NOTES AND CORRESPONDENCE The Skillful Time Scale of Climate Models

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1 Journal January of 2016 the Meteorological Society of Japan, I. TAKAYABU Vol. 94A, pp. and , K. HIBINO DOI: /jmsj NOTES AND CORRESPONDENCE The Skillful Time Scale of Climate Models Izuru TAKAYABU Meteorological Research Institute, Tsukuba, Japan Kenshi HIBINO University of Tsukuba, Tsukuba, Japan (Manuscript received 30 November 2014, in final form 2 July 2015) Abstract This paper clarifies that the skillful time-scale characteristic of a model is one of the key factors to reproduce the amount precipitation at a specific location with the model. A comparison with data from an operational weather station of the Japan Meteorological Agency in Tokyo (Ote-machi) revealed that a model needed That a model requires 5-km-grid resolution and below to represent the power spectrum of hourly precipitation. A model with a higher resolution is probably needed to simulate hourly precipitation in Tokyo during the summer monsoon season. Keywords skillful timescale; precipitation; power spectrum; probability distribution function 1. Introduction Corresponding author: Izuru Takayabu, Atmospheric Environment and Applied Meteorology Research Department, Meteorological Research Institute, Nagamine 1-1, Tsukuba, Ibaraki , Japan takayabu@mri-jma.go.jp 2015, Meteorological Society of Japan Dynamival downscaling has been performed to supply information for various end-users who need detailed information about climate change. In such cases, the scale for which the climate model can produce useful information has long been a subject of great interest. We refer to this scale as the skillful scale. Pielke (1984) has suggested that the smallest wavelength that can be represented accurately is four times the grid-point interval. However, Castro et al. (2005) and Rockel et al. (2008) have shown that the skillful scale is much larger than that scale. The need for information about extreme events has recently increased, and there are also signs of increases in heavy precipitation caused by increasing temperatures (Utsumi et al. 2011). Therefore, discussion of the skillful time scale has also become useful. Although many studies have already shown a relationship between model grid size and the reproducibility of daily or hourly precipitation intensity (e.g., Kimoto et al. 2005, Sasaki et al. 2011), no analysis of the cause of the relationship has been performed yet. In this paper, we discuss the cause of the impact of horizontal grid size on representation of short-timescale precipitation intensity by comparing the power spectrum of short-time-scale precipitation with that of weather station data. 2. Methods This study used a 60-km mesh Meteorological Research Institute atmospheric general circulation model (MRI-AGCM) version 3.2H (AGCM60), a 20-km mesh MRI-AGCM version 3.2S (AGCM20; Mizuta et al. 2012), and a 5-km grid regional climate model (NHRCM05; Sasaki et al. 2011). Table 1 shows the specifications for these models. The AGCM20/60 models were driven by using Hadley Centre sea

2 192 Journal of the Meteorological Society of Japan Vol. 94A Table 1. Configuration of models used in this study. Official model name (CMIP5) Map projection Horizontal grid system Grid size (equivalent) Dynamics Vertical coordinates Vertical levels Convection scheme Radiation scheme Cloud microphysics Land surface schemes Planetary boundary layer Reference AGCM60 AGCM20 NHRCM05 MRI-AGCM3.2H Global model TL319 (60 km) Hydrostatic Eta-scheme 64 Yoshimura Japan Meteorological Agency (2007) MJ-SiB Hirai et al. (2007) M-Y level-2 Mizuta et al. (2012) MRI-AGCM3.2S Global model TL959 (20 km) Hydrostatic Eta-scheme 64 Yoshimura Japan Meteorological Agency (2007) MJ-SiB Hirai et al. (2007) M-Y level-2 Mizuta et al. (2012) Lambert projection Grid model 5 km Non-hydrostatic Stretched grid 50 Kain and Fritsch (1993) Shortwave: Two stream with delta-eddington Bulk method MJ-SiB Hirai et al. (2007) MYNN Level-3 Sasaki et al. (2011) Fig. 1. Probability density function (PDF) of hourly precipitation data at the (blue) Tokyo weather station and PDFs simulated with the (purple) AGCM60, (green) AGCM20, and (red) NHRCM05 models at the Tokyo weather station. Table 2. Longitude and Latitude of Tokyo observing stations and the nearest grid point of the climate models. Tokyo Station AGCM60 AGCM20 NHRCM05 Longitude E E E E Latitude N N 35.7 N N ice and sea surface temperature data as the bottom boundary condition, was integrated between 1979 and The NHRCM05 model used AGCM20 model calculation results as the lateral boundary conditions and was integrated for 20 years between September 1980 and August To focus on the skillful time scale, we validated model data with the observational data at specific points. For that purpose, we chose an operational weather station in Tokyo managed by the Japan Meteorological Agency. Table 2 indicates each

3 January 2016 I. TAKAYABU and K. HIBINO 193 Fig. 2. Power spectrum of hourly precipitation data at the Tokyo weather station is shown. The numbers in the legend are the annual mean precipitation rate in mm h 1. Shaded area indicates the 95 % confidence interval of the mean value of the power spectrum. Fig. 3. Results of t-test to determine the significance of the difference between model precipitation and observed precipitation in Fig. 2. The three horizontal dashed lines indicate the 99 %, 95 %, and 90 % confidence levels from top to bottom, respectively. grid point at the stations. Data validation was done with the probability distribution function (PDF) and power spectrum of hourly precipitation data. 3. Results Kimoto et al. (2005) and Sasaki et al. (2011) have shown that a relatively high-resolution model with a temporal resolution of 1 hour to 1 day is needed to represent heavy precipitation. Figure 1 indicates the PDF of hourly precipitation around the Tokyo station. It was difficult to characterize extreme hourly precipitation by using the AGCM20/60 models; however, the

4 194 Journal of the Meteorological Society of Japan Vol. 94A Fig. 4. Same as Fig. 2, but for the (a) Sapporo and (b) Naha weather stations are shown. The numbers in the legend are the annual mean precipitation rates in mm h 1. NHRCM05 model could simulate extreme precipitation events. To clarify the cause of this difference, we obtained the power spectrum of precipitation data (Fig. 2). When we compared the simulated power spectrum with that of the observational data, we found that they were very similar at frequencies lower than 1 cycle per day (CPD). However, at frequencies greater than 1 CPD, the simulated power was lower in the lower resolution model. Here we designate f c (CPD) as the frequency at which two power spectra start to differ at the 99 % confidence level. Because there were years of hourly precipitation data, we could generate power spectra. The variances from the mean of these spectra are proportional to inverse years. We could estimate f c (CPD) by applying a t-test to these results. Figure 3 indicates the p-values associated with the t-tests. However, before applying the t-test, the power spectrum was smoothed by a simple moving average (SMA) of 240 points in the frequency domain to decrease the error in the power spectrum. After SMA was applied, there were 365 points within

5 January 2016 I. TAKAYABU and K. HIBINO 195 Fig. 5. Same as Fig. 2, but for seasons at Tokyo. Numbers in the legend represent the seasonal mean precipitation in mm h 1 for (a) December January February (DJF) and (b) June July August (JJA). 1 CPD. The error in the frequency data was therefore 120/365 = 0.33 CPD on both sides. The results were as follows. AGCM60 and AGCM20 followed the observed data at frequencies of up to 3.2 and 6.0 CPD, respectively. However, the NHRCM05 followed the observed power spectrum at frequencies of up to 12.0 CPD. This result suggests that daily precipitation can be simulated by using a 60-km mesh size model, but a 5-km-grid model is needed to simulate hourly precipitation. 4. Discussion Because the islands of Japan extend from subarctic to subtropical climate zones, the climate regime of each weather station therefore depends on the location of the station and season. The Tokyo station (35.7 N, E) is near the center of the Japanese island arc and experiences a temperate climate. To estimate changes in the representativeness of the precipitation power spectrum because of the location of the station, we compared the power spectrum

6 196 Journal of the Meteorological Society of Japan Vol. 94A Fig. 6. (Blue) PDFs of observed hourly precipitation at Tokyo, including the original PDF. (Others) PDF with high-frequency information cut off at (red) 8 CPD, (green) 4 CPD, and (purple) 2 CPD. at the Tokyo station with spectra at northern Japan (Sapporo: 43.1 N, E; Fig. 4a) and southern Japan (Naha: 26.2 N, E; Fig. 4b) stations. The comparison between Tokyo (temperate) and Sapporo (subarctic) indicated that the 5-km-grid NHRCM accurately represented the sub-daily precipitation power density, but at Naha (subtropical), even the 5-km-grid NHRCM failed to represent the sub-daily precipitation power density. Figure 5 compares the power spectrum at Tokyo from season to season. During the winter monsoon season of December January February (DJF; Fig. 5a), the coarser grid models represented the high-cpd precipitation data. On the other hand, during the summer monsoon season of June July August (JJA; Fig. 5b), even the 5-km-grid model failed to represent the sub-daily precipitation power spectrum. The characteristics of the precipitation pattern reflected the climate regime around the Tokyo area. During the winter monsoon season, the mean wind direction was from the northwest. Because Tokyo is located on the lee side of a mountainous region, the amount of precipitation is very small during the winter, and synoptic-scale, extra-tropical cyclones control the precipitation pattern around the Tokyo area at that time. In contrast, during the summer monsoon season, the mean wind direction is from the southwest, and the southwesterly wind pushes very humid air over the Pacific Ocean to the Tokyo area. The amount of precipitation is therefore high during the summer. The climate of the Tokyo area enters to the subtropical climate regime during the summer, and the spatial scale of precipitation system become smaller than that during the winter monsoon season. Olranski (1975) has shown that the spatial scale and time scale of atmospheric disturbances are strongly related, and changes of the pattern of disturbances affect the skillful time scale. A simultaneous analysis of the spatial and temporal skillful scales would be the next step in this research. When we removed the high-frequency signal from the observed data by applying a high-frequency cutoff filter, the maximum hourly precipitation was decreased. Figure 6 shows the PDF of the original data and of the high-frequency cutoff data. To represent high-frequency precipitation, it is necessary to take into consideration extreme precipitation events. 5. Conclusion The use of results of model calculations to study the impact of climate change has increased the demand for statistical information about extreme events. It is already known that the horizontal resolution of models affects the representativeness of simulated precipitation. In this paper, we focused on the skillful time scale and estimated the power spectrum of precipitation in Tokyo. In the case of daily precipitation, even a 60-km-mesh model had

7 January 2016 I. TAKAYABU and K. HIBINO 197 the capacity to represent the precipitation power spectrum of, but The model requires 5-km-grid resolution and below to represent the power spectrum of hourly precipitation. The horizontal resolution of the models affected the representation of the PDF of hourly precipitation. It is necessary to pay attention to the skillful time scale of the model when information about extreme events is used to evaluate the impact of climate change in various studies. Finally, we should be careful to determine to what extent the results obtained in a study depend on the climate regime and season. The results for other climatic variables may be different from those obtained for precipitation. All these issues should be addressed in the next stage of this research. Acknowledgments This work was supported by the SOUSEI programs of the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan. References Castro, C. L., R. A. Pielke, Sr., and G. Leoncini, 2005: Dynamical downscaling: Assessment of value retained and added using the Regional Atmospheric Modeling System (RAMS). J. Geophys. Res., 110, D05108, doi: /2004jd Hirai, M., T. Sakashita, H. Kitagawa, T. Tsuyuki, M. Hosaka, and M. Oh izumi, 2007: Development and validation of a new land surface model for JMA s operational global model using the CEOP observation dataset. J. Meteor. Soc. Japan, 85A, Japan Meteorological Agency, 2007: Outline of the operational numerical weather prediction at the Japan Meteorological Agency. (Appendix to WMO technical report on the global data-processing and forecasting system and numerical weather prediction progress report). Japan Meteorological Agency, 194 pp. [Available at jma-center/nwp/outline-nwp/index.htm.] Kain, J. S., and J. M. Fritsch, 1993: Convective parameterization for mesoscale models: The Kain-Fritsch scheme. The Representation of Cumulus Convection in Numerical Models. Meteor. Monogr., 46, Amer. Meteor. Soc., Kimoto, M., N. Yasutomi, C. Yokoyama, and S. Emori, 2005: Projected changes in precipitation characteristics around Japan under the global warming. SOLA, 1, Mizuta, R., H. Yoshimura, H. Murakami, M. Matsueda, H. Endo, T. Ose, K. Kamiguchi, M. Hosaka, M. Sugi, S. Yukimoto, S. Kusunoki, and A. Kitoh, 2012: Climate simulation using MRI-AGCM3.2 with 20-km grid. J. Meteor. Soc. Japan, 90A, Orlanski, I., 1975: A rational subdivision of scales for atmospheric processes. Bull. Amer. Meteor. Soc., 56, Pielke, Sr., R. A., 1984: Mesoscale Meteorological Modeling. Academic Press Inc., 612 pp. Rockel, B., C. L. Castro, R. A. Pielke, Sr., H. von Storch, and G. Leoncini, 2008: Dynamical downscaling: Assessment of model system dependent retained and added variability for two different regional climate models. J. Geophys. Res., 113, D21107, doi: /2007jd Sasaki, H., A. Murata, M. Hanafusa, M. Oh izumi, and K. Kurihara, 2011: Reproducibility of present climate in a non-hydrostatic regional climate model nested within an atmosphere general circulation model. SOLA, 7, Utsumi, N., S. Seto, S. Kanae, E. E. Maeda, and T. Oki, 2011: Does higher surface temperature intensify extreme precipitation? Geophys. Res. Lett., 38, L16708, doi: /2011gl