Extended-range forecast method and system based on CFSv2-WRF model

By combining the CFSV2 and WRF models, the problems that existing technology cannot meet the needs of the extension period can be solved, and a more accurate and reliable climatic trend and atmospheric circulation forecast have been realized.

CN118821495BActive Publication Date: 2025-01-21SHANDONG PROVINCIAL CLIMATE CENT
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Patent Information

Application Number
CN202411296238.3
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2024-09-18
Publication Date
2025-01-21
Estimated Expiration
2044-09-18

AI Technical Summary

Technical Problem

The existing numerical model set forecast cannot meet the needs of extended forecast services, especially when considering the initial value and boundary value issues.

Method used

Adopt an extension forecasting method based on the CFSV2-WRF model, provides initial and boundary conditions by combining the CFSV2 mode data with the WRF mode, and scoring through the power reduction scale and land surface process scheme to obtain multiple forecast results and choose the best choice plan.

Benefits of technology

Improve the accuracy, simulation ability, stability and reliability of the extension forecast, and provide more powerful support for meteorological forecasting and decision -making.

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Abstract

The present invention relates to the field of meteorological forecasting technology, and in particular to an extended-range forecasting method and system based on a CFSv2-WRF model, the method comprising: S1, providing an initial field for a WRF model based on CFSv2 model data, and providing boundary conditions for the WRF model in combination with ground data and high-altitude data in the CFSv2 model data; S2, selecting a physical process scheme, and performing dynamic downscaling based on the WRF model; S3, modifying the land process scheme in the physical process scheme, and repeating S2 to obtain multiple forecast results; S4, scoring the forecast effect of each land process scheme based on the forecast results and actual information, and selecting the one with the highest score as the best land process scheme. By combining CFSv2 model data with the WRF model, the accuracy, simulation capability, stability and reliability of the forecast can be improved, providing more powerful support for meteorological forecasting and decision-making.
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Description

Technical Field

[0001] The present invention relates to the technical field of meteorological forecasting, and in particular to an extended-range forecasting method and system based on a CFSv2-WRF model. Background Art

[0002] Extended-range forecast refers to the weather forecast for the next 10 to 30 days or even longer. Its time span is between the medium-term forecast (generally 3 to 10 days) and the seasonal climate forecast (more than 1 month). The characteristic of the extended-range forecast is that it does not focus on specific weather conditions (such as specific sunshine or rain, temperature, etc.), but predicts the climate trend of the weather and the possible development of atmospheric circulation.

[0003] The significance of the extended-range forecast is that it can provide early warnings for agriculture, water resources management, energy scheduling and other fields, helping decision makers prepare in advance for future climate anomalies or extreme weather phenomena. The extended-range forecast is a crucial part of building a refined and seamless forecasting system, and plays an important role in major meteorological services for disaster prevention and mitigation.

[0004] Extended-range forecasts must consider both initial value problems and boundary value problems, which makes forecasts on this time scale very difficult. The existing numerical model ensemble forecasts cannot meet the needs of extended-range forecast services. Summary of the invention

[0005] In order to solve the problem that the existing numerical model ensemble forecast cannot meet the needs of extended-range forecast business, the present invention provides an extended-range forecast method and system based on the CFSv2-WRF model.

[0006] In a first aspect, the present invention provides an extended-range forecast method based on the CFSv2-WRF model, which adopts the following technical solution: an extended-range forecast method based on the CFSv2-WRF model, comprising the following steps:

[0007] S1, based on the CFSv2 model data, provides the initial field for the WRF model, and combines the ground data and upper air data in the CFSv2 model data to provide boundary conditions for the WRF model;

[0008] S2, select the physical process scheme and perform dynamic downscaling based on the WRF model;

[0009] S3, modifying the land surface process scheme in the physical process scheme, and repeating S2 to obtain multiple forecast results;

[0010] S4, based on the forecast results and actual information, the forecast effect of each physical process scheme is scored, and the one with the highest score is selected as the best land surface process scheme.

[0011] Optionally, the WRF mode settings include:

[0012] The WRF model uses the Lambert projection with a horizontal resolution of 30 km, 80 grid points in both longitude and latitude, and 38 layers in the vertical direction.

[0013] Optionally, providing the initial field and boundary conditions in step S1 specifically includes:

[0014] The CFSv2 model is used to generate 6-hour forecast results. Each forecast generates 16 samples based on different initial conditions, and the initial field of the WRF model is generated based on all samples.

[0015] The boundary conditions of the WRF model at the initial moment are determined by combining the ground data observed by the ground station and the upper air data observed by the upper air station. After a preset interval, the boundary conditions of the WRF model are updated with new ground data and upper air data.

[0016] Optionally, the physical process schemes selected specifically include: the microphysical process scheme adopts the WSM3 simple ice scheme, the longwave radiation scheme adopts the rrtm scheme, the shortwave radiation scheme adopts the Dudhia scheme, the near-surface layer scheme adopts the Monin-Obukhov scheme, the land surface process scheme adopts the Noah or CLM or RUC land surface process scheme, the boundary layer scheme adopts the YSU scheme, and the cumulus convection parameterization scheme adopts the shallow convection Kain-Fritsch scheme.

[0017] Optionally, step S4 specifically includes configuring different weights based on the success probability PS score, the spatial correlation coefficient ACC score and the mean square error RMSE score to comprehensively score the forecast effect of each land surface process scheme, which is calculated as: comprehensive score = PS score*0.5+ACC score*0.3+RMSE score*0.2.

[0018] Optionally, the success probability PS score is calculated as:

[0019]

[0020] Where j represents different land surface process scenarios, represents the number of times precipitation is predicted and actually occurs in the jth land process scenario; represents the number of times precipitation is predicted in the jth land surface process scenario but there is no precipitation in reality; It represents the number of times no precipitation is predicted in the jth land surface process scenario but there is precipitation in reality.

[0021] Optionally, the spatial correlation coefficient ACC score is calculated as:

[0022]

[0023] Where j represents different land surface process scenarios, represents the spatial average of the temporal anomalies of all grid points in the observation area in the jth land surface process scenario, represents the spatial average of the temporal anomalies of all grid points in the prediction area in the jth land surface process scenario, represents the observed value at the i-th time point in the j-th land surface process scenario, represents the predicted value at the i-th time point in the j-th land surface process scenario, and M represents the total number of spatial grid points.

[0024] Optionally, the mean square error RMSE score is calculated as:

[0025]

[0026] Where j represents different land surface process scenarios, represents the observed value at the i-th time point in the j-th land surface process scenario, represents the predicted value at the i-th time point in the j-th land surface process scenario, and M represents the total number of spatial grid points.

[0027] In the second aspect, an extended-range forecast system based on the CFSv2-WRF model includes:

[0028] Data acquisition module, which acquires data based on CFSv2 model data, ground data and high-altitude data in CFSv2 model data;

[0029] The dynamic downscaling module provides the initial field for the WRF model based on the CFSv2 model data, and combines the ground data and high-altitude data in the CFSv2 model data to provide boundary conditions for the WRF model; selects the physical process scheme and performs dynamic downscaling based on the WRF model;

[0030] The land surface process scheme scoring module modifies the land surface process scheme in the physical process scheme and returns the modified land surface process scheme to the dynamic downscaling module to obtain multiple forecast results; the forecast effect of each land surface process scheme is scored based on the forecast results and actual information, and the one with the highest score is selected as the best land surface process scheme.

[0031] Optionally, the WRF model uses the Lambert projection with a horizontal resolution of 30 km, 80 grid points in both longitude and latitude, and 38 levels in the vertical direction.

[0032] In summary, the present invention has the following beneficial technical effects:

[0033] As a climate prediction system, CFSv2 can provide large-scale climate background information and have a good grasp of long-term weather trends. It can provide macro-climate trends for extended-term forecasts and help determine the approximate scope and development trend of possible weather systems; land data can accurately grasp the conditions of the land surface and improve the ability to predict weather changes in local areas; high-altitude data is critical for predicting the movement and evolution of high-altitude weather systems, and these high-altitude systems often have a significant impact on ground weather. By combining CFSv2 model data with the WRF model, the accuracy, simulation ability, stability and reliability of the forecast can be improved, providing stronger support for meteorological forecasting and decision-making. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 It is a flow chart of an extended-range forecast method based on the CFSv2-WRF model according to an embodiment of the present invention.

[0035] Figure 2 It is a structural schematic diagram of an extended-range forecast system based on the CFSv2-WRF model according to an embodiment of the present invention. DETAILED DESCRIPTION

[0036] The following is combined with Figure 1 -Attached Figure 2 The present invention is described in further detail.

[0037] Example 1

[0038] Reference Figure 1 , an extended-range forecast method based on the CFSv2-WRF model of this embodiment comprises the following steps:

[0039] S1, based on the CFSv2 model data, provides the initial field for the WRF model, and combines the ground data and upper air data in the CFSv2 model data to provide boundary conditions for the WRF model;

[0040] CFSv2 (Climate Forecast System version 2) is an important climate prediction model. CFSv2 is able to simulate and predict climate on a global scale. It covers multiple climate system components such as the atmosphere, ocean, land and sea ice, providing a powerful tool for studying global climate change. The model can make climate predictions at different time scales, from short-term seasonal predictions to long-term climate trend predictions. This makes it widely used in meteorological forecasting, agricultural planning, water resources management and other fields. CFSv2 contains detailed descriptions of physical processes such as atmospheric circulation, ocean circulation, cloud physics, radiation transfer, etc. Accurate simulation of these physical processes is crucial to improving the accuracy of climate prediction.

[0041] The CFSv2-WRF model is a modeling system that combines the National Centers for Environmental Prediction (NCEP) Climate Forecast System version 2 (CFSv2) and the Mesoscale Weather Model (WRF).

[0042] The WRF model uses the Lambert projection with a horizontal resolution of 30 km, 80 grid points in both longitude and latitude, and 38 layers in the vertical direction.

[0043] The construction of the initial field includes: using the CFSv2 model 6-hour forecast products with 16 samples at the end of each decade in the summer of 1982-2023 as the initial field, which means that during this long period of time, researchers or forecasters choose to use the CFSv2 model to generate 6-hour forecast results at the end of each decade in the summer of each year (such as June 10, June 20, etc.). Each forecast will generate 16 samples based on different initial conditions to more comprehensively evaluate possible changes in future climate. These samples are the model data generated by CFSv2.

[0044] Preprocess the ground data and high-altitude data in the CFSv2 model data, including data cleaning, interpolation and standardization. Ensure that the format and unit of the data are consistent, and remove outliers and erroneous data. According to the determined weight distribution principle, weighted fusion is performed on the ground data and high-altitude data. For each boundary condition parameter, different weights can be assigned to fuse the ground data and high-altitude data to determine the boundary conditions at the initial moment, and after a preset interval, the boundary conditions are updated using new ground data and high-altitude data. In this embodiment, the preset interval is set to 12 hours, and the new ground data and high-altitude data are also weighted fused. The updated boundary condition data is re-entered into the WRF model to replace the old boundary condition data.

[0045] Surface data (Surface and Radiative Fluxes, horizontal resolution is T126), the surface and radiation flux information in the surface data can reflect the energy exchange process between the earth's surface and the atmosphere. After the surface absorbs solar radiation, part of the energy is transferred to the atmosphere in the form of sensible heat and latent heat, affecting the temperature and humidity distribution of the atmosphere. Surface data with a horizontal resolution of T126 has a higher spatial resolution and can provide more detailed surface feature information. It can help the WRF model better simulate terrain effects and provide the WRF model with more realistic near-surface energy exchange conditions, thereby improving the simulation accuracy of near-surface meteorological conditions.

[0046] High-altitude data (3D Pressure Level, horizontal resolution of 0.5°×0.5°) The three-dimensional pressure level information in the high-altitude data can reflect the structure and changes of the atmosphere in the vertical direction. Meteorological elements such as air pressure, temperature, wind direction and wind speed at different altitudes are crucial to understanding the movement of the atmosphere and the development and evolution of weather systems. High-altitude data with a horizontal resolution of 0.5°×0.5° are well applicable in regional and global meteorological studies. Although its resolution is relatively low compared to ground data, it can provide sufficient information in large-scale weather system analysis and climate simulation. It can provide key atmospheric vertical structure information for the WRF model, enabling the WRF model to more accurately simulate the dynamic process of the weather system.

[0047] S2, select the physical process scheme and perform dynamic downscaling based on the WRF model;

[0048] The selected physical process schemes include: the WSM3 type simple ice scheme is used for the microphysical process scheme, the rrtm scheme is used for the longwave radiation scheme, the Dudhia scheme is used for the shortwave radiation scheme, the Monin-Obukhov scheme is used for the near-surface layer scheme, the Noah or CLM or RUC land surface process scheme is used for the land surface process scheme, the YSU scheme is used for the boundary layer scheme, and the shallow convection Kain-Fritsch scheme is used for the cumulus convection parameterization scheme;

[0049] S3, modifying the land surface process scheme in the physical process scheme, and repeating S2 to obtain multiple forecast results;

[0050] Modifying the physical process scheme specifically includes: modifying the land surface process scheme Noah or CLM or RUC in the physical process scheme;

[0051] Noah land surface process scheme: It simulates soil temperature and humidity more accurately, and can better reflect the water and heat exchange process between the land surface and the atmosphere. Taking into account the role of vegetation, it can better simulate the land-atmosphere interaction in vegetation-covered areas. The computational efficiency is relatively high, and it runs faster in practical applications. It is widely used in various weather and climate studies, and can provide relatively reliable results for general meteorological simulations, short-term weather forecasts, and mesoscale meteorological studies. For example, in daily meteorological forecasting operations, the Noah scheme can provide forecasters with information on the impact of land surface conditions on the atmosphere, helping to improve the accuracy of weather forecasts; when studying the climate characteristics and climate change in different regions, the Noah scheme is often used to simulate the role of land surface processes.

[0052] CLM Land Surface Process Scheme (Community Land Model): It has a relatively complete description of physical processes, including biogeophysical processes, hydrological processes, biogeochemical processes and dynamic vegetation processes. It can simulate in detail the physical processes related to vegetation cover, the physical processes related to soil water and heat conduction, and hydrological cycle variables such as surface runoff, base flow, vegetation canopy evaporation, vegetation transpiration, and soil evaporation. It has strong simulation capabilities for complex terrain and surface cover types such as urban underlying surfaces, and can better describe the changes in characteristics and non-uniformity within the city. For example, for research on urban heat island effects and urban climate, the CLM scheme can provide more detailed simulation results. With continuous development and improvement, its simulation accuracy and functions are constantly improving. The latest version has improvements in major dynamic processes such as soil and vegetation hydrological processes, snow accumulation and snowmelt dynamic processes, carbon and nitrogen cycle and coupling simulation, and vegetation simulation. It is often used in climate simulation, global change research, and regional climate research with high requirements for land surface processes. For example, when studying the impact of global climate change on different ecosystems, the CLM scheme can more comprehensively consider various factors in land surface processes; when analyzing urban climate characteristics and the impact of urban planning on climate, the use of the CLM scheme can more accurately simulate the complex interactions between the urban underlying surface and the atmosphere.

[0053] RUC Land Surface Process Scheme (Rapid Update Cycle): It can quickly update the land surface state, adjust the land surface parameters in a timely manner, and better adapt to rapidly changing weather conditions. It has certain advantages in data assimilation and can effectively combine observational data to improve the simulation of land surface states. For example, in areas with many ground observation stations, the RUC scheme can make better use of these observational data to improve the accuracy of the simulation. It is often used in real-time weather forecasts and short-term forecast systems, and can provide more accurate land surface information for meteorological changes in a short period of time. For example, in some business scenarios that require rapid updates to meteorological information, such as impending severe convective weather warnings, short-term precipitation and temperature change forecasts, the RUC scheme can take advantage of its rapid updates and data assimilation to provide more accurate land surface initial fields and boundary conditions for forecasts.

[0054] S4, based on the forecast results and actual information, the forecast effect of each physical process scheme is scored, and the one with the highest score is selected as the best land surface process scheme.

[0055] Based on the success probability PS score, spatial correlation coefficient ACC score and mean square error RMSE score, different weights are configured to give a comprehensive score to the forecast effect of each land surface process scheme, which is calculated as: comprehensive score = PS score*0.5+ACC score*0.3+RMSE score*0.2.

[0056] The success probability PS score is calculated as:

[0057]

[0058] Where j represents different land surface process scenarios, represents the number of times precipitation is predicted and actually occurs in the jth land process scenario; represents the number of times precipitation is predicted in the jth land surface process scenario but there is no precipitation in reality; It represents the number of times no precipitation is predicted in the jth land surface process scenario but there is precipitation in reality.

[0059] The spatial correlation coefficient ACC score is calculated as:

[0060]

[0061] Where j represents different land surface process scenarios, represents the spatial average of the temporal anomalies of all grid points in the observation area in the jth land surface process scenario, represents the spatial average of the temporal anomalies of all grid points in the prediction area in the jth land surface process scenario, represents the observed value at the i-th time point in the j-th land surface process scenario, represents the predicted value at the i-th time point in the j-th land surface process scenario, and M represents the total number of spatial grid points.

[0062] The mean square error RMSE score is calculated as:

[0063]

[0064] Where j represents different land surface process scenarios, represents the observed value at the i-th time point in the j-th land surface process scenario, represents the predicted value at the i-th time point in the j-th land surface process scenario, and M represents the total number of spatial grid points.

[0065] In other embodiments, the hit rate, false alarm rate, time correlation coefficient (TCC), etc. may be added for scoring, and it is necessary to ensure that the sum of all assigned weights is 1.

[0066] In summary, the dynamic downscaling experiment was carried out using the high-resolution regional climate model WRF with different parameterization schemes and different time data of the global climate model as the initial field. Through numerical experiments and diagnostic analysis methods, the predictability of the extended period extreme high temperature in Shandong summer was evaluated, the optimal land surface process scheme suitable for the local area was selected, and the extended period dynamic downscaling prediction method suitable for Shandong was established. The 30km extended period extreme high temperature grid and dynamic downscaling ensemble forecast in Shandong was achieved, which provided a reference for the construction of a seamless forecasting system, further improved the meteorological disaster prevention and mitigation capabilities, and provided services for agricultural and economic and social development.

[0067] Example 2

[0068] Reference Figure 2 The difference between this embodiment and embodiment 1 is that this embodiment provides an extended-range forecast system based on the CFSv2-WRF model, including:

[0069] Data acquisition module, which acquires data based on CFSv2 model data, ground data and high-altitude data in CFSv2 model data;

[0070] The dynamic downscaling module provides the initial field for the WRF model based on the CFSv2 model data, and combines the ground data and high-altitude data in the CFSv2 model data to provide boundary conditions for the WRF model; selects the physical process scheme and performs dynamic downscaling based on the WRF model;

[0071] The land surface process scheme scoring module modifies the land surface process scheme in the physical process scheme and returns the modified land surface process scheme to the dynamic downscaling module to obtain multiple forecast results; the forecast effect of each land surface process scheme is scored based on the forecast results and actual information, and the one with the highest score is selected as the best land surface process scheme.

[0072] The WRF model uses the Lambert projection with a horizontal resolution of 30 km, 80 grid points in both longitude and latitude, and 38 layers in the vertical direction.

[0073] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the method disclosed in the embodiment, since it corresponds to the system disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0074] Professionals may further appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of the two. In order to clearly illustrate the interchangeability of hardware and software, the composition and steps of each example have been generally described in the above description according to function. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professionals and technicians may use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of the present invention.

[0075] The above disclosure is only a preferred embodiment of the present invention, but the present invention is not limited thereto. Any non-creative changes that can be thought of by a person skilled in the art, as well as several improvements and modifications made without departing from the principle of the present invention, should fall within the protection scope of the present invention.

Claims

1. An extended-range forecast method based on the CFSv2-WRF model, characterized in that: The following steps are involved: S1, based on the CFSv2 model data, provides the initial field for the WRF model, and combines the ground data and upper air data in the CFSv2 model data to provide boundary conditions for the WRF model; Providing the initial field and boundary conditions in step S1 specifically includes: The CFSv2 model is used to generate 6-hour forecast results. Each forecast generates 16 samples based on different initial conditions, and the initial field of the WRF model is generated based on all samples. Combine the ground data and upper air data in the CFSv2 model data to determine the boundary conditions of the WRF model at the initial time, and update the WRF model boundary conditions with new ground data and upper air data after a preset interval; S2, select the physical process scheme and perform dynamic downscaling based on the WRF model; The selected physical process schemes include: the WSM3 type simple ice scheme is used for the microphysical process scheme, the rrtm scheme is used for the longwave radiation scheme, the Dudhia scheme is used for the shortwave radiation scheme, the Monin-Obukhov scheme is used for the near-surface layer scheme, the Noah or CLM or RUC land surface process scheme is used for the land surface process scheme, the YSU scheme is used for the boundary layer scheme, and the shallow convection Kain-Fritsch scheme is used for the cumulus convection parameterization scheme; S3, modifying the land surface process scheme in the physical process scheme, and repeating S2 to obtain multiple forecast results; Modifying the physical process scheme specifically includes: modifying the land surface process scheme in the physical process scheme; S4, based on the forecast results and actual information, the forecast effect of each physical process scheme is scored, and the one with the highest score is selected as the best land surface process scheme.

2. The extended-range forecast method based on the CFSv2-WRF model according to claim 1, characterized in that: The WRF mode settings include: The WRF model uses the Lambert projection with a horizontal resolution of 30 km, 80 grid points in both longitude and latitude, and 38 layers in the vertical direction.

3. The extended-range forecast method based on the CFSv2-WRF model according to claim 2, characterized in that: Step S4 specifically includes configuring different weights based on the success probability PS score, spatial correlation coefficient ACC score and mean square error RMSE score to comprehensively score the forecast effect of each land surface process scheme, which is calculated as: comprehensive score = PS score * 0.5 + ACC score * 0.3 + RMSE score * 0.

2.

4. The extended-range forecast method based on the CFSv2-WRF model according to claim 3, characterized in that: The success probability PS score is calculated as: in, j Represents different land surface process scenarios, Indicates j The number of times precipitation was predicted and actually occurred in each land process scenario; Indicates j The number of times precipitation was predicted in each land surface process scenario but no precipitation actually occurred; Indicates j The number of times no precipitation is forecast in a land surface process scenario but precipitation actually occurs.

5. The extended-range forecast method based on the CFSv2-WRF model according to claim 3, characterized in that: The spatial correlation coefficient ACC score is calculated as: Where j represents different land surface process scenarios, represents the spatial average of the temporal anomalies of all grid points in the observation area in the jth land surface process scenario, represents the spatial average of the temporal anomalies of all grid points in the prediction area in the jth land surface process scenario, represents the observed value at the i-th time point in the j-th land surface process scenario, represents the predicted value at the i-th time point in the j-th land surface process scenario, and M represents the total number of spatial grid points.

6. The extended-range forecast method based on the CFSv2-WRF model according to claim 3, characterized in that: The mean square error RMSE score is calculated as: Where j represents different land surface process scenarios, represents the observed value at the i-th time point in the j-th land surface process scenario, represents the predicted value at the i-th time point in the j-th land surface process scenario, and M represents the total number of spatial grid points.

7. An extended-range forecast system based on the CFSv2-WRF model, characterized in that: When the system is executed, the method according to any one of claims 1 to 6 is implemented, and the system includes: Data acquisition module, which acquires data based on CFSv2 model data, ground data and high-altitude data in CFSv2 model data; The dynamic downscaling module provides the initial field for the WRF model based on the CFSv2 model data, and combines the ground data and high-altitude data in the CFSv2 model data to provide boundary conditions for the WRF model; selects the physical process scheme and performs dynamic downscaling based on the WRF model; The land surface process scheme scoring module modifies the land surface process scheme in the physical process scheme and returns the modified land surface process scheme to the dynamic downscaling module to obtain multiple forecast results; the forecast effect of each land surface process scheme is scored based on the forecast results and actual information, and the one with the highest score is selected as the best land surface process scheme.

8. The extended-range forecast system based on the CFSv2-WRF model according to claim 7, characterized in that: The WRF model uses the Lambert projection with a horizontal resolution of 30 km, 80 grid points in both longitude and latitude, and 38 layers in the vertical direction.

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