Numerical mode vertical shear base flow terrain gravity wave parameterization evaluation method

Abstract

The invention relates to vertical shear base flow terrain gravity wave parameterization, in particular to a numerical mode vertical shear base flow terrain gravity wave parameterization evaluation method. According to the numerical mode vertical shear base flow terrain gravity wave parameterization evaluation method, a new terrain gravity wave parameterization scheme considering the vertical shear effect in the numerical mode is researched and developed through a vertical shear base flow terrain gravity wave analytic solution, and the vertical shear effect can be represented; therefore, the distribution of the terrain gravity fluctuation quantity flux in the numerical mode can be better described; by considering the vertical shear effect, the basic features of the large-scale circulation field can be better described, and the simulation effect of the numerical mode is further improved.

Description

Technical Field

[0001] The invention relates to vertical shear base flow terrain gravity wave parameterization, and in particular to a numerical model vertical shear base flow terrain gravity wave parameterization evaluation method. Background Art

[0002] my country has a vast territory, with intricate land and sea borders. The complex and ever-changing terrain has an important impact on the weather and climate of my country and even the East Asian continent. Since small and medium-scale topographic gravity waves cannot be fully resolved by numerical weather prediction (NWP) and general circulation models (GCMs), their impact on atmospheric circulation can only be described by topographic gravity wave parameterization.

[0003] However, due to the lack of observations and inaccurate theoretical assumptions, the existing orographic gravity wave drag parameterization schemes in numerical models do not fully characterize the wave volume transmission. Their inaccurate representation is also an important source of systematic deviations in atmospheric circulation simulations. For example, the orographic gravity wave drag parameterization schemes in current numerical models are all based on the assumption of a steady base flow (the background wind field does not change with height, i.e. like Figure 2 ), ignoring the actual atmospheric vertical wind shear (including wind direction and wind speed shear, such as Figure 3 Therefore, it is necessary to establish a new parameterization scheme for terrain gravity wave drag that takes into account the vertical shear effect in numerical models, so as to improve the simulation ability and prediction level of numerical models under complex terrain. Summary of the invention

[0004] The purpose of the present invention is to provide a method for evaluating the parameterization of terrain gravity waves in the vertical shear base flow of a numerical model, so as to solve the technical problem that the existing terrain gravity wave parameterization schemes in numerical models are all based on the assumption of a steady base flow, ignoring the actual atmospheric environmental vertical wind shear, resulting in systematic deviations in the atmospheric circulation simulation.

[0005] In order to solve the above technical problems, the present invention provides a method for parameterizing and evaluating vertical shear base flow terrain gravity waves in a numerical model, comprising the following steps:

[0006] Step S1, calculating the terrain gravity wave momentum flux D0 on the reference layer under the steady base flow;

[0007] Step S2, calculating the correction term of the vertical shear effect on the reference layer terrain gravity wave momentum flux;

[0008] Step S3, above the reference layer, the wave momentum flux propagates vertically upward layer by layer, and the following steps are performed:

[0009] Step S3.1: If the terrain gravity wave does not meet the wave saturation, the wave flux remains unchanged and continues to be uploaded vertically, that is, the wave flux of the upper layer is equal to the wave flux of the lower layer D i+1 =D i , and the amplitude of the upper wave of the model is calculated (h d ) i , using (h d ) i Obtain the modified Richardson number Ri m ;

[0010] Step S3.2, according to the wave saturation hypothesis theory, when Ri m When the wave saturation condition is not met, the terrain gravity wave will not break in this layer, and the D of this layer remains unchanged; when the Ri m When Ri is less than 0.25, the topographic gravity wave reaches saturation and breaks in this layer, D decreases, and some energy is lost until it returns to the critical saturation point. m = 0.25 Calculate the critical amplitude h d , using this critical amplitude, further calculate the residual wave momentum flux D of this layer;

[0011] Step S3.3, repeat steps S3.1 to S3.2 to calculate the wave flux of each layer of the model until D i =0 or top of mode layer;

[0012] Step S3.4 calculates the changing trend of the wind field due to wave drag by performing gradient calculation on the total wave momentum flux of each layer;

[0013] Step S4, performing online testing and model result evaluation and verification in the numerical mode.

[0014] The beneficial effects of the present invention are:

[0015] The numerical model vertical shear base flow terrain gravity wave parameterization evaluation method of the present invention develops a new terrain gravity wave parameterization scheme considering the vertical shear effect in the numerical model through the analytical solution of the vertical shear base flow terrain gravity wave. It can characterize the vertical shear effect, so as to better describe the distribution of terrain gravity wave momentum flux in the numerical model; by considering the vertical shear effect, it can better describe the basic characteristics of the large-scale circulation field, and further improve the simulation effect of the numerical model. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] In order to more clearly illustrate the specific implementation methods of the present invention or the technical solutions in the prior art, the drawings required for use in the specific implementation methods or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some implementation methods of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0017] Figure 1 It is a schematic flow chart of the parameterized evaluation method of the vertical shear base flow terrain gravity wave of the numerical model of the present invention;

[0018] Figure 2 is a schematic diagram of steady base flow;

[0019] Figure 3 The left picture in the middle is a schematic diagram of vertical shear of wind speed, and the right picture is a schematic diagram of vertical shear of wind direction;

[0020] Figure 4 Schematic diagram of the spatial distribution of surface wave momentum flux in the austral winter from 1995 to 2014; (a) is the steady base flow scheme, and (b) is the vertical shear scheme minus the steady base flow scheme;

[0021] Figure 5 Schematic diagram of the vertical distribution of the zonal average zonal wind in the austral hemisphere winter from 1995 to 2014; among them, (a) is the actual observation, (b) is the steady base flow scheme, (c) is the steady base flow scheme minus the actual observation, and (d) is the vertical shear scheme minus the steady base flow scheme. DETAILED DESCRIPTION

[0022] The parameterization schemes of terrain gravity wave drag in current numerical models are all based on the assumption of a steady base flow, such as Figure 2 As shown in Figure 2, the background wind field does not change with height, that is, The actual atmospheric vertical wind shear, including wind direction and wind speed shear, is ignored. Figure 3 As shown, the impact on the wave source and momentum transfer.

[0023] Based on this, see Figure 1 This embodiment provides a method for parameterizing and evaluating vertical shear base flow terrain gravity waves in a numerical model, which includes the following steps:

[0024] Step S1, calculating the terrain gravity wave momentum flux D0 on the reference layer under the steady base flow;

[0025] Step S2, calculating the correction term of the vertical shear effect on the reference layer terrain gravity wave momentum flux;

[0026] Step S3, above the reference layer, the wave momentum flux propagates vertically upward layer by layer, and the following steps are performed:

[0027] Step S3.1: If the terrain gravity wave does not meet the wave saturation, the wave flux remains unchanged and continues to be uploaded vertically, that is, the wave flux of the upper layer is equal to the wave flux of the lower layer D i+1 =D i , and the amplitude of the upper wave of the model is calculated (h d ) i , using (h d ) i Obtain the modified Richardson number Ri m ;

[0028] Step S3.2, according to the wave saturation hypothesis theory, when Ri m When ≥0.25 does not meet the wave saturation condition, the terrain gravity wave will not break in this layer, and the D of this layer remains unchanged; when Ri m When Ri is less than 0.25, the topographic gravity wave reaches saturation and breaks in this layer, D decreases, and some energy is lost until it returns to the critical saturation point. m = 0.25 Calculate the critical amplitude h d , using this critical amplitude, further calculate the residual wave momentum flux D of this layer;

[0029] Step S3.3, repeat steps S3.1 to S3.2 to calculate the wave flux of each layer of the model until D i =0 or top of mode layer;

[0030] Step S3.4 calculates the changing trend of the wind field due to wave drag by performing gradient calculation on the total wave momentum flux of each layer;

[0031] Step S4, performing online testing and model result evaluation and verification in the numerical mode.

[0032] Specifically, in step 1, the method for calculating the terrain gravity wave momentum flux D0 on the reference layer under the steady base flow includes:

[0033] For a steady, adiabatic, inviscid atmosphere, the Boussinesq approximation is used, and the atmospheric motion equations are as follows:

[0034]

[0035] Using two-dimensional Fourier transform, we can get the vertical velocity in spectral space The wave equation is as follows:

[0036]

[0037]

[0038] in represents the vertical wind shear term, K is the horizontal wave number, and the steady base flow assumption is adopted. The polar coordinate system (ρ, θ) is further introduced. The expression of the momentum flux of topographic gravity waves on the reference layer under the steady base flow is:

[0039]

[0040] The coefficients are:

[0041]

[0042] in is the dimensionless Fourier transform of the terrain height, and γ = a / b is the ratio of the horizontal major and minor axes of an elliptical mountain. It is worth noting that for axisymmetric mountains, B = C = π / 4; for two-dimensional ridges, B = 1 and C = 0 (if the ridge axis is along the y direction).

[0043] Furthermore, the method of calculating the correction term of the vertical shear effect on the reference layer terrain gravity wave momentum flux in step S2 includes:

[0044] Based on the wave analytical solution of vertical shear terrain gravity wave, considering the vertical shear (wind direction and wind speed) effect, the terrain gravity wave momentum flux on the reference layer under the vertical shear base flow is calculated. Assuming that the background flow is horizontally uniform and isolated mountains are considered, the terrain height and all fluid disturbances can be expressed as Fourier integrals along the x and y directions; when the equation of motion is expressed in Fourier space, the following can be obtained: The single equation for is as follows:

[0045]

[0046] where the derivative represents the differential with respect to z, (U,V) is the horizontal wind vector, (k1,k2) is the horizontal wave number vector, and

[0047] The second-order WKB approximation is used to simultaneously consider the correction of the first-order vertical shear and the second-order vertical shear on the surface wave momentum flux of topographic gravity waves, thereby deriving the expression for the correction of the surface wave momentum flux due to the first-order vertical shear and the second-order vertical shear (D x ,D y )as follows:

[0048]

[0049] Among them (D 0x ,D 0y ) is the surface wave momentum flux calculated under steady base flow, (U0,V0) is the surface horizontal wind, (U'0,V'0) and (U'0',V'0') ​​are the first and second order vertical shears of wind speed, respectively, and the coefficients α and β depend on the anisotropy of the mountain range.

[0050] Furthermore, in step S3, based on the theoretical solution of the momentum flux of the vertical shear base flow terrain gravity wave, a new parameterization scheme of terrain gravity waves considering the vertical shear effect in the numerical model is developed.

[0051] Specifically, above the reference layer, the wave momentum flux propagates vertically upward layer by layer, and the following steps are performed:

[0052] Step S3.1, according to the wave theory, if the terrain gravity wave does not meet the wave saturation, the wave flux remains unchanged and continues to be uploaded vertically, that is, the wave flux of the upper layer is equal to the wave flux of the lower layer D i+1 =D i , and the amplitude of the upper wave of the model is calculated (h d ) i , using (h d ) i Obtain the modified Richardson number Ri m ; The calculation formula is as follows:

[0053]

[0054] Step S3.2, according to the wave saturation hypothesis theory, when Ri m When ≥0.25 does not meet the wave saturation condition, the topographic gravity wave will not break in this layer, and the D of this layer remains unchanged;

[0055] When Ri is satisfied m When Ri is less than 0.25, the topographic gravity wave reaches saturation and breaks in this layer, D decreases, and some energy is lost until it returns to the critical saturation point. m = 0.25 Calculate the critical amplitude h d , using the critical amplitude, further calculate the residual wave momentum flux D of this layer; the calculation formula is:

[0056]

[0057] Step S3.3, repeat steps S3.1 to S3.2 to calculate the wave flux of each layer of the model until D i =0 or top of mode layer;

[0058] Step S3.4 calculates the change trend of the wind field due to wave drag by performing gradient calculation on the total wave momentum flux of each layer:

[0059]

[0060] In an application scenario, in step S4, specifically, numerical simulation can be carried out using my country's BCC-AGCM3-MR (middle-atmosphere version of Beijing Climate Center Atmospheric General Circulation Model version 3) numerical model, and a new vertical shear terrain gravity wave parameterization scheme can be used in the physical parameterization module to study the influence of the vertical shear effect on the terrain gravity wave momentum flux.

[0061] Specifically, the two groups of simulation experiments are the old experiment using the steady base flow orographic gravity wave parameterization scheme and the new experiment using the vertical shear base flow orographic gravity wave parameterization scheme. Each group of experiments has 20 simulations for three months, that is, from June to August every year from 1995 to 2014 (austral winter), and each group of experiments is started 10 days in advance as the start time. The horizontal resolution of the model is set to 1°×1°, there are 80 layers in the vertical direction, the simulation top is set to 1hPa (about 50km), and the top 5km of the model is used as a sponge layer. The initial field of the model uses a 1°×1° GFS analysis field. Through the numerical prediction results, the impact of the vertical shear effect on the momentum flux of the orographic gravity wave and the atmospheric circulation is evaluated, so as to improve the simulation ability and prediction level of the numerical model under complex terrain.

[0062] Figure 4 The spatial distribution of the average surface wave flux in the southern hemisphere winter from 1995 to 2014 is given. The results show that the new vertical shear scheme generally presents a negative correction to the surface wave flux in the northern hemisphere compared with the old steady base flow scheme, and the new scheme also has a significant negative correction to the surface wave flux in the Antarctic region.

[0063] Figure 5 The vertical distribution of the mean zonal wind in the southern hemisphere winter from 1995 to 2014 is given. There are still significant differences between the old steady base flow scheme and observations, such as weak westerly winds in the mid-latitude stratosphere and strong westerly winds in the high-latitude stratosphere, which generally shows the characteristics of the polar night jet shifting to high latitudes. The new vertical shear scheme can significantly reduce this strong deviation of the polar night jet in the southern hemisphere winter, making the simulated circulation field closer to observations.

Claims

1. A method for parameterizing the vertical shear base flow terrain gravity wave in a numerical model, characterized in that: The following steps are involved: Step S1, calculating the terrain gravity wave momentum flux D0 on the reference layer under the steady base flow; Step S2, calculating the correction term of the vertical shear effect on the reference layer terrain gravity wave momentum flux; Step S3, above the reference layer, the wave momentum flux propagates vertically upward layer by layer, and the following steps are performed: Step S3.1: If the terrain gravity wave does not meet the wave saturation, the wave flux remains unchanged and continues to be uploaded vertically, that is, the wave flux of the upper layer is equal to the wave flux of the lower layer D i+1 =D i , and the amplitude of the upper wave of the model is calculated (h d ) i , using (h d ) i Obtain the modified Richardson number Ri m ; Step S3.2, according to the wave saturation hypothesis theory, when Ri m When ≥0.25 does not meet the wave saturation condition, the terrain gravity wave will not break in this layer, and the D of this layer remains unchanged; when Ri m When Ri is less than 0.25, the topographic gravity wave reaches saturation and breaks in this layer, D decreases, and some energy is lost until it returns to the critical saturation point. m = 0.25 Calculate the critical amplitude h d , using this critical amplitude, further calculate the residual wave momentum flux D of this layer; Step S3.3, repeat steps S3.1 to S3.2 to calculate the wave flux of each layer of the model until D i =0 or top of mode layer; Step S3.4 calculates the changing trend of the wind field due to wave drag by performing gradient calculation on the total wave momentum flux of each layer; Step S4, performing online testing and model result evaluation and verification in the numerical mode.

2. The method for parameterizing the vertical shear base flow terrain gravity wave of a numerical model according to claim 1, characterized in that: In step S1, the method for calculating the terrain gravity wave momentum flux D0 on the reference layer under the steady base flow includes: For a steady, adiabatic, inviscid atmosphere, the Boussinesq approximation is used, and the atmospheric motion equations are as follows: Using two-dimensional Fourier transform, the wave equation for the vertical velocity w in the spectral space is obtained as follows: in represents the vertical wind shear term, K is the horizontal wave number, and the steady base flow assumption is adopted. The polar coordinate system (ρ, θ) is further introduced. The expression of the momentum flux of topographic gravity waves on the reference layer under the steady base flow is: The coefficients are: in is the dimensionless Fourier transform of terrain height, and γ = a / b is the ratio of the horizontal major and minor axes of an elliptical mountain range.

3. The method for parameterizing the vertical shear base flow terrain gravity wave of the numerical model according to claim 2, characterized in that: The method of calculating the correction term of the vertical shear effect on the momentum flux of the reference layer terrain gravity wave in step S2 includes: The second-order WKB approximation is used to simultaneously consider the correction of the first-order vertical shear and the second-order vertical shear on the surface wave momentum flux of topographic gravity waves, thereby deriving the expression for the correction of the surface wave momentum flux due to the first-order vertical shear and the second-order vertical shear (D x ,D y )as follows: Among them (D 0x ,D 0y ) is the surface wave momentum flux calculated under steady base flow, (U0,V0) is the surface horizontal wind, (U'0,V'0) and (U'0',V'0') ​​are the first and second order vertical shears of wind speed, respectively, and the coefficients α and β depend on the anisotropy of the mountain range.

4. The method for parameterizing the vertical shear base flow terrain gravity wave of the numerical model according to claim 3, characterized in that: In step S3.1, using (h d ) i Obtain the modified Richardson number Ri m The calculation formula is:

5. The method for parameterizing the vertical shear base flow terrain gravity wave of the numerical model according to claim 4, characterized in that: In step S3.2, the critical amplitude h d The calculation formula is:

6. The method for parameterizing the vertical shear base flow terrain gravity wave of a numerical model according to claim 5, characterized in that: In step S3.2, the critical amplitude is used to calculate the residual wave momentum flux D of the layer as follows:

7. The method for parameterizing the vertical shear base flow terrain gravity wave of a numerical model according to claim 6, characterized in that: In step S3.4, the formula for calculating the changing trend of wave drag on the wind field is:

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