An application of statistical downscaling to estimate surface air temperature in Japan

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 107, NO. D10, 4095, 10.1029/2001JD000762, 2002 An application of statistical downscaling to estimate surface air temperature in Japan Naoko Oshima, Hisashi Kato, and Shinji Kadokura Central Research Institute of Electric Power Industry, Tokyo, Japan Received 10 April 2001; revised 20 August 2001; accepted 15 October 2001; published 24 May 2002. [1] In this study, a statistical downscaling model based on singular value decomposition was applied to estimate the monthly mean temperature field in Japan for January and July. The regression model estimated surface air temperature in Japan from upper air temperature in east Asia with root-mean-square errors of around 1.0 C for an independent verification period. The method was applied to the output of a CO 2 transient run of NCAR-CSM, and the result was compared with the output of NCAR-RegCM2.5 nested in CSM. The statistical model reproduced the spatial distribution of the temperature more realistically than the CSM output. In January the results corresponded well between the models except that the climate simulated by RegCM was generally cooler than that estimated using the statistical method mainly due to the unrealistic RegCM topography. In July the results did not correspond well between the methods, since the climate is more complex and difficult to be estimated solely from the upper air temperature field. Temperature rise from 1CO 2 climate to 2CO 2 climate was larger in RegCM than in the statistical method for both months reflecting the influence of sea surface temperature rise. It was concluded that this statistical downscaling method can be applied to estimate the January mean temperature in Japan, although other predictor variables such as sea surface temperature should be included to improve the estimation in July. INDEX TERMS: 1610 Global Change: Atmosphere (0315, 0325); 9320 Information Related to Geographic Region: ASIA; KEYWORDS: climate change, statistical downscaling, singular value decomposition, temperature, east Asia, Japan 1. Introduction [2] The increase in the concentration of greenhouse gases in the atmosphere is said to cause global warming, and the resulting climate changes and their impact upon the natural environment and on human society are of great concern [International Panel on Climate Change (IPCC), 2001]. General circulation models (GCMs) are widely used as an important method of predicting global climate changes induced by the increase of carbon dioxide (CO 2 ). The spatial resolution of the present state-of-the-art GCMs, which is about 200 300 km, is sufficiently fine to predict the principal features of the global climate change. However, the resolution is too coarse to provide the regionalscale information required for regional impact assessments, particularly in areas with complicated geography such as east Asia [Giorgi and Mearns, 1999]. Therefore downscaling methods for extracting regional-scale information from the output of GCMs have been considered. [3] High-resolution GCMs, regional climate models nested in GCMs, and statistical downscaling methods are the three main tools for downscaling. Regional climate models (RegCMs) are dynamic models nested in GCMs and are used to translate GCM output information given as boundary conditions into regional scales. RegCMs can simulate physically convincing regional climates. However, they require a considerable amount of computer resources. Statistical downscaling methods, on the other hand, are methods for estimating a regional-scale climate from GCM output using the statistical relationship between the largescale climate and the regional-scale climate. In this method, to begin with, the relationship between a large-scale climate field and Copyright 2002 by the American Geophysical Union. 0148-0227/02/2001JD000762 a regional-scale climate field is described on the basis of observational data. Then, the relationship is applied to GCM output in order to extract a regional-scale climate estimate. [4] The present GCMs are considered to entail a considerable degree of uncertainty. Therefore to compare the regional climate estimates translated from different GCMs and to investigate the variability between the scenarios is more favorable than relying on only one scenario for a reliable impact assessment. Since statistical methods are less computer intensive and can be applied regardless of model structures, it is easier to use the methods for translation. On the other hand, in the results of statistical downscaling methods, the physical mechanisms of phenomena should be supported by results obtained through dynamic models. Hence the results of dynamic models and statistical downscaling methods should support each other. [5] Statistical downscaling methods can be classified into the following three main groups: transfer function methods, weathertyping methods, and weather generator models [IPCC, 2001; Wilby and Wigley, 1997]. In transfer function methods, a direct quantitative relationship, typically a regression equation is established between large-scale climate variables and regional-scale climate variables based on observed time series data. Complicated multivariate analyses are applied in order to extract regional-scale climate information from large-scale climate information. A considerable number of studies have been made on statistical downscaling using multivariate analyses [Kim et al., 1984; Wigley et al., 1990; Huth, 1999; Murphy, 2000; Landman and Tennant, 2000; Wilby et al., 2000; Benestad, 2001]. For example, Zorita et al. [1992] used a principal component analysis combined with a canonical correlation analysis to reveal that large-scale pressure patterns over the North Atlantic Ocean affect precipitation in the Iberian Peninsula and the seasonal fluctuation of the sea surface temperature in the Atlantic Ocean. von Storch et al. [1993] used this relationship to downscale the output of a GCM. ACL 14-1

ACL 14-2 OSHIMA ET AL.: STATISTICAL DOWNSCALING FOR TEMPERATURE IN JAPAN [6] In weather-typing methods, certain atmospheric conditions are related to regional climate variables based on the concept of a synoptic climate. First, the large-scale climate field is subjectively or objectively classified into patterns. Then the patterns are related to the regional-scale meteorological observational data [Hay et al., 1991, 1992; Bardossy and Plate, 1991, 1992; Matyasovszky et al., 1993, 1994; Enke and Spekat, 1997; Conway and Jones, 1998]. For example, Bogardi et al. [1993] identified nine circulation pattern types based on the 500 hpa height field data for 40 years in the western central United States and found that both the probability and the amount of daily precipitation in eastern Nebraska are strongly related to these types. Aspects of daily precipitation patterns are controlled by large-scale weather patterns, and thus the use of this method is recommended [Mearns et al., 1999]. [7] Stochastic weather generator models produce realistic time series of meteorological variables as random variables. For example, the amount of precipitation in a given day is predicted using Markov chains conditioned by the precipitation of the previous day. For the purpose of downscaling, the parameters of the chaindependent processes are conditioned by large-scale atmospheric circulation [Katz and Parlange, 1993, 1996; Katz, 1996]. Semenov and Barrow [1997] first conducted regression downscaling and used the downscaled values to fit the parameters of a weather generator model in order to simulate site-specific daily weather data. Other relevant works were conducted by Richardson [1981] and Wilks [1992, 1999]. [8] Numerous attempts have been made to downscale climate information statistically. However, the methods have been applied mainly to Europe and the United States, and little attention has been given to the region of east Asia, including Japan. In this study, a statistical downscaling method was applied to the air temperature field in east Asia, and the applicability of the method to the region was examined. Among the three methods mentioned above, the regression approach is the most direct method to statistically relate predictor variables and predictand variables. Since the surface air temperature field is expected to be controlled most strongly by the large-scale upper air temperature field, it was decided to use the regression approach for downscaling in this study. [9] This paper is organized as follows: The data used in the analysis are described in section 2. The methodology is then given in some detail in section 3. Results and discussion are given in section 4. Finally, a concluding section is provided in section 5. 2. Data [10] In this study, the January and July monthly mean upper air temperature field in east Asia was downscaled to the surface air temperature field in Japan. Data domains used for the analysis are shown in Figure 1. With regard to the predictor field, gridded January and July monthly mean upper air temperature data for three pressure levels (namely, 850, 700, and 500 hpa) for east Asia from 1966 to 1995 (1996 for January) were used (Figure 1a). These observed data come from the Monthly Northern Hemisphere 72 19 Tropospheric Analyses data set prepared by the National Center for Atmospheric Research (NCAR) Data Support Section (http://dss.ucar.edu). The data at higher levels (300 and 200 hpa) were also used in the preliminary analysis. The resolution of the grid is 5 by 5, and the data were interpolated into a 2.81 by 2.81 grid to match the GCM output mentioned below. To eliminate the effect of topography, 850 hpa data were omitted for grid points of over 1500 m above sea level, and 700 and 850 hpa data were omitted for grid points of over 3000 m above sea level. With regard to the predictand field, January and July monthly mean surface air temperature data obtained at 51 observation stations in Japan (observed by Japan Meteorological Agency) for the same period were used (Figure 1b). Figure 1. Domains used in this analysis: (a) the grid points for the upper air temperature field and (b) the observation stations for the surface air temperature field. [11] The upper air temperature estimate in east Asia for the present and doubled CO 2 climates (9 and 10 years of simulated values for 1CO 2 and 2CO 2 climates, respectively), calculated using the NCAR climate system model (CSM, version1.0), was used as the GCM output for downscaling [Boville and Gent, 1998; Maruyama et al., 1997]. The model was forced with a gradual increase of CO 2 concentration, 1% increase per year compounded. The statistically downscaled surface air temperature estimate was compared with the output of the NCAR RegCM2.5 (regional climate model version2.5) nested in CSM [Giorgi and Mearns, 1999; Kato et al., 2001a]. 3. Procedure [12] In this study we applied a regression method based on singular value decomposition (SVD) in order to relate the predictor and predictand fields statistically. A regression method based on a variant of canonical correlation analysis (CCA) prefiltered and orthogonized by principal component analysis (PCA) (hereinafter

OSHIMA ET AL.: STATISTICAL DOWNSCALING FOR TEMPERATURE IN JAPAN ACL 14-3 referred to as PCA + CCA) was also examined for comparison. Bretherton et al. [1992] compared several methods for finding coupled patterns in climate data by applying them to an artificial model field created by adding signals with noise. The result showed that methods based on SVD and PCA + CCA show smaller system error and reproduction error than the combined PCA and single-field-based PCA methods. These methods are superior to the much simpler multiple regression analysis since they can describe the relationship between the plural predictors and the plural predictands in the form of the most closely correlated pairs of patterns. [13] SVD identifies the pairs of spatial patterns from the two fields that share maximum covariance, while CCA identifies the pairs of patterns that share maximum correlation. The second pairs maximize covariance or correlation for the residual vectors, and so on. A detailed description of SVD can be found in the work of Bretherton et al. [1992]. In this study, SVD pairs were first identified from the observed data of upper air temperature (predictors X ) and surface air temperature (predictands Y ), both transformed to deviations from the mean states of the years for model fitting. Let X(i,t) be the observed data of X at grid point i (i = 1, 2,..., N X ) and time t (t =1,2,..., T ), and let Y( j,t) bethe observed data of Y at station j ( j =1,2,..., N Y ) and time t. The two sets of data can be expanded on the basis of SVD as follows: Xði; tþ XK a k ðþp t k ðþ i k¼1 Yðj; tþ XK b k ðþq t k ðþ; j k¼1 where p k and q k are kth SVD patterns, and a k and b k are called kth SVD/CCA expansion coefficient time series. These expansions can be used to estimate predictand data for an independent time period (t 0 ) based on a least squares method: Yðj; t 0 Þ XK CORREL½a k ðþ; t b k ðþ t Š STDEV ½ b kðþ t Š a k ðt 0 Þq k ðþ: j STDEV ½a k¼1 k ðþ t Š The climatological means for the fitting period were added to the regressed values to obtain the downscaled result. A detailed description of PCA + CCA can be found in the work of Barnett and Preisendorfer [1987]. In the PCA + CCA method, predictor variables and predictand variables were summarized into several principal components (PCs) in the respective fields. Then, weighted sums of the two PC variable fields (canonical variables) were selected, so the correlation coefficients between the pairs of canonical variables were maximized. Finally, simple regression equations between the pairs of canonical variables were derived in the same way as in the case of SVD. [14] The SVD method and the PCA + CCA method are similar in the sense that the relationship between the weighted sums of the two data fields is optimized. Actually, the PCA + CCA method is identical to SVD of the temporal cross-covariance matrix between the leading mode PC sets standardized to have variances of 1. Therefore if PCs are not standardized with their variances and the higher mode PCs are not truncated in the PCA + CCA method, then the result will be exactly the same as that of the SVD method. The major difference between the two methods is that in the PCA + CCA method, small fluctuations such as random noise which may worsen a correlation between parameters are filtered out from each data field using PCA prior to the analysis of the relationship between the two data fields, whereas in the SVD method, they remain unfiltered before the two fields are related. In the PCA + CCA method the number of PCs retained for CCA must be selected arbitrarily. If the number is too small, PCs, which explain only a small fraction of the variance of the field but have a strong connection with the other data field, are filtered out before CCA. Therefore strongly related patterns could remain undescribed. However, if too many PCs are retained for CCA, estimate errors could become larger due to noise, particularly because the higher mode PCs tend to strongly affect the result because of the standardization of PCs. Thus the number of PCs should be chosen carefully. On the other hand, the SVD method maximizes covariance of predictors and predictands rather than the correlation coefficient, so the coupled modes that are not only closely correlated between the fields but also show large fluctuation in the respective field tend to become the leading modes. Therefore there is no possibility that closely correlated modes are eliminated before the two fields are related. Although the linear transformation matrix between the SVD expansion coefficient time series is not identical to that of original data except in the special cases [Newman and Sardeshmukh, 1995], the leading modes that correlate strongly can describe the principal relationship between the fields. [15] Comparing these two methods, PCA + CCA has the merit that we can compare the spatial structures of patterns with large fluctuations in one field only and patterns that fluctuate together with the other field by comparing PCA patterns and CCA patterns. However, its demerit is that the choice of the number of variables is subjective. The merits of the SVD method are that subjective noise removal is unnecessary, and the computational process is simpler. 4. Results and Discussion 4.1. Comparison of the Methods [16] The basic concepts of SVD and PCA + CCA are similar except for the maximization target (covariance for SVD and correlation coefficient for PCA + CCA) and noise removal, so the results are expected to resemble each other. However, since the properties of the regional climate field, such as the variance explained by the selected PCs, affect the level of necessity of noise removal, a preliminary analysis was conducted to compare the two methods for the east Asia region. [17] The SVD and the PCA + CCA methods were applied to the January and July monthly mean observed data for the upper air temperature in east Asia and the surface air temperature in Japan. In the PCA + CCA method, PCs, which account for 70% of the variance of their respective fields, were used for CCA as recommended by Bretherton et al. [1992]. However, at least three leading PCs were retained in this analysis due to the reason explained later. The leading modes derived by these methods were dominant in the fields, and the spatial structures of the modes were similar between the methods. For example, both the SVD first mode and the PCA + CCA second mode described the close relationship between the second PC of the upper air field and the first PC of the surface field in January (not shown). Similarly, the SVD second mode and the PCA + CCA first mode described the relationship between the first PC of the upper air field and the second PC of the surface field in January. The distribution patterns, which showed a high correlation between the upper air temperature field and the surface air temperature field, were dominant in the respective fields. Therefore there was no significant difference between the two methods so long as only the dominant modes were considered. [18] In the case of the surface air temperature field, the first mode of PCA was so dominant (with the explained variance of 82% in January and 76% in July) that the second mode of PCA was eliminated as noise if 70% variance was used as a threshold. Since the second mode of the surface PC actually showed a strong correlation with the first mode of the upper air temperature PC, noise removal based solely on the threshold of the proportion of the variance might not represent the good relationship between the

ACL 14-4 OSHIMA ET AL.: STATISTICAL DOWNSCALING FOR TEMPERATURE IN JAPAN Table 1. Squared Covariance Fraction (SCF) and Cumulative Squared Covariance Fraction (CSCF) for Five Leading Modes of the SVD Expansion and the Temporal Correlation Coefficient r Between SVD Expansion Coefficients of Upper and Surface Air Temperature Fields Associated With the Same Mode (January and July) k SCF k,% CSCF k,% r(a k,b k ) January 1 85.08 85.08 0.88 2 13.89 98.98 0.88 3 0.46 99.43 0.68 4 0.22 99.65 0.72 5 0.10 99.75 0.81 July 1 88.00 88.00 0.89 2 8.53 96.53 0.62 3 1.58 98.11 0.70 4 0.76 98.87 0.65 5 0.28 99.15 0.69 fields. On the other hand, the third modes of the SVD method and the PCA + CCA method described the correlation between the third PC of the surface field and both the fourth and the fifth PCs of the upper field. Hence it was confirmed that the simple regression analysis between the PCs could cause errors. From the above discussion, it is clear that the use of the SVD method, which does not require subjective prefiltering, is preferable in this case. Therefore the SVD method was chosen for this study. [19] The temperature fluctuation at 300 and 200 hpa levels did not contribute to the fluctuation of the leading modes in both methods, so only the data at 850, 700, and 500 hpa were used in the following analysis. 4.2. Application to Temperature 4.2.1. Relationship derived by SVD. [20] Table 1 summarizes the squared covariance fraction (SCF), the cumulative squared covariance fraction (CSCF), and the temporal correlation coefficient (r) for the five leading modes (k) of the SVD expansion derived from the observed data for the upper and surface air temperature fields. SCF is defined as the percentage of the squared covariance explained by a pair of patterns, and it indicates how successful the method has been in explaining the observed covariance matrix between the fields using the mode [Bretherton et al., 1992]. [21] Since more than 96% of the squared covariance was explained by the two leading SVD modes in both January and July, it was evident that these leading modes were dominant in the relationship between the two fields. Therefore a large degree of regional climate fluctuation is controlled by the large-scale climate field, which is the basic assumption for the applicability of statistical downscaling methods. The correlation coefficients between the expansion coefficients associated with these two leading modes were higher than 0.8 for the first, second, and fifth modes in January and the first mode in July. For the leading five modes of these months, the correlation coefficients were statistically significant at 1% level. [22] Figure 2 shows the spatial distributions of the correlation coefficients between the SVD expansion coefficients and the temperature anomaly data at each station or grid point for the two SVD leading modes in January which are defined as CORREL½a k ðþ; t Xði; tþš CORREL½b k ðþ; t Yðj; tþš for upper air and surface air temperature fields, respectively. These patterns indicate the extent to which the SVD modes describe a temperature anomaly at each station or grid point. In the areas where correlation coefficients are relatively high, the temperature anomaly correlates with the SVD mode relatively strongly. Such areas are called action center hereinafter. In January the first SVD mode for the surface field explained 82% of the total variance of the surface air temperature observed data (Figure 2a), so it was the dominant mode that governed the fluctuation in the surface field. The pattern related strongly to the surface air temperature anomaly and was almost identical to the spatial pattern of factor loading of the first PC of the surface air temperature (not shown). This pattern showed a very strong negative correlation coefficient (< 0.9) over a wide area, except in Hokkaido (the most northern of the four main islands of Japan (Figure 1)). The corresponding SVD first mode for the upper air field had a strong negative action center over a wide area in the center of the domain (Figure 2b) and showed positive over the Kamchatka Peninsula, which is located to the northeast of Japan. This pattern was similar to the spatial pattern of the second principal component of the upper air temperature. Accordingly, the SVD first mode mainly expressed the overall temperature fluctuation around Japan and was the same for both upper and surface fields. The correlation pattern for the surface second mode of SVD showed a strong positive in eastern Hokkaido (Figure 2c), and the pattern was similar to the second principal component pattern of the surface air temperature field (not shown). The corresponding SVD upper air second mode showed a strong positive over the southeastern region of Russia (Figure 2d) and was similar to the first principal component pattern. The SVD second pair of patterns also had a strong correlation in the same area for both the upper air field and the surface field. This mode expressed a relationship between the north-south temperature gradient of the upper air and the surface air temperature anomaly in Hokkaido. [23] Figures 2e, 2f, 2g, and 2h show correlation coefficient patterns for the first and second SVD modes in July. Variances of 76% and 15% of the surface and upper air temperature data were explained by the first mode, respectively, so the mode was dominant particularly in the surface field. In Figures 2e and 2f, a marked positive action center in the middle was evident, although it occupied a smaller region compared with the action center in January. Therefore it can be said that the first SVD mode described the overall temperature fluctuation around Japan, which is common for both surface and upper air temperature fields. The second mode correlation pattern for the surface air temperature (Figure 2g) described the north-south gradient of the surface air temperature pattern. The upper air pattern (Figure 2h) described the temperature fluctuation in the southwestern part of the domain and was limited to the height lower than the 700h Pa level. [24] The spatial patterns of the two SVD leading modes were similar to the spatial patterns of the two leading PC patterns of the respective fields both in January and in July. Therefore it was concluded that the principal fluctuations in the upper air temperature field were correlated to those in the surface air temperature field as well. 4.2.2 Regression analysis between the two fields. [25] Regression equations between the coupled expansion coefficients of the SVD analysis were derived. The surface air temperature reconstructed from the upper air temperature data using the regression equations was compared with the observed data. The observed climatological means were added to the regressed values to be compared directly with the observed data. Table 2 illustrates the fraction of the variance of surface air temperature explained by regression from the upper air temperature. In January the first SVD mode was by far the most dominant mode, and the top two modes together explained more than 70% of the variance of the surface air temperature data. Including the third- or higher-order modes did not improve the reproduction significantly, except for Hokkaido where the second and third modes contributed to the improvement considerably (not shown). In July the first mode was by far the

OSHIMA ET AL.: STATISTICAL DOWNSCALING FOR TEMPERATURE IN JAPAN ACL 14-5 Figure 2. Correlation patterns for the first mode in the SVD expansion for the (a) surface and (b) upper air temperature fields in January. The second SVD mode correlation patterns for the (c) surface and (d) upper air temperature fields in January. Figures 2e, 2f, 2g, and 2h are the same as in Figures 2a, 2b, 2c, and 2d, respectively, except for July. The black areas in the upper air fields were not used in the analysis to remove the effect of topography, and the shaded areas are where correlation coefficients were statistically significant at 99% confidence level. Fractions of variances in the respective fields explained by the mode are shown as VF. most dominant mode compared to other modes, as in the case of January, and the mode explained about 60% of the total variance. The leading two modes together explained nearly 65% of the total variance, and including the higher-order modes did not improve the reproduction significantly. [26] The number of leading modes used for the regression was chosen so that the regression accounted for at least 99.00% of squared covariance, namely three in the case of January and five in the case of July. The root-mean-square errors (RMSEs) for the fitting period were around 0.7 C in both January and July. In January the RMSEs were relatively large (0.8 1.1 C) in Hokkaido, although they had decreased as the second and third modes were included in the regression analysis. The RMSE, averaged over seven stations in Hokkaido, decreased from 1.3 to 0.9 C by including the second SVD mode to the regression. This corresponds to the fact that the second SVD mode has its geographical action center around Hokkaido and is important for the estimation of surface air temperature in Hokkaido. The second SVD mode seems to represent the cold airflow from Siberia, which makes the winter temperature of Hokkaido cooler than other places on the same latitude. Therefore although the SCF of the first mode was about 6 times larger than that of the second mode, the less dominant mode could be important for some predictands. Nevertheless, even the third- or higher-order modes could not improve the errors for Hokkaido to the same level as for the other areas. The height-latitude cross sections of the correlation coefficients between the surface air temperature at observation station and the upper air temperature on the same latitude revealed that the surface air temperature in Hokkaido showed a weaker relationship with the upper air temperature field compared to other areas (figure not shown). In addition to the effect of the cold airflow from Siberia, Hokkaido is cooled down by the sea ice over the Okhotsk

ACL 14-6 OSHIMA ET AL.: STATISTICAL DOWNSCALING FOR TEMPERATURE IN JAPAN Figure 2. Sea. Radiational cooling further affects the surface air temperature at some locations in the middle of Hokkaido where the wind is weak. Thus other variables such as sea surface temperature and cold or warm airflow near the surface should be considered in order to improve the estimate in Hokkaido. [27] In a strict sense, the above discussion did not provide a reliable verification of the regression model, since the data used for reproduction were the same as the data used for deriving regression coefficients. To verify the regression method, we divided the observed data into two periods: the years 1966 1985 for model estimation (fitting) and the years 1986 1996 (1995 in July) for model verification. A comparison between the observed data and the estimated values for the years 1986 1996 is shown in Figure 3. The temperature was reproduced well in the estimate, but the variance was generally smaller in the reproduced values than in the observed data (Figures 3a and 3d). This is due to the fact that not all the local temperature fluctuations could be explained by largescale climate, and some factors other than the upper air temperature, such as sea surface temperature, also account for the surface air temperature anomaly. The RMSEs were around 1.0 C for the verification period both in January and in July (Figures 3b, 3e). These were partly due to the cumulated errors attached to the free parameters estimated in calculating the SVD. The standard deviations of the surface air temperature observed data are identical to (continued) RMSEs if the estimated temperatures were replaced with the climatic mean. Therefore the standard deviations can be considered as a lower benchmark for downscaling methods [Huth, 1999]. Since the RMSEs for the verification period were smaller than the Table 2. Relationship Between the Number of SVD Modes Used in the Regression Analysis and the Cumulative Fraction of the Variance of Surface Data Explained by Estimates (January and July) k Variance Explained,% January 1 63.09 2 72.08 3 72.59 4 73.01 5 73.40 30 75.57 July 1 60.04 2 64.64 3 66.53 4 67.32 5 67.82 30 70.85

OSHIMA ET AL.: STATISTICAL DOWNSCALING FOR TEMPERATURE IN JAPAN ACL 14-7 Figure 3. Comparison between the observed surface air temperatures and the values estimated using the statistical downscaling method for January. The regression equation was established on the basis of the 1966 1985 data, and the estimate is for 1986 1996 (1995 for July). Units are degrees Celsius. (a) Temperature averaged over all 51 stations, (b) root-mean-square errors (RMSEs) at each observation station, (c) comparison between the observed standard deviations and the RMSEs. The 51 station averages of RMSEs, and the temporal correlation coefficients (r) are printed. Figures 3d, 3e, and 3f are the same as in Figures 3a, 3b, and 3c, respectively, except for July and the estimate is for 1986 1995. standard deviations of the observed data except only at several stations, it is meaningful to apply the model to the CSM output at most stations (Figures 3c, 3f ). 4.2.3. Application to the CSM output. [28] We applied the regression model to the output of a transient run using the CSM. Figure 4 shows a comparison between the spatial distributions of surface air temperature in January for the observation, the spatially interpolated CSM output, and the statistical downscaling result. The results were shown for the area covered by four CSM grids for central Japan where the topography is complex. Compared with the observation, the CSM climate is warmer due to the strong effect of surrounding warm seawater, and isothermal lines were uniform and showed less regional variation. On the other hand, the statistical downscaling model reproduced a realistic temperature distribution. Figure 4. Comparison of January mean surface air temperatures by (a) observation (1966 1996 average), (b) CSM output (interpolated; 10-year average for 1CO 2 climate), and (c) statistical downscaling result (9-year average for 1CO 2 climate). Units are degrees Celsius.

ACL 14-8 OSHIMA ET AL.: STATISTICAL DOWNSCALING FOR TEMPERATURE IN JAPAN Figure 5. Comparison between the observed surface air temperatures (1966 1996 average) for the 51 stations and the estimated values by (a) the statistical downscaling method and (b) RegCM (both 9-year average for 1CO 2 climate) for January. (c, d) Same as in Figures 5a and 5b, respectively, except for July, and the observed values are 1966 1995 average. Units are degrees Celcius. January. A pattern analysis of the CSM output showed that the global model may not represent the present climate statistics in July very precisely [Kato et al., 2001b], in which case the downscaled estimates do not agree well with the observation. [30] A comparison of the estimated results of the surface air temperature by RegCM and the statistical downscaling method under the 1CO 2 climate is shown in Figure 6. At most stations in January, the results corresponded well between the methods (Figure 6a), except that the climate simulated by RegCM was cooler at most stations than that estimated using the statistical downscaling method. The difference between the methods was particularly marked (larger than 3 C) in some peripheral areas, including Hokkaido and Shikoku (Figure 6b). The difference for Hokkaido could be attributable to the relatively poor performance of this statistical downscaling, whereas the difference in other areas was attributed to the tendency of RegCM to reproduce temperature low. Figures 6c and 6d show the same result for July. As in the case of January, the statistically downscaled climate was warmer than that of RegCM except at several peripheral stations like eastern Hokkaido and isolated islands. Unlike January, temperatures did not correspond well between the methods. This is probably because the climate in July was more complex than that in January, and the influence of other variables, such as precipitation, which were not included in this statistical downscaling, was relatively large. [31] Figure 7 shows a comparison between the estimated surface air temperatures by RegCM and the statistical downscaling method under the doubled CO 2 concentration condition. In January the temperature rise from 1CO 2 climate to 2CO 2 climate averaged over 51 stations was 0.6 C for the statistical downscaling method and 1.4 C for RegCM (Figures 7a, 7b). The temperature rise is relatively large in Hokkaido due to the melting of sea ice [Kato et al., 2001a]. The rise in sea surface temperature around Japan was Thus it was confirmed that the application of the statistical downscaling model to a coarse-resolution global model would improve the estimate of regional-scale climate characteristics. Not only the temperature estimate at each year and location but also the statistics such as temporal or spatial mean temperature is expected to improve due to downscaling, since the downscaled values include effect of topography. [29] The statistical downscaling result was compared with the observed climate and the output of RegCM2.5 nested in CSM. Figures 5a and 5b show a comparison between the observed and the estimated present climates at the 51 stations in Japan in January. Statistical downscaling reproduced the observed climate fairly well, while RegCM tended to reproduce temperature lower than the observation. Comparison between the climatological means of the observation and the CSM 1CO 2 output in the upper air temperature field revealed that the CSM-simulated climate is warmer over Japan (with a maximum difference of +4 C at the 850 hpa level over the middle of Honshu), except Hokkaido. As the estimation by statistical downscaling agreed with this tendency of CSM, it was confirmed that the downscaled estimate was strongly controlled by the upper air temperature. The estimated climate in Hokkaido is particularly cooler than the observed climate, since the CSM overestimated the area of sea ice especially over the east Okhotsk Sea [Kato et al., 2001a], and the bias was as large as 14 C at 850 hpa over the Kamchatka Peninsula. In the north of Shikoku, topography of RegCM describes the nearby inland sea as land, and this rendered the RegCM-estimated climate in the vicinity cooler [Kato et al., 1999]. Figures 5c and 5d show the same result for July. The correspondences between observation and estimates were not so good as those for January. Compared with the observation, upper air climate simulated by CSM is cooler over Japan (the bias is 1 Cin Hokkaido to 4 C in Kyushu at 850 hpa). However, the bias was not directly reflected to the statistically downscaled result, showing that the influences of other factors were stronger than in the case of Figure 6. Comparison between the estimated January mean surface air temperatures for 1CO 2 condition by RegCM and the statistical downscaling: (a) temperature averaged over all 51 stations and (b) temperature difference (statistical downscaling minus RegCM; 9-year average for 1CO 2 climate) at each station. (c, d) Same as in Figures 6a and 6b, respectively, except for July. Units are degrees Celsius.

OSHIMA ET AL.: STATISTICAL DOWNSCALING FOR TEMPERATURE IN JAPAN ACL 14-9 Figure 7. Same as in Figure 6 except the 10-year average for the 2CO 2 condition. larger than that in the upper air temperature [Kato et al., 2001b], and it strongly influenced the surface air temperature rise in Japan [Kato et al., 2001a]. Therefore the average temperature rise estimated by RegCM was larger than that estimated by statistical downscaling. The temperatures corresponded well between the methods (Figure 7a). The geographical distribution pattern of the difference between the methods was basically similar to that of 1CO 2, and the temperature difference was within ±3 C at most stations (Figure 7b). The doubled CO 2 result for July is shown in Figures 7c and 7d. The average temperature rise from 1CO 2 climate was 0.4 C for the statistical downscaling method and 1.6 C for RegCM. As in the case of January, the sea surface temperature rise, which was larger than the upper air temperature, raised the estimate by RegCM. As in the case of 1CO 2 climate, the estimates did not correspond well between the methods in July. The geographical distribution of the temperature difference between the results of the methods was similar to the 1CO 2 climate result. 5. Conclusions [32] In this study, a statistical downscaling model for estimating the monthly mean surface air temperature in Japan from the monthly mean upper air temperature field in east Asia based on the SVD method was established for January and July. The RMSEs for an independent verification period were around 1.0 C, and they were smaller than the standard deviations of the observed data at most stations. [33] The method was then applied to the output of a transient run using NCAR-CSM, and the result was compared with the output of NCAR-RegCM2.5 nested in CSM. Since the geographical distribution of the statistically downscaled temperature was more realistic compared with spatially interpolated CSM output, the statistical downscaling method was confirmed to improve the estimate of regional-scale climate characteristics. In January the statistically downscaled result under 1CO 2 climate corresponded well to the RegCM output, except that the climate simulated by RegCM was cooler at most stations. The difference between the methods was mainly due to the effect of unrealistic model topography in RegCM. In July the temperature did not correspond well between the methods. This was probably because the Japanese climate in July is more complex than in January, and thus the statistical estimation solely from large-scale upper air temperature is more difficult. The temperature rise due to the doubling of CO 2 was larger in RegCM than in the statistical method in both January and July, reflecting the large influence of sea surface temperature around Japan, which was not included as predictor variables in this statistical downscaling. [34] It was indicated through the analysis that the monthly mean temperature in January in Japan could be estimated from the upper air temperature field in east Asia by using the statistical downscaling method, which is less computer intensive than RegCM, although some factors other than the upper air temperature should be considered for July. Introducing other parameters such as sea surface temperature, solar radiation, and sea level pressure as predictor variables is expected to contribute to improving the estimation for July. 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