first guess surface skin temperature Even though a big reduction of temperature bias up to 12-hour forecast was observed in the upper troposphere and around the tropopause (Fig. 1) when changing the predictors (SB4P and SB3P cases), similar root mean square errors (RMSE) were found. Changing the predictors (SB4P and SB3P), we observed higher bias of relative humidity at the mentioned atmospheric levels (not shown) that also had no impact on the RMSE values. In the lower troposphere we observed an opposite effect of bias, which had also no impact on the RMSE (Fig. 2). Figure 1. Time series day-to-day bias and root mean square error (RMSE) of the analysis of temperature at 250 hpa for the different runs at 12 UTC.

3 Figure 2. Time series day-to-day bias and root mean square error (RMSE) of the analysis of temperature at 850 hpa for the different runs at 12 UTC. The impact of the changes in the mid-troposphere was more clear, we observed a reduction in both bias and RMSE (Fig. 3). Figure 3. Time series day-to-day bias and root mean square error (RMSE) of the analysis of temperature at 500 hpa for the different runs at 12 UTC.

4 Investigation of different periods in the computation of the bias correction for LAM data assimilation system Estimating the air-mass bias coefficients with the global model we have almost all available meteorological conditions (cyclonic, anticyclonic, winter, summer, etc ) within a relatively short time. While, with the LAM we have only those meteorological events passing through the model domain and for only one season. It is important to estimate the suitable period and the frequency for the update to be taken into account when estimating the bias correction for LAM. This paper reports the results of a study related to the estimation/computation of the bias correction coefficients within different periods (within one and several months). The experiments were repeated for two seasons (winter and summer) as follows: Summer case: Long period: the bias correction was estimated for the period from to Short period: the bias correction was estimated during the month of May A one month (during June 2006) experiment have been performed to evaluate the impact of the bias correction files (BC01- long period; BC02- short period) Winter case: Long period: the bias correction was estimated for the period from to Short period: the bias correction was estimated during the month of November A one month (during December 2005) experiment have been performed to evaluate the impact of the bias correction files (BC03- long period; BC04- short period). The impact of the bias correction coefficients was evaluated comparing the different runs for the same month. The scores of each run were evaluated objectively. The bias and root-mean-square error (RMSE) were computed from the differences between the analysis/forecasts and observations (surface and radiosondes) as well as analysis/forecasts and long cut-off ARPEGE analyses. Significance tests of the objective verification scores were also performed. The significance was examined based on statistical t-test regarding the difference in the expected values of the RMSE scores of the compared experiments. Plots were provided together with error bars that represent the interval in which the RMSE difference falls within 90% confidence. Consequently we considered a difference to be significant if the corresponding error bar did not include the zero difference line. Analysing the results from all runs, performed during the summer (June) and winter (December), we can conclude that the comparison against the observations did not show any significant differences. But the comparison against the long cut-off ARPEGE analyses showed some differences, especially during the summer period. Although almost similar bias was observed from the day-to-day scores, except few days, we noticed a remarkable difference in RMSE (Fig. 4). The differences, mainly on temperature, humidity and wind speed, are significant for the day-1 (until 24-h) forecast of wind speed (Fig 5). The difference between the scores from the comparison against observation versus against long cut-off analyses indicates that the impacts are locale and might be fare from the observed places (surface and radiosonde stations). Comparing the 10m wind fields, for example, we observe differences mainly over sea (Fig. 6). Although the impact of the bias correction coefficients on the analysis and forecasts for the relative humidity was not significant, the mean RMSE was negative in the lower troposphere (Fig. 7). Case Study: We investigated also the impact of the bias correction coefficients on the analysis and forecasts for precipitation and wind gust. The comparison was done against the surface measurements. In Figure 8 the RMSE time series of the cumulative precipitation are given for the whole ALADIN/HU domain and Hungary. For the summer period, the statistical investigation showed better forecast of precipitation when using the bias estimated during the longer period (case of 4-month update). Differences between the RMSE values were higher for the whole domain than those, calculated for Hungary. Our subjective verification, however, showed better forecast when using the bias, calculated for the shorter (one month) period. According to the map of the predicted precipitation over Hungary (Fig. 9) one can see differences between the precipitation fields (colored areas) and

5 corresponding surface measurements (white numbers) in the 36-h and 12-h forecasts in the highlighted areas. According to the subjective evaluation, the area without any precipitation in N-E Hungary was not predicted by the 36h forecast, that was performed using the bias correction calculated for the longer period. Also the precipitation fields in Western Hungary were closer to the measured data when applying the bias correction, calculated using the shorter period. Similar conclusions could be drawn regarding the 12h precipitation forecast. Most probably the calculated values were closer to the measured ones when using the bias calculated for the longer period, but the general spatial distribution of the precipitation fields were better in the other case. Concerning the winter period study, no valuable differences between the forecasts of precipitation were found between the forecasts obtained with the bias calculated for longer and shorter periods. According to the objective verification, better forecast of the wind gust was obtained for cases, when the bias correction was calculated using the short period information (Figure 10), except the forecast for June 10. The subjective comparison of the measured and predicted wind gust for that particular day was performed (Fig. 11). In general, the 12h forecast fields were better for the short-period case, but the predicted values were overestimated. Because of the overestimation, the objective verification gave better results for the forecasts, obtained using the bias correction based on the long period calculation. That means, that even for the only day when the long-period bias calculations gave better results (lower RMSE values), the subjective verification would prefer the forecast of the short-period case. Figure 4. Time series day-to-day bias and root mean square error (RMSE) for the analysis of 10m wind for the runs with the bias correction file computed during the short (BC02) and the long (BC01) periods at both (00 and12 UTC) networks for the summer case.

6 Figure 5. Significance test based on daily score from both 00 and 12 UTC runs for 10m wind speed fields associated to the summer case (left) and the winter case (right). Figure 6. Objective verification against the long cut-off ARPEGE analyses for the analysis of 10m wind speed. These graphs show the RMSE difference between BC02 and BC01 runs estimated from June 2006.

7 Figure 7. Significance test based on daily score from both 00 and 12 UTC runs for 2m relative humidity fields associated to the summer case (left) and the winter case (right). Verification days Verification days Figure 8. RMSE of the cumulated precipitation for the last 6-h of the 12-h forecast (mm/6h) evaluated for the whole ALADIN/HU domain (left) and for the Hungarian surface measurements only (right) for the period of 09 to 28 June The red lines refer to the long, while the green ones to the short-period calculations.

8 Long period (BC01) - 36h Long period (BC01) - 12h One month (BC02) - 36h One month (BC02) - 12h Figure 9. Cumulated precipitation for the last 6-h of the 36-h (left, from 9 th of June 2006) and 12-h (right, from 10 th of June 2006) forecasts valid for 12 UTC 10 th of June Numbers indicate the measured 6-h cumulated precipitation. days Figure 10. RMSE of the wind gust for the last 6-h of the 12-h forecast (mm/6h) evaluated over Hungary for the period of 09 to 28 June The red lines refer to the long, while the green ones to the short-period calculations.

9 Long period (BC01) - 36h Long period (BC01) - 12h One month (BC02) - 36h One month (BC02) - 12h Figure 11. Forecasted wind gust for the last 6-h of the 36-h (left, from 9 th of June 2006) and 12-h (right, from 10 th of June 2006) valid for 12 UTC 10 th of June Numbers indicate the measured wind gust. Preliminary conclusions Our investigations proved the importance of air-mass bias correction when assimilating satellite radiances in limited area models. Air-mass bias corrections calculated using three different combinations of five predictors were investigated. It was shown, that the bias correction can be improved by changing the combination of the predictors. The optimisation should also concern the reduction of the number of predictors used for bias correction. These conclusions are in agreement with those, drawn by Bjarne Amstrup (HIRLAM newsletter 51), who found, that excluding the model first guess surface skin temperature and the total column water vapor from the predictors improved the bias correction in DMI HIRLAM model. The objective verifications against observations and long cut-off analyses showed that differences in the forecasts when using bias correction estimated within different periods were mainly over sea. In this study bias corrections, calculated using data of different time periods (a 1 month short and a 4-5 months long period) were compared for both, summer and winter periods. The evaluation was based on the comparison of the measured precipitation and wind data with the forecasts, obtained using different air-mass bias correction methods. Better forecasts of wind speed and wind gusts were observed when using a monthly update for bias correction. Nevertheless, long term computation of bias correction appeared to be more efficient in case of the forecast of precipitation. Some differences in the results from summer and winter cases were found when investigating the impact of the period for the computation of bias coefficients. Our additional experiment showed, that these differences were not coming from the fact that there was one common month in the periods for the computation of bias correction coefficients for the winter cases. Further investigations are needed to optimise the predictors and the calculation period of the bias correction estimation for limited area models.

10 Acknowledgements The financial support from the TOVS organizing committee to attend the workshop is highly acknowledged. The research for this paper was supported by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences and by the Hungarian National Scientific Foundation (OTKA T049579). The help from Andrea Lőrincz and the fruitful discussion with the colleagues of the numerical modeling and climate dynamics division of the Hungarian Meteorological Service are highly appreciated. References Atkinson N., Cameron J., Candy B. and English S., 2005: Bias correction of satellite data at the Met Office, ECMWF/NWP-SAF Workshop on Bias estimation and correction in data assimilation, 8-11 November 2005, Reading, UK. Berre, L., 2000: Estimation of synoptic and meso scale forecast error covariances in a limited area model. Mon. Wea. Rev. 128, Bjarne Amstrup 2006: Note on the use of bias predictors for bias correction of AMSU data in DMI- HIRLAM, HIRLAM Newsletter N 51 (Available on Harris, B.A. and Kelly, G., 2001: A satellite radiance-bias correction scheme for data assimilation. Quarterly Journal of the Royal Meteorological Society, Randriamampianina, R.., 2005: Radiance-bias correction for a limited area model, Időjárás, 109, Rabier, F., Gérard É., Sahlaoui Z., Dahoui M. and Randriamampianina R., 2001: Use of ATOVS and SSMI observations at Météo-France. 11 th Conference on Satellite Meteorology and Oceanography, Madison, WI, October 2001 (preprints). Boston, MA, American Meteorological Society Saunders, R., Matricardi, M. and Brunel, P., 1998: An improved fast radiative transfer model for assimilation of satellite radiance observations. Quarterly Journal of the Royal Meteorological Society Široká, M., Fischer, C., Cassé, V., Brožková R. and Geleyn, J.-F., 2003: The definition of mesoscale selective forecast error covariances for a limited area variational analysis. Meteorology and Atmospheric Physics