Terrain gravity wave parameterization method considering mountain range sharpness change

Abstract

The invention discloses a terrain gravity wave parameterization method considering mountain range sharpness change. The terrain gravity wave parameterization method comprises the following steps: calculating a high-resolution sub-grid terrain truth value in each grid of a numerical mode; calculating a sub-grid terrain error for terrain heights on # imgabs0 # sub-grid points represented based on an elliptical mountain function; calculating the ellipse range sharpness in each pattern grid by minimizing the secondary grid topographic error, and traversing all grids to obtain global distribution of the range sharpness; after the mountain range sharpness in each grid is obtained, the drag coefficient of each pattern grid is obtained through calculation; and calculating terrain gravity wave surface stress and vertical distribution of gravity wave stress. According to the method, the regional sensing algorithm of the sub-grid mountain sharpness is developed in the terrain gravity wave parameterization, the terrain gravity wave parameterization scheme is improved, the mountain sharpness factor changing along with the region is incorporated, and the requirement of high-precision numerical forecasting of the complex terrain region is met.

Description

Technical Field

[0001] The present invention belongs to the field of meteorological technology, and particularly relates to a terrain gravity wave parameterization method considering the change of mountain sharpness. Background Art

[0002] The terrain affects the atmospheric circulation through various complex processes and on various spatial and temporal scales. For example, the gravity waves excited by the terrain can significantly affect the tropospheric circulation and the atmospheric state of the stratosphere. However, the atmospheric state of the stratosphere is very important for medium-range weather forecasting, seasonal prediction, and climate prediction. Under the current limited computing power conditions, numerical weather prediction models generally can only resolve the terrain above the horizontal scale of 3 to 8 times the grid spacing, and cannot well represent the influence of small-scale terrain on the atmosphere. Small-scale terrain effects include terrain gravity wave drag, airflow blockage drag, and turbulent terrain drag. The latter two processes mainly occur in the lower troposphere, and the terrain gravity wave drag process can not only decelerate the tropospheric wind field, but also propagate to the stratosphere and significantly affect the stratospheric circulation. In current numerical weather prediction models, parameterization schemes are usually used to describe the terrain gravity wave drag process, and it has been proven to be a key factor for numerical models to improve prediction accuracy.

[0003] The terrain gravity wave parameterization scheme is based on the assumption of sub-grid elliptical mountains and linear gravity wave theory. Due to the lack of constraints on the terrain parameterization process, there are a large number of assumptions, empirical approximations, and settings of uncertain parameters in the parameterization scheme. Currently, when integrating the elliptical mountains, the mountain sharpness is regarded as a constant, which means that the mountain sharpness in all grid boxes is the same. The consistent mountain sharpness makes it lose the "regional perception" ability, and causes the terrain gravity wave drag coefficient to become a constant. For example, in the study of Van Niekerk et al. (2018), it is shown that the terrain gravity wave drag coefficient in the parameterization scheme of the UK Met Office MetUM model is 0.5, while the terrain gravity wave drag coefficient in the parameterization scheme of the European Centre for Medium-Range Weather Forecasts IFS model is 0.6. The uncertainty of the terrain gravity wave drag coefficient and the mountain sharpness parameter that loses the "regional perception" ability bring errors to the parameterization scheme and numerical models.

[0004] In the traditional terrain gravity wave parameterization scheme (Lott and Miller, 1997), the terrain gravity wave surface stress is obtained by integrating the mountain function in the following formula (1); where is the near-surface mean density, is the near-surface mean wind speed, is the near-surface mean buoyancy frequency, is the elliptical mountain function The Fourier expression form, where represents the sub-grid mountain height, and are the semi-minor axis and semi-major axis of the elliptical mountain range respectively, is the sharpness of the elliptical mountain range. After integrating the mountain function, the expression of the surface stress of the orographic gravity wave is obtained: (2); is the effective mountain height obtained by subtracting the airflow blocking height from the sub-grid mountain height, and are the anisotropic functions of the elliptical mountain range, and represent the components parallel and perpendicular to the wind direction respectively, is the angle between the mountain range azimuth and the wind direction, is the drag coefficient, which is the only function of the sharpness of the elliptical mountain range and is as follows: (3); where is the gamma function. Since in the traditional orographic gravity wave parameterization scheme, the sharpness of the elliptical mountain range is set as a constant, the drag coefficient also becomes a constant, that is, it has the same drag coefficient under different terrain conditions and loses the ability to sense the surrounding terrain conditions, which will obviously introduce errors.

[0005] In summary, in order to meet the needs of high-precision numerical forecasting in complex terrain areas, it is necessary to develop a regional sensing algorithm for the sharpness of sub-grid mountain ranges in orographic gravity wave parameterization. On this basis, improve the orographic gravity wave parameterization scheme and develop a new orographic gravity wave parameterization scheme to incorporate the factor of mountain range sharpness varying with the region. Summary of the Invention

[0006] Aiming at the problem that the mountain range sharpness parameter in the current orographic gravity wave parameterization scheme is usually taken as a constant, resulting in the loss of the regional sensing ability of the orographic gravity wave drag coefficient, this application combines high-resolution terrain elevation data and model terrain data, studies a high-precision calculation method for the sharpness of sub-grid mountain ranges, and proposes a new orographic gravity wave parameterization method considering the change of mountain range sharpness to meet the needs of high-precision numerical simulation and improve the simulation ability of the numerical model for the tropospheric and stratospheric circulations.

[0007] To achieve the above object, this application proposes an orographic gravity wave parameterization method considering the change of mountain range sharpness, including the following steps: Using the global 1km high-resolution terrain elevation data and the model grid terrain data, calculate the high-resolution sub-grid terrain true value in each grid of the numerical model; Within each grid, for the number of sub-grid points, calculate the sub-grid terrain error represented by the elliptical mountain function; After minimizing the sub-grid terrain error, calculate the sharpness of the elliptical mountain within each model grid , and traverse all grids to obtain the global distribution of mountain sharpness; According to the mountain sharpness within each model grid , calculate the gravity wave drag coefficient for each model grid , and the gravity wave drag coefficient varies with the model grid area; Calculate the vertical distribution of the topographic gravity wave surface stress and the gravity wave stress.

[0008] Preferably, using the global 1 km high-resolution terrain elevation data and the model grid terrain data, calculate the high-resolution sub-grid terrain truth value within each grid of the numerical model, and the mathematical representation is as follows: ; is the global 1 km high-resolution terrain elevation data, is the model grid terrain data, is the grid coordinate, and are located at the th sub-grid point index within the model grid box.

[0009] Preferably, within each grid, for the number of sub-grid points, calculate the sub-grid terrain error represented by the elliptical mountain function, and the mathematical representation is as follows: ; This is a non-linear optimization problem, represents the sub-grid mountain height, and are the semi-minor axis and semi-major axis of the elliptical mountain respectively, is the mountain sharpness, is the total number of sub-grid points within the model grid box, and are located at the th sub-grid point index within the model grid box.

[0010] Preferably, take the logarithm of the sub-grid terrain error formula of the elliptical mountain function to become: ; , , , After that, the non - linear optimization problem becomes a least - squares problem, obtaining: ; The azimuth angle of the elliptical mountain range, that is, the angle between the major axis and the meridional coordinate axis, is ; Therefore, when calculating the mountain sharpness, the rotation coordinate system keeps the mode coordinates consistent with the elliptical mountain function coordinates, that is , , is the angle between the mountain azimuth and the wind direction.

[0011] Preferably, the elliptical mountain sharpness within each mode grid is calculated by the following expression: ; is the number of sub - grid points, is the number of the grid point.

[0012] Preferably, the drag coefficient of each mode grid is calculated by the following formula : ; where is the gamma function.

[0013] Preferably, after obtaining the gravity wave drag coefficient within each mode grid box, substitute it into the following formula to obtain the surface stress of the topographic gravity wave: ; is the near - surface average density, is the near - surface average wind speed, is the near - surface average buoyancy frequency, is the effective mountain height obtained by subtracting the airflow blocking height from the sub - grid mountain height, and are the elliptical mountain anisotropy functions, and respectively represent the components parallel and perpendicular to the wind direction, is the angle between the mountain azimuth and the wind direction, is the drag coefficient.

[0014] Preferably, during the upward propagation of the topographic gravity wave stress, the following steps are taken: First, calculate the gravity wave amplitude layer by layer: ; represents the gravity wave amplitude on the th mode layer, Denote the gravitational wave stress on the th mode layer, , , are respectively the density, buoyancy frequency, and wind speed on the th mode layer; Calculate the local Richardson number: ; where is the mean Richardson number of the air flow, , where Fr represents the gravitational wave frequency, U is the mean wind speed near the ground, is the local gravitational wave amplitude, is the mean buoyancy frequency near the ground; Determine whether the gravitational wave breaks in this layer; compare the local Richardson number with the critical value. If it is greater than the critical value, the topographic gravitational wave stress in this layer continues to propagate upward; if it is less than the critical value, calculate the gravitational wave amplitude at which the gravitational wave breaks and the gravitational wave stress in this layer: ; where is the critical wave amplitude obtained when the local Richardson number is equal to the critical value; by gradually iterating and propagating upward, the vertical distribution of the gravitational wave stress is determined.

[0015] This application develops a regional perception algorithm for sub-grid mountain sharpness in topographic gravity wave parameterization, improves the topographic gravity wave parameterization scheme, incorporates the mountain sharpness factor that varies with the region, and develops a new topographic gravity wave parameterization scheme, meeting the requirements of high-precision numerical forecasting in complex terrain regions. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 The flow chart of the gravity wave parameterization method provided by the embodiment of this application; Figure 2 The probability density of the global distribution of the sub-grid topographic gravity wave drag coefficient; Figure 3 The global zonal wind distribution. Among them, 3(a) is ERA5, 3(b) is the control experiment, 3(c) is the control experiment minus ERA5, and 3(d) is the new experiment minus the control experiment. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0017] The present invention will be further described below with reference to the drawings, but the present invention is not limited in any way. Any transformation or substitution made based on the teachings of the present invention falls within the protection scope of the present invention.

[0018] As mentioned above, using the same drag coefficient for different terrain conditions loses the ability to perceive regional terrain information, which obviously introduces errors. Therefore, this application combines high-resolution terrain elevation data with model terrain data to study a high-precision calculation method for sub-grid mountain sharpness and proposes a new terrain gravity wave parameterization method that considers changes in mountain sharpness.

[0019] First, we need to use the global 1km high-resolution terrain elevation data and model grid terrain data , in each grid of the numerical model The high-resolution subgrid terrain truth is calculated internally as follows: (4); Then, in each grid, The calculation of the number of subgrid points is based on the subgrid terrain error represented by the elliptical mountain function: (5); This is a nonlinear optimization problem. However, taking the logarithm of the above equation, it becomes: ; set up , , , After that, except is an unknown quantity, and the others are known quantities, which turns it into a least squares problem. We can get: (6); The azimuth of the elliptical mountain range, that is, the angle between the main axis and the longitudinal coordinate axis is Therefore, when calculating the mountain sharpness, the coordinate system needs to be rotated to keep the pattern coordinates consistent with the elliptical mountain function coordinates, that is, , .

[0020] Finally, the calculation expression for the sharpness of the elliptical mountains in each pattern grid is obtained as follows: (7); is the number of subgrid points, is the grid point number.

[0021] By using this calculation formula to traverse all grids, we can get the global distribution of mountain sharpness. The sub-grid mountain sharpness is mainly distributed in some complex terrain areas, such as the Qinghai-Tibet Plateau, the Rocky Mountains, etc. Get the mountain sharpness in each grid Then, the drag coefficient of each mode grid can be obtained by formula (3): , thus making It is no longer a constant for different regions, but becomes a more accurate topographic gravity wave drag coefficient that varies with the model grid region.

[0022] The probability density distribution of the global distribution of the sub-grid topographic gravity wave drag coefficient is as Figure 2 shown. The sharpness of the sub-grid mountains is mainly distributed below 1, with a peak around 0.6.

[0023] After obtaining the gravity wave drag coefficient within each model grid box, substituting it into formula (2) gives the topographic gravity wave surface stress. Then, during the upward propagation of the topographic gravity wave stress, the following steps are taken: First, calculate the gravity wave amplitude layer by layer: (8); Then calculate the local Richardson number: (9); where is the mean Richardson number of the airflow, , where Fr represents the gravity wave frequency, U is the mean near-surface wind speed, is the mean near-surface buoyancy frequency, represents the local gravity wave amplitude. Then determine whether the gravity wave breaks in this layer. Compare the local Richardson number with the critical value. If it is greater than the critical value, the topographic gravity wave stress in this layer continues to propagate upward; if it is less than the critical value, calculate the gravity wave amplitude at which the gravity wave breaks and the gravity wave stress in this layer: (10); where is the critical wave amplitude obtained when the local Richardson number is equal to the critical value. Iteratively propagate upward in this way to determine the vertical distribution of the gravity wave stress.

[0024] The following takes the simulated global zonal wind from January 1 to 10, 2023 as an example, and further illustrates the present invention in combination with the accompanying drawings. As Figure 3 shown, the ERA5 data has a tropospheric jet and a stratospheric jet in the mid-latitude region of the Northern Hemisphere ( Figure 3 a). The control experiment successfully simulated the structural characteristics of the jet, but the wind speed intensity is greater than that of ERA5 ( Figure 3 b). It can also be seen from the differences between the control experiment and ERA5 that the control experiment using the original mountain sharpness and drag coefficient has a strong positive deviation for both the stratospheric jet and the tropospheric jet ( Figure 3 c). However, after considering the mountain sharpness that varies with the region and using the newly calculated drag coefficient, the new experiment alleviates the positive wind speed deviation in the troposphere and stratosphere of the control experiment ( Figure 3 d).

[0025] The beneficial effects of this application are as follows: In this application, a regional perception algorithm for developing sub-grid mountain sharpness is developed in terrain gravity wave parameterization, improving the terrain gravity wave parameterization scheme, incorporating the factor of mountain sharpness that varies with the region, and developing a new terrain gravity wave parameterization scheme, meeting the requirements of high-precision numerical forecasting in complex terrain regions.

[0026] As used herein, the term "preferred" is meant to be used as an example, illustration, or exemplification. Any aspect or design described herein as "preferred" need not be construed as more advantageous than other aspects or designs. Instead, the use of the term "preferred" is intended to present concepts in a specific manner. As used in this application, the term "or" is intended to mean an inclusive "or" rather than an exclusive "or". That is, unless otherwise specified or clear from the context, "X uses A or B" is meant to naturally include any one of the permutations. That is, if X uses A; X uses B; or X uses both A and B, then "X uses A or B" is satisfied in any of the foregoing examples.

[0027] Moreover, although the present disclosure has been shown and described with respect to one or more implementations, equivalent variations and modifications will occur to those skilled in the art based on a reading and understanding of this specification and the drawings. The present disclosure includes all such modifications and variations and is limited only by the scope of the appended claims. In particular, with respect to the various functions performed by the above-described components (e.g., elements, etc.), the terms used to describe such components are intended to correspond to any component that performs the specified function of the component (unless otherwise indicated), even if not structurally equivalent to the disclosed structure that performs the functions in the exemplary implementations of the present disclosure shown herein. Additionally, although a particular feature of the present disclosure has been disclosed with respect to only one of several implementations, such feature may be combined with one or other features of other implementations as may be desired and advantageous for a given or particular application. Also, insofar as the terms "comprises," "has," "contains," or variations thereof are used in the detailed description or claims, such terms are intended to include in a manner similar to the term "includes."

[0028] Each functional unit in the embodiments of the present invention may be integrated into one processing module, or each unit may exist physically alone, or multiple or more than multiple units may be integrated into one module. The above-mentioned integrated module may be implemented in the form of hardware or in the form of a software functional module. When the above-mentioned integrated module is implemented in the form of a software functional module and sold or used as an independent product, it may also be stored in a computer-readable storage medium. The above-mentioned storage medium may be a read-only memory, a magnetic disk, or an optical disc, etc. The above-mentioned various devices or systems may execute the storage method in the corresponding method embodiments.

[0029] In summary, the above embodiments are one implementation manner of the present invention. However, the implementation manners of the present invention are not limited by the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications made under the premise of departing from the spirit and principle of the present invention shall be equivalent replacement manners and are all included in the protection scope of the present invention.

Claims

1. A terrain gravity wave parameterization method considering the change of mountain sharpness, characterized in that, Including the following steps: Using the global 1-km high-resolution terrain elevation data and the model grid terrain data, calculate the true value of the high-resolution sub-grid terrain within each grid of the numerical model; Within each grid, for the number of sub-grid points, the sub-grid terrain error represented by the elliptic mountain function is calculated; After minimizing the sub-grid topographic error, calculate the elliptical mountain sharpness within each model grid , and traverse all grids to obtain the global distribution of mountain sharpness; According to the sharpness of the mountains within each model grid the gravity wave drag coefficient of each model grid is calculated The gravity wave drag coefficient varies with the change of the model grid area; Calculate the vertical distribution of the topographic gravity wave surface stress and the gravity wave stress.

2. The terrain gravity wave parameterization method considering the change of mountain sharpness according to claim 1, characterized in that, The step of using the global 1-km high-resolution terrain elevation data and the model grid terrain data to calculate the true value of the high-resolution sub-grid terrain within each grid of the numerical model is mathematically expressed as follows: ； is the global 1-km high-resolution terrain elevation data, is the model grid terrain data, are the grid coordinates, and is located at the index of the sub-grid grid point within the model grid box.

3. The terrain gravity wave parameterization method considering the change of mountain sharpness according to claim 2, characterized in that, Within each grid, for the number of sub-grid points, the sub-grid terrain error represented by the elliptic mountain function is calculated, and the mathematical representation is as follows: ； The above equation is a non-linear optimization problem. represents the sub-grid mountain height, and are the semi-minor axis and semi-major axis of the elliptical mountain respectively, is the mountain sharpness, is the total number of sub-grid points within the model grid box, and is located at the th index of the sub-grid grid point within the model grid box.

4. The terrain gravity wave parameterization method considering the change of mountain sharpness according to claim 3, characterized in that Take the logarithm of the sub-grid terrain error formula of the elliptical mountain function to become: ； , , , After that, the non-linear optimization problem becomes a least squares problem, obtaining: ； The azimuth angle of the elliptical mountain range, that is, the angle between the major axis and the meridional coordinate axis, is ; Therefore, when calculating the sharpness of the mountain range, the rotation coordinate system keeps the mode coordinates consistent with the elliptical mountain range function coordinates, that is, the mode coordinates are , , is the angle between the mountain range azimuth angle and the wind direction.

5. The terrain gravity wave parameterization method considering the change of mountain sharpness according to claim 4, characterized in that, The sharpness of the elliptical mountains within each pattern grid The calculation expression is as follows: ； is the total number of pattern grids, is the number of the pattern grid.

6. The terrain gravity wave parameterization method considering the change of mountain sharpness according to claim 5, characterized in that The drag coefficient of each pattern grid is calculated by the following formula :[[]]END]] ； wherein is the gamma function 7. The terrain gravity wave parameterization method considering the change of mountain sharpness according to claim 6, characterized in that After obtaining the gravity wave drag coefficient within each model grid box, substitute it into the following formula to obtain the topographic gravity wave surface stress: ； Among them, is the near-surface average density, is the near-surface average wind speed, is the near-surface average buoyancy frequency, is the effective mountain height obtained by subtracting the airflow blocking height from the sub-grid mountain height, and are the anisotropic functions of the elliptical mountain range, and represent the components parallel and perpendicular to the wind direction respectively, is the angle between the mountain range azimuth and the wind direction, is the drag coefficient.

8. The terrain gravity wave parameterization method considering the change of mountain sharpness according to claim 7, characterized in that, During the upward propagation of the topographic gravity wave stress, perform the following steps: First, calculate the gravity wave amplitude layer by layer ； Denote the amplitude of gravity wave on the th mode layer, denote the gravity wave stress on the , , are respectively the density, buoyancy frequency, and wind speed on the Calculate the local Richardson number: ； Among them is the average Richardson number of the air flow, , where Fr represents the gravity wave frequency, U is the average near-surface wind speed, is the local gravity wave amplitude, is the average near-surface buoyancy frequency; Determine whether the gravity wave breaks in this layer; compare the local Richardson number with the critical value. If it is greater than the critical value, the topographic gravity wave stress in this layer continues to propagate upward; if it is less than the critical value, calculate the gravity wave amplitude at which the gravity wave breaks and the gravity wave stress in this layer: ； wherein, is the critical wave amplitude obtained when the local Richardson number is equal to the critical value; the vertical distribution of the gravity wave stress is determined by gradually propagating upward iteratively.

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