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Ensemble-Based Using a Global Coupled Atmosphere–Ocean GCM

a b c a NOBUMASA KOMORI, TAKESHI ENOMOTO, TAKEMASA MIYOSHI, AKIRA YAMAZAKI, d e AKIRA KUWANO-YOSHIDA, AND BUNMEI TAGUCHI a Application Laboratory, Japan Agency for Marine-Earth Science and Technology, Yokohama, Japan b Disaster Prevention Research Institute, Kyoto University, Uji, Kyoto, and Application Laboratory, Japan Agency for Marine-Earth Science and Technology, Yokohama, Japan c RIKEN Center for Computational Science, RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program, and RIKEN Cluster for Pioneering Research, Kobe, and Application Laboratory, Japan Agency for Marine-Earth Science and Technology, Yokohama, Japan, and Department of Atmospheric and Oceanic Science, University of Maryland, College Park, College Park, Maryland d Disaster Prevention Research Institute, Kyoto University, Shirahama, Wakayama, and Application Laboratory, Japan Agency for Marine-Earth Science and Technology, Yokohama, Japan e Research Center for Advanced Science and Technology, The University of Tokyo, Tokyo, and Application Laboratory, Japan Agency for Marine-Earth Science and Technology, Yokohama, Japan

(Manuscript received 28 November 2017, in final form 29 July 2018)

ABSTRACT

Ensemble-based atmospheric (DA) systems are sometimes afflicted with an underesti- mation of the ensemble spread near the surface caused by the use of identical boundary conditions for all ensemble members and the lack of atmosphere–ocean interaction. To overcome these problems, a new DA system has been developed by replacing an atmospheric GCM with a coupled atmosphere–ocean GCM, in which atmospheric observational data are assimilated every 6 h to update the atmospheric variables, whereas the oceanic variables are subject to no direct DA. Although SST suffers from the common biases among many coupled GCMs, two months of a retrospective analysis–forecast cycle reveals that the ensemble spreads of air temperature and specific humidity in the surface boundary layer are slightly increased and the forecast skill in the midtroposphere is rather improved by using the coupled DA system in comparison with the atmospheric DA system. In addition, surface atmospheric variables over the tropical Pacific have the basinwide horizontal correlation in ensemble space in the coupled DA system but not in the atmospheric DA system. This suggests the potential benefit of using a coupled GCM rather than an atmospheric GCM even for atmospheric reanalysis with an ensemble-based DA system.

1. Introduction Atmospheric General Circulation Model for the Earth Simulator (AFES; Ohfuchi et al. 2004; Enomoto et al. Ensemble-based data assimilation (DA) techniques 2008) to construct the AFES–LETKF ensemble DA sys- such as the ensemble Kalman filter (Evensen 1994, 2003) tem. Miyoshi et al. (2007a) performed one and a half years have been rapidly growing because of their advantages of the AFES–LETKF experimental ensemble reanalysis of the flow-dependent estimation of analysis and fore- using the observational dataset of the Japan Meteorolog- cast errors, relative ease of implementation, and effi- ical Agency operational system. Enomoto et al. (2013) ciency with parallel computers. constructed the second generation of the DA system Miyoshi and Yamane (2007) applied the local ensemble (ALEDAS2) using the latest version of AFES with an transform Kalman filter (LETKF; Hunt et al. 2007)tothe improved cloud scheme for better representation of low-level clouds (Kuwano-Yoshida et al. 2010)and Denotes content that is immediately available upon publica- LETKF employing physical distances for localization tion as open access. instead of using local patches (Miyoshi et al. 2007b), and performed five years of an experimental ensemble re- Corresponding author: Nobumasa Komori, komori@jamstec. analysis (ALERA2) assimilating observational data of go.jp the NCEP global DA system (PREPBUFR) archived at

DOI: 10.1175/MWR-D-17-0361.1 Ó 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses). Unauthenticated | Downloaded 09/28/21 06:08 AM UTC 3312 MONTHLY WEATHER REVIEW VOLUME 146

UCAR. The ALERA2 has been used as the reference strongly coupled DA in a realistic situation and dem- dataset for a series of observing system experiments onstrated its usefulness based on their regional opera- using the ALEDAS2 (e.g., Yamazaki et al. 2015; Hattori tional system. Additionally, modern techniques such et al. 2016, 2017; Kawai et al. 2017). as a particle filter are also applied to CGCMs to deal In many ensemble DA systems based on AGCMs with the intrinsic nonlinearity of the coupled DA (e.g., including the ALEDAS2, surface boundary conditions Browne and van Leeuwen 2015). such as SST and sea ice distribution are identical among In this study, to enhance the capability of the all ensemble members. It leads to an underestimated ALEDAS2, a new system has been developed by ensemble spread near the surface, or equivalently an replacing AFES with the Coupled Atmosphere–Ocean overestimate of the accuracy of the first-guess fields, and General Circulation Model for the Earth Simulator may eventually lead to a degradation of the resulting (CFES; Komori et al. 2008). As a first step toward a fully analyses. Kunii and Miyoshi (2012) showed that intro- coupled version of the CFES–LETKF ensemble DA ducing SST perturbations in the LETKF for a regional system (CLEDAS), the new system assimilates only at- atmospheric DA system improves the analyses and sub- mospheric observational data to update the atmospheric sequent forecasts. In addition, air–sea coupled phenom- variables and is referred to as CLEDAS-A. Using this ena, such as the lead–lag relationship between SST and system, two months of experimental ensemble analysis precipitation over the tropics, are not well reproduced in has been conducted, and two-month-averaged fields are AGCM-based systems (Arakawa and Kitoh 2004; Saha compared with those of ALERA2. This approach is et al. 2010). By using a coupled atmosphere–ocean GCM categorized as quasi-weakly coupled DA (Penny et al. (CGCM) instead of an AGCM in an ensemble DA sys- 2017) and could be considered as the atmospheric coun- tem, it is expected that the effects of perturbed surface terpart of the attempt by Fujii et al. (2009),inwhichocean boundary conditions and atmosphere–ocean interaction DA constrains the ocean component of their CGCM to are naturally introduced into the system. construct a coupled reanalysis dataset. Data assimilation into CGCMs has progressed in the The rest of this article is organized as follows. Section last decade. Zhang et al. (2007) conducted a series of perfect 2 describes the ensemble DA system using a CGCM. model experiments, assimilating pseudo-observations Section 3 describes the setting of experimental ensemble made from a CGCM simulation with an ensemble fil- retrospective analysis. The results are presented in sec- ter to reconstruct climate variability and trends. Sugiura tion 4. Finally, a summary and conclusions are provided et al. (2008) assimilated 10-day-averaged atmospheric in section 5. and oceanic observational data using a four-dimensional variational method and controlled surface fluxes by in- troducing adjustment factors for the coupled state esti- 2. Ensemble data assimilation system mation from 1996 to 1998. Several operational centers a. Forecast model have constructed their global coupled DA systems mainly for seasonal to interannual prediction or climate CFES is used as the forecast model in CLEDAS-A reanalysis based on their existing operational atmo- (Fig. 1), and its configuration is the same as used in the spheric and oceanic DA systems. In these systems, previous studies (Richter et al. 2010; Taguchi et al. 2012; CGCMs are used in the forecast step to construct the Bajish et al. 2013; Sasaki et al. 2013; Kuwano-Yoshida first-guess fields but atmospheric and oceanic DA are et al. 2013; Miyasaka et al. 2014; Taguchi and Schneider conducted separately in the analysis step (e.g., Saha 2014). CFES consists of AFES as an atmospheric com- et al. 2010; Lea et al. 2015), or atmospheric and oceanic ponent including a land surface process and OFES systems are integrated only in a limited portion of the (Masumoto et al. 2004)asanoceaniccomponent DA process (e.g., Laloyaux et al. 2016). The former including a sea ice process. Surface variables such as SST, methodology is called weakly coupled DA and the latter sea surface and sea ice velocities, sea ice concentration, sea quasi-strongly coupled DA by the definition of Penny ice thickness, and snow depth over sea ice are transferred et al. (2017). Recently, some studies show the effec- from OFES to AFES, while the surface fluxes and sea level tiveness of strongly coupled DA, in which atmospheric pressure are passed from AFES to OFES. AFES is cou- and oceanic DA are conducted integrally in the whole pled with OFES every hour in CLEDAS-A (Fig. 1b), DA process and observational data in one component whereas it is forced with prescribed surface boundary are directly used to update the state of the other, in an conditions (BC) of the NOAA 1/48 daily OISST (Reynolds idealized or simplified framework (e.g., Smith et al. 2015; et al. 2007; Banzon et al. 2016)inALEDAS2(Fig. 1a). Lu et al. 2015a,b; Sluka et al. 2016). On the other hand, AFES is an AGCM and solves the primitive equa- Frolov et al. (2016) proposed an ‘‘interface solver’’ for tions using the spectral transform method and Eulerian

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Vertical mixing is parameterized by the Noh model (Noh and Kim 1999; Noh et al. 2005), in which mixing depends on both the Richardson and Prandtl numbers. In addition, the shortwave penetration scheme is im- proved especially for the use with the free surface (Komori et al. 2012). It should be noted that the treatment of sea ice is different between AFES and CFES, besides the differ- ence of whether sea ice concentration and thickness are the boundary conditions (AFES) or the prognostic variables (CFES). In AFES, sea ice concentration is treated as one (full ice) if observed sea ice concentration is greater than 0.1 and otherwise treated as zero (no ice), and sea ice thickness is parameterized as a linear func- tion of observed concentration with the maximum of 0.5 m. In CFES, sea ice concentration varies between zero and one, and sea ice thickness has no upper limit. Such a difference may affect the accuracy of atmo- spheric (re)analyses over the marginal ice zone (Inoue et al. 2011). b. Analysis scheme and analysis–forecast cycle

FIG. 1. The data flow charts of (a) ALEDAS2 [adapted from CLEDAS-A uses the LETKF for analysis as in Fig. 21.2 of Enomoto et al. (2013)] and (b) CLEDAS-A. Rectan- ALEDAS2 (Fig. 1), and the analysis is made only for gles represent input/output data, and round rectangles represent atmospheric variables every 6 h with a 6-h window of processes. DA. In the forecast step, each ensemble member is in- tegrated in time with CFES for 9 h from the initial advection. The resolution is T119 (the triangle truncation conditions (IC) to produce the restart file, which con- at wavenumber 119, ;100 km) in the horizontal and tains hourly forecasts at 3–9 h (63 h from analysis time t) 48 s layers in the vertical with the top level placed at and is used for input of the LETKF. In the analysis step, s 5 0:003 (about 3 hPa), the same as used in ALEDAS2. atmospheric observations (obs) from t 2 3tot 1 3 are In AFES, the broadband radiative transfer model assimilated using the 4D-EnKF (Hunt et al. 2004) (MstrnX; Sekiguchi and Nakajima 2008) and the land technique to produce analysis at time t of atmospheric surface model, the Minimal Advanced Treatments of prognostic variables (temperature, specific humidity, Surface Interaction and RunOff (MATSIRO; Takata zonal and meridional , cloud water, and surface et al. 2003) are incorporated. The cumulus convection is pressure). The guess file represents the forecast at time represented by the Emanuel scheme (Emanuel 1991; t of these variables. Finally, the analyses replace the Emanuel and Zivkovic ´-Rothman 1999; Peng et al. 2004), prognostic variables in restart at time t to produce the and the gridscale cloud scheme uses statistical partial next IC for the atmospheric component. Note that condensation based on joint-Gaussian probability distri- prognostic variables of the land surface model (soil bution functions of the liquid water potential temperature temperature, soil moisture, snow amount, and so on) in and total water content (Kuwano-Yoshida et al. 2010). restart, as well as diagnostic variables such as surface OFES is a z-coordinate OGCM based on the GFDL’s turbulent heat fluxes and precipitations, are not updated , version 3 (MOM3; Pacanowski and by the LETKF. The oceanic variables are also kept Griffies 1999), and contains a dynamic–thermodynamic unchanged throughout the assimilation procedure, and sea ice model (Komori et al. 2005). It has a resolution of restart is simply used as the next IC for the oceanic 1/28 (;50 km at the equator) in the directions of both component. longitude and latitude and 54 levels in the vertical with Parameters for the LETKF used in CLEDAS-A are varying cell thicknesses from 5 m at the surface to 330 m the same as those used in ALEDAS2. The ensemble at the maximum depth of 6065 m. Isoneutral diffusion size is 63. The error covariance is localized by physical (Redi 1982) and thickness diffusion (Gent and McWilliams distance (Miyoshi et al. 2007b), and the localization 1990) are adopted for tracers, and the Smagorinsky scheme length, defined as a standard deviation of the Gaussian (Smagorinsky 1963) is adopted for horizontal friction. weighting function, is 400 km in the horizontal and

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63-member outputs of ALERA2, and the model is in- tegrated for another 5 months from 1 January to 2 June 2008. Finally, 63-member ensemble ocean simulations are carried out from 2 June to 1 August 2008, in which the model is forced by each member of ALERA2. The ensemble ocean simulations, hereafter referred to as EnOFES, are extended to the end of the experiment (30 September 2008) to be compared with the oceanic component of CLERA-A. Temporal evolution of the ensemble spread of SST and a snapshot at the beginning of the experiment (1 August 2008) are shown in Figs. 2 and 3 , respectively. Two months of ensemble simulations successfully create FIG. 2. Temporal evolution of SST ensemble spread for EnOFES the perturbed initial conditions of the oceanic compo- (from 2 Jun 2008; with closed circles) and for CLERA-A (from nent, and the amplitude of the ensemble spread of SST 1 Aug 2008; with open circles) averaged over the globe (black), in the extratropical Northern Hemisphere (NH, blue tropics (red), extratropical Northern Hemisphere (blue), and ex- line in Fig. 2) is about 0.1 K at 1 August 2008, which is tratropical Southern Hemisphere (purple). comparable to that of the previous experimental study (about 0.2 K; Kunii and Miyoshi 2012) in which SST 0.4 lnp in the vertical, where p is pressure. The constant is artificially perturbed to investigate a typhoon in the inflation parameter of 10% spread inflation (equiva- North Pacific. lent to 21% covariance inflation) is used (Miyoshi and It would be worth mentioning that the ensemble Yamane 2007). spread of SST in the NH is much larger than that in the extratropical Southern Hemisphere (SH, purple line), despite that the ensemble spreads of surface variables in 3. Experimental ensemble reanalysis ALERA2 are larger in the SH, especially over the ice- An experimental retrospective analysis–forecast covered regions, than those in the tropics and NH (not cycle with CLEDAS-A is conducted from 1 August to shown). The ensemble spread of SST in the NH turns 30 September 2008, assimilating the atmospheric ob- from rapid increasing into decreasing in late July, servations (NCEP PREPBUFR archived at UCAR) whereas that in the SH continue to increase. Their am- every 6 h. The result is referred to as CLERA-A. plitudes are finally reversed in early November when The 63-member initial conditions of the atmospheric EnOFES is further extended (not shown). In the case component at 0000 UTC 1 August are taken from when EnOFES is started from 3 December instead of ALERA2. The initial conditions of the oceanic com- 2 June, the situation becomes entirely opposite: the ponent are made by stand-alone ocean simulations using ensemble spread of SST in the SH is much larger than OFES as follows. First, the surface boundary conditions that in the NH at the beginning, and their amplitudes are (surface air temperature, specific humidity, zonal and reversed in early May 2009 (not shown). Thus, the en- meridional winds, downward shortwave and longwave semble spread of SST shows clear seasonality that is radiations, rainfall, snowfall, and sea level pressure) are larger in the tropics (red line) and summer hemisphere taken from the Common Ocean-ice Reference Experi- than that in the winter hemisphere. We consider the ments (CORE; Large and Yeager 2004, 2009) Corrected reason as follows. 1) Incident solar radiation is the pri- Interannual Forcing, version 2, and the river runoff data mary source of surface heating, and the response of the are from the CORE Corrected Normal Year Forcing, ocean to the thermal forcing potentially generates the version 2. OFES is integrated for 60 years from the be- ensemble spread of SST. 2) The thick mixed layer is ginning of 1948 to the end of 2007 from the initial con- formed at the ocean surface in winter, and the thermal ditions of the climatological temperature and salinity inertia of the surface ocean becomes larger than in fields for January in the World Ocean Atlas 2005 summer. In other words, the surface ocean is less (more) (WOA05; Locarnini et al. 2006; Antonov et al. 2006) sensitive to the atmospheric disturbances in winter with no ocean currents and sea ice, while sea surface (summer). 3) Ensemble members with higher (lower) salinity is restored to the climatological monthly value of SST than ensemble mean tend to lose more (less) heat WOA05 with a restoration time scale of 30 days. Then through surface cooling by sensible and latent heat the surface boundary conditions (except for river fluxes. This mechanism acts to make ensemble mem- runoff) are switched to the ensemble-mean fields of bers converge, or equivalently, reduce ensemble spread.

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FIG. 3. Ensemble mean (contour) and spread (color) of SST at the initial time of the experiment (0000 UTC 1 Aug 2008). The contour interval is 2 K.

4) SST under sea ice is very close to the freezing tem- perature in our model. This also acts to reduce ensemble spread in the ice-covered regions. In addition to the large-scale contrast between the summer and winter hemispheres, we find some notice- able local maxima of the ensemble spread (Fig. 3). The local maximum around 408N in the North Pacific is probably induced by the atmospheric disturbances, and that around 108N in the eastern tropical Pacific corre- sponds to the ITCZ. On the other hand, the local maxima in the eastern equatorial Pacific and Atlantic are likely FIG. 4. Differences (CLERA-A minus ALERA2) in (a) the caused by tropical instability waves (Legeckis 1977)inthe ensemble mean and (b) spread of forecast surface temperature ocean. Thus, both the atmospheric and oceanic variations (K) averaged over the experimental period. may contribute to increase the SST ensemble spread. in CLERA-A compared with observations, and partly 4. Results because an effective surface temperature in a model grid is an average of ocean and sea ice surface temperatures a. Comparison between ALERA2 and CLERA-A (the former is much warmer than the latter) weighted Figure 4a shows the difference of the ensemble mean with sea ice concentration in CLERA-A over these re- of forecast surface temperature (land, ocean, or sea ice gions, whereas it is a purely sea ice surface temperature surface temperature) between ALERA2 and CLERA-A in ALERA2 (see section 2a for difference in sea ice averaged over the entire experimental period (from treatment between AFES and CFES). 0600 UTC 1 August to 0000 UTC 30 September 2008). Figure 4b shows the difference of the ensemble spread SST in ALERA2 is a given boundary condition (NOAA of forecast surface temperature between ALERA2 and daily OISST) rather than a prognostic variable, and the CLERA-A. As mentioned above, the boundary condi- difference represents the model bias in CLERA-A. tion of SST is identical among the all ensemble members Regions of negative SST bias are found in the mid- in ALERA2, and the ensemble spread of SST is exactly and high latitudes in the North Pacific and Atlantic, and zero. Therefore, the difference in the ensemble spread those of positive SST bias are found in the eastern side of of SST originates in CLERA-A. The ensemble spread of the subtropical Pacific (off California and Peru) and SST is 0.1–0.3 K in the tropics and summer hemisphere South Atlantic (off Namibia). These are common fea- and kept (or slightly increased) during the experiment in tures even among the state-of-the-art CGCMs (e.g., the coupled system, but is much smaller in the winter Richter 2015). In addition, a surface temperature in hemisphere where the thick mixed layer is formed in the CLERA-A over the ice-covered regions is much higher ocean (see also Fig. 2). Remarkably, the introduction than that in ALERA2. This is partly because the sea ice of atmosphere–ocean coupling increases the ensemble concentration in the Southern Ocean is underestimated spread of land surface temperature particularly over

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Africa and southern Eurasia although the ensemble mean of land surface temperature is almost the same between ALERA2 and CLERA-A. This might be related to per- turbed monsoonal winds from the ocean and the associ- ated precipitation in this season. The ensemble spread of surface temperature over the ice-covered regions, partic- ularly in the Southern Ocean, in CLERA-A is much smaller than that in ALERA2. Because the surface ocean heat content is much larger than the sea ice heat content, the effective surface heat content in CLERA-A is much larger than that in ALERA2 because of a fractional treat- ment of sea ice concentration. This implies that surface temperature over the ice-covered regions in CLERA-A is less sensitive to the atmospheric disturbances than that in ALERA2, which may lead to the decrease of the en- semble spread of surface temperature in these regions. The difference in the ensemble mean and spread of analyzed surface pressure between ALERA2 and CLERA-A is shown in Fig. 5. The spatial patterns of the difference in ensemble mean, especially over the ocean, well correspond to those of surface temperature (Fig. 4a): higher (lower) surface temperature causes lower (higher) surface pressure in CLERA-A than in ALERA2. The magnitude of the difference is, however, less than 1 hPa except for the ice-covered regions in the Southern Ocean, which implies that CLERA-A reproduces a similar atmospheric circulation to ALERA2 because FIG.5.AsinFig. 4, but for analyzed surface pressure (hPa). The of the assimilation of atmospheric observations. The averaged ensemble mean of surface pressure in ALERA2 is also ensemble spread of surface pressure in CLERA-A plotted in the gray contour in (a), and the interval is 4 hPa. slightly increases almost all over the world and partic- ularly over the eastern tropical Pacific. Figure 6 compares the ensemble spread of forecast air Atlantic, where low-level clouds are underestimated temperature and specific humidity in the surface boundary probably because of the significant warm bias in surface layer (at the height of s 5 0:97, which roughly corresponds temperature in CLERA-A (Fig. 4a). It should be noted to the 970-hPa surface) between ALERA2 and CLERA-A. that the difference in the ensemble spread of air tem- The overall patterns of the ensemble spread in CLERA-A perature between ALERA2 and CLERA-A is larger in are very similar to those in ALERA2. Meanwhile, the en- the lower troposphere (Fig. 7c) than that in the surface semble spread in CLERA-A is larger than that in ALERA2 boundary layer (Fig. 6c). particularly in the regions where the ensemble spread in Figure 8 shows the spread–skill diagram of forecast air ALERA2 is relatively small, and over the tropics and sum- temperature over the ocean for ALERA2 (Figs. 8a–c) mer hemisphere, where the ensemble spread of SST is and CLERA-A (Figs. 8d–f). We define the skill as the more increased by the atmosphere–ocean coupling (Fig. 4b). RMS difference from the corresponding analysis of the A similar comparison is made for the lower troposphere ERA-Interim (Dee et al. 2011), and both the ensemble (at the height of s 5 0:86, which roughly corresponds to spread and RMS difference are averaged over the entire the 860-hPa surface) in Fig. 7. The ensemble spread of experimental period. Table 1 summarizes the spatio- forecast air temperature and specific humidity has temporally averaged values of the ensemble spread, local maxima over the eastern side of the subtropical RMS difference, and their ratio. At the 975-hPa surface, Pacific and South Atlantic, as well as over the equatorial the ensemble spread in ALERA2 (Fig. 8a) is very small eastern Pacific and Atlantic, for both ALERA2 and (0.25 K on average) in comparison with the RMS dif- CLERA-A. Similar to the boundary layer situation ference (1.60 K on average), or the system is under- (Fig. 6), the ensemble spread in CLERA-A is larger dispersive in the surface boundary layer. In CLERA-A than that in ALERA2 at this height except for the (Fig. 8d), the ensemble spread is increased especially in eastern side of the subtropical Pacific and South the region where the ensemble spread in ALERA2 is

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21 FIG. 6. Ensemble spread of (a)–(c) forecast air temperature (K) and (d)–(f) specific humidity (g kg ) at the height of s 5 0:97 averaged over the experimental period for (top) ALERA2, (middle) CLERA-A, and (bottom) their difference (CLERA-A minus ALERA2). smaller than 0.2 K as shown in Fig. 6. However, the RMS by simply using a CGCM, and the better representation difference is also increased (1.87 K) possibly because of of model error, for example, would be needed in the the model bias. At the 850-hPa surface, the ratio of the future. At the 500-hPa surface, the ensemble spread ensemble spread to the RMS difference is improved in is almost comparable to the RMS difference in both both ALERA2 (Fig. 8b) and CLERA-A (Fig. 8e). No ALERA2 (Fig. 8c; the average ratio is 0.70) and CLERA-A significant differences are found between them. Thus, (Fig. 8f; 0.75). Interestingly, the RMS difference in the spread–skill relationship is not necessarily improved CLERA-A (1.11 K) is smaller than that in ALERA2

FIG.7.AsinFig. 6, but for the height of s 5 0:86. Note that the color bars are different from those in Fig. 6.

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FIG. 8. Density plot for spread–skill diagram of forecast air temperature over the ocean between 458S and 458N for (a)–(c) ALERA2 and (d)–(f) CLERA-A at the heights of (a),(d) 975 hPa; (b),(e) 850 hPa; and (c),(f) 500 hPa. Both the ensemble spread and skill (defined as the RMS difference from the ERA-Interim analysis) are averaged over the entire experimental period.

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TABLE 1. Spatiotemporally averaged ensemble spread, RMS difference, and their ratio.

ALERA2 CLERA-A Height (hPa) Spread (K) RMSD (K) Ratio Spread (K) RMSD (K) Ratio 975 0.25 1.60 0.16 0.27 1.87 0.14 850 0.54 1.39 0.39 0.54 1.42 0.38 500 0.82 1.16 0.70 0.83 1.11 0.75

(1.16 K) at this height. This might suggest the potential with higher SST than the ensemble mean have more benefits of using a CGCM for an atmospheric analysis cumulus precipitation on the next day possibly because instead of an AGCM. of the enhanced convective activity. The ensemble-based covariance without lag between SST and cumulus pre- b. Ensemble covariance and correlation among cipitation (Fig. 9b) is still positive over the ITCZ regions, variables but it turns negative over the warm water pools. When Ensemble-based reanalysis has the advantage that one cumulus precipitation leads SST by 1 day (Fig. 9c), the can calculate the statistics from the ensemble members ensemble-based covariance is unclear over the ITCZ and can estimate the relationship among the variables regions, whereas it is strongly negative over the warm from relatively short time series. water pools. This negative covariance implies that the Figure 9 shows the lag covariance, estimated from the ensemble members with more cumulus precipitation ensemble, between forecast SST and precipitation in- than the ensemble mean have lower SST on the next day duced by cumulus convection (Figs. 9a–c) and large- possibly because of the decreased solar irradiance, a scale condensation (Figs. 9d–f) in CLERA-A averaged feature that is never seen when using an AGCM. over the experimental period. When SST leads cumulus The relationship between SST and large-scale pre- precipitation by 1 day (Fig. 9a), the ensemble-based cipitation is totally different from that between SST and covariance is mostly positive over the regions with heavy cumulus precipitation. When SST leads large-scale pre- precipitation such as the warm water pools in the west- cipitation by 1 day (Fig. 9d), the ensemble-based covari- ern tropical Pacific, Atlantic, and Indian Oceans and the ance is slightly negative but not a robust signal over the ITCZs in the eastern tropical Pacific and Atlantic. This ITCZ regions. The ensemble-based covariance without a positive covariance implies that the ensemble members lag between SST and large-scale precipitation (Fig. 9e)is

FIG. 9. Ensemble-based lag covariance between forecast SST and precipitation induced by (a)–(c) cumulus convection and (d)–(f) large-scale condensation in CLERA-A. (top) SST leads precipitation by 1 day, (middle) simultaneous, and (bottom) precipitation leads SST by 1 day. The averaged ensemble mean of SST is also plotted in the contour, and the interval is 2 K.

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FIG. 10. Ensemble-based vertical correlation between forecast FIG. 11. Ensemble-based horizontal correlation of forecast 2-m SST and tropospheric air temperature at the height of (a) s 5 0:86 air temperature (color), 10-m winds (green arrows), and surface and (b) s 5 0:51 in CLERA-A averaged over the experimental pressure (gray contour) with respect to 2-m air temperature in the period. The averaged ensemble mean of SST is also plotted in the Niño-3.4 region (58S–58N, 1708–1208W; indicated by the white contour, and the interval is 2 K. rectangle) averaged over the experimental period for (a) ALERA2 and (b) CLERA-A. The arrows for 10-m winds smaller than 0.1 are omitted for visibility. The contour interval for surface pressure is strongly negative over the ITCZ regions in the eastern 0.05, and the dashed contours represent negative values. tropical Pacific and Atlantic, and the negative ensemble- based covariance becomes stronger in these regions when temperature has a much broader and larger ensemble- large-scale precipitation leads SST by 1 day (Fig. 9f). based horizontal correlation over the tropics and sub- For the future extension of our system to assimilate tropics in the summer hemisphere. The 10-m winds in oceanic observational data, Fig. 10 shows the ensemble- CLERA-A also tend to converge into the Niño-3.4 re- based vertical correlation between forecast SST and tro- gion but from a much broader area over the tropical pospheric air temperature in CLERA-A. The correlation Pacific. In addition, 10-m winds over the Arabian Sea, is calculated every 6 h and then averaged over the entire Bay of Bengal, South China Sea, and Philippine Sea are experimental period to reduce noises. SST has positive correlated with 2-m air temperature within the Niño-3.4 correlation with air temperature in the lower troposphere region, and their directions are opposite to the typical (at the height of s 5 0:86, Fig. 10a) over the tropics and monsoonal winds in this season. Surface pressure over subtropics in the summer hemisphere, and the correlation the tropical Pacific is negatively correlated with 2-m air coefficient almost reaches 0.3 in some regions. (The cor- temperature within the Niño-3.4 region. In the ensemble relation coefficient greater than 0.250 is significant at the ocean simulation driven by each member of ALERA2 95% confidence level for 60 degrees of freedom.) Such a (EnOFES), tropical SST exhibits similar (but weaker) relatively high correlation is also seen even in the mid- ensemble-based correlation with respect to SST aver- troposphere (at the height of s 5 0:51, which roughly aged within the Niño-3.4 region (not shown). Therefore, corresponds to the 510-hPa surface, Fig. 10b) over the this large-scale structure of ensemble-based horizontal warm water pool in the western tropical Pacific. correlation over the tropics in CLERA-A might be in- Finally, we compare remote effects of the tropical duced by the ocean and amplified through some coupled Pacific in CLERA-A with that in ALERA2. Figure 11 atmosphere–ocean processes, although the detailed shows the ensemble-based horizontal correlation of analysis is beyond the scope of this paper. forecast 2-m air temperature (color), 10-m winds (green arrows), and surface pressure (gray contour) with respect 5. Summary and conclusions to 2-m air temperature averaged within the Niño-3.4 re- gion (58S–58N, 1708–1208W). In ALERA2 (Fig. 11a), the In this study, to enhance the capability of the local area of high ensemble-based correlation among these ensemble transform Kalman filter (LETKF) with the variables is primarily confined to the Niño-3.4 region. Atmospheric General Circulation Model for the Earth The 10-m winds tend to converge into the region, and Simulator (AFES), a new system has been devel- surface pressure is positively correlated with 2-m air opedbyreplacingtheAFESwiththeCoupled temperature there. In CLERA-A (Fig. 11b), 2-m air Atmosphere–Ocean General Circulation Model for the

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Earth Simulator (CFES). Using the coupled system, two author ([email protected]). PREPBUFR, which is months of experimental retrospective analysis, CLERA-A, compiled by NCEP and archived at UCAR, is used as have been conducted from 1 August 2008 by assimilating the observations (http://rda.ucar.edu). The authors are atmospheric observational data (NCEP PREPBUFR) grateful to three anonymous reviewers for their valuable every 6 h to update only the atmospheric variables. comments. This work was supported by MEXT/JSPS Comparison of the CLERA-A with the AFES–LETKF KAKENHI (22106008, 22244057, 22740319, 25400474, experimental ensemble reanalysis, version 2 (ALERA2), and 17K05663). 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