CN113011037B - Non-static terrain gravitational wave parameterization method - Google Patents

Abstract

The invention discloses a non-hydrostatic terrain gravity wave parameterization method, comprising the following steps: calculating the surface momentum flux of the static terrain gravity wave and the correction factor of the non-hydrostatic effect on the terrain gravity wave flux; calculating the non-hydrostatic terrain gravity wave surface momentum flux; starting from the first model layer located above the terrain height, the following steps are processed: calculating the amplitude of the terrain gravity wave; calculating the fluctuation Richardson number and the saturation amplitude and momentum flux of the terrain gravity wave; if the fluctuation Richardson If the number is greater than the critical value R _c , it will continue to propagate vertically until the top layer of the model. The method of the present invention processes the non-hydrostatic effects of terrain gravity waves, which can better characterize the transmission of subgrid terrain gravity fluctuations in high-resolution numerical models and their influence on atmospheric circulation, and improve the performance of models under complex terrain. simulation forecasting capabilities.

Description

Parameterization method of non-hydrostatic terrain gravity waves

technical field

The invention relates to a method for parameterizing terrain gravity waves in numerical models, in particular to a method for parameterizing non-static terrain gravity waves in high-resolution numerical models, and belongs to the field of atmospheric science research.

Background technique

Terrain gravity waves are an important sub-grid physical process in numerical models, and play an important role in accurate numerical weather prediction and climate prediction. The horizontal resolution of the traditional numerical model is relatively coarse, so the horizontal scale of the subgrid terrain is also large, and the excited gravity waves are fluctuations of static equilibrium (McFarlane 1987). In recent years, with the development of numerical models, the horizontal resolution of the models has also been continuously improved, and has reached the order of ten kilometers from hundreds of kilometers. For example, the IFS forecast system of ECMWF adopts a global resolution of 9km. In this case, the dynamic structural characteristics and momentum transfer of orographic gravity waves will be significantly affected by non-hydrostatic effects (Xue et al.2000), so they are non-hydrostatic orographic gravity waves.

For non-hydrostatic orographic gravity waves, it is usually impossible to obtain an analytical solution, so the momentum flux of non-hydrostatic orographic gravity waves cannot be obtained, which brings great challenges to parameterization. For this reason, Smith (1980) proposed to use the two-dimensional fast Fourier transform method to solve the gravitational wave, that is, numerical solution. Obviously, this numerical method cannot be used in the parameterization scheme of terrain gravity waves. Afterwards, Shutts (1998) et al. adopted the physical space ray tracing method (spatial-ray tracing) to approximate the solution of terrain gravity waves. However, this method can only obtain the far-field solution of gravitational waves, and there are caustic points directly above the terrain, and the wave-ray theory is no longer suitable. In order to overcome this problem, Broutman et al. (2002) developed a wave ray tracing method in spectral space, that is, Fourier-ray tracing technology, which effectively avoids the caustics above the terrain in physical space. However, this method still has caustics at the turning point of the buoyancy frequency. In recent years, Pulido and Rodas (2011) adopted a high-order wave ray approximation method (ie Gaussian beam approximation method) to approximate the terrain gravity wave. Compared with the traditional wave-ray method, this method considers the contribution of different wave-rays to the central wave-ray, so it can effectively avoid the caustics problem in the traditional ray tracing theory. Using this method, Xu et al. (2017) studied the influence of directional shear on the dynamic structure and momentum transmission of terrain gravity waves, and achieved good results. However, the Gaussian beam approximation needs to consider the contribution of different wave rays, and the calculation amount is very huge, which cannot be applied to the operational terrain gravity wave parameterization.

In summary, in order to meet the development needs of high-resolution numerical models, it is necessary to develop calculation methods for non-hydrostatic terrain gravity fluctuation fluxes. On this basis, the traditional static terrain gravity wave parameterization scheme is improved, and the non-static terrain gravity wave parameterization scheme is developed.

Contents of the invention

The technical problem to be solved by the present invention is to propose a new non-static terrain gravity wave parameterization scheme to meet the development needs of high-resolution numerical models, aiming at the fact that the existing topographic gravity wave parameterization scheme cannot characterize the non-hydrostatic effect. Improve the model's ability to simulate and predict complex terrain.

In order to solve the above-mentioned technical problems, the non-hydrostatic terrain gravity wave parameterization method proposed by the present invention includes the following steps:

Step 1: Calculate the surface momentum flux τ _s of the static terrain gravity wave.

Step 2: Calculate the correction term α of the non-hydrostatic effect on the terrain gravity fluctuation flux.

Step 3: Calculate the surface momentum flux τ ₀ =(1+α)τ _s of the non-hydrostatic terrain gravity wave.

Step 4: Starting from the first pattern layer above the terrain height of the secondary grid, proceed as follows,

Step 4.1: According to the model's horizontal wind field U _i , V _i , atmospheric density ρ _i and stratification N _i , calculate the orographic gravity wave amplitude H _i .

Step 4.2: Calculate the fluctuation Richardson number Ri according to the amplitude of the terrain gravity wave.

Step 4.3: Judgment of gravity wave breaking. If the fluctuating Richardson number Ri is less than the critical value Ri _c , the terrain gravity wave is saturated, and the saturation amplitude H _{i_sat} of the terrain gravity wave and the momentum flux τ _i of the terrain gravity wave in this model layer are calculated; if the fluctuating Richardson number Ri is greater than the critical value R _c , the topographic gravity wave does not reach saturation and continues to propagate vertically. The momentum flux of the topographic gravity wave in this mode layer is equal to that of the i-1th layer, that is, τ _i =τ _i-1 .

Step 4.4: Repeat steps 4.1 to 4.3 until the pattern top level is reached.

Among the above technical solutions,

where _ρ0 is the surface air density, _N0 is the surface atmospheric stratification, is the square of the sub-grid terrain height, γ=a/b is the anisotropy of the sub-grid terrain, a and b are the width of the sub-grid terrain in the east-west and north-south directions respectively, U ₀ and V ₀ are the east-west and north-south directions surface level wind, χ is the surface level wind direction, φ and /> for /> The direction and magnitude of , where k and l are the horizontal wavenumbers in the east-west and north-south directions.

Among the above technical solutions,

in is the horizontal Froude number.

Among the above technical solutions,

where /> are the vertical wavenumbers of gravity waves on the surface and the i-th layer of the model, respectively, and the subscript i represents the i-th layer of the model.

Among the above technical solutions,

in is the Richardson number of the average airflow, U _zi and V _zi are the vertical wind shear of the east-west wind and north-south wind in layer i of the model, respectively.

Among the above technical solutions,

Among the above technical solutions,

In the above technical solution, R _c =0.25.

The non-hydrostatic terrain gravity wave parameterization method of the present invention has the following advantages:

1. Be able to characterize the impact of non-hydrostatic effects on the flux of terrain gravity fluctuations.

Figure 1 shows the variation of the anisotropic gravitational fluctuation flux with the Fr number excited by the isotropic terrain. As the Fr number increases, the orographic gravity fluctuation flux decreases gradually. In addition, because the Fr number is related to the horizontal scale of the terrain, it can represent the change of the terrain gravity fluctuation flux caused by the change of the terrain scale, that is, scale adaptation.

2. It still has high accuracy for anisotropic terrain.

Figure 2 shows the ratio of the non-hydrostatic gravity fluctuation flux induced by anisotropic terrain to the isotropic terrain gravity fluctuation flux. As the Fr number increases, the influence of anisotropy on the topographic gravity fluctuation flux increases gradually, but the error does not exceed 5%. Therefore, for different anisotropic terrains, the flux of terrain gravity fluctuations is very similar to that of isotropic terrain gravity fluctuations.

Description of drawings

Fig. 1 Variation of non-hydrostatic gravity fluctuation flux with Fr number excited by isotropic terrain.

Fig. 2 The ratio of the non-hydrostatic gravity fluctuation flux induced by anisotropic terrain to the gravity fluctuation flux of isotropic terrain.

Figure 3 Distribution map of global terrain (a) and subgrid terrain (b).

Figure 4. The topographic gravity wave amplitude in the western Qinghai-Tibet Plateau. The dashed line is the static parameterization scheme, the dotted line is the non-hydrostatic parameterization scheme, and the solid line is the vertical distribution of saturation amplitude.

Detailed ways

Taking the topographic gravity wave in the western region of the Qinghai-Tibet Plateau in December 2013 as an example, the non-static topographic gravity wave parameterization scheme proposed by the present invention is specifically described.

The first step is the preprocessing of terrain and ambient atmosphere. According to the 2.5° reanalysis data provided by the European Center for Mesoscale Weather Forecasting, the global terrain and sub-grid terrain distribution including the Qinghai-Tibet Plateau can be obtained, as shown in Figure 3. At the same time, the vertical profile of wind speed and buoyancy frequency in the western plateau in December 2013 can also be obtained. This step is manually processed offline, and can be skipped directly in the mode system.

The second step is to calculate the surface momentum flux of the static terrain gravity wave. The maximum height of the terrain is 5864 meters, so the average wind speed, average buoyancy frequency and average density below this height are calculated as U ₀ =6.8ms ^-1 , V ₀ =2.1ms ^-1 , N ₀ =0.0085s ^-1 , ρ ₀ =1.12 kg m ⁻³ . In addition, it can be seen from the sub-grid terrain data that the east-west and north-south widths of the sub-grid terrain are respectively a=20km and b=16km, so γ=1.25. According to the above data, the surface momentum flux of the static terrain gravity wave is finally calculated as τ _s =(0.000238,0.000817)N m ^-1 .

The third step is to calculate the non-hydrostatic terrain gravity fluctuation flux. First calculate the non-hydrostatic factor α. According to the data, the horizontal Froude number can be obtained as Fr=0.311, which can be substituted into the α expression to get α=-0.011. Therefore, the non-static terrain gravity fluctuation flux is τ ₀ =(1+α)τ _s =(0.000212,0.000727)N m ^-1 .

In the fourth step, since the terrain height is below the 6th layer (5915 m) of the model, the terrain gravity wave amplitude and saturation amplitude are calculated layer by layer starting from this layer. For the convenience of comparison, the gravity wave amplitude calculated according to the static terrain gravity wave parameterization scheme is given at the same time. As shown in Fig. 4, the amplitude of the non-static terrain gravity wave is always smaller than that of the static terrain gravity wave. The static orographic gravity wave is saturated in the altitude range of 22-28 km (the fluctuation amplitude is greater than the saturation amplitude), while the saturation range of the non-static orographic gravity wave is about 24-27 km. Therefore, under the action of non-hydrostatic effects, the fragmentation of terrain gravity waves will be suppressed, effectively solving the problem of excessive drag of stratospheric terrain gravity waves in the parameterization scheme of static terrain gravity waves.

Claims (5)

1. The non-static terrain gravitational wave parameterization method is characterized by comprising the following steps of:

step 1, calculating the earth surface momentum flux tau of the gravity wave of the static terrain _s ；

Wherein ρ is ₀ To the surface air density, N ₀ Is the junction of the earth surface and the atmosphere,gamma = a/b is the subgrid terrain anisotropy, a, b is the subgrid terrain width in east-west and north-south directions, respectively, U, as the square of the subgrid terrain height ₀ 、V ₀ Earth surface horizontal wind in east-west and north-south directions, χ is earth surface horizontal wind direction, phi and +.>Is->Where k and l are horizontal wavenumbers in the east-west and north-south directions;

step 2, calculating a correction term alpha of the non-static effect on the fluctuation quantity flux of the terrain gravity;

wherein the method comprises the steps ofIs the number of horizontal Froude;

step (a)3, calculating the earth surface momentum flux tau of the non-static terrain gravitational wave ₀ ＝(1+α)τ _s ；

Step 4, starting from a first mode layer positioned above the subgrid terrain height, performing the following steps;

step 4.1, horizontal wind field U according to the mode _i 、V _i Atmospheric density ρ _i And layer junction N _i Calculating the amplitude H of the gravitational wave of the terrain _i ；

Wherein->Vertical wave numbers of gravity waves on the earth surface and the mode ith layer respectively, wherein the subscript i represents the mode ith layer;

step 4.2, calculating a fluctuation Richardson number Ri according to the amplitude of the terrain gravity wave;

wherein the method comprises the steps ofRichardson number, U, of average gas flow _zi And V _zi Vertical wind cuts of east-west wind and north-south wind of the ith layer of modes respectively;

step 4.3 if the ripple Richardson number Ri is less than the threshold Ri _c Calculating saturation amplitude H of gravitational wave of terrain _{i_sat} Momentum flux tau of the terrain gravity wave at the mode layer _i The method comprises the steps of carrying out a first treatment on the surface of the If the fluctuation Richardson number Ri is greater than the critical value Ri _c Continuing to propagate vertically, the momentum flux of the gravitational wave in this mode layer is equal to that of layer i-1, i.e. τ _i ＝τ _i-1 ；

Step 4.4: steps 4.1 to 4.3 are repeated until the pattern top layer is reached.

2. A method of parameterizing gravitational waves of non-static terrain as claimed in claim 1, wherein:

3. a method of parameterizing gravitational waves of non-static terrain according to claim 1 or 2, characterized in that:

4. a method of parameterizing gravitational waves of non-static terrain according to claim 1 or 2, characterized in that: ri (Ri) _c ＝0.25。

5. A method of parameterizing gravitational waves of non-static terrain as claimed in claim 3, wherein: ri (Ri) _c ＝0.25。