1. Ensemble version | ||||||
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Ensemble identifier code | JMA CPS3 | JMA GEPS2203 | JMA GEPS2103 | JMA GEPS2003 | JMA GEPS1701 | GSM1403C |
Short Description | Coupled 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 operational | Operational | Operational | Operational | Operational | Operational | Operational |
Data time of first forecast run | 19/02/2023 | 15/03/2022 | 30/03/2021 | 24/03/2020 | 22/03/2017 | 05/03/2014 |
2. Configuration of the EPS | ||||||
Is the model coupled to an ocean model? | Yes, from day 0 | No | No | No | No | No |
If yes, please describe ocean model briefly including frequency of coupling and any ensemble perturbation applied | Ocean 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/A | N/A | N/A | N/A | N/A |
If no, please describe the sea surface temperature boundary conditions (climatology, reanalysis ...) | ||||||
Is the model coupled to a sea Ice model? | Yes | No | No | No | No | No |
If yes, please describe sea-ice model briefly including any ensemble perturbation applied | Interactive sea-ice model (MRI.COMv4.6). Initial perturbations of sea-ice from the 5-ensemble ocean. No stochastic perturbations. | N/A | N/A | N/A | N/A | N/A |
Is the model coupled to a wave model? | No | No | No | No | No | No |
If yes, please describe wave model briefly including any ensemble perturbation applied | N/A | N/A | N/A | N/A | N/A | N/A |
Ocean model | MRI.COM 0.25-degree resolution | N/A | N/A | N/A | N/A | N/A |
Horizontal resolution of the atmospheric model | TL319 (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 levels | 100 | 128 | 128 | 100 | 100 | 60 |
Top of model | 0.01 hPa | 0.01 hPa | 0.01 hPa | 0.01 hPa | 0.01 hPa | |
Type of model levels | hybrid (sigma-p) coordinate | hybrid (sigma-p) coordinate | hybrid (sigma-p) coordinate | hybrid (sigma-p) coordinate | hybrid (sigma-p) coordinate | sigma |
Forecast length | 34 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 Frequency | every day at 00Z | once 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? | Yes | Yes | Yes | Yes | Yes | Yes |
Number of perturbed ensemble members | 4 (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 step | 20 minutes | 10 minutes up to 18 days and 12 minutes after 18 days | 12 minutes up to 18 days and 20 minutes after 18 days | 12 minutes up to 18 days and 20 minutes after 18 days | 12 minutes up to 18 days and 20 minutes after 18 days | 20 minutes |
3. Initial conditions and perturbations | ||||||
Data assimilation method for control analysis | hybrid 4D Var-LETKF | hybrid 4D Var-LETKF | hybrid 4D Var-LETKF | hybrid 4D Var-LETKF | 4D Var | 4D Var |
Resolution of model used to generate Control Analysis | TL959L128 | TL959L128 | TL959L128 | TL959L100 | TL959L100 | TL959L100 |
Ensemble initial perturbation strategy | Bred vectors (Northern Hemisphere, Tropics and Southern Hemisphere) | LETKF + singular vectors (initial SV; Northern Hemisphere, Tropics and Southern Hemisphere) + Lagged Average Forecasting | LETKF + singular vectors (initial SV; Northern Hemisphere, Tropics and Southern Hemisphere) + Lagged Average Forecasting | LETKF + singular vectors (initial SV; Northern Hemisphere, Tropics and Southern Hemisphere) + Lagged Average Forecasting | LETKF + singular vectors (initial SV; Northern Hemisphere, Tropics and Southern Hemisphere) + Lagged Average Forecasting | Bred vectors (extratropics (NH) plus tropics) + Lagged Average Forecasting |
Horizontal and vertical resolution of perturbations | TL319L100 | TL319L128 (LETKF), TL63L40 (SV) | TL319L128 (LETKF), TL63L40 (SV) | TL319L100 (LETKF), TL63L40 (SV) | TL319L100 (LETKF), T63L40 (SV) | TL319L60 |
Perturbations in +/- pairs | Yes | Yes (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;
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;
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;
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;
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 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 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 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 forecast | Soil 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 methods | Stochastically perturbed physics tendencies (SPPT) scheme | Stochastically perturbed physics tendencies (SPPT) scheme | Stochastically perturbed physics tendencies (SPPT) scheme | Stochastically perturbed physics tendencies (SPPT) scheme | Stochastically perturbed physics tendencies (SPPT) scheme | Stochastic physics |
Do all ensemble members use exactly the same model version? | Same | Same | Same | Same | Same | Same |
Is model dynamics perturbed? | No | No | No | No | No | No |
Are the above model perturbations applied to the control forecast? | No | No | No | No | No | No |
5. Surface boundary perturbations | ||||||
Perturbations to sea surface temperature? | Yes | Yes | Yes | Yes | Yes | No |
Perturbation to soil moisture? | No | No | No | No | No | No |
Perturbation to surface stress or roughness? | No | No | No | No | No | No |
Any other surface perturbation? | No | No | No | No | No | No |
Are the above surface perturbations applied to the Control forecast? | No | No | No | No | No | No |
Additional comments | None | None | None | None | None | None |
6. Other details of the models | ||||||
Description of model grid | Linear grid | Quadratic grid | Linear grid | Linear grid | Linear grid | Linear grid |
List of model levels in appropriate coordinates | See appendix | See appendix | See appendix | See appendix | See appendix | http://jra.kishou.go.jp/JRA-55/document/JRA-55_handbook_TL319_v2_en.pdf |
What kind of large scale dynamics is used? | Spectral semi-lagrangian | Spectral semi-lagrangian | Spectral semi-lagrangian | Spectral semi-lagrangian | Spectral semi-lagrangian | Spectral 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? |
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| Outline of the operational numerical weather prediction at the Japan Meteorological Agency |
7. Re-forecast configuration | ||||||
Number of years covered | 30 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 advance | Fixed re-forecasts in advance | Fixed re-forecasts in advance | Fixed re-forecasts in advance | Fixed re-forecasts in advance | Fixed 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 members | 13 members | 13 members | 5 members | 5 members |
Initial conditions | JRA-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-3Q | JRA-55 (TL319L60) + land surface values estimated with the land-surface model in the Global EPS using atmospheric forcing from JRA-55 | JRA-55 (TL319L60) + land surface values estimated with the land-surface model in the Global EPS using atmospheric forcing from JRA-55 | JRA-55 (TL319L60) + land surface values estimated with the land-surface model in the Global EPS using atmospheric forcing from JRA-55 | JRA-55 (TL319L60) + JRA-55 land analysis (TL319) |
Is the model physics and resolution the same as for the real-time forecasts | Yes | Yes | Yes | Yes | Yes | Yes |
If not, what are the differences | N/A | N/A | N/A | N/A | N/A | N/A |
Is the ensemble generation the same as for real-time forecasts? | Yes | No | No | No | No | Yes, except for lagged average forecasting. |
If not, what are the differences | LETKF perturbations are not used and singular vectors (initial SV + evolved SV) are used | LETKF perturbations are not used and singular vectors (initial SV + evolved SV) are used | LETKF perturbations are not used and singular vectors (initial SV + evolved SV) are used | LETKF perturbations are not used and singular vectors (initial SV + evolved SV) are used | N/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:
| 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:
| 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:
| 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:
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;
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;
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:
| 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:
|
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 |