A Semiempirical Downscaling Approach for Predicting Regional Temperature Impacts Associated with Climatic Change

Transcription

1 JANUARY 1999 SAILOR AND LI 103 A Semiempirical Downscaling Approach for Predicting Regional Temperature Impacts Associated with Climatic Change DAVID J. SAILOR AND XIANGSHANG LI Department of Mechanical Engineering, Tulane University, New Orleans, Louisiana (Manuscript received 24 June 1997, in final form 30 January 1998) ABSTRACT A statistical downscaling approach is developed for generating regional temperature change predictions from GCM results. The approach utilizes GCM free atmosphere output and surface observations in a framework conceptually similar to the model output statistics approach common in the forecasting community. The appropriateness of this approach is demonstrated through a comparison of GCM and observed free atmosphere variables. Seasonal downscaling models are presented for eight sites within four community climate model (CCM) grid cells in the United States. The majority of these models are capable of eplaining more than 90% of the variance in the temperature time series. The results indicate a wide range of differences between downscaled climate change predictions and grid cell level CCM predictions. 1. Introduction General circulation model (GCM) predictions typically indicate that the doubling of atmospheric CO 2 and concomitant increase in aerosol concentrations will lead to an elevation of global average temperature by a few degrees (e.g., IPCC 1995). There is little agreement, however, regarding temperature or precipitation predictions at regional scales. As pointed out by Grotch and MacCracken (1991) very low confidence is placed on the climate change scenarios produced by GCM predictions at the subcontinental or regional scale. There are several eplanations for this uncertainty. First, the typical GCM implementations involve very coarse grids. At a more fundamental level, all atmospheric models suffer from limitations in model physical and dynamical representation. Also, the forcing mechanisms for synoptic and mesoscale circulation patterns are quite different, and mesoscale influences on regional climate are not adequately accounted for within GCMs. Thus, GCMs generally perform well in capturing the largescale atmospheric motion, but must be viewed skeptically at regional scales. As pointed out numerous times in the literature, impact analysis of climatic change requires a regional or local focus beyond the scale limitations of the GCMs (e.g., Wigley et al. 1990; Robock et al. 1993; Gutowski et al. 1991). Several approaches have been suggested to overcome Corresponding author address: Dr. David J. Sailor, Dept. of Mechanical Engineering, 400 Lindy Boggs Center for Bioenvironmental Research, Tulane University, New Orleans, LA sailor@mailhost.tcs.tulane.edu these deficiencies by combining regional-scale surface information with the output from GCMs. Giorgi and Mearns (1991) present a review of some of the first significant attempts at downscaling. These downscaling efforts generally fall into three categories: regional nested climate modeling systems (e.g., Giorgi et al. 1993; Giorgi et al. 1994), empirical downscaling (e.g., Jager and Kellogg 1983), and statistical downscaling (e.g., Wilks 1992; Wilson 1992; von Storch et al. 1993; Zorita et al. 1995; Matyasovszky et al. 1994a,b). The statistical downscaling approach is rooted in the National Weather Service s (NWS) numerical statistical (N S) methods, which are used for daily weather forecasting. Klein (1982) reviewed three NWS statistical techniques, including two N S methods perfect prognosis (PP; Klein et al. 1959) and model output statistics (MOS; Glahn and Lowry 1972). These N S methods first derive statistical equations between the free atmospheric variables and local climate variables, then substitute the model-predicted free atmospheric variables into the equations to generate weather forecasts. MOS uses model output free atmospheric variables to develop the equations, and PP uses observations. Because MOS is able to take into account the internal bias and inaccuracy of numerical models, it has the potential to outperform PP (Klein 1982). A variety of techniques have been applied to develop the statistical relationships required for N S downscaling. Zorita et al. (1995) provide a brief description of some of the techniques that they group into regressionbased and weather-type-based techniques. The regression-based techniques normally are good for predicting the time-continuous local variables such as temperature, 1999 American Meteorological Society

2 104 JOURNAL OF CLIMATE VOLUME 12 wind speed, and humidity. Weather-type-based approaches can be used to predict both continuous and discrete local variables. Among the regression-based techniques, Karl et al. (1990) developed an approach referred to as climate projection by model statistics (CPMS), which uses a suite of three multivariate statistical components to relate the free atmospheric variables to surface observations. They found that a MOSlike version of CPMS closely approimated the observed local climate whereas the corresponding PP version did not. Hewitson (1994) developed a lag/ polynomial transfer function between the atmospheric circulation and surface temperature. He applied this transfer function to daily surface circulation predictions from the Goddard Institute GCM control run. Both of these studies looked only at current climate simulations, however. Winkler et al. (1995) presented a different transfer function approach, linking free atmospheric variables to surface temperature by using stepwise multiple regression. Downscaled predictions of future temperature were obtained by applying the output from the Canadian Climate Centre (CCC) GCM to the transfer functions for two specific locations one in the state of Michigan and one in Spain. In a weather-type-based approach, Matyasovszky et al. (1994a,b) stochastically linked climate pattern types to daily mean temperature using a conditional space time model. Both current and future climate downscaled temperatures were calculated using the 500-hPa geopotential height output from two GCMs for the central Nebraska region. Zorita et al. (1995) pointed out three assumptions behind the statistical downscaling approach. First, the GCMs are assumed to predict large-scale atmospheric variables more realistically than surface-based variables. The second assumption is that the relationships between the large-scale and local variables remain fundamentally unchanged under altered climate. Finally, the statistical procedure is assumed to not only replicate the historical data but to do so using physically meaningful variables and relationships. With respect to the first assumption, Portman et al. (1992) compared the National Center for Atmospheric Research (NCAR) Community Climate Model (CCM) grid-bo temperatures with observations at the surface, 850-hPa, 500- hpa, and 300-hPa levels. They found grid-bo to station differences decrease with height. A similar temperature comparison is conducted in this paper and a similar result is obtained. Palutikof (1995) showed that daily time series of maimum and minimum temperature directly from CCC output can be unrealistic, whereas the 500-hPa geopotential height and sea level pressure are in better agreement with observations. Risbey and Stone (1996), however, tested the ability of two GCMs to simulate large-scale and synoptic-scale processes for the Sacramento Basin and concluded that the GCM simulations showed major differences from observations. The synoptic processes that they investigated included stationary waves, jet streams, and storm tracks. Their results suggest that the quality of GCM large-scale variables can vary significantly. In fact, for any particular variable, the quality can differ from region to region. Therefore a preliminary quality checking procedure is required prior to using any candidate large-scale variable in a downscaling model. 2. Methodology Both temperature and precipitation changes are important to regional climate change impact modeling efforts. For many applications precipitation is a more important variable, but it is also much more difficult to predict. For the development of our downscaling approach, therefore, we have chosen to conduct an initial analysis focusing on temperature. Specifically, in this paper we develop and present a MOS-like downscaling approach to predict surface temperatures. The approach relates free atmosphere GCM predictions to surface observations. To motivate and justify the use of free atmosphere GCM output, we conducted a comparison analysis of GCM and observed temperature at the surface, 850-hPa, and 500-hPa levels. As discussed below, this comparison revealed that the 850-hPa temperatures and additional free atmosphere variables are strong indicators of actual surface temperature. Following the approach of the NWS we initially investigated 21 GCM free atmosphere variables as predictors. After some data preprocessing, the predictors and predictand (surface temperature) were directly linked using multiple linear regression (MLR) models. This analysis immediately revealed that many of these variables were relatively unimportant for predicting surface temperature. After further evaluation the initial best linear regression models were revised, using a subset of 7 of the original 22 free atmosphere variables. As the 850-hPa temperature was included in most of the initial models, we decided to force its inclusion in each of the final revised models. This decision is also justified on physical grounds as discussed later in this section. Using this final set of models, 2 CO 2 downscaled temperatures were then computed by applying the established models to the GCM 2 CO 2 output. The methodology developed here is applicable to any GCM. For the purposes of this paper we have used output from the CCM. The specific set of simulations is described in Henderson-Sellers (1993). To demonstrate the usefulness of this methodology over a wide range of regional domains, we selected four diverse regions across the United States to serve as test domains for our analysis. These regions are defined by specific CCM grid cells, and are nominally the same size as a typical state. We, therefore refer to these CCM grid cells by the name of the associated state: Louisiana, Nebraska, New York, and Washington. As our methodology results in very localized predictions, we chose to apply the analysis to two specific cities within each of these grid cells. These cities (indicated in Fig. 1) correspond

3 JANUARY 1999 SAILOR AND LI 105 FIG. 1. Locations of the CCM grid cells and specific downscaling sites investigated in the present paper. to locations of first-order weather stations from which we etracted the required surface observations for the present study. This range of grid cells allows an investigation of the role of geographical location in affecting the differences between downscaled temperature predictions and the baseline GCM predictions. The central cell covering much of Nebraska was intentionally selected for this study as it corresponds to the site of an independent downscaling effort by Matyasovszky et al. (1994a), which used a different driving GCM and a substantially different approach. Thus, we are able to compare our approach to an independent, conceptually different approach using a different driving GCM. a. Observation dataset Observational surface temperature data were obtained from two different first-order reporting stations in each of the four CCM grid cell regions for a period of yr, depending upon the site. The data are all daily observations, typically from large airports near major urban centers. As a result the downscaling estimates will be strictly applicable only to a small region surrounding the measurement sites. Nevertheless, there is typically a fairly strong correlation between temperature observations separated by short distances over similar terrain. Thus, it should be fairly straightforward to combine multiple downscaling analyses for scaling of these results up to larger regions of interest. In addition to the surface observations, free atmospheric variables for four sites (one within each grid cell) were etracted from the National Climatic Data Center s (NCDC) Radiosonde Data of North America ( ). Specifically, temperature, height, relative humidity, and wind components at 850- and 500-hPa level were obtained for the validation and comparison effort. The period of data availability depended upon the monitoring station and ranged from 30 yr for New Orleans to 45 yr for Omaha. b. GCM output dataset The driving GCM used in this study is version 1 of the NCAR CCM (Williamson et al. 1987). We etracted 12 large-scale atmospheric variables from a paired run (1 CO 2 and 2 CO 2 ) by Henderson-Sellers et al. (1993). The 12 variables include geopotential height, temperature, zonal and meridional wind components, and relative humidity all at both the 850- and 500-hPa levels. We also etracted the sea level pressure for use in the analysis. All CCM output were obtained using the CCM processor available on the Cray at NCAR. The selected variables are similar to those used by Karl et al. (1990), with only a few differences. Karl s variable list is similar to that developed by NWS s Technique Development Lab (TDL), but includes 500-hPa rather than 700-hPa data in an attempt to include information from higher altitude circulation patterns. Since this paper focuses on downscaling temperature, the K-Inde used by Karl was dropped from consideration because it is believed to be mostly relevant for precipitation studies. Although not used by Karl, our use of 850- and 500-hPa-level temperatures is justified from a historical basis (i.e., MOS from NWS). As in Karl s work, we calculated backward changes and forward changes of some variables, using values separated by 24 h. The final 21 predictor variables considered in this study are listed in Table 1. The choice of pressure levels at which predictors were selected was not arbitrary. The geopotential height of the 850-hPa level is usually at or above the top of the boundary layer. It therefore represents the lowest level

4 106 JOURNAL OF CLIMATE VOLUME 12 TABLE 1. Complete set of CCM1 variables considered in this analysis. Variable abbreviation T850 T500 U850 T500 V850 V500 SLP RH850 RH500 HT500 THKAV THK THK SLP SLP HT500 HT500 RH850 RH850 RH500 RH500 Description Temperature at 850-hPa level Temperature at 500-hPa level U wind speed at 850-hPa level U wind speed at 500-hPa level V wind speed at 850-hPa level V wind speed at 500-hPa level Sea level pressure RH at 850-hPa level RH at 500-hPa level Geopot. height of 500-hPa level Thickness of hPa levels Forward 24-h change of THKAV Backward 24-h change of THKAV Forward 24-h change in SLP Backward 24-h change in SLP Forward 24-h change of HT500 Backward 24-h change of HT500 Forward 24-h change in RH850 Backward 24-h change in RH850 Forward 24-h change in RH500 Backward 24-h change in RH500 in the GCM output for which we epect useful and consistent results. On the other hand, the 500-hPa level variables are generally a useful proy for large-scale circulation patterns. These two levels also represent common levels for which free atmosphere observations are available. c. Comparison of observed and CCM temperature at different levels The purpose of comparing observed and CCM predicted parameters is twofold. First, as discussed earlier, the quality of GCM predictions of large-scale atmospheric variables should, theoretically, be better than the surface predictions. Nevertheless, a real comparison between CCM and observed parameters is important for validating the necessity and appropriateness of using free atmosphere GCM predictions in this downscaling approach. Second, a prescreening of candidate free variables can prevent variables that are poorly modeled by the GCM from entering the downscaling models for a particular region. As will be shown later in this paper, the 850-hPa temperature is the most significant variable in our downscaling models. Therefore it is etremely important to make sure that the CCM 850-hPa temperature predictions are consistently of high quality when compared to actual observational data. One representative site from each of the four grid cells was chosen for this comparison effort. The four sites are New Orleans, Albany, Omaha, and Spokane. An approach first proposed by Chervin (1981) and later followed by Portman et al. (1992) is adopted here to compare the observed and CCM-predicted temperatures. Chervin used two test variates to check the agreement of variance and mean between GCM and observed variables. The first test variate is a scaled difference of the means of the GCM and observed time series of temperature: 2 2 r1 ( a b) a b. (1) Here, a and b are the variances of the GCM and observed time series, respectively, and a and b are the means. This variate takes on a value of 0.0 if the two means are equal. For a confidence level of 95% and nine degrees of freedom (see below), the null hypothesis (equal mean) is accepted when r 1 is in the range from 0.71 to The second test variate of importance is a simple ratio of the variances of the two time series: r 2 a / b. (2) This variate takes on a value of 1.0 if the GCM time series has the same variance as that of the observations. For a confidence level of 90% (as suggested by Chervin) and nine degrees of freedom, the null hypothesis (equal variance) is accepted when r 2 is in the range 0.56 to Following Portman s approach, 50 epanded datasets of observed 10-yr time series were created using a resampling procedure. Each time series set was obtained by randomly selecting 10 yr from the available period of analysis. This choice of 10-yr time series gives rise to the nine degrees of freedom discussed above. For each time series, interannual statistics were calculated for four seasons. Because only one set of CCM 10-yr time series is available, one set of CCM interannual statistics was calculated. For each season and for each of the three atmospheric levels, 50 values of r 1 and r 2 were then computed. Figures 2 and 3 show the statistical bo plots for the two test variates for each of the four sites. From these plots it is clear that the CCM mean 850-hPa temperature fairly consistently shows equal or better agreement with observations than is demonstrated by the CCM surface temperature predictions. One eample is Spokane, where the median of surface r 1 is about 4.7 in summer and 2.3 in fall, both well out of the 95% confidence range ( 0.71, 0.71). On the other hand, the r 1 variate for the 850-hPa level is always within this confidence range. In the case of Albany the surface and 850-hPa values for r 1 are roughly comparable. The r 2 test variate demonstrates similar behavior, although it falls into a relatively smaller range than r 1. This indicates that the CCM performed better at capturing the interannual variation than the mean. This analysis lends credibility to the choice of 850-hPa-predicted temperature as the primary predictor variable in this downscaling approach. d. Data preprocessing The CCM and observational datasets required some manipulation prior to conducting the analysis. The first

5 JANUARY 1999 SAILOR AND LI 107 FIG. 2. Statistical bo plots of test variate r 1 [Eq. (1)] for representative sites in each of the four CCM grid cells. The test statistic is shown for the surface, 850-hPa, and 500-hPa levels for each season. step was to remove the interannual variation by creating an average meteorological year (AMY) from each of the three datasets. The AMY was defined for the surface observations by taking day-by-day averages of surface temperature over the entire period of record. The AMY is similar to the concept of climate normal, though here daily normal is computed instead of the usual monthly normal. Since GCM output is not representative of any specific time period, a direct temporal comparison with observations is not appropriate. The averaging procedure implemented thus creates current climate normals suitable for comparison. Most of the observed AMY temperature curves were quite smooth, however, the variability in the winter was so large that even a 45-yr average demonstrated significant scatter. This suggests that simply averaging the observational data does not yield a true daily climate normal. Hence, a smoothing procedure was conducted for all observed temperature datasets. Several different smoothing approaches were investigated, each with essentially the same downscaling result. Ultimately, a single continuous curve is desired for the observational climate normal. To develop such a curve we divided the raw data into four segments and fit each segment with sith-order polynomial curves. To decrease the discontinuity at the boundaries between these four segments, 45 days of preseason and 45 days of postseason data were added to each segment prior to the curve fitting procedure. The curve fit data for each segment were then recombined to form a smoothed annual temperature profile. Each of the final smoothed observational datasets ehibited slight discontinuities of less than 0.4 C at the seasonal break points. The result for each site was a smoothed observational dataset, which when compared to the original data has an R 2 greater than 98%. An eample of the output from this smoothing technique is shown in Fig. 4 for Albany. This smoothing can be viewed as an etension to the above AMY averaging to achieve a true climate normal. It serves to remove the weather factors that cannot be captured by the GCM model. Seasonal aggregation has been used in most previous statistical downscaling studies. The usual seasonal division is into four seasons of 3 months each: DJF, MAM, JJA, and SON. We noted, however, that the temperature profile in the traditional winter season has a relatively small slope for all sites in this study, and that this seasonal division is incapable of yielding strong statistical models for winter. To alleviate this problem we shifted the seasonal groupings by 1 month, resulting in an overall improvement in model quality significant improvement in winter, while maintaining almost the same quality for the models in the other seasons. Development of seasonal models introduces one con-

6 108 JOURNAL OF CLIMATE VOLUME 12 FIG. 3. Same as Fig. 2 for r 2 [Eq. (2)]. cern that must be addressed. Specifically, models for neighboring seasons should give approimately continuous predictions at the seasonal boundaries. To reduce the magnitude of the discontinuities that naturally arise from the seasonal aggregation, we included 15 preseason and 15 postseason days in the development of the model for any particular season. For eample, the JFM seasonal model uses data from 16 December through 15 April. The average meteorological year for the CCM free atmosphere results was developed by simply taking the day-by-day average of each upper-atmosphere parameter over the 10-yr period of the simulation. This was done for both 1 CO 2 and 2 CO 2 simulations. It should be noted that the interannual variability of some CCM output variables is significantly larger than observed interannual variability, and that the inclusion of more years of CCM output from longer control runs should stabilize the specification of the CCM AMY. These AMY data were also grouped into four seasonal sets as discussed above. Although the observational dataset was smoothed to generate a representative climate normal, we chose not to smooth the CCM output so that we could investigate the capability of generating strong downscaling models directly from GCM output. It must also be pointed out that while the fluctuations in the observational AMY represent weather effects, which we wish to remove from the climate normal, fluctuations in the CCM AMY are due to other causes. Also, the CCM output consisted of only 10 yr of simulated data. As a result, smoothing the CCM AMY is not justified, and was not done. e. Statistical model development Using the two current climate seasonal datasets (observations and the CCM control run) a series of regression equations was developed relating free atmosphere parameters to surface temperature observations. Since the CCM is not capable of simulating the influence of detailed surface characteristics, the regression approach is used to implicitly include factors such as regional topography and land use. The regression analysis was performed independently for each city and for each season, resulting in a total of 32 seasonal models (four seasons eight cities). The initial modeling approach was to start with the single predictor that demonstrated the highest correlation with the dependent variable (observed surface temperature). Subsequently, the strongest possible multiple variable models were identified from all possible combinations of independent parameters. For each city and for each season the strongest model was identified as the best n-variable model, such that the adjusted R 2 was improved by less than 1.5% by the incremental addition of any other variable. The result, summarized in Table 2, was that slightly different sets

7 JANUARY 1999 SAILOR AND LI 109 FIG. 4. Sample of the smoothing approach applied to the raw observational data for the Albany site. of independent variables were used in each of the four seasonal models, and variable sets were inconsistent from location to location. Most models contained fewer than four independent variables, and had an adjusted R 2 greater than 90%. The winter models were a consistent eception, requiring four or five variables to produce models with R 2 between 70% and 90%. At this point in the analysis we found that 6 of the original 21 independent variables did not appear in any of the models. We also identified seven other variables that appeared in fewer than four of the models. As simplicity is greatly favored in the downscaling analysis, we removed these variables from our dataset resulting in a total of eight independent variables. We then conducted an analysis of correlation coefficients to verify that the CCM large-scale variables (used in the models) were well correlated with their observational counterparts. For all sites this annual correlation was above 0.95 for the temperature at the 850- hpa level (T850) and above 0.92 for the temperature at the 500-hPa level (T500). For the free atmosphere wind parameters, geopotential heights, and sea level pressures the correlations were less strong, but generally in the range of 0.7 to 0.9. The only variable that was not satisfactory for use in the downscaling for any site was the CCM prediction of V500, which generally had correlation coefficients in the range of 0.2 to 0.5. V500 was therefore removed from the list of independent variables. We also identified the 850-hPa temperature, which appeared in 24 of the original models, as the singlemost important variable. After the 850-hPa temperature, the net most significant variables showed up only in nine of the initial models and were related to geopotential heights. Hence, it was decided to force the 850-hPa temperature into every model. Another round of best linear regressions was then conducted using a similar approach to that described above. After identifying the appropriate set of independent variables for each model, a stepwise regression was conducted for each model to illustrate the relative importance of each variable. The results of this refined regression model development (with seven independent variables) (shown in Table 3) are quite similar to the preliminary models in Table 2. In fact, many are identical. Those that differ still produce similar results for both 1 CO 2 and 2 CO 2 temperature predictions. The T850 column in Table 3 lists the adjusted R 2 for models with T850 as the only independent variable. The role of each additional parameter is illustrated by indicating the order of the variable in the model (shown in parentheses) and the accumulated adjusted R 2. For eample, the model for New Orleans has an R 2 of 84.2% if T850 is the only parameter, but 91.6% if U500 is added as a second parameter, and 92.9% if HT500 is used along with T850 and U500. The revised models shown in Table 3 are preferred over the initial models for several reasons. First, they demonstrate more conformity, each using the 850-hPa temperature as the primary predictor. Also, after rerunning the above regressions with the 7 variables, we found the new models have almost the same strength as the models with 15 variables. Only the winter models suffer a noticeable decrease in adjusted R-square. The most significant impact was a decrease of roughly 5% in the adjusted R 2 in the winter model of New Orleans. This trade-off is minor compared to the benefit of model simplicity. As indicated in Table 3, the quality of the regression models is quite good. All the spring, summer, and fall season models have adjusted R 2 over 90%. The only significant limitations occur in the winter month models, which consistently have the lowest adjusted R 2. Even so, the winter models all have adjusted R 2 above 65% with two cities over 90%, and another two cities over 80%. For the sites in Washington and New York our approach was able to generate spring, summer, and fall models with R 2 greater than 90% using only the temperature at the 850-hPa level. By adding one more variable, models for sites in the other two states all ehibited R 2 above 90%. As epected from the adjusted R 2 values, the predicted current climate surface temperatures are all in good agreement with observations as shown in Fig. 5. The partial validation shown in Fig. 5 indicates the overall strength of the fit but does not provide an independent test of the method. The usual validation approach involves dividing the data into two sets, one for training the model, and one for testing it. Due to the limited 10-yr time series from the CCM it is not practical to divide these simulation data into two distinct parts. Therefore, we have conducted a methodological validation using a training testing approach that involves division of the observational record into two parts, but relies upon the same 10-yr CCM output in both training

8 110 JOURNAL OF CLIMATE VOLUME 12 TABLE 2. Variable selection for initial models with 15 variables. Independent variables State and city Season* Adj. R 2 (%) T850 T500 U850 U500 V850 V500 SLP RH- 850 RH- 500 HT- 500 TH- KAV THK THK SLP HT- 500 Louisiana New Orleans Lake Charles New York New York City Albany Washington Seattle Spokane Nebraska Omaha N. Platte * : Apr Jun, summer: Jul Sep, fall: Oct Dec, winter: Jan Mar. and testing phases. Depending upon the site, yr of data were used for the training, and yr of data were used for testing. The training data were used to generate regression models substantially similar to the operational models shown in Table 3. The predictors from the test dataset were then substituted into these models to generate test set estimates of surface temperatures. Table 4 presents a comparison of the mean annual temperature from the trained model applied to the test data, and the actual surface temperatures from the test data. This table clearly demonstrates the agreement between the training and testing phases of model validation. The modeling approach selected the 850-hPa temperature as the primary predictor for all final models because it demonstrated the strongest correlation to the observed surface temperature. This use of T850 as the primary predictor is justified on the statistical basis mentioned above, but also on a more fundamental physical basis. Specifically, the 850-hPa level generally resides at the top of the atmospheric boundary layer (ABL). The miing pattern in the ABL largely determines the temperature profile from the surface to the 850-hPa level. Since miing processes in the ABL are strongly affected by the local surface characteristics, the physical relationship between surface temperature and T850 is inherently influenced by surface characteristics. This argument was supported by a correlation analysis, which revealed T850 to be the dominant variable for all locations, with R 2 values generally above 0.90, and always above 0.95 for seasons other than winter. 3. Downscaled temperature results Each of the 32 regression models summarized in Table 3 were applied to the free atmosphere dataset from

9 JANUARY 1999 SAILOR AND LI 111 TABLE 3. Variable selection for final downscaling models with seven variables. State and city Louisiana New Orleans Lake Charles New York New York City Albany Washington Seattle Spokane Nebraska Omaha Season* N. Platte T850 only adj. R 2 (%) Additional independent variables. Order of variable model in parentheses followed by accumulated adjusted R 2 for model including that variable. T500 U850 U500 SLP HT500 THKAV 2 (91.9) 2 (91.9) 3 (68.7) 3 (68.2) 2 (93.1) 2 (91.6) 3 (94.4) 2 (93.5) 2 (91.8) 3 (94.4) 2 (65.5) 2 (64.9) 3 (92.9) 3 (93.2) (94.1) (80.5) 2 (75.1) 3 (78.0) (80.8) 2 (74.3) 3 (78.1) (93.3) (73.6) 2 (70.2) (73.9) 2 (70.5) (92.5) 3 (70.8) 3 (92.7) 3 (70.1) 2 (90.3) 4 (93.1) 2 (91.2) 4 (94.3) 4 (95.7) 2 (68.6) 4 (95.6) 2 (67.4) * : Apr Jun, summer: Jul Sep, fall: Oct Dec, winter: Jan Mar. the future climate scenario of the paired CCM runs. The results are plotted in Fig. 6 along with the predictions obtained by direct subtraction of surface temperature output of the baseline CCM simulation from the future climate simulation. It is evident from this figure that our downscaling approach results in predictions that are sometimes significantly higher or lower than the raw CCM output. There is no clear annual effect, nor is there a consistent bias from one state to another. Within New York State, the CCM predicted a 5 6 C increase in winter surface temperatures. Our downscaling suggests that this magnitude of temperature change will occur in fall months, but that for most other months New York will ehibit a warming of less than 4 C, with Albany warming more than New York City. The ability to differentiate impacts within a grid cell is one of the key benefits of any downscaling method. In the particular case of the New York grid cell, the smaller coastal impact is likely a result of the moderating influence of the Atlantic Ocean. This difference between two sites within the same grid cell stems from differing surface responses to changes in the large-scale variables. For the states of Washington and Nebraska, our downscaling suggests a similar trend to that of the CCM, but with substantially less warming in the winter months. For the state of Louisiana, our results suggest a significant fall warming for both New Orleans and Lake Charles, with Lake Charles also eperiencing significant warming in the winter months. Although the direct temperature change prediction from the GCM gives one value for each grid cell, the downscaling approach here has the ability to differentiate among different locations in one grid cell. It is also interesting to note that for two sites in a single grid cell the MLR results can be virtually identical for certain months, and quite different in others. This observation

10 112 JOURNAL OF CLIMATE VOLUME 12 FIG. 5. Comparison of current climate observations with multiple linear regression (MLR) downscaling output for representative sites in each of the four states. is particularly evident for Louisiana where Lake Charles is epected to eperience warming 2 C in ecess of that predicted for New Orleans in winter, but about the same (within 0.2 C) for all other months. Although this paper does not seek to conduct a thorough modeling intercomparison effort, it is useful to TABLE 4. Comparison of training and testing phases of model validation. Site r 2 Mean (pred)* Mean (test) New Orleans Lake Charles New York City Albany Seattle Spokane Omaha North Platte * Mean (pred) is the yearly mean of the predicted temperature by substituting the test datasets into the trained model. Mean (test) is the actual yearly mean of the test data. present the corresponding results from another researcher using a distinctly different approach. Matyasovszky et al. (1994a) applied a climate categorization approach to the CCC model. Their analysis covered the state of Nebraska, and they present specific results for Valentine, Nebraska, which is about 165 km from the North Platte site of our analysis. As the regions surrounding Valentine and North Platte have comparable topography and surface characteristics, as well as similar historical climate, it is reasonable to compare downscaled climatic change predictions for these two sites. In Fig. 7 we compare temperature change results for North Platte using the direct output from both the CCC and CCM, as well as the downscaled results from our analysis and that of Matyasovszky (for Valentine). Clearly there are distinct differences in the output from the two GCMs for this particular location. The CCM model predicts slightly less warming than the CCC, with peaks in the winter months in the range of 8 10 C. The annual profiles of regional warming (for Nebraska) from the two GCMs, however, are actually quite similar. Although

11 JANUARY 1999 SAILOR AND LI 113 FIG. 6. Climate change predictions from GCM direct output and from revised MLR downscaling models (Table 3). FIG. 7. Comparison of downscaling from the MLR of the present paper with the work of Matyasovszky (Mat) for the N. Platte site in Nebraska. For reference, direct climate change predictions from the CCC and CCM are shown. Matyasovszky predicts a fairly large spring summer oscillation, our results indicate a smoother trend in temperature change. The fact that these downscaling results are in general agreement does not validate either method. On the other hand, if this comparison had indicated large discrepancies in downscaled results, this information would be quite important in assessing the uncertainties associated with downscaling in general. 4. Discussion and conclusions An important feature of the results presented here is that downscaling for specific cities within a GCM grid cell reveals some of the anticipated variability within the grid cell. First, it is clear that the current climate can vary substantially within a single grid cell, and over the course of the year. One good eample is the mean temperature difference between New York City and Albany, which is typically about 6 C in the winter, but less than 3 C during the summer. Clearly, the direct GCM output is incapable of distinguishing these differences. Our downscaling results indicate that the magnitude of predicted temperature change can ehibit a similar spatial and temporal variability. It is also important to note that for a particular region of study statistical downscaling analysis may indicate warming that is significantly higher or lower than the direct output from the GCM runs. Strictly speaking this downscaling approach scales GCM output down to specific sites from which the observational data are obtained. If one wishes to apply such an analysis over a larger region it could be scaled up by applying it to data from several sites within a region and averaging. The appropriate means of averaging depends upon the ultimate use of the regional

12 114 JOURNAL OF CLIMATE VOLUME 12 climate change predictions. For eample, if one wished to simply revise the GCM grid cell level output to reflect a more representative surface level response with mesoscale forcing, several weather stations within the grid cell could be used for downscaling and then aggregated using an appropriate spatial average. Although the approach presented here is simpler than those introduced by other researchers, the quality of the resulting models is quite good. The eplained variance of the temperature time series is over 90% for spring, summer, and fall, and in the range of 70% 90% for winter. It is useful to note that Hewitson (1994) developed models that were 86% accurate for winter and 76% for summer. Winkler (1995) generated models for Michigan with R 2 in the range of 64% 86%, and lower quality models for his Spain site. Clearly, since these researchers used different methods and were studying different regions, we cannot use this comparison as a quantitative demonstration of the relative strength of our approach. Nevertheless, this comparison indicates general support for the statement that we have developed a relatively simple downscaling approach that generates very strong models. Additional development of this approach and application to other GCMs and other surface variables should help to further establish its utility. Acknowledgments. The authors wish to thank three anonymous reviewers for their insightful comments, Dr. Steve Lambert for supplying the CCC data, and Mr. Tianmiao Hu for his assistance with the test variate analysis and downloading of free atmosphere observations. One author (XL) would like to acknowledge a student computing services grant from the Scientific Computing Division at NCAR. 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