1. Ensemble version







Ensemble identifier codeJMA CPS3JMA GEPS2203JMA GEPS2103JMA GEPS2003JMA GEPS1701GSM1403C
Short DescriptionCoupled Prediction System that simulates initial atmospheric uncertainties using the Breeding Growth Mode (BGM), its oceanic uncertainties approximating the analysis error covariance using oceanic 4DVAR minimization history and model uncertainties due to physical parameterizations using a stochastically perturbed physics tendencies (SPPT) scheme.Global ensemble system that simulates initial uncertainties using the Local Ensemble Transform Kalman Filter (LETKF), the singular vectors and lagged averaging forecasts, model uncertainties due to physical parameterizations using a stochastically perturbed physics tendencies (SPPT) scheme, and uncertainties on surface boundary conditions using sea surface temperature (SST) perturbation. Although it is uncoupled model, SST is relaxed to the ensemble-mean SST based on prediction using coupled model after lead time of 6 days. Ensembles are based on 50 members run once a week with 2 start dates (Tuesday and Wednesday at 12Z) up to day 34.Global ensemble system that simulates initial uncertainties using the Local Ensemble Transform Kalman Filter (LETKF), the singular vectors and lagged averaging forecasts, model uncertainties due to physical parameterizations using a stochastically perturbed physics tendencies (SPPT) scheme, and uncertainties on surface boundary conditions using sea surface temperature (SST) perturbation. Although it is uncoupled model, SST is relaxed to the ensemble-mean SST based on prediction using coupled model after lead time of 12 days. Ensembles are based on 50 members run once a week with 2 start dates (Tuesday and Wednesday at 12Z) up to day 34.Global ensemble system that simulates initial uncertainties using the Local Ensemble Transform Kalman Filter (LETKF), the singular vectors and lagged averaging forecasts, model uncertainties due to physical parameterizations using a stochastically perturbed physics tendencies (SPPT) scheme, and uncertainties on surface boundary conditions using sea surface temperature (SST) perturbation. Although it is uncoupled model, SST is relaxed to the ensemble-mean SST based on prediction using coupled model after lead time of 12 days. Ensembles are based on 50 members run once a week (Tuesday and Wednesday at 00Z and 12Z) up to day 34.Global ensemble system that simulates initial uncertainties using the Local Ensemble Transform Kalman Filter (LETKF), the singular vectors and lagged averaging forecasts, model uncertainties due to physical parameterizations using a stochastically perturbed physics tendencies (SPPT) scheme, and uncertainties on surface boundary conditions using sea surface temperature (SST) perturbation. Ensembles are based on 50 members run once a week (Tuesday and Wednesday at 00Z and 12Z) up to day 34.Global ensemble system that simulates initial uncertainties using the bred vectors and lagged averaging forecasts and model uncertainties due to physical parameterizations using a stochastic scheme. Ensembles are based on 50 members, run once a week (Tuesday, Wednesday at 12Z) up to day 34.
Research or operationalOperationalOperationalOperationalOperationalOperationalOperational
Data time of first forecast run19/02/202315/03/202230/03/202124/03/202022/03/201705/03/2014

2. Configuration of the EPS







Is the model coupled to an ocean model?Yes, from day 0NoNoNoNoNo
If yes, please describe ocean model briefly including frequency of coupling and any ensemble perturbation appliedOcean model is MRI.COMv4.6 with a 0.25-degree horizontal resolution, 60 vertical levels, initialized from MOVE-G3 (Fujii et al. 2023) Analysis + 4 perturbed analyses produced by approximating the analysis error covariance using oceanic 4DVAR minimization history (Niwa and Fujii, 2020). Frequency of coupling is hourly.N/AN/AN/AN/AN/A
If no, please describe the sea surface temperature boundary conditions (climatology, reanalysis ...) 




Is the model coupled to a sea Ice model?YesNoNoNoNoNo
If yes, please describe sea-ice model briefly including any ensemble perturbation appliedInteractive sea-ice model (MRI.COMv4.6). Initial perturbations of sea-ice from the 5-ensemble ocean. No stochastic perturbations.N/AN/AN/AN/AN/A
Is the model coupled to a wave model?NoNoNoNoNoNo
If yes, please describe wave model briefly including any ensemble perturbation appliedN/AN/AN/AN/AN/AN/A
Ocean modelMRI.COM 0.25-degree resolutionN/AN/AN/AN/AN/A
Horizontal resolution of the atmospheric modelTL319 (about 55 km).TQ479 (about 27 km) up to 18 days, TQ319 (about 40 km) after 18 days.TL479 (about 40 km) up to 18 days, TL319 (about 55 km) after 18 days.TL479 (about 40 km) up to 18 days, TL319 (about 55 km) after 18 days.TL479 (about 40 km) up to 18 days, TL319 (about 55 km) after 18 days.TL319 (about 55 km)
Number of model levels10012812810010060
Top of model0.01 hPa0.01 hPa0.01 hPa0.01 hPa0.01 hPa
Type of model levelshybrid (sigma-p) coordinatehybrid (sigma-p) coordinatehybrid (sigma-p) coordinatehybrid (sigma-p) coordinatehybrid (sigma-p) coordinatesigma
Forecast length34 days (816 hours)34 days (816 hours), but archived up to 32.5 days (780 hours)34 days (816 hours), but archived up to 32.5 days (780 hours)34 days (816 hours), but archived up to 32.5 days (780 hours)34 days (816 hours), but archived up to 32.5 days (780 hours)34 days (816 hours)
Run Frequencyevery day at 00Zonce a week (combination of Tuesday and Wednesday at 12Z)once a week (combination of Tuesday and Wednesday at 12Z)once a week (combination of Tuesday and Wednesday at 00Z and 12Z)once a week (combination of Tuesday and Wednesday at 00Z and 12Z)once a week (combination of Tuesday and Wednesday at 00Z and 12Z)
Is there an unperturbed control forecast included?YesYesYesYesYesYes
Number of perturbed ensemble members4 (1 control)48 (totally 2 controls from 2 initial dates)48 (totally 2 controls from 2 initial dates)46 (4 controls from each initial date), but archived as 49 (1 control from each initial date)46 (4 controls from each initial date), but archived as 49 (1 control from each initial date)48 (2 controls from each initial date)
Integration time step20 minutes10 minutes up to 18 days and 12 minutes after 18 days12 minutes up to 18 days and 20 minutes after 18 days12 minutes up to 18 days and 20 minutes after 18 days12 minutes up to 18 days and 20 minutes after 18 days20 minutes

3. Initial conditions and perturbations







Data assimilation method for control analysishybrid 4D Var-LETKFhybrid 4D Var-LETKFhybrid 4D Var-LETKFhybrid 4D Var-LETKF4D Var4D Var
Resolution of model used to generate Control AnalysisTL959L128TL959L128TL959L128TL959L100TL959L100TL959L100
Ensemble initial perturbation strategyBred vectors (Northern Hemisphere, Tropics and Southern Hemisphere)LETKF + singular vectors (initial SV; Northern Hemisphere, Tropics and Southern Hemisphere) + Lagged Average ForecastingLETKF + singular vectors (initial SV; Northern Hemisphere, Tropics and Southern Hemisphere) + Lagged Average ForecastingLETKF + singular vectors (initial SV; Northern Hemisphere, Tropics and Southern Hemisphere) + Lagged Average ForecastingLETKF + singular vectors (initial SV; Northern Hemisphere, Tropics and Southern Hemisphere) + Lagged Average ForecastingBred vectors (extratropics (NH) plus tropics) + Lagged Average Forecasting
Horizontal and vertical resolution of perturbationsTL319L100TL319L128 (LETKF), TL63L40 (SV)TL319L128 (LETKF), TL63L40 (SV)TL319L100 (LETKF), TL63L40 (SV)TL319L100 (LETKF), T63L40 (SV)TL319L60
Perturbations in +/- pairsYesYes (SV), No (LETKF), No (SST)Yes (SV), No (LETKF), No (SST)Yes (SV), No (LETKF), No (SST)Yes (SV), No (LETKF), No (SST)Yes
Initialization of land surface





3.1 What is the land surface model (LSM) and version used in the forecast model, and what are the current/relevant references for the model? Are there any significant changes/deviations in the operational version of the LSM from the documentation of the LSM?

See Land Surface Processes Chapter 3.2.10 by JMA (2022).

LSM is the JMA SIB. The JMA SIB is based on the Simple Biosphere (SiB) developed by Sellers et al.(1986) and implemented by Sato et al.(1989a) and Sato et al.(1989b) for the land surface process in forecast model, and overall specifications are comprehensively updated and refined schemes are introduced. Significant changes from SiB are;

  • replacement the force-restore method for soil temperature prediction with a multilayer soil heat and water flux model and separate layers for snow

  • introduction of an equation of heat conduction with seven soil levels

  • consideration of the release or absorption of latent heat from phase change for soil temperature prediction

  • introduction of a new snow model with up to four layers with consideration for thermal diffusion, increased density from snow compaction and reduction of albedo due to snow aging

The Simple Biosphere (SiB) developed by Sellers et al.(1986), Sato et al.(1989a)

LSM is the JMA SIB. The JMA SIB is based on the Simple Biosphere (SiB) developed by Sellers et al.(1986) and implemented by Sato et al.(1989a) and Sato et al.(1989b) for the land surface process in forecast model, and overall specifications are comprehensively updated and refined schemes are introduced. Significant changes from SiB are;

  • replacement the force-restore method for soil temperature prediction with a multilayer soil heat and water flux model and separate layers for snow

  • introduction of an equation of heat conduction with seven soil levels

  • consideration of the release or absorption of latent heat from phase change for soil temperature prediction

  • introduction of a new snow model with up to four layers with consideration for thermal diffusion, increased density from snow compaction and reduction of albedo due to snow aging

The Simple Biosphere (SiB) developed by Sellers et al.(1986), Sato et al.(1989a)

LSM is the JMA SIB. The JMA SIB is based on the Simple Biosphere (SiB) developed by Sellers et al.(1986) and implemented by Sato et al.(1989a) and Sato et al.(1989b) for the land surface process in forecast model, and overall specifications are comprehensively updated and refined schemes are introduced. Significant changes from SiB are;

  • replacement the force-restore method for soil temperature prediction with a multilayer soil heat and water flux model and separate layers for snow

  • introduction of an equation of heat conduction with seven soil levels

  • consideration of the release or absorption of latent heat from phase change for soil temperature prediction

  • introduction of a new snow model with up to four layers with consideration for thermal diffusion, increased density from snow compaction and reduction of albedo due to snow aging

The Simple Biosphere (SiB) developed by Sellers et al.(1986), Sato et al.(1989a)

LSM is the JMA SIB. The JMA SIB is based on the Simple Biosphere (SiB) developed by Sellers et al.(1986) and implemented by Sato et al.(1989a) and Sato et al.(1989b) for the land surface process in forecast model, and overall specifications are comprehensively updated and refined schemes are introduced. Significant changes from SiB are;

  • replacement the force-restore method for soil temperature prediction with a multilayer soil heat and water flux model and separate layers for snow

  • introduction of an equation of heat conduction with seven soil levels

  • consideration of the release or absorption of latent heat from phase change for soil temperature prediction

  • introduction of a new snow model with up to four layers with consideration for thermal diffusion, increased density from snow compaction and reduction of albedo due to snow aging

The Simple Biosphere (SiB) developed by Sellers et al.(1986), Sato et al.(1989a)

The Simple Biosphere (SiB) developed by Sellers et al.(1986), Sato et al.(1989a) and Sato et al.(1989b) has been implemented for the land surface process in forecast model.
3.2 How is soil moisture initialized in the forecasts? (climatology / realistic / other)? If “realistic”, does the soil moisture come from an analysis using the same LSM as is coupled to the GCM for forecasts, or another source? Please describe the process of soil moisture initialization. Is there horizontal and/or vertical interpolation of initialization data onto the forecast model grid? If so, please give original data resolution(s).  Does the LSM differentiate between liquid and ice content of the soil? If so, how are each initialized? If all model soil layers are not initialized in the same way or from the same source, please describe.

Soil moisture cycled from JMA’s offline surface simulation forced by JMA Global Analysis (GA) and JRA-3Q (Kobayashi et al. 2021) is separately run and used for forecasts. No horizontal and vertical interpolation are applied. The LSM defines two soil moisture state variables, liquid and ice. The amounts of liquid and ice are determined by soil temperature and the ratio of the two soil moisture state variables cycled from the model forecast in GA. To prevent unrealistic soil moisture drifting after long-term integration, initial soil moisture deeper than or equal to the 4th layer is set to the climatological value. See Ochi (2020) for details.

Soil moisture is initialized realistically by JMA’s soil moisture analysis based on Simplified Extended Kalman Filter (SEKF). Soil moisture and other initialization data are interpolated from the resolution of the deterministic system (TL959) to the resolution of the EPS forecast model grid (TQ479). No vertical interpolation is applied. The LSM defines two soil moisture state variables, liquid and ice. The amounts of liquid and ice are determined by soil temperature and the ratio of the two soil moisture state variables cycled from the model forecast in the JMA Global Analysis (GA). To prevent unrealistic soil moisture drifting after long-term integration, initial soil moisture deeper than or equal to the 4th layer is set to the climatological value. See Ochi (2020) for details.Soil moisture is initialized realistically by JMA’s soil moisture analysis based on Simplified Extended Kalman Filter (SEKF). Soil moisture and other initialization data are interpolated from the resolution of the deterministic system (TL959) to the resolution of the EPS forecast model grid (TL479). No vertical interpolation is applied. The LSM defines two soil moisture state variables, liquid and ice. The amounts of liquid and ice are determined by soil temperature and the ratio of the two soil moisture state variables cycled from the model forecast in the JMA Global Analysis (GA). To prevent unrealistic soil moisture drifting after long-term integration, initial soil moisture deeper than or equal to the 4th layer is set to the climatological value. See Ochi (2020) for details.Soil moisture is initialized  with climatology derived from the offline simulations of the LSM with resolution of TL959. Soil moisture and other initialization data are interpolated from the resolution of the deterministic system (TL959) to the resolution of the EPS forecast model grid (TL479). No vertical interpolation is applied. The LSM defines two soil moisture state variables, liquid and ice. The amounts of liquid and ice are determined by soil temperature and the ratio of the two soil moisture state variables cycled from the model forecast in the JMA Global Analysis (GA).Soil moisture is initialized with climatology derived from the offline simulations of the LSM with resolution of TL959. Soil moisture and other initialization data are interpolated from the resolution of the deterministic system (TL959) to the resolution of the EPS forecast model grid (TL479). No vertical interpolation is applied. The LSM defines two soil moisture state variables, liquid and ice. The amounts of liquid and ice are determined by soil temperature and the ratio of the two soil moisture state variables cycled from the model forecast in the JMA Global Analysis (GA).Initial soil moisture data (which consists of three layers) is produced by the offline simulations of the land surface model. The land processes in this simulations are similar to the one set in forecast model, and no horizontal and vertical interpolations are introduced in this analysis. Soil ice is handled as soil water, and no soil ice is used as initial condition specifically.
3.3 How is snow initialized in the forecasts? (climatology / realistic / other)? Is there horizontal and/or vertical interpolation of data onto the forecast model grid? If so, please give original data resolution(s) Are snow mass, snow depth or both initialized? What about snow age, albedo, or other snow properties?The global snow depth is analyzed using SYNOP snow depth data on the day. The forecasted snow depth corrected by satellite-estimated snow area is employed as first guess of the snow depth analysis. A two-dimensional optimum interpolation (OI) is employed for the analysis method. The analyzed snow depth is converted to the EPS forecast model grid (TL319). In addition, snow depth on Japan land grids is replaced with interpolated latest observation value of AMeDAS (Automated Meteorological Data Acquisition System) snow depth as well as Japanese SYNOP. The analyzed snow depth is converted to snow mass using snow density cycled from the GA model forecast and the snow mass is used as an initial condition for the LSM. Snow age is cycled from the GA model forecast and albedo is calculated with the snow age.The global snow depth is analyzed using SYNOP snow depth data on the day. The forecasted snow depth corrected by satellite-estimated snow area is employed as first guess of the snow depth analysis. A two-dimensional optimum interpolation (OI) is employed for the analysis method. The analyzed snow depth is converted to the EPS forecast model grid (TQ479). In addition, snow depth on Japan land grids is replaced with interpolated latest observation value of AMeDAS (Automated Meteorological Data Acquisition System) snow depth as well as Japanese SYNOP. The analyzed snow depth is converted to snow mass using snow density cycled from the GA model forecast and the snow mass is used as an initial condition for the LSM. Snow age is cycled from the GA model forecast and albedo is calculated with the snow age.The global snow depth is analyzed using SYNOP snow depth data on the day. The forecasted snow depth corrected by satellite-estimated snow area is employed as first guess of the snow depth analysis. A two-dimensional optimum interpolation (OI) is employed for the analysis method. The analyzed snow depth is converted to the EPS forecast model grid (TL479). In addition, snow depth on Japan land grids is replaced with interpolated latest observation value of AMeDAS (Automated Meteorological Data Acquisition System) snow depth as well as Japanese SYNOP. The analyzed snow depth is converted to snow mass using snow density cycled from the GA model forecast and the snow mass is used as an initial condition for the LSM. Snow age is cycled from the GA model forecast and albedo is calculated with the snow age.The global snow depth with 1.0 degree latitude/longitude resolution is analyzed using SYNOP snow depth data on the day. A two-dimensional optimum interpolation (OI) is employed for the analysis method. The analyzed snow depth is interpolated to the EPS forecast model grid (TL479). In addition, snow depth on Japan land grids are replaced with interpolated latest observation value of AMeDAS (Automated Meteorological Data Acquisition System) snow depth as well as Japanese SYNOP. The analyzed snow depth is converted to snow mass using snow density cycled from the GA model forecast and the snow mass is used as an initial condition for the LSM. Snow age is cycled from the GA model forecast and albedo is calculated with the snow age.The global snow depth with 1.0 degree latitude/longitude resolution is analyzed using SYNOP snow depth data on the day. A two-dimensional optimum interpolation (OI) is employed for the analysis method. The analyzed snow depth is interpolated to the EPS forecast model grid (TL479). In addition, snow depth on Japan land grids are replaced with interpolated latest observation value of AMeDAS (Automated Meteorological Data Acquisition System) snow depth as well as Japanese SYNOP. The analyzed snow depth is converted to snow mass using snow density cycled from the GA model forecast and the snow mass is used as an initial condition for the LSM. Snow age is cycled from the GA model forecast and albedo is calculated with the snow age.Initial snow data is also produced by using the offline simulation of the land surface model, and no horizontal interpolation is introduced. In the offline simulation, snow depth data is updated once a day (00UTC) by the two-dimensional Optimal Interpolation using the SYNOP snow depth data. The first guess is calculated by snow depth data from the offline simulation and snow cover data estimated by satellite observation. Forecast model calculates the snow water equivalent, so snow depth data is converted to the snow water equivalent. Snow density is set as a function related to the snow water equivalent (Verseghy 1991). Snow albedo is set as a function of wavelength and snow temperature. The age of snow is not considered.
3.4 How is soil temperature initialized in the forecasts? (climatology / realistic / other) Is the soil temperature initialized consistently with soil moisture (frozen soil water where soil temperature ≤0°C) and snow cover (top layer soil temperature ≤0°C under snow)? Is there horizontal and/or vertical interpolation of data onto the forecast model grid? If so, please give original data resolution(s)  If all model soil layers are not initialized in the same way or from the same source, please describe.Soil temperature cycled from JMA’s offline surface simulation forced by GA and JRA-3Q is separately run and used for forecasts. No horizontal and vertical interpolation are applied. The liquid and ice content of the soil initialized in the forecasts are determined by the soil temperature cycled from the GA model forecast.Soil temperature cycled from the GA model forecast with resolution of TL959 is used as an initial condition for the LSM. It is interpolated to the EPS forecast model grid. The liquid and ice content of the soil initialized in the forecasts are determined by the soil temperature cycled from the GA model forecastSoil temperature cycled from the GA model forecast with resolution of TL959 is used as an initial condition for the LSM. It is interpolated to the EPS forecast model grid. The liquid and ice content of the soil initialized in the forecasts are determined by the soil temperature cycled from the GA model forecastSoil temperature cycled from the GA model forecast with resolution of TL959 is used as an initial condition for the LSM. It is interpolated to the EPS forecast model grid. The liquid and ice content of the soil initialized in the forecasts are determined by the soil temperature cycled from the GA model forecastSoil temperature cycled from the GA model forecast with resolution of TL959 is used as an initial condition for the LSM. It is interpolated to the EPS forecast model grid. The liquid and ice content of the soil initialized in the forecasts are determined by the soil temperature cycled from the GA model forecastSoil temperature is also initialized by the offline simulations of the land surface model. No horizontal and vertical interpolation is implemented. Note that soil layers are three for soil moisture, while it is only one layer for soil temperature. Snow cover is updated at each 00UTC based on the snow depth analysis. At the same time, soil temperature for all grids where snow exists is set as less than 0 deg. Once the soil temperature becomes less than 0deg, soil water changes soil ice (No consideration about freeze latent heat). No soil water scatters or moves in the freezing soil.
3.5 How are time-varying vegetation properties represented in the LSM? Is phenology predicted by the LSM? If so, how is it initialized? If not, what is the source of vegetation parameters used by the LSM? Which time-varying vegetation parameters are specified (e.g., LAI, greenness, vegetation cover fraction) and how (e.g., near-real-time satellite observations? Mean annual cycle climatology? Monthly, weekly or other interval?)There is no consideration about time-varying of vegetation properties. The climatology for each vegetation based on Dorman and Sellers (1989) is set as outer parameters (Some parameters are monthly data, such as LAI, the ratio of green leaves, the ratio of vegetation)There is no consideration about time-varying of vegetation properties. The climatology for each vegetation based on Dorman and Sellers (1989) is set as outer parameters (Some parameters are monthly data, such as LAI, the ratio of green leaves, the ratio of vegetation)There is no consideration about time-varying of vegetation properties. The climatology for each vegetation based on Dorman and Sellers (1989) is set as outer parameters (Some parameters are monthly data, such as LAI, the ratio of green leaves, the ratio of vegetation)There is no consideration about time-varying of vegetation properties. The climatology for each vegetation based on Dorman and Sellers (1989) is set as outer parameters (Some parameters are monthly data, such as LAI, the ratio of green leaves, the ratio of vegetation)There is no consideration about time-varying of vegetation properties. The climatology for each vegetation based on Dorman and Sellers (1989) is set as outer parameters (Some parameters are monthly data, such as LAI, the ratio of green leaves, the ratio of vegetation)There is no consideration about time-varying of vegetation properties. The climatology for each vegetation based on Dorman and Sellers (1989) is set as outer parameters (Some parameters are monthly data, such as LAI, the ratio of green leaves, the ratio of vegetation)
3.6 What is the source of soil properties (texture, porosity, conductivity, etc.) used by the LSM?

Soil thermal and hydraulic properties are calculated using soil texture from the HWSD (Harmonized World Soil Database).

Soil thermal and hydraulic properties are calculated using soil texture from the HWSD (Harmonized World Soil Database).

Soil thermal and hydraulic properties are calculated using soil texture from the HWSD (Harmonized World Soil Database).

Soil thermal and hydraulic properties are calculated using soil texture from the HWSD (Harmonized World Soil Database).

Soil thermal and hydraulic properties are calculated using soil texture from the HWSD (Harmonized World Soil Database).

The source of soil properties is different depending on the property. For example, soil porosity is set as outer parameters for each type of vegetation, while soil heat conductivity is set as a function related to the porosity and soil moisture in the first soil layer. In addition, some parameters are not considered such as difference of soil texture.
3.7 If the initialization of the LSM for re-forecasts deviates from the procedure for forecasts, please describe the differences.Land surface values are estimated with the offline land-surface model in the CPS3 using atmospheric forcing from JRA-3Q.Land surface values are estimated with the land-surface model in the Global EPS using atmospheric forcing from JRA-3Q (Kobayashi et al. 2021)Land surface values are estimated with the land-surface model in the Global EPS using atmospheric forcing from JRA-55 (Kobayashi et al. 2015)Land surface values are estimated with the land-surface model in the Global EPS using atmospheric forcing from JRA-55 (Kobayashi et al. 2015)Land surface values are estimated with the land-surface model in the Global EPS using atmospheric forcing from JRA-55 (Kobayashi et al. 2015)There is no difference between re-forecast and operational forecast about the procedure for initialization of land surface. For the re-forecast, land analysis data of JRA-55 is utilized as the land initial data and it is derived from the offline system forced by JRA-55 atmospheric field. This system is similar to the operational system, but note that the atmospheric forcing for operational offline system is given from the operational Global Analysis.

4. Model uncertainties perturbations







Is model physics perturbed?  If yes, briefly describe methodsStochastically perturbed physics tendencies (SPPT) schemeStochastically perturbed physics tendencies (SPPT) schemeStochastically perturbed physics tendencies (SPPT) schemeStochastically perturbed physics tendencies (SPPT) schemeStochastically perturbed physics tendencies (SPPT) schemeStochastic physics
Do all ensemble members use exactly the same model version?SameSameSameSameSameSame
Is model dynamics perturbed?NoNoNoNoNoNo
Are the above model perturbations applied to the control forecast?NoNoNoNoNoNo

5. Surface boundary perturbations







Perturbations to sea surface temperature?YesYesYesYesYesNo
Perturbation to soil moisture?NoNoNoNoNoNo
Perturbation to surface stress or roughness?NoNoNoNoNoNo
Any other surface perturbation?NoNoNoNoNoNo
Are the above surface perturbations applied to the Control forecast?NoNoNoNoNoNo
Additional commentsNoneNoneNoneNoneNoneNone

6. Other details of the models







Description of model gridLinear gridQuadratic gridLinear gridLinear gridLinear gridLinear grid
List of model levels in appropriate coordinatesSee appendixSee appendixSee appendixSee appendixSee appendixhttp://jra.kishou.go.jp/JRA-55/document/JRA-55_handbook_TL319_v2_en.pdf
What kind of large scale dynamics is used?Spectral semi-lagrangianSpectral semi-lagrangianSpectral semi-lagrangianSpectral semi-lagrangianSpectral semi-lagrangianSpectral semi-lagrangian
What kind of boundary layer parameterization is used?Mellor and Yamada level 2 and diffusive coefficients based on Han and Pan (2011) for stable BL, JMA (2022)Mellor and Yamada level 2 and diffusive coefficients based on Han and Pan (2011) for stable BL, JMA (2022)Mellor and Yamada level 2 and diffusive coefficients based on Han and Pan (2011) for stable BL, JMA (2019)Mellor and Yamada level 2 and diffusive coefficients based on Han and Pan (2011) for stable BL, JMA (2019)Mellor and Yamada level 2 and diffusive coefficients based on Han and Pan (2011) for stable BL, Yonehara et al. (2014)Mellor and Yamada level 2.5
What kind of convective parameterization is used?Arakawa and Schubert (1974), Tokioka et al. (1988), Bechtold et al. (2008), Komori et al. (2020), JMA (2022)Arakawa and Schubert (1974), JMA (2022)Arakawa and Schubert (1974), JMA (2019)Arakawa and Schubert (1974), JMA (2019)Arakawa and Schubert (JMA 2013), Yonehara et al. (2014), Yonehara et al. (2017)Arakawa and Schubert (JMA 2013)
What kind of large-scale precipitation scheme is used?Sundqvist (1978), JMA (2022)Sundqvist (1978), JMA (2022)Sundqvist (1978), JMA (2019)Sundqvist (1978), JMA (2019)Sundqvist (1978), Yonehara et al. (2017)Sundqvist (1978)
What cloud scheme is used?Smith (1990), Kawai et al. (2017), Chiba and Kawai (2021)Smith (1990), Kawai and Inoue (2006), JMA (2022)Smith (1990), Kawai and Inoue (2006), JMA (2019)Smith (1990), Kawai and Inoue (2006), JMA (2019)Smith (1990), Kawai and Inoue (2006), Yonehara et al. (2017)Smith (1990), Kawai and Inoue (2006), Yonehara et al. (2017)
What kind of land-surface scheme is used?JMA-SIB, JMA (2022), Yonehara et al. (2020)JMA-SIB, JMA (2022), Yonehara et al. (2020)JMA-SIB, JMA (2019), Yonehara et al. (2020)JMA-SIB, JMA (2019), Yonehara et al. (2020)JMA-SIB, Yonehara et al. (2017)SiB (Sato et al. 1989)
How is radiation parametrized?
  • Longwave radiation: JMA (2022)
  • Shortwave radiation: JMA (2022)
  • Longwave radiation: JMA (2022)
  • Shortwave radiation: JMA (2022)
  • Longwave radiation: JMA (2019)
  • Shortwave radiation: JMA (2019)
  • Longwave radiation: JMA (2019)
  • Shortwave radiation: JMA (2019)
  • Longwave radiation: Yabu (2013)
  • Shortwave radiation: JMA (2013), Nagasawa (2012)
Outline of the operational numerical weather prediction at the Japan Meteorological Agency

7. Re-forecast configuration







Number of years covered30 years (1991-2020)30 years (1991-2020)40 years (1981-2020)30 years (1981-2010)32 years (1981-2012)30 years (1981-2010)
Produced on the fly or fix re-forecasts?Fixed re-forecasts in advanceFixed re-forecasts in advanceFixed re-forecasts in advanceFixed re-forecasts in advanceFixed re-forecasts in advanceFixed re-forecasts in advance
Frequency

2 start dates lagged by 15 days

The re-forecasts consist of a 13-member ensemble starting the 15th and the last dates of calendar months.The re-forecasts consist of a 13-member ensemble starting the 15th and the last dates of calendar months.The re-forecasts consist of a 13-member ensemble starting the 15th and the last dates of calendar months.The re-forecasts consists of a 5 member ensemble starting the 10th, 20th, the last dates of calendar months.The re-forecasts consists of a 5 member ensemble starting the 10th, 20th, the last dates of calendar months.
Ensemble size

5 members

13 members13 members13 members5 members5 members
Initial conditionsJRA-3Q (TL479L100) + land surface values estimated with the land-surface model in the CPS3 using atmospheric forcing from JRA-3Q + MOVE-G3 ocean initial conditions (0.25 degree)JRA-3Q (TL479L100) + land surface values estimated with the land-surface model in the Global EPS using atmospheric forcing from JRA-3QJRA-55 (TL319L60) + land surface values estimated with the land-surface model in the Global EPS using atmospheric forcing from JRA-55JRA-55 (TL319L60) + land surface values estimated with the land-surface model in the Global EPS using atmospheric forcing from JRA-55JRA-55 (TL319L60) + land surface values estimated with the land-surface model in the Global EPS using atmospheric forcing from JRA-55JRA-55 (TL319L60) + JRA-55 land analysis (TL319)
Is the model physics and resolution the same as for the real-time forecastsYesYesYesYesYesYes
If not, what are the differencesN/AN/AN/AN/AN/AN/A
Is the ensemble generation the same as for real-time forecasts?YesNoNoNoNoYes, except for lagged average forecasting.
If not, what are the differences
LETKF perturbations are not used and singular vectors (initial SV + evolved SV) are usedLETKF perturbations are not used and singular vectors (initial SV + evolved SV) are usedLETKF perturbations are not used and singular vectors (initial SV + evolved SV) are usedLETKF perturbations are not used and singular vectors (initial SV + evolved SV) are usedN/A
Other relevant information

The JMA re-forecasts dataset is a "fixed" dataset which means that the re-forecasts are produced once from a "frozen" version of the model and are used for a number of years to calibrate real-time forecast. The JMA re-forecasts consist of a 5-member ensemble running twice a month from 1991 to 2020. The start dates are the following list.

16/31 January - 10/25 February - 12/27 March - 11/26 April - 16/31 May - 15/30 June - 15/30 July - 14/29 August - 13/28 September - 13/28 October - 12/27 November and 12/27 December 1991-2020

The S2S database contains the complete JMA re-forecast dataset.


The JMA re-forecasts are archived in the S2S database with 2 date attributes:

  • hdate which corresponds to the actual starting date of the re-forecast
  • date which corresponds to the ModelVersionDate. Since the JMA re-forecasts are "fixed" re-forecasts this ModelVersiondate is the same for all the re-forecasts and equal to 20220930. This variable will change when a new version of the JMA model for extended-range forecasts will be implemented.

The JMA re-forecasts dataset is a "fixed" dataset which means that the re-forecasts are produced once from a "frozen" version of the model and are used for a number of years to calibrate real-time forecast. The JMA re-forecasts consist of a 13-member ensemble running twice a month from 1991 to 2020. The start dates correspond to 1st and 16st of each month at 00Z minus 12 hours (28 February instead of 29 February). Here is the complete list of re-forecast start dates:

15/31 January - 15/28 February - 15/31 March - 15/30 April - 15/31 May - 15/30 June - 15/31 July - 15/31 August - 15/30 September - 15/31 October - 15/30 November and 15/31 December 1991-2020

The S2S database contains the complete JMA re-forecast dataset.


The JMA re-forecasts are archived in the S2S database with 2 date attributes:

  • hdate which corresponds to the actual starting date of the re-forecast
  • date which corresponds to the ModelVersionDate. Since the JMA re-forecasts are "fixed" re-forecasts this ModelVersiondate is the same for all the re-forecasts and equal to 20220331. This variable will change when a new version of the JMA model for extended-range forecasts will be implemented.

The JMA re-forecasts dataset is a "fixed" dataset which means that the re-forecasts are produced once from a "frozen" version of the model and are used for a number of years to calibrate real-time forecast. The JMA re-forecasts consist of a 13-member ensemble running twice a month from 1981 to 2020. The start dates correspond to 1st and 16st of each month at 00Z minus 12 hours (28 February instead of 29 February). Here is the complete list of re-forecast start dates:

15/31 January - 15/28 February - 15/31 March - 15/30 April - 15/31 May - 15/30 June - 15/31 July - 15/31 August - 15/30 September - 15/31 October - 15/30 November and 15/31 December 1981-2020

The S2S database contains the complete JMA re-forecast dataset.


The JMA re-forecasts are archived in the S2S database with 2 date attributes:

  • hdate which corresponds to the actual starting date of the re-forecast
  • date which corresponds to the ModelVersionDate. Since the JMA re-forecasts are "fixed" re-forecasts this ModelVersiondate is the same for all the re-forecasts and equal to 20210331. This variable will change when a new version of the JMA model for extended-range forecasts will be implemented.

The JMA re-forecasts dataset is a "fixed" dataset which means that the re-forecasts are produced once from a "frozen" version of the model and are used for a number of years to calibrate real-time forecast. The JMA re-forecasts consist of a 13-member ensemble running twice a month from 1981 to 2010. The start dates correspond to 1st and 16st of each month at 00Z minus 12 hours (28 February instead of 29 February). Here is the complete list of re-forecast start dates:

15/31 January - 15/28 February - 15/31 March - 15/30 April - 15/31 May - 15/30 June - 15/31 July - 15/31 August - 15/30 September - 15/31 October - 15/30 November and 15/31 December 1981-2010

The S2S database contains the complete JMA re-forecast dataset.


The JMA re-forecasts are archived in the S2S database with 2 date attributes:

  • hdate which corresponds to the actual starting date of the re-forecast
  • date which corresponds to the ModelVersionDate. Since the JMA re-forecasts are "fixed" re-forecasts this ModelVersiondate is the same for all the re-forecasts and equal to 20200331. This variable will change when a new version of the JMA model for extended-range forecasts will be implemented.

The JMA real-time ensemble forecasts include 4 start dates (Tuesdays at 00Z and 12Z + Wednesdays at 00Z + 12Z). The ensemble size is 13 members for Tuesdays 12Z and Wednesdays 00 and 12Z and 11 members for Tuesdays 00Z. For user convenience, ensemble data from 4 start dates are archived as a single 50-member ensemble starting on Wednesdays at 12Z. List of initialize date and index of archived member in final 50 member ensemble are as follows;

  • Wednesday 12 Z : 0,1, …, 12
  • Wednesday 00 Z : 13,14, …, 25
  • Tuesday 12 Z : 26, 27, …, 38
  • Tuesday 00 Z : 39, 40, …, 49

Note that member 0, 13, 26 and 39 are control forecast from each initial date, however, they are encoded as pf for user convenience.

The JMA re-forecasts dataset is a "fixed" dataset which means that the re-forecasts are produced once from a "frozen" version of the model and are used for a number of years to calibrate real-time forecast. The JMA re-forecasts consist of a 5-member ensemble running three times a month from 1981 to 2012. The start dates correspond to 1st / 11th and 21st of each month at 00Z minus 12 hours (28 February instead of 29 February). here is the complete list of re-forecast start dates:

10/20/31 January - 10/20/28 February - 10/20/31 March - 10/20/30 April - 10/20/31 May - 10/20/30 June - 10/20/31 July - 10/20/31 August - 10/20/30 September - 10/20/31 October - 10/20/30 November and 10/20/31 December 1981-2012

The S2S database contains the complete JMA re-forecast dataset.

The JMA real-time ensemble forecasts include 4 start dates (Tuesdays at 00Z and 12Z + Wednesdays at 00Z + 12Z). The ensemble size is 13 members for Tuesdays 12Z and Wednesdays 00 and 12Z and 11 members for Tuesdays 00Z. For user convenience, ensemble data from 4 start dates are archived as a single 50-member ensemble starting on Wednesdays at 12Z. List of initialize date and index of archived member in final 50 member ensemble are as follows;

  • Wednesday 12 Z : 0,1, …, 12

  • Wednesday 00 Z : 13,14, …, 25

  • Tuesday 12 Z : 26, 27, …, 38

  • Tuesday 00 Z : 39, 40, …, 49

Note that member 0, 13, 26 and 39 are control forecast from each initial date, however, they are encoded as pf for user convenience.

The JMA re-forecasts are archived in the S2S database with 2 date attributes:

  • hdate which corresponds to the actual starting date of the re-forecast

  • date which correspond to the ModelVersionDate. Since the JMA re-forecasts are "fixed" re-forecasts this ModelVersiondate is the same for all the re-forecasts and equal to 20170131. This variable will change when a new version of the JMA model for extended-range forecasts will be implemented.

The JMA re-forecasts dataset is a "fixed" dataset which means that the re-forecasts are produced once from a "frozen" version of the model and are used for a number of years to calibrate real-time forecast. The JMA re-forecasts consist of a   5-member ensemble running three times a month from 1981 to 2010. The start dates correspond to 1st / 11th and 21st of each month at 00Z minus 12 hours (28 February instead of 29 February). here is the complete list of re-forecast start dates:

10/20/31 January - 10/20/28 February - 10/20/31 March - 10/20/30 April - 10/20/31 May - 10/20/30 June - 10/20/31 July - 10/20/31 August - 10/20/30 September - 10/20/31 October - 10/20/30 November and 10/20/31 December 1981-2010

The S2S database contains the complete JMA re-forecast dataset.

As for the other models, JMA re-forecasts are archived in the S2S database with 2 date attributes:

  • hdate which corresponds to the actual starting date of the re-forecast
  • date which correspond tot he ModelVersionDate.Since the JMA re-forecasts are "fixed" re-forecasts this ModelVersiondate is the same for all the re-forecasts and equal to  20140304. This variable will change when a new version of the JMA model for extended-range forecasts will be implemented.

8. References

  • Arakawa, A. and W. H. Schubert, 1974: Interaction of a Cumulus Cloud Ensemble with the Large-Scale Environment, Part I. J. Atmos. Sci., 31, 674-701.
  • Bechtold, P., M. Köhler, T. Jung, F. Doblas-Reyes, M. Leutbecher, M. J. Rodwell, F. Vitart, and G. Balsamo, 2008: Advances in simulating atmospheric variability with the ECMWF model: From synoptic to decadal time-scales. Quart. J. Roy. Meteor. Soc., 134, 1337–1351.
  • Chiba, J. and H. Kawai, 2021: Improved SST-shortwave radiation feedback using an updated stratocumulus parameterization. WGNE blue book, Res. Activ. Earth Sys. Modell., 51, 4–03.
  • Dorman, J. L. and P. J. Sellers, 1989: A global climatology of albedo, roughness length and stomatal resistance for atmospheric general circulation models as represented by the simple biosphere model (SiB). J. Appl.Meteor., 28, 833–855.
  • Fujii, Y., T. Yoshida, H. Sugimoto, I. Ishikawa, and S. Urakawa, 2023: Evaluation of a global ocean reanalysis generated by a global ocean data assimilation system based on a Four-Dimensional Variational (4DVAR) method. Front Clim, accepted.
  • Han, J. and H-L, Pan. 2011: Revision of convection and vertical diffusion schemes in the NCEP global forecast system. Weather and Forecasting, 26.4, 520-533.
  • Hirahara, S., Y. Kubo, T. Yoshida, T. Komori, J. Chiba, T. Takakura, T. Kanehama, R. Sekiguchi, K. Ochi, H. Sugimoto, Y. Adachi, I. Ishikawa, and Y. Fujii, 2023: Japan Meteorological Agency/Meteorological Research Institute Coupled Prediction System version 3 (JMA/MRI-CPS3). J. Meteor. Soc. Japan, accepted.
  • Japan Meteorological Agency, 2022: Outline of the operational numerical weather prediction at the Japan Meteorological Agency. https://www.jma.go.jp/jma/jma-eng/jma-center/nwp/outline2022-nwp/index.htm
  • Japan Meteorological Agency, 2019: Outline of the operational numerical weather prediction at the Japan Meteorological Agency.
  • Kawai, H., T. Koshiro, and M. J. Webb, 2017: Interpretation of factors controlling low cloud cover and low cloud feedback using a unified predictive index. J. Climate, 30, 9119–9131.
  • Kobayashi, S., Y. Kosaka, J. Chiba, T. Tokuhiro, Y. Harada, C. Kobayashi, and H. Naoe, 2021: JRA-3Q: Japanese reanalysis for three quarters of a century. WCRP-WWRP Symposium on Data Assimilation and Reanalysis/ECMWF annual seminar 2021, WMO/WCRP, O4–2, available at https://symp-bonn2021.sciencesconf.org/data/355900.pdf.
  • Kobayashi, S., Y. Ota, Y. Harada, A. Ebita, M. Moriya,H. Onoda, K. Onogi, H. Kamahori, C. Kobayashi, H. Endo, K. Miyaoka, and K. Takahashi, 2015: The JRA-55 reanalysis: General specifications and basic characteristics. J. Meteor. Soc. Japan. 93, 5-48.
  • Komori, T., S. Hirahara, and R. Sekiguchi, 2020: Improved representation of convective moistening in JMA ’s next-generation coupled seasonal prediction system. WGNE blue book, Res. Activ. Earth Sys. Modell., 50, 4–05.
  • Lott, F. and M.J. Miller, 1997: A new subgrid-scale orographic drag parameterization: Its formulation and testing. Quart. J. Roy. Meteor. Soc., 123, 101–127.
  • Niwa, Y. and Y. Fujii, 2020: A conjugate BFGS method for accurate estimation of a posterior error covariance matrix in a linear inverse problem. Quart. J. Roy. Meteor. Soc., 146, 3118-3143.
  • Ochi, K., 2020: Preliminary results of soil moisture data assimilation into JMA Global Analysis. CAS/JSC WGNE Res. Activ. Atmos. Oceanic Modell., 50, 1.15-1.16.
  • Sato, N., P. J. Sellers, D. A. Randall, E. K. Schneider, J. Shukla, J. L. Kinter III, Y-T Hou, and E. Albertazzi, 1989a: Effects of implementing the simple biosphere model (SiB) in a general circulation model. J. Atmos. Sci., 46, 2757–2782.
  • Sato, N., P. J. Sellers, D. A. Randall, E. K. Schneider, J. Shukla, J. L. Kinter III, Y-T Hou, and E. Albertazzi, 1989b: Implementing the simple biosphere model (SiB) in a general circulation model: Methodologies and results. NASA contractor Rep. 185509, NASA. 76pp.
  • Scinocca, J. F. 2003: An accurate spectral nonorographic gravity wave drag parameterization for general circulation models. J. Atmos. Sci., 60(4), 667-682.
  • Sellers, P. J., Y. Mintz, Y. C. Sud, and A. Dalcher, 1986: A simple biosphere model (SiB) for use within general circulation models. J. Atmos. Sci., 43, 505–531.
  • Simmons, A. J. and D. M. Burridge, 1981: An Energy and Angular-Momentum Conserving Vertical Finite-Difference Scheme and Hybrid Vertical Coordinates. Mon. Wea. Rev., 109, 758-766.
  • Smith, R. N. B., 1990: A scheme for predicting layer clouds and their water content in a general circulation model. Quart. J. Roy. Meteor. Soc., 116, 435–460.
  • Sundqvist, H., 1978: A parameterization scheme for non-convective condensation including prediction of cloud water content. Quart. J. Roy. Meteor. Soc., 104, 677–690.
  • Takakura, T., and T. Komori, 2020: Two-tiered sea surface temperature approach implemented to JMA’s Global Ensemble Prediction System, CAS/JSC WGNE Res. Activ. Atmos. Oceanic Modell., 50, 6.15-6.16.
  • Tokioka, T., K. Yamazaki, A. Kitoh, and T. Ose,1988: The equatorial 30-60 day oscillation and the Arakawa-Schubert penetrative cumulus parameterization. J. Meteor. Soc. Japan, 66, 883–901.
  • Tsujino, H., H. Nakano, K. Sakamoto, S. Urakawa, M. Hirabara, H. Ishizaki, and G. Yamanaka, 2017: Reference manual for the Meteorological Institute Community Ocean Model version 4 (MRI.COMv4), Technical Reports of the Meteorological Research Institute, 80, doi:10.11483/mritechrepo.80.
  • Yonehara, H., C. Matsukawa, T. Nabetani, T. Kanehama, T. Tokuhiro, K. Yamada, R. Nagasawa, Y. Adachi, and R. Sekiguchi, 2020: Upgrade of JMA’s Operational Global Model. CAS/JSC WGNE Res. Activ. Atmos. Oceanic Modell., 50, 6.19-6.20.

Appendix. Hybrid coordinates

Model level fields are produced for 100 hybrid levels. Each hybrid level is defined with half-levels 𝑝𝑘+ 1 as the boundary;

𝑝𝑘+ 1/2 = 𝐴𝑘+ 1/2 + 𝐵𝑘+ 1/2 𝑝s

where 𝑝s is the surface pressure. Coefficients A and B are given in Table A for k = 0, 1, 2, …, 100. The following equation by Simmons and Burridge (1981) gives full-level pressure;

𝑝𝑘 = 𝑒𝑥𝑝 [ 1 /𝛥𝑝𝑘 (𝑝𝑘− 1/2 𝑙𝑛 𝑝𝑘− 1/2 − 𝑝𝑘+ 1/2 𝑙𝑛 𝑝𝑘+ 1/2 ) − 𝐶]

where C=1 and k=1, 2, …, 99. The full-level pressure for the uppermost level (k=100) is given by

𝑝100 = 1/2 𝑝99.5.

Table A gives half-level and full-level pressures with a surface pressure of 1000hPa.

Table A. Model level from 1 to 120.

k

A[Pa]

B

Ph [Pa]

Pf [Pa]

1

0.000000000000

1.000000000000

100000.000000000000

99904.290840579200

2

0.381960202384

0.998082302745

99808.612234744800

99670.173246024500

3

2.282910582686

0.995295154130

99531.798323590500

99347.919685101000

4

7.263029910790

0.991568913910

99164.154420887900

98932.524217222700

5

17.501408483548

0.986835732358

98701.074644256400

98419.772700848500

6

35.837785954245

0.981029007209

98138.738506895400

97806.231077202200

7

65.788528045194

0.974083114968

97474.100024808800

97089.234993263200

8

111.534392415342

0.965933434382

96704.877830603100

96266.880120736900

9

177.878399880397

0.956516672775

95829.545677392600

95338.012570768100

10

270.172962859622

0.945771497843

94847.322747197800

94302.218827432700

11

394.216325080918

0.933639468705

93758.163195576900

93159.814637500400

12

556.119328049108

0.920066250467

92562.744374765500

91911.832303038100

13

762.144528509426

0.905003086587

91262.453187183600

90560.005835827300

14

1018.520729177840

0.888408493058

89859.370034940100

89106.753449905900

15

1331.237027835890

0.870250128253

88356.249853163600

87555.156896884000

16

1705.821506076210

0.850506782430

86756.499749027800

85908.937189891400

17

2147.110630500550

0.829170421862

85064.152816714400

84172.426318215500

18

2659.016282299730

0.806248214805

83283.837762814500

82350.534627023000

19

3244.298018195740

0.781764460392

81420.744057349000

80448.713625802900

20

3904.348647413270

0.755762337749

79480.582422272000

78472.914092492300

21

4639.001437858670

0.728305391427

77469.540580591400

76429.539458441800

22

5446.367197228410

0.699478671155

75394.234312718700

74325.394586804000

23

6322.709077375450

0.669389449218

73261.653999201500

72167.630192822300

24

7262.362201659950

0.638167447649

71079.106966589700

69963.683291679100

25

8257.704110039350

0.605964519813

68854.156091381300

67721.214196734600

26

9299.180569138790

0.572953746817

66594.555250834700

65448.040719169400

27

10375.389539015100

0.539327927949

64308.182333870500

63152.070338304300

28

11473.224080521700

0.505297465547

62002.970635264500

60841.231211752800

29

12578.072802905200

0.471087667443

59686.839547171500

58523.402974039900

30

13674.074183704900

0.436935513458

57367.625529535900

56206.348326637900

31

14744.418848362500

0.403085955334

55053.014381784300

53897.646448443100

32

15771.691788626800

0.369787840613

52750.475849926500

51604.629252389200

33

16738.244640660300

0.337289569439

50467.201584557700

49334.321479924800

34

17626.586642451900

0.305834607737

48210.047416192100

47093.385561382200

35

18419.781837842800

0.275656989982

45985.480836070300

44888.072078245200

36

19101.839561775500

0.246976949037

43799.534465497900

42724.176546770400

37

19658.085271638000

0.219996808968

41657.766168447000

40607.003104238100

38

20075.526860069500

0.194896994550

39565.226315109000

38541.335525382200

39

20348.203855336900

0.171782286883

37526.432543591400

36531.415831917500

40

20482.864348214500

0.150624878506

35545.352198787400

34580.930588915300

41

20488.765176917900

0.131366272807

33625.392457601600

32693.004813927300

42

20375.969116023400

0.113934288681

31769.397984114500

30870.203263861700

43

20155.124803274900

0.098245309992

29979.655802511500

29114.538716257400

44

19837.251425764500

0.084206555089

28257.906934664100

27427.486730006300

45

19433.533168591100

0.071718310588

26605.364227357400

25810.006259845500

46

18955.127764879100

0.060676079296

25022.735694518300

24262.565411487900

47

18412.992715443800

0.050972599092

23510.252624625100

22785.171561890400

48

17817.731910349000

0.042499697435

22067.701653843300

21377.405032399900

49

17179.464524154800

0.035149954572

20694.459981371100

20038.455490812100

50

16507.717210577500

0.028818156934

19389.532904015600

18767.160270414400

51

15811.339825110100

0.023402530452

18151.592870315500

17562.043827637700

52

15098.444184614000

0.018805751134

16979.019298027200

16421.357612071200

53

14376.364752906400

0.014935737065

15869.938459396100

15343.119690217800

54

13651.639635522500

0.011706231774

14822.262812901500

14325.153543749600

55

12930.009882453200

0.009037193620

13833.729244465200

13365.125550654600

56

12216.434835214000

0.006855009366

12901.935771811700

12460.580749913600

57

11515.121108602900

0.005092552507

12024.376359264000

11608.976583855000

58

10829.562757481700

0.003689108260

11198.473583477900

10807.714403949500

59

10162.590230693600

0.002590187498

10421.608980493000

10054.168612764700

60

9516.425841105990

0.001747251473

9691.150988404960

9345.713394664660

61

8892.743664671200

0.001117368110

9004.480475650450

8679.747058445850

62

8292.732003956980

0.000662819064

8359.013910400600

8053.714074693860

63

7717.156794907570

0.000350674853

7752.224280169770

7465.124937566750

64

7166.424582956140

0.000152353280

7181.659910971780

6911.574013559450

65

6640.643930896120

0.000043174299

6644.961360805330

6390.755557203870

66

6139.684332954040

0.000001922387

6139.876571614700

5900.478074345070

67

5664.274455875150

0.000000000000

5664.274455875150

5438.677196337180

68

5216.157067389680

0.000000000000

5216.157067389680

5003.427192121430

69

4793.670459729050

0.000000000000

4793.670459729050

4592.951188831610

70

4395.114269365740

0.000000000000

4395.114269365740

4205.630095053620

71

4018.949974054140

0.000000000000

4018.949974054140

3840.010124851320

72

3663.807671750400

0.000000000000

3663.807671750400

3494.808707459600

73

3328.491104611250

0.000000000000

3328.491104611250

3168.918441738340

74

3011.980522341890

0.000000000000

3011.980522341890

2861.408623813800

75

2713.432848941730

0.000000000000

2713.432848941730

2571.523752587070

76

2432.178500685180

0.000000000000

2432.178500685180

2298.678317361130

77

2167.714119867010

0.000000000000

2167.714119867010

2042.447116130520

78

1919.690462218170

0.000000000000

1919.690462218170

1802.550367850080

79

1687.894733586160

0.000000000000

1687.894733586160

1578.832995713020

80

1472.226842483650

0.000000000000

1472.226842483650

1371.237698850850

81

1272.669345516910

0.000000000000

1272.669345516910

1179.771818607930

82

1089.251329298170

0.000000000000

1089.251329298170

1004.468550946980

83

922.007094507183

0.000000000000

922.007094507183

845.343744829332

84

770.931257919772

0.000000000000

770.931257919772

702.350312854100

85

635.932704095892

0.000000000000

635.932704095892

575.333082759937

86

516.790597980398

0.000000000000

516.790597980398

463.987615559623

87

413.116273736551

0.000000000000

413.116273736551

367.826956159841

88

324.325080743701

0.000000000000

324.325080743701

286.160302444110

89

249.622034667881

0.000000000000

249.622034667881

218.087038143596

90

188.004271574095

0.000000000000

188.004271574095

162.508397634113

91

138.281806013939

0.000000000000

138.281806013939

118.157251081607

92

99.116049913469

0.000000000000

99.116049913469

83.644292565773

93

69.073210161771

0.000000000000

69.073210161771

57.516604928473

94

46.687438729531

0.000000000000

46.687438729531

38.322593975469

95

30.526924411285

0.000000000000

30.526924411285

24.676084366670

96

19.255421744700

0.000000000000

19.255421744700

15.312305272479

97

11.682279666395

0.000000000000

11.682279666395

9.129700358650

98

6.795855105220

0.000000000000

6.795855105220

5.213807582741

99

3.777949731857

0.000000000000

3.777949731857

2.842405863603

100

2.000000000000

0.000000000000

2.000000000000

1.000000000000

101

0.000000000000

0.000000000000

0.000000000000