Reproducibility of Regional-Mean Probable Precipitation by High-Resolution Climate Models

: We assessed the reproducibility of regional-mean probable precipitation in Japan estimated based on the results of three runs of a 20km-mesh global climate model (MRI-GCM20) and one run of a 20km-mesh regional climate model (MRI-RCM20). These models inappropriately simulate the annual maximum daily precipitation at individual grid points, especially in relation to the spatial pattern, but estimate the regional mean reasonably well. MRI-GCM20 runs simulated data over annual maximum regional-mean 10-day precipitation better than 1-day. Precipitation and return values estimated by MRI-GCM20 were quite different from those by MRI-RCM20. Among the three MRI-GCM20 runs, one forced by SST without year-to-year variability estimated the standard deviation of the annual maximum precipitation as smaller than those forced by SST with year-to-year variability. The reproducibility of the average and standard deviation of the annual maximum precipitation is correlated with the reproducibility of 30-year return values.


INTRODUCTION
Increasing extreme weather events is one of the most important concerns, so the Japan Meteorological Agency (JMA) published the Climatic Risk Map of Extreme Events (JMA, 2007; hereafter Riskmap07) on the JMA web site. Riskmap07 presents probable precipitation based on observed precipitation at observatories in Japan and indicates the present risk of heavy rainfall.
In recent years, the Meteorological Research Institute (MRI) has developed several high-resolution climate models to project future climate change. The 20km-mesh global climate model (MRI-GCM20) and the 20km-mesh regional climate model (MRI-RCM20) were confirmed to accurately reproduce the present climate around Japan, including average temperature and annual precipitation (Mizuta et al., 2006;Kurihara et al., 2005;JMA, 2005b).
Some studies estimate future changes in extreme events and present several suggestions for estimating probable precipitation using these climate models. Wada et al. (2006) found that it was necessary that the assessment of probable precipitation using MRI-RCM20 be based on values averaged over a region of about 60 kilometers square in extent. In contrast, Wada et al. (2008) showed that it was possible to assess the reproducibility of the probable precipitation at individual grid points with MRI-GCM20. In general, however, the smallest scale of weather events that can be represented by a climate model is a few times the horizontal resolution of the model.
As for the time scale, Fowler et al. (2007) indicated that models they used underestimated return values of 1-day precipitation in the UK but reasonably simulate longerduration (5-or 10-day) extremes. They studied 1, 2, 5 and 10-day precipitation totals. In their paper, results have been presented for only 1-and 10-day totals, because they said that 1-and 10-day totals represented short and long-duration precipitation events respectively.
We focused on the regional mean of precipitation totals, and checked their reproducibility by MRI-GCM20 and MRI-RCM20. We showed results of 1-and 10-day precipitation similar to Fowler et al. (2007).

Models
Two models (MRI-GCM20 and MRI-RCM20) were used in this study (Table I). MRI-GCM20 is a 20km-mesh global climate model (Mizuta et al., 2006;Noda et al., 2007) developed by MRI under the "Kyousei Project." We used three runs of MRI-GCM20 that had been integrated for 20 years or more (AM, AT, AJ). These experiments are forced with different sea-surface temperatures (SSTs). The SST for AM is the result of an MRI Coupled General Circulation Model (CGCM) run and is warmer around northern Japan and colder in the south of Japan than the observed SST. AJ and AT are prescribed by the observed SSTs. The SST for AJ is the 12-year mean without year-to-year variability. MRI-RCM20 is a 20km-mesh regional climate model (Kurihara et al., 2005;JMA, 2005b) developed by MRI. Although the integration period of MRI-RCM20 slightly differs from that of MRI-GCM20, this is not likely to have influenced our results.

Observations
To assess the reproducibility of the models, we used daily precipitation data observed at 151 observatories in Japan from 1979 to 1998 and at AMeDAS (Automated Meteorological Data Acquisition System) stations from 1981 to 2000 (only for assessing annual mean daily precipitation).

METHODOLOGY
The 10-day precipitation is the sum of the daily precipitation in any continuous period of 10 days. We defined the periods of our 10-day precipitation data starting with January 1 to 10 and running through December 22 to 31 for every year.
The regional mean is defined as the average of the data within each region defined for the seasonal forecast by JMA ( Figure 1) in this study. The model's grid-point values over land nearest to the observatories are used. It must be noted that, in this study, the annual maximum regional-mean value refers to the annual maximum value of the regional averaged precipitation, not the regional average of annual maximum precipitation at each observatory or grid point.
Moreover, R1 denotes the daily precipitation, and R10 the 10-day precipitation. The regional means of R1 and R10 are referred to as R1 and R10. The annual maxima of R1, R10, R1 and R10 are called R1 max , R10 max , R1 max and R10 max .

Probable Precipitation
The algorithm used for selecting extreme value distributions fitting the annual maximum precipitation is illustrated in Figure 2. The algorithm is based on that used for Riskmap07 but has been partially modified. We used the bootstrap resampling method as the evaluation criterion for extreme value distributions instead of the jackknife procedure in the algorithm of Riskmap07, in order to get a number of probable precipitation samples large enough to estimate a confidence interval. The resampling was repeated 1000 times. The 1000 probable precipitations were made by applying each resample data set to the selected distribution. The range between 5th and 95th percentiles of the probable precipitation is considered to be the 90% confidence interval in this study.

Average and Frequency of Precipitation
MRI-GCM20 and MRI-RCM20 generally reproduce the spatial pattern of the annual average precipitation observed by AMeDAS (Figures 3 and S1). All of the MRI-GCM20 runs underestimate the precipitation on the Pacific side of Table I. Models used in this study a CGCM: MRI Coupled General Circulation Model (Yukimoto et al., 2001;Yukimoto et al., 2006). b SST for MRI-GCM20-AJ is the 12-year mean from 1982 to 1993. c SST for MRI-RCM20 was adjusted so that the 20-year average of daily SST was equal to the 20-year average of the observed SST for each day (Kurihara et al., 2005).   Japan, but MRI-RCM20 overestimates it. The boundary condition of MRI-RCM20 is supposed to contribute to inadequate precipitation especially in Northern Japan (JMA, 2005b). MRI-GCM20 also underestimates the frequency of days with precipitation of 50 mm or more, but MRI-RCM20 overestimates it ( Figure S2). Figure 4 illustrates the 20-year means of R1 max and R1 max of the observation and MRI-GCM20-AT (see also Figure  S3). Figure 4a indicates that the model underestimates the daily precipitation all over Japan, particularly around western Japan. The spatial pattern of R1 max seems to suggest a problem in that the difference of R1 max produced by the model between the northern part and the southern part is smaller than that of the observation. In the case of R1 max (Figure 4b), the spatial pattern is relatively accurate when compared to R1 max , although the amount is underestimated.

Comparison of Regional-mean Value with Grid-Point Value
MRI-GCM20-AM and -AJ exhibit the same tendency as AT. MRI-RCM20 simulates the regional mean better as well, but the amount is overestimated (not shown).

Annual Maximum Regional-Mean Precipitation
The models basically reproduce the 20-year means of R1 max and R10 max ( Figure S4). For R1 max , the difference between the models and the observations is about 25%. The difference among the MRI-GCM20 runs is small relative to that between MRI-RCM20 and MRI-GCM20. In the case of MRI-GCM20, R10 max is generally reproduced better than R1 max . MRI-RCM20, however, tends to overestimate R10 max more than R1 max .
The standard deviation of R1 max and R10 max is reproduced worse by the models when compared to the 20-year mean. The standard deviation by MRI-GCM20-AJ is smaller than that of the other MRI-GCM20 runs (Figures 6 and S4). This is likely to have been caused by use of the SST without year-to-year variability for this run.

Probable Precipitation
The probable precipitation (30-year return value) of R1 and R10 is underestimated by MRI-GCM20 and overestimated by MRI-RCM20 ( Figure 5). The differences among the MRI-GCM20 runs are small except for Okinawa and Amami, where the value of MRI-GCM20-AJ is smaller than that of the other runs.
The 90% confidence intervals estimated by the bootstrap method are 20% to 60% of the probable precipitation, so the errors are 10% to 30%. The errors are thought to be basically due to the small sample size (Takara and Takasao, 1988).
The relation between the reproducibility of R1 max and R10 max and that of the 30-year return value is depicted in Figure 6. The reproducibility of the average and standard deviation of the annual maximum precipitation is correlated with the reproducibility of 30-year return values for both R1 and R10, whether the types of the distributions of the observation and the models are the same or not.

DISCUSSION AND CONCLUSIONS
This study assessed the reproducibility of the regionalmean probable precipitation in Japan estimated from MRI-GCM20 and MRI-RCM20. The results are summarized as follows: • The models reproduce the spatial pattern of the annual maximum regional-mean daily precipitation (R1 max ) better than that of grid-point values (R1 max ). It is supposed that R1 max often occurs with larger scale events such as a typhoon or extratropical cyclone that can be reproduced by climate models better than smaller scale events. • MRI-GCM20 simulated R10 max better than R1 max , but MRI-RCM20 tended to overestimate R10 max more than R1 max . It is consistent with the result in Fowler et al. (2007) that the reproducibility of longer-duration extremes is better than that of 1 day. • There are smaller differences among the three runs of MRI-GCM20 than between MRI-RCM20 and MRI-GCM20. MRI-GCM20-AJ, which is forced by the 12year mean SST without year-to-year variability, tends to have smaller standard deviations than the other MRI-GCM20 runs. This study demonstrated that the regional mean and 10day sum are likely to improve the reproducibility of the probable precipitation estimated by the model. We hereafter will estimate the change in probable precipitation using regional-mean 10-day values.

SUPPLEMENTS
Supplement 1 includes 4 figures. Figure S1. Enlargement of Figure 3. Figure S2. Frequency of daily precipitation intensity. Figure S3. Enlargement of Figure 4. Figure S4. 20-year Average and Standard Deviation of Annual Maximum Regional-Mean Precipitation.