Table of Contents |
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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. |
2. Configuration of the EPS
3. Initial conditions and perturbations
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
Soil thermal and hydraulic properties are calculated using soil texture from the HWSD (Harmonized World Soil Database).
4. Model uncertainties perturbations
5. Surface boundary perturbations
6. Other details of the models
7. Re-forecast configuration
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.
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.
- 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.
- 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.
- Japan Meteorological Agency, 2019: Outline of the operational numerical weather prediction at the Japan Meteorological Agency.
- 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.
- 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.
- 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.
- 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.
- 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 128 hybrid levels. Each hybrid level is defined with half-levels as the boundary;
where is the surface pressure. Coefficients A and B are given in Table A for k = 0, 1, 2, …, 128. The following equation by Simmons and Burridge (1981) gives full-level pressure;
where C=1 and k=1, 2, …, 127. The full-level pressure for the uppermost level (k=128) is given by
Table A gives half-level and full-level pressures with a surface pressure of 1000hPa.
Table A. Model level from 1 to 128.
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 |
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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 |
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? |
|
|
|
|
| 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
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- 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 |
k
A[Pa]
B
Ph [Pa]
Pf [Pa]
1
0.000000000000
1.000000000000
100000.000000000000
99906.149328801500
2
0.367279053361
0.998119607566
99812.328035645300
99707.078615143900
3
1.651295433209
0.996002149193
99601.866214743700
99480.841827595100
4
4.263935162251
0.993556025633
99359.866498482900
99219.297574726400
5
8.818642865415
0.990699763605
99078.795003366000
98915.476159705600
6
16.153564274720
0.987360935873
98752.247151551600
98563.497767488800
7
27.352655050102
0.983475161368
98374.868791829000
98158.495693304200
8
43.760653705889
0.978985208099
97942.281463645000
97696.543075913600
9
66.989186167242
0.973840213666
97451.010552792600
97174.582116438100
10
98.912437237234
0.967995031094
96898.415546672800
96590.355173546100
11
141.651809373079
0.961409701475
96282.621956901400
95942.337440485500
12
197.549799934382
0.954049049521
95602.454752054800
95229.671150837900
13
269.133969108446
0.945882393768
94857.373345948900
94452.101429317500
14
359.072347557138
0.936883359805
94047.408328036600
93609.914021442900
15
470.121954299976
0.927029782579
93173.100212176600
92703.875201491000
16
605.072274485724
0.916303682526
92235.440527052200
91735.174189560300
17
766.685600539283
0.904691299836
91235.815584124600
90705.368407497400
18
957.636088881686
0.892183171556
90175.953244477800
89616.331877189700
19
1180.449250079540
0.878774237209
89057.872970937400
88470.207023681400
20
1437.443395530380
0.864463960067
87883.839402250300
87269.360090425000
21
1730.674330567250
0.849256452964
86656.319626988400
86016.340312364600
22
2061.884332303790
0.833160599383
85377.944270597100
84713.842927258300
23
2432.456198180200
0.816190162450
84051.472443213600
83364.676041107800
24
2843.372912386710
0.798363876191
82679.760531518600
81971.731299931800
25
3295.183263110750
0.779705514941
81265.734757235400
80537.958263339100
26
3787.973561424270
0.760243938082
79812.367369670600
79066.342322563600
27
4321.345466897210
0.740013108242
78322.656291106200
77559.885961130400
28
4894.399817081290
0.719052081756
76799.607992665500
76021.593118835800
29
5505.726286743880
0.697404970581
75246.223344854400
74454.456390393700
30
6153.398665018050
0.675120874964
73665.486161433700
72861.446768227600
31
6834.975529818620
0.652253786076
72060.354137414400
71245.505624873700
32
7547.506113219540
0.628862457583
70433.751871486600
69609.538623254500
33
8287.541182649680
0.605010244769
68788.565659596100
67956.411242983100
34
9051.148804124690
0.580764909450
67127.639749119800
66288.945616008800
35
9833.934898763650
0.556198388528
65453.773751564300
64609.918376429900
36
10631.068546365100
0.531386523789
63769.720925242600
62922.059244645800
37
11437.312024228700
0.506408750331
62078.187057363800
61228.050086197400
38
12247.055590877300
0.481347741058
60381.829696701600
59530.524208817900
39
13054.357028916700
0.456289004840
58683.257512887600
57832.065687358200
40
13852.985946051900
0.431320436397
56985.029585744600
56135.208534621000
41
14636.472796443700
0.406531816609
55289.654457338000
54442.435566027300
42
15398.162525485300
0.382014262845
53599.588809964400
52756.176837013500
43
16131.272660216100
0.357859630043
51917.235664546200
51078.807563275800
44
16828.955566715800
0.334159864585
50244.942025257400
49412.645465099300
45
17484.364477778600
0.311006314494
48584.995927132800
47759.947507769900
46
18090.722762945100
0.288489001104
46939.622873350700
46122.906038724200
47
18641.395773489400
0.266695859038
45310.981677293800
44503.644350057200
48
19129.964452997900
0.245711952979
43701.159750914300
42904.211719761400
49
19550.299766124400
0.225618681387
42112.167904844900
41326.578007900800
50
19896.636870744900
0.206492978760
40545.934746732300
39772.627903007100
51
20163.980086975300
0.188403206951
39004.300782028000
38244.154930225900
52
20351.944344566100
0.171370679911
37489.012335655400
36742.855344864500
53
20463.342581962100
0.155383728414
36001.715423361600
35270.322043458200
54
20501.374046673500
0.140425756613
34543.949708016400
33828.038628992400
55
20469.538812267800
0.126476038663
33117.142678580100
32417.373767254300
56
20371.603412767300
0.113510007752
31722.604187988600
31039.575968092000
57
20211.564215127300
0.101499572658
30361.521480941200
29695.768918140300
58
19993.608937901800
0.090413458959
29034.954833767600
28386.947481304800
59
19722.076787294600
0.080217571292
27743.833916544400
27113.974469751500
60
19401.417732755300
0.070875372401
26488.954972838800
25877.578272274200
61
19036.151481018200
0.062348274144
25270.978895384400
24678.351408969000
62
18630.826728478400
0.054596035287
24090.430257184200
23516.750061661900
63
18189.981276200600
0.047577160614
22947.697337580200
22393.094609378300
64
17718.103579492800
0.041249295828
21843.033162334100
21307.571177633000
65
17219.596275363200
0.035569612810
20776.557556335600
20260.234190198700
66
16698.742187492900
0.030495180003
19748.260187780400
19251.009892823500
67
16159.673251338300
0.025983313127
18758.004564073600
18279.700800639100
68
15606.342733896800
0.021991901889
17805.532922819900
17345.991005115600
69
15042.501046123400
0.018479709003
16890.471946455900
16449.452262833600
70
14471.675363861100
0.015406638528
16012.339216706500
15589.550777349100
71
13897.153188406700
0.012733971269
15170.550315345700
14765.654577045400
72
13321.969893417000
0.010424565774
14364.426470857500
13977.041386529500
73
12748.900223548600
0.008443024230
13593.202646582800
13222.906886473900
74
12180.453634514400
0.006755823303
12856.035964764400
12502.373257022700
75
11618.873296265500
0.005331410662
12152.014362450400
11814.497902710800
76
11066.138522444300
0.004140268568
11480.165379269900
11158.282262021800
77
10523.970341313200
0.003154946421
10839.464983428800
10532.680612040700
78
9993.839886724720
0.002350064638
10228.846350531500
9936.608787727700
79
9476.979262550330
0.001702292571
9647.208519692700
9368.952745786510
80
8974.394520051310
0.001190303424
9093.424862452510
8828.576914590710
81
8486.880384221110
0.000794709276
8566.351311844540
8314.332283627920
82
8015.036371079950
0.000497979401
8064.834311166120
7825.064198118570
83
7559.283951848330
0.000284345023
7587.718454119770
7359.619836325270
84
7119.884440234330
0.000139693594
7133.853799600960
6916.855358210030
85
6696.957303929350
0.000051455511
6702.102855046850
6495.642724032220
86
6290.498628904240
0.000008486026
6291.347231482130
6094.876189775000
87
5900.493980737070
0.000000000000
5900.493980737070
5713.478492448980
88
5528.481630297230
0.000000000000
5528.481630297230
5350.406741907360
89
5174.285933388900
0.000000000000
5174.285933388900
5004.658036279840
90
4836.925350720490
0.000000000000
4836.925350720490
4675.274815057110
91
4515.466275302810
0.000000000000
4515.466275302810
4361.349956723390
92
4209.028002503950
0.000000000000
4209.028002503950
4062.031616233200
93
3916.787433562190
0.000000000000
3916.787433562190
3776.527781221010
94
3637.983481907540
0.000000000000
3637.983481907540
3504.110504425720
95
3371.921127743180
0.000000000000
3371.921127743180
3244.119743480640
96
3117.975037623500
0.000000000000
3117.975037623500
2995.966708364220
97
2875.592632860050
0.000000000000
2875.592632860050
2759.136582338770
98
2644.296454685800
0.000000000000
2644.296454685800
2533.190445678590
99
2423.685637127690
0.000000000000
2423.685637127690
2317.766195254820
100
2213.436263278170
0.000000000000
2213.436263278170
2112.578220408930
101
2013.300350929100
0.000000000000
2013.300350929100
1917.415570860470
102
1823.103194212330
0.000000000000
1823.103194212330
1732.138341042090
103
1642.738784867620
0.000000000000
1642.738784867620
1556.672003523160
104
1472.163056683520
0.000000000000
1472.163056683520
1390.999458895190
105
1311.384746465990
0.000000000000
1311.384746465990
1235.150637357940
106
1160.453751007800
0.000000000000
1160.453751007800
1089.189593919690
107
1019.446986748220
0.000000000000
1019.446986748220
953.199187899828
108
888.451928822532
0.000000000000
888.451928822532
827.263627663412
109
767.548215932542
0.000000000000
767.548215932542
711.449386955591
110
656.787947376753
0.000000000000
656.787947376753
605.785246379858
111
556.175551249932
0.000000000000
556.175551249932
510.242460795943
112
465.648342355864
0.000000000000
465.648342355864
424.716270813441
113
385.059081069088
0.000000000000
385.059081069088
349.010127626377
114
314.161951254557
0.000000000000
314.161951254557
282.824045691573
115
252.603356889854
0.000000000000
252.603356889854
225.748400577188
116
199.918760089339
0.000000000000
199.918760089339
177.264223682977
117
155.536429527503
0.000000000000
155.536429527503
136.750604725015
118
118.788443103480
0.000000000000
118.788443103480
103.499217296971
119
88.928627808076
0.000000000000
88.928627808076
76.735284754437
120
65.156391730376
0.000000000000
65.156391730376
55.643586362110
121
46.644705017873
0.000000000000
46.644705017873
39.397472794456
122
32.569931284291
0.000000000000
32.569931284291
27.188427315847
123
22.140906946455
0.000000000000
22.140906946455
18.253569151567
124
14.624692644256
0.000000000000
14.624692644256
11.898702444718
125
9.366805063801
0.000000000000
9.366805063801
7.515060935547
126
5.804438422468
0.000000000000
5.804438422468
4.588710053849
127
3.472094398676
0.000000000000
3.472094398676
2.702510420768
2.000000000000 | 0.000000000000 | 2.000000000000 | 1.000000000000 |
101 | 0.000000000000 | 0.000000000000 | 0.000000000000 |