A simple bias correction technique for modeled monsoon precipitation applied to West Africa

Transcription

1 GEOPHYSICAL RESEARCH LETTERS, VOL. 38,, doi: /2010gl045909, 2011 A simple bias correction technique for modeled monsoon precipitation applied to West Africa L. Feudale 1 and A. M. Tompkins 1 Received 19 October 2010; revised 19 November 2010; accepted 30 November 2010; published 4 February [1] Seasonal forecast systems suffer from biases in location and intensity of precipitation for the West African monsoon which require correction especially if used for impacts modeling. A simple global bias correction technique based on empirical orthogonal function analysis has been applied specifically to the West African monsoon region. It is demonstrated to improve the operational forecasts made by the European Centre for Medium Range Weather Forecasts seasonal forecasts which suffer from a systematic southerly shift in precipitation in this region. Citation: Feudale, L., and A. M. Tompkins (2011), A simple bias correction technique for modeled monsoon precipitation applied to West Africa, Geophys. Res. Lett., 38,, doi: / 2010GL Introduction [2] Predicting precipitation anomalies is one of the most difficult tasks for forecasts at seasonal lead times and the prediction of monsoon precipitation in particular remains a major challenge. Considering the West African monsoon (WAM) system, the June to September (JJAS) monsoon precipitation undergoes a high level of intraseasonal, interannual and inter decadal variability relative to other regions of the world [Sultan and Janicot, 2003; Nicholson, 2008]. A realistic representation of the precipitation field in forecasts is crucial, especially for impact and vulnerability applications in the Sub Saharan region, where agriculture is predominantly rain fed and transmission seasons of vector borne disease are demarked by precipitation anomalies. [3] Current seasonal forecasts of precipitation using dynamical models have not performed well in the WAM region with respect to other parts of the globe [Wang et al., 2009]. Part of this deficiency stems from the inability to reproduce a reasonable annual cycle of sea surface temperature (SST) in the tropical Atlantic [Huang et al., 2004; Tompkins and Feudale, 2010]. Along the African coastal areas of tropical Atlantic Ocean there is a strong interaction between SST anomalies, convection and associated surface winds, ocean upwelling [e.g., Dommenget and Latif, 2000] and this feedback can modulate errors in model parametrization schemes for subgrid scale physical processes and complicates the process of understanding the model shortcomings. [4] Forecasting centers are continually improving the representation of the physical processes to correct model deficiencies. This is a long term evolution and while significant biases in models persist, they must in the meantime 1 Earth System Physics Section, Abdus Salam International Centre for Theoretical Physics, Trieste, Italy. Copyright 2011 by the American Geophysical Union /11/2010GL be tackled using bias correction and calibration techniques, especially if the forecast output is to be used to drive enduser models for health, agriculture and socio economic impacts. [5] Rescaling is the most straightforward bias correction method, rectifying the systematic error in the mean and possibly variance of the precipitation amount, but this procedure may leave substantial frequency and intensity biases if the higher order moments of the observed and modeled precipitation probability density (PDF) exist. A quantilebased bias correction is also a useful approach to statistically transform the precipitation simulated by GCM to bias corrected data [Wood et al., 2002; Hopson and Webster, 2010], while a closely related technique maps the cumulative distribution functions (CDF) using best fit monotonic polynomials [Ines and Hansen, 2006; Piani et al., 2009]. [6] While quantile regression and CDF based approaches are able to correct higher order moments of the distribution of precipitation intensity, they are applied on a point wise basis and thus can not take advantage of known spatial correlation patterns of precipitation. This also implies that they are difficult to apply in data sparse regions. This is addressed by techniques that correlate models and observed regions of covariation, as, for example, singular value decomposition analysis (SVDA) and canonical correlation analysis (CCA). Ward and Navarra [1997], Feddersen et al. [1999] and Kang et al. [2004] used the SVDA to biascorrect their model simulations of seasonal prediction of precipitation. They corrected the systematic errors of the predicted anomaly by first identifying which leading modes of variability were well correlated between the observational and model precipitation fields. For these, they replaced the SVDA mode by the corresponding observed mode, demonstrating improved skill scores with the application of this post processing method. Feddersen et al. [1999] compared the SVDA method to one based on leading CCA modes and the two methods have shown to give similar results. One potential drawback is that even when two fields are spatially uncorrelated and have no common signal, the SVDA technique may result in an erroneous high correlation pattern [Cherry, 1996], which can be avoided using instead a technique based on empirical orthogonal functions (EOFs). Feddersen et al. [1999] also applied this third method, showing that the method works well on tropical precipitation, but that the skill was slightly below that of the SVDA and CCA based techniques. The EOF method was also applied to the multi model super ensemble of the DEME- TER forecasts and the forecast produced by their proposed method slightly improved the normal forecast [Yun et al., 2005]. [7] The EOF, CCA and SVDA based algorithms were applied on a global scale, with the performance of the 1of5

2 Figure 1. Total precipitation in the African region for JJAS for (a) SYS3 ensemble mean and (b) GPCP; (c) in the SYS3 bias. Units are mm day 1. methods determined by how well the model modes are correlated to the observed ones. It is possible that the application of this methodology may be even more beneficial if applied on a focused regional scale subject to a dominant mode of variability that can be well reproduced by a model. The WAM is one such example, where the predominate summer precipitation variability is defined by the progression inland and subsequent regression of the monsoon rains [Nicholson and Grist, 2003; Nicholson and Webster, 2007]. Many models can represent this precipitation progression well, but misplace the location of the summer rains. Thus the region is an excellent candidate to test the application of the mode based correction on the regional scale. This study applies and evaluates the simplest implementation of the EOF technique targeted for the WAM system to adjust the spatial distribution of the seasonal precipitation anomaly. 2. Model and Data [8] The precipitation hindcasts of the WAM region to be corrected were produced by the system 3 operational seasonal forecast (SYS3) of the European Centre for Medium Range Weather Forecasts (ECMWF). ECMWF SYS3 has been operational since March 2007 and consists of the atmospheric component, based on version 31R1 with resolution T L 159 with 62 vertical sigma levels, coupled to the Hamburg Ocean Primitive Equation (HOPE) ocean model, running with 29 vertical levels. Technical information about the model is available from Anderson et al. [2008]. The forecasts with 1st May start dates are corrected in this study since these contribute to the annual probabilistic consensus forecasting process in West Africa known as Prévision Saisonniéres en Afrique de l Ouest, or PRE SAO, thus the June to September rains are predicted with a 1 4 month lead time. Each forecast ensemble consists of 11 members. [9] The data used for precipitation validation is the Global Precipitation Climatology Project (GPCP) [Huffman et al., 1995] dataset, which consists of station data merged with satellite information. Data uncertainties and their covariances are not considered in this study. The precipitation is available as monthly mean values from 1979 onwards and so the study uses hindcasts made for the period 1979 to [10] To concentrate on West Africa the analysis is restricted to the domain between 27.5W 60E and 40S 40N. In Figure 1 the mean JJAS precipitation from SYS3 (Figure 1a) is compared with GPCP data (Figure 1b). Even if the model precipitation spatial distribution agrees reasonably well with observations, reproducing also the peak of precipitation close by the West coast and the Cameroonian region, the predicted mean precipitation shows an obvious shortcoming: an underestimation of precipitation over equatorial Africa and along all the Sahelian region (in evidence in the precipitation bias of Figure 1c). This bias is evident in the long term model summer climate and also every year, mainly due to the inability of the model to accurately reproduce the annual cycle of SST in the Tropical Atlantic. The reader is referred to Tompkins and Feudale [2010] for further analysis and explanations of the possible causes for this deficiency. 3. Method [11] A simple technique based on EOFs is applied to the hindcast dataset. As the methodology has been previously documented by Ward and Navarra [1997] and Feddersen et al. [1999], only a brief overview is given here. The EOF approach identifies independent patterns of variability, in this application specifically in the mean summer JJAS monsoon precipitation, that accounts for high amounts of statistical variance. Let X o =X o (x, y, t) be the GPCP data (anomaly with respect the mean summer precipitation) at a fixed point in space (x, y) and time (t), and X m =X m (x, y, t) the same for SYS3. The EOF decomposition derives the respective eigenvectors e o j and e m j (the subscript refers to the jth EOF). The principal component (PC) is then calculated as projection of the data vector X onto each eigenvector: where T stands for transpose. u o j ¼ e ot j X o ð1þ u m j ¼ e mt j X m ð2þ 2of5

3 Figure 2. First EOF of (a) SYS3 and (b) GPCP (mm day 1 ), and (c) their relative PCs (SYS3, solid and GPCP, dashed) calculated on the JJAS season for The spatial pattern of variability accounts for the 60% in SYS3 and 51% in GPCP of their total variability. [12] The data field can be approximately reconstructed from the principal component analysis according to: X m e m 1 um 1 þ em 2 um 2 þ...þ em N um N ¼ XN e m j um j j¼1 where N is the number of eigenvectors required to represent the desired proportion of the variance of the full field [Wilks, 2006]. In the following analysis N = 10 is used which represents about the 90 95% of the variance. [13] As introduced by Ward and Navarra [1997] and Feddersen et al. [1999], if the model s leading M EOFs are demonstrated to be good analogues of the observed principle modes, then a simple bias correction consists of projecting these EOFs of the model onto the equivalent modes calculated from the GPCP data. Therefore, the corrected dataset X c consists in the following linear combination: X c XM e o j um j þ XN e m j um j j¼1 j¼mþ1 Here for simplicity it is assumed that the coherent leading modes are consecutive while the implementation of Feddersen et al. [1999] also allowed for non consecutive modes. [14] Analyzing the leading EOFs, the first EOF of the precipitation anomaly identifies the latitudinal migration of the tropical rainband during the monsoon season showing a north south dipole pattern (Figure 2). The comparison between the first EOF calculated from model (Figure 2a) and observations (Figure 2b) again reveals the main deficiency of the model to concentrate the precipitation in the coastal region at the expense of the Sahel area, with the rain belt in the model shifted southward by about 3 4 degrees. ð3þ ð4þ The first EOF on GPCP data accounts for 51% of total precipitation variability and on SYS3 for about 60%. The first PC calculated from the SYS3 ensemble mean is closely related to the first PC of the GPCP data, with the greatest difference occurring in 1988, 1989 and 1999 where the model underestimates the intraseasonal variability (Figure 2c). The high correlation (0.83) shows that the model first EOF is a good analogue of the EOF calculated from the data. [15] The second EOF (not shown) captures instead the east west (between the Guinea Coast and the Cameroonian area) variability and accounts for 13% and the 15% of total variability of GPCP and SYS3, respectively. The correlation of the second EOFs is not significant (0.40) and thus in this implementation of the bias correction only the first EOF is retained (i.e., M = 1 above). In summary, only the bias of the principle mode is corrected, while the model s higher order modes of variability are unaltered. The number of corrected modes is smaller than in the global implementation of Feddersen et al. [1999] mainly due to the fact that precipitation variability is dominated by the first mode in this region. The bias correction is implemented using a crossvalidation technique [Michaelsen, 1987], in which data from one year at a time are withheld from the dataset and the EOF patterns calculated with the remaining years. 4. Results [16] The effect of the correction is most beneficial in the peak of the season in August when the tropical rain belt reaches its most northern position (Figure 3). The application of the method is able to place the peak precipitation in the correct latitudinal location. A running skill score [World Meteorological Organization, 2002] for the previous 10 years for precipitation in the upper boundary (between 16N 20N) in Figure 3g shows that the uncorrected model 3of5

4 Figure 3. EOF correction applied to the August precipitation in the WAM region from 1979 to (a) Total precipitation in the SYS3, (b) in SYS3 after the correction, (c) in GPCP. (d f) are the same as Figures 3a 3c only for the precipitation anomaly with respect the seasonal mean. (g) Skill score calculated for the upper boundary area (10W 10E, 16N 20N) on SYS3 (dotted), SYS3 after EOF correction (solid black) and SYS3 after a mean bias correction (solid grey). (h) Meridional profiles of precipitation zonal averaged between 10W 10E for June (solid), July (dots) and August (dot dash) of GPCP (thick black) compared with SYS3 (thick grey), SYS3 EOF corrected (thin black) and SYS3 mean corrected (thin grey). (mm day 1 ). has apparently little skill in predicting precipitation in the northern West African region, which improves significantly after correction with the EOF technique. As stated by Feddersen et al. [1999], it is important to emphasize that the correction technique does not improve underlying skill of the model, but simply improves the integrated point wise skill by correcting misplaced anomalies. If the model had no ability to predict seasonal anomalies in monsoon precipitation, the application of the bias correction would only be able to translate the large scale pattern of the model precipitation climatology to approximately match the observed climatology. Note also that the method outperformed a simple correction of the mean precipitation bias. [17] The profiles of monthly precipitation averaged over a longitude band 10W to 10E clearly show the improvement in latitudinal positioning of monsoon precipitation after the correction is applied, especially at latitudes northward of 12N (Figure 3h). This is most apparent in the month of August, where the original model underestimated precipitation by more than 2 mm day 1. [18] The improvement is further demonstrated by the mean square skill score (MSSS) in Table 1 calculated for two regions in the Sahel, a large (10W 10E, 12N 20N) and a small area (10W 10E, 16N 20N) close to the northern boundary of the rain belt, and for the two months of the summer season of June before the onset, and August when the monsoon is at a maximum. The MSSS for the corrected dataset increases especially for the area in the northern Table 1. MSSS calculated for the Entire Time Period a SYS3 Original SYS3 Correction SS (12N 20N) 0.54 (JUN: 0.74) 0.56 (JUN: 0.77) (AUG: 0.55) (AUG: 0.65) SS (16W 20W) 0.24 (JUN: 0.34) 0.40 (JUN: 0.74) (AUG: 0.25) (AUG: 0.55) a Top row: (10W 10E, 12N 20N); bottom row: (10W 10E, 16W 20W). The first column shows the results for the original SYS3 dataset, the second column for the corrected SYS3 dataset. In parenthesis the MSSS is calculated for the two months of the monsoon season in which the rainband reaches the two antipodes. 4of5

5 region where the skill score is almost doubled (Table 1). Clearly the correction improves the precipitation spatial distribution in SYS3 not only in the monthly mean, but also in the monthly accumulated precipitation during the entire monsoon seasons (JJAS) from 1979 to 2007 (Table 1). 5. Conclusions [19] Models are imperfect and their precipitation forecasts suffer from biases which require correction. Many correction methodologies exist, some operating on a point wise basis, while other methods use canonical correlation analysis, singular value decomposition analysis or empirical orthogonal functions analysis to identify model leading modes of variability that are well correlated with observed ones and then directly substituting the observed anomaly patterns for these modes. These methods have the advantage of maintaining the spatial coherence of precipitation anomalies and have previously been applied to global model output, but could be particularly useful on a regional scales with a dominant mode of variability that could be well represented by models. One example is the West African monsoon system where models can represent the onset and progression of the rains into the continent, but often with a spatial offset due to model deficiencies, as it is the case with the European Centre for Medium Range Weather Forecasts seasonal ensemble forecasts. In an empirical orthogonal function decomposition of precipitation variability in observations and the forecasts, the first mode of variability represents the monsoon progression and accounts for the majority of the precipitation variability in both the model and observations over the region. The higher model modes explain little variability and correlate poorly with observed modes, thus the bias correction was only applied to the first mode. The correction technique was found to improve the location of monthly and seasonal average precipitation anomalies and in consequence was able to maximize a point wise precipitation skill score. In conclusion, the spatial bias correction techniques are shown to have value applied on the regional scale. Future work will determine if the performance of EOF based techniques can be further enhanced by their combination with a point wise approach. [20] Acknowledgments. We thank Franco Molteni, Fred Kucharski and Claudio Piani for useful and constructive comments. This research was supported by the Research grant FISR CMCC (Fondo Integrativo Speciale per la Ricerca of the Centro Euro Mediterraneo per i Cambiamenti Climatici). References Anderson, D., et al. (2008), Development of the ECMWF Seasonal Forecast System 3, technical report, Eur. 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