Adjustment of GCM Precipitation Intensity over the United States

Transcription

1 876 JOURNAL OF APPLIED METEOROLOGY VOLUME 37 Adjustment of GCM Precipitation Intensity over the United States MINGXUAN CHEN, XUBIN ZENG, AND ROBERT E. DICKINSON Department of Atmospheric Sciences, The University of Arizona, Tucson, Arizona (Manuscript received 9 December 1996, in final form 5 January 1998) ABSTRACT A regression equation is developed to adjust the simulated monthly averaged intensity of hourly precipitation over the continental United States using air temperature at the first model level (about 80 m above ground) simulated by a revised version of NCAR s Community Climate Model version coupled with the Biosphere Atmosphere Transfer Scheme. The adjusted precipitation intensity is in much closer agreement with the locally observed precipitation intensity, both in pattern and magnitude, than is the simulated intensity produced by climate models. The multiresponse randomized block permutation analysis shows that the authors adjustment method is statistically significant. The equation is robust with respect to seasonal and interannual variations, as demonstrated by applying it to independent months of different years. The relationship between precipitation intensity and near-surface air temperature likely reflects a linkage among precipitation, precipitable water, and vertical velocity. It can be applied to estimate fractional precipitation coverage with temporal and spatial variability over the continental United States, and to help statistically construct a time series of local precipitation events both for the present climate and for the studies of climate change. 1. Introduction Precipitation is usually characterized by its volume (i.e., the total amount of precipitation in a given period). Volume depends on intensity (i.e., precipitation amount divided by the precipitation period only) and frequency (i.e., precipitation rate divided by intensity). Both intensity and frequency are also important for surface hydrology (e.g., Rutter 1975; Pitman et al. 1993; Eltahir et al. 1993). In particular, climate studies of land surface processes need locally observed precipitation data containing information on intensity and frequency (BAHC 1993). Without such realistic precipitation input, it may be impossible to simulate realistic land surface hydrological processes (Dickinson 199a,b; Johnson et al. 1993). General circulation models (GCMs) generally do not reproduce local precipitation intensity (Chen et al. 1996). The large differences between observed intensity of hourly precipitation and that simulated by a climate model are illustrated in Fig. 1. On average, the simulated intensity of hourly precipitation is about one-tenth of that observed, a disparity caused by differences in concepts and methods used in calculating the two intensities. Although the precise interpretation of model precipitation is unclear, it is usu- Corresponding author address: Ms. Mingxuan Chen, Department of Atmospheric Sciences, The University of Arizona, PAS Building #81, Tucson, AZ chen@air.atmo.arizona.edu ally assumed to represent a grid-box average. In addition, inevitable errors occur in simulations of a climate model. Therefore, adjustment of simulated intensities to locally observed values may be necessary. Various statistical approaches have been proposed to relate local precipitation to GCM simulations. For example, Karl et al. (1990) built an empirical relationship between simulated free atmospheric variables and local surface variables and applied it to five stations; von Storch et al. (1993) related large-scale North Atlantic sea level pressure to winter mean Iberian peninsula rainfall; Matyasovzky et al. (1994) used daily atmospheric circulation patterns to predict daily precipitation amounts in the state of Nebraska; Wilby (1994) discussed the relationship between weather type and daily precipitation occurrence and amount in southern England; Gao and Sorooshian (1994) used a stochastic precipitation disaggregation scheme to generate hourly rainfall for a summer in the southwestern United States. However, most of the preceding work adjusted only the amount of precipitation and used formulations applicable only to relatively small areas and specific seasons. The intent here is to provide a practical method for the adjustment of simulated hourly precipitation intensity on a large scale that is suitable for the entire continental United States in all four seasons. The data and method used in this study are described in section, results are presented in section 3, a plausible physical mechanism is suggested in section 4, and potential applications of our results in hydrological studies are addressed in section American Meteorological Society

2 SEPTEMBER 1998 CHEN ET AL. 877 FIG. 1. Observed averaged intensity (mm h 1 ) of hourly precipitation in (a) January and (c) July. A revised version of NCAR CCM (Hahmann et al. 1995) coupled with BATS (Dickinson et al. 1993) simulated intensity of hourly precipitation in (b) January, year 10, and (d) July, year 10.

3 878 JOURNAL OF APPLIED METEOROLOGY VOLUME 37. Data and method Observational data consist of hourly precipitation (EarthInfo 1989) from 57 carefully selected gauge stations, typically for years over the continental United States. The data are interpolated onto a Community Climate Model version (CCM) T4 grid. Details regarding data selection and interpolation are described in our previous study (Chen et al. 1996). To discuss the applicability of our method, the climatological data from the National Centers for Environmental Prediction National Center for Atmospheric Research (NCEP NCAR) reanalysis project (Kalnay et al. 1996) are also used. The model data are derived from simulations using a revised version of NCAR s CCM (Hahmann et al. 1995) at T4 resolution (.8.8 ) coupled with the Biosphere Atmosphere Transfer Scheme (BATS) (Dickinson et al. 1993). The sea surface temperature and ozone data used in the simulations are prescribed from climatological data with seasonal change. In all, 16 months (January in years 10 and 11, July in years 10 and 11, plus all 1 months in year 1) of revised CCM/BATS simulation data with hourly sampling and 10 years (years 6 15) of simulations with daily sampling are used. Here model precipitation intensity refers to the average intensity in a given month (i.e., the ratio of the total amount of precipitation to the total number of hours with precipitation during a given month), and observed intensity refers to the monthly average intensity in the same month during the total period of data. Our statistical method consists of the following steps: first, observed intensity and model variables are standardized by their spatial mean and standard deviation in the same month as z i (x i x m )/ x, where z is the standardized variable; x is the original variable; x m and x are the mean and standard deviation of x, respectively, over the continental United States ( N, W) covered by 0 grid points; and i is the index of location. Such a standardization may in principle be problematic for a bounded variable such as precipitation intensity, but it is useful in practice, as demonstrated and discussed later. In the absence of a priori analytical relations between precipitation and other variables, the following functional form is assumed: O ap (bz cz d ), int int j j j j j j where O int and P int are the standardized observed and simulated intensity of hourly precipitation, respectively, and z j denotes one of the variables listed in Table 1. The coefficients a, b j, c j, and d j can then be obtained through regression analysis, and a best functional form, as discussed in section 3, can be found. The terms z j and z j are likely correlated (Christensen 1996), but this does TABLE 1. List of simulated monthly averaged variables from NCAR CCM/BATS used in this study. The values of the generalized terrainfollowing vertical coordinates 0.99, 0.831, 0.786, 0.649, and correspond with reference pressures of 99, 831, 786, 649, and 598 mb, respectively. Symbols P int P fre ratio t 7 t 5 dt 75 u 7 u 5 du v 7 v 5 dv w 7 w 5 dw cmfq 7 cmfq 5 dcmfq pcmfq effc 7 effc 5 deffc peffc t max t min dt m t s t leaf t skin t b es tb q b mse 1 mse mse 3 e1 e e3 eb Simulated variables Intensity of hourly precipitation Frequency of hourly precipitation Ratio of convective to total precipitation Temp at Temp at t 7 t 5 Latitudinal wind at Latitudinal wind at u 7 u 5 Meridional wind at Meridional wind at v 7 v 5 Vertical velocity at Vertical velocity at w 7 w 5 Convective moist flux at Convective moist flux at cmfq 7 cmfq 5 cmfq 7 cmfq 5 Effective cloud fraction at Effective cloud fraction at effc 7 effc 5 effc 7 effc 5 Daily max surface air temp Daily min surface air temp t max t min Avg surface temp Avg leaf temp Avg skin temp Avg temp at 0.99 Saturated water vapor pressure at t b Avg specific humidity at 0.99 Surface moist static energy using max temp Surface moist static energy using min temp Surface moist static energy using avg temp Surface equivalent potential temp using max temp Surface equivalent potential temp using min temp Surface equivalent potential temp using avg temp Equivalent potential temp at 0.99 not seriously undermine the analysis, as briefly addressed in section 4. Finally, the statistical significance and robustness of the relationship are addressed through the multiresponse randomized block permutation (MRBP) procedure (Mielke 1991) [which does not assume a specific (e.g., normal) distribution] and through independent data testing. A least absolute deviation (LAD) regression (Mielke 1987), instead of the traditional least square deviation (LSD) regression, is used in this study. LAD is based on linear Euclidean distances, while LSD is based on squared Euclidean distances. The analysis space for the statistical testing of the observations is linear Euclidean (Mielke 1986). The geometrical inconsistency of analysis space between LSD and observations can cause deviant data points to excessively affect the results of the test (Mielke 1986). Thus, using LAD regression may be more reasonable.

4 SEPTEMBER 1998 CHEN ET AL. 879 The MRBP method compares one or more numerical models with each other or with observations. It has been applied to verify numerical models (Tucker et al. 1989; Cotton et al. 1994), to evaluate seasonal forecasts of Atlantic basin tropical cyclone activity (Gray et al. 1993), and to verify parameterization algorithms (Zeng and Pielke 1995). In this study, it is used to evaluate the statistical significance of the results. The MRBP output includes the agreement coefficient and the probability that the numerical results could happen by chance alone. The agreement coefficient is defined as the fractional change in the forecasting skill over chance. An agreement coefficient of unity indicates a perfect agreement between the model output and observations, whereas a coefficient close to zero would indicate little agreement. Hence, an agreement coefficient is like a correlation coefficient. Correlation coefficients are based on squared Euclidean distances and cannot be expected to give a proper quantitative measure of agreement between the predicted and observed fields (Tucker et al. 1989; Zeng and Pielke 1995). However, they are also given since they are widely used and familiar. 3. Results In the regression analysis discussed in section, 1 8 variables out of 39 model simulated variables in Table 1 are used. The best regression equation is selected as the one involving one to two variables only but having a high agreement coefficient over the continental United States. The following regression equation is obtained for the simulated precipitation: O int 0.359P int 0.907t b 0.195t b , (1) where O int is the standardized locally observed intensity of hourly precipitation, P int is the standardized simulated intensity of hourly precipitation, and t b is the standardized monthly average air temperature at the first model level (about 80 m) above ground. Both P int and O int are standardized variables; therefore, a zero or negative value means the actual intensity is equal to or less than the mean of intensity. The index of location used in the previous two equations is omitted in (1) for clarity. Equation (1) is derived from January of year 10. Figures 1a,b display the observed intensity and the CCM/BATS simulated intensity for January of year 10. The intensity after adjustment using Eq. (1) (Fig. a) is much closer to that observed (Fig. 1a), both in magnitude and pattern, than is the simulated intensity without adjustment (Fig. 1b). The agreement coefficient between observed and simulated intensity is increased from 0. to 0.64, while the correlation coefficient between them is increased from 0.33 to The probability value in the first row of Table shows that Eq. (1) substantially reduces the probability that the agreement between observed and modeled monthly average hourly precipitation intensity could be obtained by chance alone. Because spatial autocorrelations are neglected in the statistical test, magnitudes of the agreement and correlation coefficients are likely overestimated, but the above qualitative conclusion should be unchanged. Besides statistical significance, robustness is another important criterion for evaluating a statistical method. After demonstrating the statistical significance of Eq. (1) through the MRBP procedure, we now address its robustness through an independent data test. When Eq. (1) is applied to January of year 11, the agreement and correlation coefficients drop only slightly to 0.58 and 0.81, respectively. Figures b,c show that the adjusted precipitation intensity patterns for January of years 11 and 1 agree closely with that of year 10, hence, Eq. (1) is robust for January data. However, because the CCM simulations were forced by climatological sea surface temperature (with seasonal variation), part of the reason for the above results could be that the three Januarys are not significantly different statistically (e.g., with similar mean and standard deviation of precipitation, as shown in Table 3). Next, Eq. (1) is applied to July data of years Even though winter and summer precipitation are mainly characterized by large-scale and convective precipitation, respectively, Table shows that the agreement coefficient is still as high as 0.51 to 0.58 in contrast to 0.15 to 0.7 without adjustment. Correspondingly, the correlation coefficient for the three Julys are 0.77, 0.83, and 0.78 in contrast to 0.45, 0.46, and 0.34 without using Eq. (1). Figures d f show that the adjusted precipitation intensity patterns in the three Julys are much closer to the observed pattern (in Fig. 1c) than is the unadjusted July pattern (in Fig. 1d). Therefore, Eq. (1) can also significantly improve the results in July. Because the largest variation is between summer and winter, an equation that is robust for both January and July should be robust for all seasons. To test this, Eq. (1) is applied to each month of year 1. Table confirms this point, listing the agreement and correlation coefficients for each month. Compared to unadjusted values for the 15 independent cases in Table, these are increased by 0.31 and 0.3, respectively, in the worst case (July, year 10), and increased by 0.70 and 0.83, respectively, in the best case (April, year 1). Because April is a transition month between winter and summer, the simulated intensity of hourly precipitation has little correspondence to that observed (not shown, see Chen et al. 1996). The adjustment dramatically increases the agreement coefficient and brings the precipitation intensity pattern very close to that observed (Fig. 3). On average, the agreement and correlation coefficients are 0.61 and 0.84, respectively, when Eq. (1) is applied, while they are only 0.17 and 0.3, respectively, without Eq. (1). Consistent with the results in Table, the adjusted precipitation intensity pattern for each month is closer to the observed pattern than is the unadjusted

5 880 JOURNAL OF APPLIED METEOROLOGY VOLUME 37 FIG.. Simulated intensity (mm h 1 ) of hourly precipitation adjusted by Eq. (1): (a) (c) in January, years 10 1, respectively, and (d) (f) in July, years 10 1, respectively.

6 SEPTEMBER 1998 CHEN ET AL. 881 TABLE. Results of the multiresponse randomized block permutation analysis for observed and simulated intensity of hourly precipitation where Prob. refers to the probability that the numerical results could happen by chance alone. Month Jan Jul Jan Jul Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Year y10 y10 y11 y11 y1 y1 y1 y1 y1 y1 y1 y1 y1 y1 y1 y1 Adjusted by Eq. (1) Agreement Prob. Correlation Unadjusted Agreement Prob. Correlation Average pattern (not shown). Evidently, Eq. (1) is robust for all seasons. Standardized data are used in our regressions since the variables involved in this study differ from each other in units, means, and standard deviations. Even for the same variable in a particular month, the mean and standard deviation are different in different years, and they are different from those in other months. For instance, Table 3 shows that both the mean and standard deviation of precipitation intensity differ between months with the observed mean value on average roughly 1 times as large as that of model data. This is consistent with the results in Fig. 1 and is largely a result of the different interpretations of observed and modeled intensities. The standard deviation of observed precipitation intensity is on average roughly six times as large as that of model data. Without standardization, such different means and standard deviations in different months would result in a strong dependence of the regression equations on seasons; that is, the regression equation based on January data would not be applicable to other months. After standardization, however, variables become dimensionless with a mean of 0 and the standard derivation of 1, so that the regression equation (1) can be applied to all months. 4. Discussion Section 3 selected Eq. (1) as an optimum regression equation for two variables involved (P int and t b ), with performance described in terms of the agreement coefficient value and adjusted precipitation intensity pattern. Several other regression equations with two different variables and only slightly less satisfactory performance were also found. Three additional examples are Oint 0.59Pint tskin tskin , () Oint 0.13Pint tmin tmin , (3) and Oint Pint qb 0.14qb 0.196, (4) where t skin is the monthly averaged skin temperature (i.e., the effective radiating temperature of the surface), t min is the monthly average of the daily minimum surface air temperature, and q b is the monthly averaged specific humidity at model level 0.99 (roughly 80 m above ground). Table 4 compares the performance of Eqs. () (4) with that of Eq. (1) based on the MRBP procedure. Overall, Eq. (4) gives a less satisfactory fit than do Eqs. (1) (3). In the worst case (October, year 1), its agreement coefficient is only 0.9, indicating that the relation between the lowest model level specific humidity field and observed precipitation intensity field is not robust. The overall performance of Eq. () is close to that of Eq. (1), reflecting the fact that skin temperature is closely related to the temperature of the first model level (t b ). It has to be calculated to get upward longwave radiation. It usually is not saved, however. The best agreement coefficient for Eq. (3) is as good as for Eq. (1), but the worst agreement coefficient for Eq. (3) is only 0.39 (in October, year 1) in contrast to 0.51 (in July, year 10) for Eq. (1). Although not as robust in all seasons, it is very good for the summer, with agreement and correlation coefficients of 0.69 and 0.90 averaged over three Julys and one August. The adjusted patterns for these months also match the observed intensity pattern very well. In summer, precipitation is mainly convective, and the daily minimum of surface air temperature (usually in early morning) may affect its development. Overall, Eq. (1) is judged to be better than Eqs. () (4). To assess the relative importance of each term in Eq.

7 88 JOURNAL OF APPLIED METEOROLOGY VOLUME 37 TABLE 3. Means (m) and std dev ( ) of precipitation intensities. The m and values of CCM are calculated from simulation years 1, 11, and 10, respectively, while observed values are calculated from multiyear averaged data. Month m Observed m CCM Y1 m CCM Y11 m CCM Y10 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec (1), the four additional equations are derived by keeping the dominant temperature term of Eq. (1) but selectively removing other terms: Oint tb 0.107tb 0.079, (5) O P t , (6) int int b Oint tb , and (7) Oint t b. (8) Equations (5) (8) have been applied to the 15 independent months that were listed in Table with results given in Table 5. In general better fits are obtained with a greater number of variables used in the regression. However, a regression relation overfitting with too many variables could perform poorly on independent datasets. In our case, 0 data points are available for each month, so that the regression equations [Eqs. (1) and (5) (8)] with one to four terms are not expected to be overfitted. Indeed, Table 5 shows that Eq. (1) consistently performs better than Eqs. (5) (8). Comparison of simulated and observed intensity patterns (not shown) also demonstrates that without the intensity or the t b term in Eq. (1) [i.e., Eqs. (5) (7)], the agreement between adjusted and observed fields is reduced. Nearly identical results from Eqs. (7) and (8) in Table 5 also imply that the constant term is relatively unimportant. A related issue is the possible collinearity among predictors in Eq. (1). A strong collinearity among predictors of a multivariable regression equation would significantly reduce the precision of regression estimation (e.g., Belsley 1991; Christensen 1996; Hocking 1996; Fox 1997). To diagnose collinearity, variance inflation factors (VIFs) of predictors in Eq. (1) are computed, and their values are 1.458, 1.151, and for P int, t b, and t b, respectively. When predictors are orthogonal to each other, all VIFs are equal to 1, while they approach infinity when the predictors are perfectly correlated. As a rule of thumb, VIF 10 indicates a strong collinearity (Hocking 1996), while VIF 4 shows a moderate collinearity (Fox 1997). Therefore, VIFs less than 1.5 in Eq. (1) indicate a relatively mild collinearity and, hence, little effect on Eq. (1). Either Eq. (1) or Eq. (8) appear to be the most useful for practical applications. With Eq. (8), the averaged agreement and correlation coefficients decrease from 0.61 and 0.84 to 0.57 and 0.81, respectively, and the pattern of hourly precipitation intensity is less realistic than with Eq. (1). However, Eq. (8) is much simpler to use by requiring only monthly averaged air temperature and not hourly sampling of model precipitation data. Climate model simulations reproduce much of the observed interannual variability outside of the Tropics even with the use of a climatological annually repeating pattern of SSTs. Table and Figs. 1 indicate the difference between the three years considered with hourly data is much smaller than the difference between the model average and observed patterns. For Eq. (8), model data for 10 years (years 6 15) were used instead of the 3 years available with hourly sampling. Figure 3 summarizes the 10-yr averaged results for January, April, July, and October. The averaged patterns (Figs. 3e h) differ much more from the observed patterns (Figs. 3a d) than from individual years (not shown). The agreement coefficients for Fig. 3 are 0.57, 0.58, 0.51, 0.51, and their correlation coefficients are 0.81, 0.83, 0.77, and 0.76 for January, April, July, and October, respectively. The coefficients for January and July are almost the same as for the 3-yr averaged data using Eq. (8), increasing confidence that the regression equations are robust with respect to seasonal and interannual variability. Equation (8) implies that over the continental United States the spatial variation of intensity of hourly precipitation is roughly proportional to the spatial variation of air temperature of the lower troposphere. Although this regression [or Eq. (1)] is simple and robust, it is not easy to explain in detail why it works, as is often the case in regression analyses. Intensity of precipitation, in general, depends on the amount of water vapor in the atmosphere and on the intensity of vertical motion, both of which are related to temperature: higher

8 SEPTEMBER 1998 CHEN ET AL. 883 FIG. 3. Observed averaged intensity (mm h 1 ) of hourly precipitation in (a) January, (b) April, (c) July, and (d) October, and adjusted intensity of hourly precipitation averaged over (e) January, (f) April, (g) July, and (h) October of years 6 15 using Eq. (8).

9 884 JOURNAL OF APPLIED METEOROLOGY VOLUME 37 TABLE 4. Comparison of adjusted intensity of hourly precipitation for 15 independent months by Eqs. (1) (4). and are agreement and correlation coefficients, respectively. Eq. (1) Eq. () Eq. (3) Eq. (4) Average Highest Lowest temperatures favor stronger vertical motion and increase the amount of water vapor that can be held by the atmosphere. Temperature in the lower troposphere where water vapor is concentrated roughly measures the atmosphere s capability to hold water vapor. The nearsurface specific humidity (q b, Table 1) used [in Eq. (4)] in the regression analysis gives a less satisfactory agreement than does air temperature [in Eq. (1)]. Using the simulated precipitable water (i.e., the vertically integrated column water vapor), we can also obtain a regression similar to Eq. (8): O int p w, (9) where p w is the standardized precipitable water. Figures 4a d show that, compared with observations (Figs. 3a d), the patterns of intensity adjusted by Eq. (9) are not as good as those adjusted by Eq. (8) (Figs. 3e h), and the MRBP analysis shows that Eq. (9) is less robust than Eq. (8). Similar conclusions are drawn for the logarithm of p w or q b. Surface saturation vapor pressure, which is a nonlinear function of temperature, was also tested, approximately evaluated from t b. It gives compatable statistical agreement but a less satisifictory pattern. Likewise, vertical velocities (see Table 1) do not give as good a fit as temperature. Evidently temperature captures the precipitation intensity better in a regression equation than either water vapor or upward velocity alone. Thus, the statistical relation between intensity and near-surface air temperature, in principle, connects precipitation to both water vapor and upward velocity. An equation similar to Eq. (9) can also be obtained for the equivalent potential temperature eb (i.e., the last variable in Table 1), but results are not as good as those using Eq. (8) either. For instance, the mean agreement and correlation coefficients are and 0.760, respectively, which are smaller than the corresponding values using Eq. (8) (see Table 5). Equations (1) and (8) were derived using the CCM/ BATS output. But, Eq. (8) appears to be simple enough to be applicable to other models. To test this, it is used to estimate precipitation intensity from the 13-yr averaged monthly air temperature at m above ground (T m ) from the NCEP NCAR reanalysis; that is, we use O int T m. (10) Figures 4e h show that the patterns of adjusted intensity given by Eq. (10) for January, April, July, and October, respectively, are very close to those from Eq. (8) (Figs. 3e h). Correspondingly, the MRBP analysis shows that the agreement and correlation coefficients using Eq. (10) are very close to those using Eq. (8). The regression coefficient in Eq. (10) is also close to the optimal value of when T m is directly used in a regression analysis, and results using either coefficient are almost the same. Although the T m field depends on both model and observation (Kalnay et al. 1996), it could give the best available estimates of the near-surface air temperature. 5. Potential applications Equations (1) and (8) have been derived to obtain the spatial pattern of precipitation intensity over the continental United States. They complement, rather than replace, relationships requiring detailed information for a specific area for which location-specific coefficients should be used (e.g., Gao and Sorooshian 1994; Matyasovzky et al. 1994). Although there are no extensive data to perform similar analyses for other regions of the globe, the seasonal temperature variation over the continental United States can be larger than the temperature differences between different parts of the world (at least at the same latitudes) in the same month. Thus, our regression equation may be adequate to estimate precipitation intensity over different regions. TABLE 5. Comparison of adjusted intensity of hourly precipitation for 15 independent months by Eq. (1) and Eqs. (5) (8). and are agreement and correlation coefficients, respectively. April, year 1, and July, year 10, are the best and the worst cases adjusted by Eq. (1), respectively. Eq. (1) Eq. (5) Eq. (6) Eq. (7) Eq. (8) Average Apr y1 Jul y

10 SEPTEMBER 1998 CHEN ET AL. 885 FIG. 4. Adjusted intensity (mm h 1 ) of hourly precipitation in (a) January, (b) April, (c) July, and (d) October by Eq. (9), and adjusted intensity of hourly precipitation averaged over (e) January, (f) April, (g) July, and (h) October by Eq. (10).

11 886 JOURNAL OF APPLIED METEOROLOGY VOLUME 37 The distribution and magnitude of the air temperature at the first model level (t b ) used in our regression equation [Eqs. (1) and (8)] vary significantly with seasons. For instance, the 10-yr averaged means of t b are 0 and 5 C, and their standard deviations are 14.0 and 4.7 C in January and July, respectively, in the domain of this study. The variation of t b between January and July is 5 C, and the standard deviation in July is only onethird of that in January. Climate change, such as that caused by increasing greenhouse gas concentrations, is likely to be much smaller than seasonal variations. Since our regression equations are not affected by seasonal changes, it is reasonable to expect that they will also be applicable under different climate scenarios. Since the results inferred from our equations are normalized precipitation intensities using the mean and standard deviation of observed precipitation intensity under current climate, they cannot give the spatial pattern of intensity over the continental United States. However, Eqs. (1) or (8) could also be used to roughly estimate changes of the absolute values of intensity under different climate scenarios, assuming the model mean and (especially) the standard deviation values do not undergo large changes. Another potential application is estimating the fractional coverage of rain in a grid cell, a concept introduced to parameterize the effect of spatial heterogeneity of precipitation in hydrological studies. In the parameterization of surface hydrology in climate models, fractional coverage of the rainfall area is often prescribed as one or two constants for all grid cells. In reality, however, as shown in Chen et al. (1996) and in the current study, the distribution of precipitation has significant temporal and spatial variabilities. These variabilities exert a significant influence on the hydrological cycle in climate models (Pitman et al. 1990; Thomas and Henderson-Sellers 1991; Johnson et al. 1993). Recently, some efforts have been made to estimate fractional coverage of rainfall area in GCM grid cells using radar data or station precipitation observations (e.g., Collier 1993; Gupta and Waymire 1993; Gong et al. 1994; Eltahir and Bras 1993). However, relationships to estimate fractional coverage in these studies could not link observations to model variables directly. In contrast, our regression equations relate simulated variables and fractional precipitation coverage for different months over the continental United States by estimating the monthly averaged fractional coverage for hourly precipitation as simply the ratio of unadjusted over adjusted model precipitation intensities. Finally, our regression equations could be used to construct weather simulations for the time series of local precipitation events for studies of hydrological processes such as infiltration that depend not only on the intensity of precipitation but also on the sequence of dry wet episodes preceding each event. Chen et al. (1996) show that the total precipitation amounts simulated by a GCM are closer to observations than the precipitation intensity. Therefore, the local frequency (i.e., the number of rain hours in a month) can be reasonably estimated from the ratio of the adjusted precipitation intensity over the precipitation amount. Using locally observed data to compute the probability of hourly precipitation in the month, this distribution with the estimated local frequency can be used to statistically construct the time series of local precipitation events. 6. Conclusions Based on the least absolute deviation regression, a simple equation has been developed to estimate local intensity of hourly precipitation for different months from the precipitation intensity and air temperature at the first model level simulated by CCM/BATS over the continental United States. After adjustment by Eq. (1), the simulated intensity of hourly precipitation is in much closer agreement with that observed both in magnitude and pattern. The multiresponse randomized block permutation analyses indicate that the results are statistically significant. The average agreement and correlation coefficients between adjusted and observed intensity of hourly precipitation over 15 independent months are 0.61 and 0.84, respectively. Even for the worst case, the agreement and correlation coefficients are higher by 0.31 and 0.3, respectively, than those between simulated (i.e., unadjusted) and observed intensity of hourly precipitation. The robustness of Eq. (1) with respect to seasonal and interannual variations has been demonstrated by applying it to different months in different years. Equation (1) includes four simulated terms: intensity of hourly precipitation (P int ), air temperature (t b ) and squared air temperature ( t b ) at model level 0.99, and a constant. Comparison of results from Eq. (1) with those from Eqs. (5) (8) indicates that the t b term explains most of the variance with the P int and t b terms providing a smaller contribution, that is, they affect the location and the strength of maximum and minimum intensity; the constant term is the least important. Equation (8) as the simplest version includes only the t b term. Although it infers an intensity field that is not as accurate as that given by Eq. (1), Eq. (8) is also quite robust. The averaged agreement and correlation coefficients are 0.54 and 0.79 for 39 independent months (9 Januarys; 10 Aprils, Julys, and Octobers). In addition, Eq. (8) needs only monthly averaged simulated t b and so is easily applied. The statistical relationship between intensity of precipitation and lower troposphere air temperature likely reflects a linkage of precipitation to both water vapor and vertical upward motion. Application of Eq. (8) to the near-surface air temperature data from the NCEP NCAR reanalysis demonstrates that, given a reasonably simulated lower troposphere air temperature, it can closely estimate the precipitation intensity. In summary, our regression equation [Eqs. (1) or (8)]

12 SEPTEMBER 1998 CHEN ET AL. 887 is likely to be valid not only for the present climate but for studies of climate change as well, provided these changes are small compared to seasonal variation. In addition, it can be used either to estimate fractional precipitation coverage in a grid box or to provide a constraint on the construction of time series of local precipitation events. Acknowledgments. This work was supported by the Department of Energy under Grant DE-FG0-91ER6116. We thank Andrea N. Hahmann for providing revised CCM/BATS simulation data and valuable suggestions, and M. Sanderson-Rae and Darcy Anderson for editing the manuscript. Three anonymous reviewers are also thanked for very helpful comments. Computations were carried out with the support of EPRI Project Number RP367-3 and on local workstations. The plots are made by GrADS written by Brian E. Doty. 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