CN105046077B - A kind of random physical perturbation motion method based on the conservation of energy - Google Patents

A kind of random physical perturbation motion method based on the conservation of energy Download PDF

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CN105046077B
CN105046077B CN201510420905.9A CN201510420905A CN105046077B CN 105046077 B CN105046077 B CN 105046077B CN 201510420905 A CN201510420905 A CN 201510420905A CN 105046077 B CN105046077 B CN 105046077B
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闵锦忠
王勇
王世璋
武天杰
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Nanjing Manxing Data Technology Co ltd
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Abstract

本发明涉及一种基于能量守恒的随机物理扰动方法,包括如下步骤:1)根据实际需要选定进行数值预报的模式,接着确定模式预报方程中各个参数的最终倾向项的位置;2)在确定了所述参数的位置后再根据扰动形式,通过积分确定所述倾向项的扰动方案,扰动形式的表达式为:,3)在水平方向上对ε(t)进行二维傅立叶分解,接着滤除高频噪声将其中1至4倍格距的波长的波的系数赋值为0,最后将调整后的系数通过逆傅立叶变换合成新的ε(t);4)重复步骤3)直至得到各个变量对应的扰动系数,并带入至所述扰动形式的表达式。有益效果为:对完全独立的物理过程进行倾向扰动,目的在于保证模式变量的倾向扰动在能量上的守恒性,使得该方法可改善边界层模式变量的集合离散度,这将显著改善风暴尺度集合预报的预报水平。The present invention relates to a random physical disturbance method based on energy conservation, which includes the following steps: 1) select the model for numerical prediction according to actual needs, and then determine the position of the final tendency item of each parameter in the model prediction equation; 2) after determining After the position of the parameter is determined, according to the disturbance form, the disturbance scheme of the tendency item is determined by integral, and the expression of the disturbance form is: , 3) Carry out two-dimensional Fourier decomposition of ε(t) in the horizontal direction, then filter out high-frequency noise and assign the coefficient of the wave with a wavelength of 1 to 4 times the grid distance to 0, and finally pass the adjusted coefficient through the inverse Fourier transform to synthesize new ε(t); 4) Repeat step 3) until the disturbance coefficient corresponding to each variable is obtained , and into the expression of the perturbed form. The beneficial effect is: the propensity perturbation is performed on completely independent physical processes, the purpose is to ensure the energy conservation of the propensity perturbation of the model variables, so that the method can improve the ensemble dispersion of the boundary layer model variables, which will significantly improve the storm-scale ensemble The forecast level of the forecast.

Description

一种基于能量守恒的随机物理扰动方法A Random Physical Perturbation Method Based on Energy Conservation

技术领域technical field

本发明涉及气象预报领域,尤其涉及一种基于能量守恒的随机物理扰动方法。The invention relates to the field of weather forecast, in particular to a random physical disturbance method based on energy conservation.

背景技术Background technique

过去的一系列研究表明,风暴尺度集合预报是可行和有效的,但是目前各风暴尺度集合预报系统的扰动方法还有待完善。如美国风暴分析和预报中心(CAPS)的风暴尺度集合预报系统,通过提高成员数和分辨率能够提高预报评分,但是其集合扰动方案是固定的,即各集合成员的初值扰动采用固定的扰动振幅,并且与特定的物理方案匹配;部分集合成员的侧边界条件由NAM模式短期预报提供,成员间相同的侧边界条件将在一定程度上限制离散度的发展;另一方面,该系统未考虑侧边界扰动与初值扰动间扰动尺度的不匹配问题。上述典型问题在各风暴尺度集合预报系统中均有所体现,初值扰动、物理(参数)扰动、侧边界扰动与初值扰动间的有机结合问题均对于风暴尺度集合预报的成功与否起到关键作用。A series of studies in the past have shown that storm-scale ensemble forecasting is feasible and effective, but the perturbation methods of various storm-scale ensemble forecasting systems still need to be perfected. For example, the storm-scale ensemble forecast system of the Center for Storm Analysis and Prediction (CAPS) in the United States can improve the forecast score by increasing the number of members and resolution, but its ensemble disturbance scheme is fixed, that is, the initial disturbance of each ensemble member adopts a fixed disturbance Amplitude, and matched with a specific physical scheme; the lateral boundary conditions of some ensemble members are provided by the short-term forecast of the NAM model, and the same lateral boundary conditions among members will limit the development of dispersion to a certain extent; on the other hand, the system does not consider Disturbance scale mismatch between side boundary disturbance and initial value disturbance. The typical problems mentioned above are reflected in all storm-scale ensemble forecast systems. The organic combination of initial value disturbance, physical (parameter) disturbance, side boundary disturbance and initial value disturbance all play an important role in the success of storm-scale ensemble forecast. play a key role in.

由于初始误差随时间的演变在斜压不稳定和对流不稳定中具有显著地差异,中期集合扰动方法构造的初始扰动无法在对流系统中快速的增长,也即初始扰动结构与风暴系统的发展不相适应,进而导致集合成员离散度低于合理的水平;另一方面,风暴尺度的初值扰动和侧边界扰动的尺度不相适应也将限制初始扰动和集合离散度的增长。多物理过程和多模式集合有助于改善离散度问题,但是模式的微物理方案中的降水预报变量和微物理过程的阈值条件判断是不同的,对降水强度和落区范围预报均有显著地影响,针对实时发生的不同类型风暴系统,采用固定不变的集合配置组合性地选取不同模式微物理方案是盲目的。Because the evolution of the initial error over time is significantly different in baroclinic instability and convective instability, the initial disturbance constructed by the medium-term ensemble disturbance method cannot grow rapidly in the convective system, that is, the initial disturbance structure is not consistent with the development of the storm system. On the other hand, the incompatibility between the initial disturbance of the storm scale and the scale of the side boundary disturbance will also limit the growth of the initial disturbance and the dispersion of the ensemble. Multi-physics processes and multi-model ensembles help to improve the dispersion problem, but the precipitation forecast variables in the micro-physics scheme of the model and the threshold condition judgment of the micro-physics process are different, and have a significant impact on the precipitation intensity and fall area forecast. For different types of storm systems that occur in real time, it is blind to use a fixed set configuration to select different modes of microphysics schemes in combination.

发明内容Contents of the invention

本发明目的在于克服以上现有技术之不足,提供一种基于能量守恒的随机物理扰动方法,具体由以下技术方案实现:The purpose of the present invention is to overcome the deficiencies of the above prior art, and provide a random physical disturbance method based on energy conservation, which is specifically realized by the following technical solutions:

所述基于能量守恒的随机物理扰动方法,包括如下步骤:The random physical disturbance method based on energy conservation comprises the steps of:

1)根据实际需要选定进行数值预报的ARPS模式,接着确定模式预报方程中各个参数化方案输出的最终倾向项的位置;1) Select the ARPS model for numerical prediction according to actual needs, and then determine the position of the final tendency item output by each parameterization scheme in the model prediction equation;

2)在确定了所述参数的位置后再根据扰动形式,通过积分确定所述倾向项的扰动方案,扰动形式的表达式为:XP=(1+rX)Xc2) After the position of the parameter is determined, according to the disturbance form, the disturbance scheme of the tendency item is determined by integral, the expression of the disturbance form is: X P =(1+r X )X c ,

其中Xc表示所有所述参数的时间倾向项,Xp表示扰动后的时间倾向项,rX表示增加的扰动,rX自回归函数的形式为其中α是去相关时间尺度,t表示当前模式时刻为t,ε(t)是满足uniform分布的随机数,每个时次使用不同的随机种子生成,uniform分布的最大值和最小值设定为0.5和-0.5,σ是扰动的方差函数,随高度变化,分布形态与上述时间倾向的形态相同;where X c represents the time propensity term for all said parameters, X p represents the time propensity term after perturbation, r X represents the added perturbation, r X autoregressive function of the form Where α is the decorrelation time scale, t indicates that the current mode time is t, ε(t) is a random number satisfying the uniform distribution, each time is generated using a different random seed, and the maximum and minimum values of the uniform distribution are set as 0.5 and -0.5, σ is the variance function of the disturbance, which changes with height, and the distribution shape is the same as the above-mentioned time tendency;

3)在水平方向上对ε(t)进行二维傅立叶分解,接着滤除高频噪声将其中1至4倍格距的波长的波的系数赋值为0,最后将调整后的系数通过逆傅立叶变换合成新的ε(t);3) Carry out two-dimensional Fourier decomposition of ε(t) in the horizontal direction, and then filter out high-frequency noise and assign the coefficient of the wave with a wavelength of 1 to 4 times the grid spacing to 0, and finally pass the adjusted coefficient through inverse Fourier Transform and synthesize new ε(t);

4)重复步骤3)直至得到各个变量对应的扰动系数rX,并带入至所述扰动形式的表达式,所述变量包括三个风场分量u,v,w,一个温度变量T以及一个水汽变量qv。4) Repeat step 3) until the disturbance coefficient r X corresponding to each variable is obtained, and brought into the expression of the disturbance form, the variables include three wind field components u, v, w, a temperature variable T and a Water vapor variable qv.

所述基于能量守恒的随机物理扰动方法的进一步设计在于,u的预报方程为:The further design of the random physical disturbance method based on energy conservation is that the prediction equation of u is:

其中可以被扰动的时间倾向项为表示次网格湍流参数化过程输出的u变量的时间倾向。其余各项不能被扰动,其中(ρ*u)t为u变量的完整时间倾向,为气压梯度力项,-ADV(u)为平流项,为地转偏向力项。Among them, the time propensity term that can be disturbed is Indicates the time tendency of the u-variables output by the subgrid turbulence parameterization process. The remaining items cannot be disturbed, where (ρ*u) t is the complete time tendency of the u variable, is the pressure gradient force term, -ADV(u) is the advection term, is the geostrophic deflection force term.

所述基于能量守恒的随机物理扰动方法的进一步设计在于,所述T的预报方程为:The further design of the random physical disturbance method based on energy conservation is that the prediction equation of the T is:

式中可以被扰动的包括次网格湍流参数化过程的倾向项和微物理方案和辐射方案的非绝热过程的倾向项其中包括积云参数化方案输出的温度倾向项和辐射方案输出的温度倾向项;其余项不能被扰动,其中(ρ*θ)t为位温的完整时间倾向项,为对流项,-ADV(θ')为位温的平流项。The propensity term that can be perturbed in the formula includes the subgrid turbulence parameterization process and propensity terms for diadiabatic processes for the microphysics and radiation schemes in Including the temperature tendency item output by the cumulus parameterization scheme and the temperature tendency item output by the radiation scheme; the remaining items cannot be disturbed, where (ρ*θ) t is the complete time tendency item of potential temperature, is the convection term, and -ADV(θ') is the advection term of the potential temperature.

所述基于能量守恒的随机物理扰动方法的进一步设计在于,所述qv的预报方程为:The further design of the random physical disturbance method based on energy conservation is that the prediction equation of the qv is:

式中可以被扰动的包括次网格湍流参数化过程的倾向项和微物理方案导致的水汽变化的倾向项其余各项不能被扰动,(ρ*q)t是水汽的完整时间倾向项,-ADV(q)是水汽的平流项,(ρ*Vqq/zζ)ζ是水汽的通量项。The propensity term that can be perturbed in the formula includes the subgrid turbulence parameterization process and the propensity term for water vapor changes caused by the microphysics scheme The other terms cannot be disturbed, (ρ*q) t is the complete time tendency term of water vapor, -ADV(q) is the advection term of water vapor, and (ρ*V q q/z ζ ) ζ is the flux term of water vapor.

本发明的优点如下:The advantages of the present invention are as follows:

本发明提供的基于能量守恒的随机物理扰动方法对完全独立的物理过程进行倾向扰动,目的在于保证模式变量的倾向扰动在能量上的守恒性,使得该方法可改善包括边界层和对流区域内部模式变量的集合离散度,这将显著改善风暴尺度集合预报的预报水平。与传统的对完整时间倾向的扰动相比,本发明的扰动方案能够通过模式本身来平衡加入的扰动,使得模式的总能量不会发生显著的变化(天气系统尤其是对流系统发展时就包含了使其消亡的因素,因此在仅仅扰动模式中的一部分物理过程时,模式的其他物理过程会做出响应的调整,在一定程度上抵消由于人为扰动引入的能量。而传统方案对完整时间倾向进行扰动,就使得所有物理过程的值都被统一的放大或缩小,因此无法保证能量的守恒)。同时,本发明的扰动方案对不同的物理过程可以根据该过程的特点使用不同的扰动形态,使得扰动与传统方法相比更具代表性。The stochastic physical disturbance method based on energy conservation provided by the present invention performs tendency disturbance on completely independent physical processes, the purpose is to ensure the energy conservation of the tendency disturbance of model variables, so that the method can improve the internal mode including boundary layer and convection area The ensemble dispersion of variables will significantly improve the forecast level of storm-scale ensemble forecasts. Compared with the traditional perturbation to the complete time tendency, the perturbation scheme of the present invention can balance the perturbation added by the model itself, so that the total energy of the model will not change significantly (weather systems, especially when convective systems develop The factors that make it disappear, so when only a part of the physical process in the model is disturbed, other physical processes in the model will make corresponding adjustments, to a certain extent offset the energy introduced by human disturbance. The traditional scheme tends to carry out the complete time Disturbance makes the values of all physical processes uniformly magnified or reduced, so the conservation of energy cannot be guaranteed). At the same time, the disturbance scheme of the present invention can use different disturbance forms for different physical processes according to the characteristics of the process, making the disturbance more representative than traditional methods.

具体实施方式Detailed ways

下面结合附图和具体实施例,进一步阐明本发明,本发明提供的基于能量守恒的随机物理扰动方法主要包括:Below in conjunction with accompanying drawing and specific embodiment, further clarifies the present invention, the random physical perturbation method based on energy conservation provided by the present invention mainly comprises:

1)根据实际需要选定进行数值预报的模式,接着确定模式预报方程中各个参数的最终倾向项的位置;1) Select the model for numerical prediction according to actual needs, and then determine the position of the final tendency item of each parameter in the model prediction equation;

2)在确定了所述参数的位置后再根据扰动形式,通过积分确定所述倾向项的扰动方案,扰动形式的表达式为:Xp=(1+rX)Xc2) After the position of the parameter is determined, according to the disturbance form, the disturbance scheme of the tendency item is determined by integral, the expression of the disturbance form is: X p =(1+r X )X c ,

其中Xc表示所有所述参数的时间倾向项,Xp表示扰动后的时间倾向项,rX表示增加的扰动,rX自回归函数的形式为 where X c represents the time propensity term for all said parameters, X p represents the time propensity term after perturbation, r X represents the added perturbation, r X autoregressive function of the form

其中ε(t)是满足uniform分布的随机数,每个时次使用不同的随机种子生成,uniform分布的最大值和最小值设定为0.5和-0.5,σ是扰动的方差函数,随高度变化,分布形态与上述时间倾向的形态相同;Where ε(t) is a random number that satisfies the uniform distribution, which is generated using a different random seed each time, the maximum and minimum values of the uniform distribution are set to 0.5 and -0.5, and σ is the variance function of the disturbance, which varies with height , the distribution form is the same as that of the above-mentioned time tendency;

3)在水平方向上对ε(t)进行二维傅立叶分解,接着滤除高频噪声将其中1至4倍格距的波长的波的系数赋值为0,最后将调整后的系数通过逆傅立叶变换合成新的ε(t);3) Carry out two-dimensional Fourier decomposition of ε(t) in the horizontal direction, and then filter out high-frequency noise and assign the coefficient of the wave with a wavelength of 1 to 4 times the grid spacing to 0, and finally pass the adjusted coefficient through inverse Fourier Transform and synthesize new ε(t);

4)重复步骤3)直至得到各个变量对应的扰动系数rX,并带入至所述扰动形式的表达式。4) Repeat step 3) until the disturbance coefficient r X corresponding to each variable is obtained, and bring it into the expression of the disturbance form.

以下给出上述方法的具体实施步骤:Provide the concrete implementation steps of above-mentioned method below:

(I.1)根据实际需要选定进行数值预报的模式,本实施例以ARPS模式为例。(I.1) Select the model for numerical forecasting according to actual needs. This embodiment takes the ARPS model as an example.

(I.2)确定模式预报方程中各个参数化方案输出的最终倾向项的位置。任意一个模式变量的预报方程都有多个时间倾向项,变量的最终时间倾向是上述时间倾向项的和。随机过程仅扰动参数化方案输出的时间倾向项。随机扰动涉及的预报方程包括三个风场分量u,v,w,一个温度变量T,一个水汽变量qv。其中u和v的形式相似,以u为例,其表达式为如下:(I.2) Determine the position of the final propensity term output by each parameterization scheme in the model forecast equation. The forecast equation of any model variable has multiple time bias items, and the final time bias of the variable is the sum of the above time bias items. The stochastic process only perturbs the time propensity term output by the parametric scheme. The prediction equation involved in the random disturbance includes three wind field components u, v, w, a temperature variable T, and a water vapor variable qv. The forms of u and v are similar, taking u as an example, the expression is as follows:

其中为次网格湍流参数化过程输出的u变量的时间倾向。确定在程序中的位置。同理需要确定v和w的的位置。in Time tendency of the u-variables output by the subgrid turbulence parameterization process. Sure position in the program. In the same way, it is necessary to determine the v and w and s position.

T的预报方程为:The prediction equation of T is:

式中,包括次网格湍流参数化过程的倾向项和微物理方案和辐射方案的非绝热过程的倾向项其中包括,但不限于微物理方案输出的温度倾向项和辐射方案输出的温度倾向项。至少要对这两项进行扰动。根据模式方程确定在程序中的位置。where the propensity term of the subgrid turbulence parameterization process is included and propensity terms for diadiabatic processes for the microphysics and radiation schemes in Including, but not limited to, the temperature propensity term output from the microphysics scheme and the temperature propensity term output from the radiation scheme. At least these two items should be perturbed. determined according to the model equation and position in the program.

qv的预报方程为:The prediction equation of qv is:

包括次网格湍流参数化过程的倾向项和微物理方案导致的水汽变化的倾向项确定在程序中的位置。Include a propensity term for the subgrid turbulence parameterization process and the propensity term for water vapor changes caused by the microphysics scheme Sure and position in the program.

(I.3)在确定了上述的位置后再确定这些倾向项的扰动方案。确定扰动的形式为:Xp=(1+rX)Xc,其中Xc表示上述7个时间倾向项,Xp表示扰动后的时间倾向项,rX表示增加的扰动。Xp=(1+rX)Xc将被应用在每一步积分上。(I.3) After determining the above and Then determine the disturbance scheme of these propensity items. The form of determining the disturbance is: X p = (1+r X ) X c , where X c represents the above seven time-inclined items, X p represents the time-prone item after the disturbance, and r X represents the added disturbance. X p = (1+r X ) X c will be applied at each step of the integration.

(I.4)rX在每一步积分上是不一样的,为了同时保证rX的随机性和连续性,使用自回归函数确定下一步积分时rX的数值,自回归函数的形式为:(I.4) r X is different in each step of integration. In order to ensure the randomness and continuity of r X at the same time, an autoregressive function is used to determine the value of rX in the next step of integration. The form of the autoregressive function is:

其中,ε(t)是满足uniform分布的随机数,每个时次使用不同的随机种子生成。uniform分布的最大值和最小值设定为0.5和-0.5。σ是扰动的方差函数,随高度变化,分布形态与上述时间倾向的形态相同。Among them, ε(t) is a random number that satisfies the uniform distribution, and is generated using a different random seed each time. The maximum and minimum values of the uniform distribution are set to 0.5 and -0.5. σ is the variance function of the disturbance, which varies with height, and the distribution shape is the same as that of the above-mentioned time tendency.

(I.5)在水平方向上对ε(t)进行二维傅立叶分解。然后将其中1-4倍格距的波长的波的系数赋值为0,用于滤除高频噪声。再将贡献小的波长的系数也赋值为0。最后将调整后的系数通过逆傅立叶变换合成新的ε(t)。(I.5) Two-dimensional Fourier decomposition of ε(t) in the horizontal direction. Then assign the coefficient of the wave with a wavelength of 1-4 times the grid pitch to 0, which is used to filter out high-frequency noise. Then, the coefficient of the wavelength with small contribution is also assigned to be 0. Finally, the adjusted coefficients are synthesized into a new ε(t) through inverse Fourier transform.

(I.6)对每个变量都进行(I.4)和(I.5)的分析,得到各个变量自己的扰动系数rX(I.6) Perform (I.4) and (I.5) analysis on each variable to obtain the disturbance coefficient r X of each variable itself.

(I.7)使用(I.6)得到的各个变量的rX,代入(I.3)的扰动方程中,将这一扰动方程再应用到不同变量的每一次积分上,就完成了随机物理过程扰动方案所要做的事情。(I.7) Use the r X of each variable obtained in (I.6) to substitute into the disturbance equation of (I.3), and then apply this disturbance equation to each integral of different variables to complete the random What the physical process perturbation scheme does.

Claims (1)

1. a kind of random physical perturbation motion method based on the conservation of energy, it is characterised in that include the following steps:
1) the ARPS patterns for carrying out numerical forecast are selected, then determine that the output of parameters scheme is most in model predictions equation The position of tendency item eventually;
2) after the position of the parameter is determined further according to disturbance form the disturbance side for being inclined to item is determined by integrating Case, the expression formula for disturbing form are:Xp=(1+rX)Xc,
Wherein XcRepresentAndTime incline Xiang Xiang, XpRepresent the time tendency item after disturbance, rXRepresent coefficient of disturbance, rXThe form of Autoregressive Functions is
Wherein α is decorrelation time scale, and t represents that the present mode moment is t, and ε (t) is the random number for meeting uniform distributions, Secondary when each to be generated using different random seeds, the maximum and minimum value of uniform distributions are set as 0.5 and -0.5, and σ is The variance function of disturbance, with height change, distributional pattern and the homomorphosis of tendency of above-mentioned time;
3) in the horizontal direction to ε (t) carry out two-dimension fourier decomposition, then filter out high-frequency noise by wherein 1 to 4 times of lattice away from The coefficient of the ripple of wavelength is assigned a value of 0, and the coefficient after adjustment is finally synthesized new ε (t) by inverse Fourier transform;
4) repeat step 3) until obtaining the corresponding coefficient of disturbance r of each variableX, and bring into the expression formula of the disturbance form, The variable includes u, v, w, one temperature variable T of a three wind field components and steam variable qv;
The prognostic equation of u is:
<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mrow> <mo>(</mo> <mi>&amp;rho;</mi> <mo>*</mo> <mi>u</mi> <mo>)</mo> </mrow> <mi>t</mi> </msub> <mo>+</mo> <mi>m</mi> <mover> <mi>&amp;rho;</mi> <mo>&amp;OverBar;</mo> </mover> <msup> <mi>&amp;rho;</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>{</mo> <msub> <mrow> <mo>&amp;lsqb;</mo> <msub> <mi>J</mi> <mn>3</mn> </msub> <mrow> <mo>(</mo> <msup> <mi>p</mi> <mo>&amp;prime;</mo> </msup> <mo>-</mo> <msub> <mi>&amp;alpha;</mi> <mi>&amp;xi;</mi> </msub> <mi>D</mi> <mi>i</mi> <mi>v</mi> <mo>*</mo> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mi>&amp;xi;</mi> </msub> <mo>+</mo> <msub> <mrow> <mo>&amp;lsqb;</mo> <msub> <mi>J</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <msup> <mi>p</mi> <mo>&amp;prime;</mo> </msup> <mo>-</mo> <msub> <mi>&amp;alpha;</mi> <mi>&amp;xi;</mi> </msub> <mi>D</mi> <mi>i</mi> <mi>v</mi> <mo>*</mo> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mi>&amp;zeta;</mi> </msub> <mo>}</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mo>-</mo> <mi>A</mi> <mi>D</mi> <mi>V</mi> <mrow> <mo>(</mo> <mi>u</mi> <mo>)</mo> </mrow> <mo>+</mo> <mi>&amp;rho;</mi> <mo>*</mo> <mo>&amp;lsqb;</mo> <mrow> <mo>(</mo> <mi>f</mi> <mo>+</mo> <msub> <mi>f</mi> <mi>m</mi> </msub> <mo>)</mo> </mrow> <mi>v</mi> <mo>-</mo> <mover> <mi>f</mi> <mo>&amp;OverBar;</mo> </mover> <mi>w</mi> <mo>-</mo> <msup> <mi>uwa</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>&amp;rsqb;</mo> <mo>+</mo> <msqrt> <mi>G</mi> </msqrt> <msub> <mi>D</mi> <mi>u</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced>
Wherein can be disturbed time tendency item beRepresent the u variables of time grid turbulence parameterized procedure output when Between be inclined to, in the prognostic equation of u exceptIt is every cannot be disturbed, it is impossible to disturbed item includes the complete of u variables Time is inclined to (ρ * u)t, pressure gradient-force itemAdvective term-ADV (u) and geostrophic deviating force item
The prognostic equation of v is:
<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mrow> <mo>(</mo> <mi>&amp;rho;</mi> <mo>*</mo> <mi>v</mi> <mo>)</mo> </mrow> <mi>t</mi> </msub> <mo>+</mo> <mi>m</mi> <mover> <mi>&amp;rho;</mi> <mo>&amp;OverBar;</mo> </mover> <msup> <mi>&amp;rho;</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>{</mo> <msub> <mrow> <mo>&amp;lsqb;</mo> <msub> <mi>J</mi> <mn>3</mn> </msub> <mrow> <mo>(</mo> <msup> <mi>p</mi> <mo>&amp;prime;</mo> </msup> <mo>-</mo> <msub> <mi>&amp;alpha;</mi> <mi>&amp;xi;</mi> </msub> <mi>D</mi> <mi>i</mi> <mi>v</mi> <mo>*</mo> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mi>&amp;xi;</mi> </msub> <mo>+</mo> <msub> <mrow> <mo>&amp;lsqb;</mo> <msub> <mi>J</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <msup> <mi>p</mi> <mo>&amp;prime;</mo> </msup> <mo>-</mo> <msub> <mi>&amp;alpha;</mi> <mi>&amp;xi;</mi> </msub> <mi>D</mi> <mi>i</mi> <mi>v</mi> <mo>*</mo> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mi>&amp;zeta;</mi> </msub> <mo>}</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mo>-</mo> <mi>A</mi> <mi>D</mi> <mi>V</mi> <mrow> <mo>(</mo> <mi>v</mi> <mo>)</mo> </mrow> <mo>+</mo> <mi>&amp;rho;</mi> <mo>*</mo> <mo>&amp;lsqb;</mo> <mrow> <mo>(</mo> <mi>f</mi> <mo>+</mo> <msub> <mi>f</mi> <mi>m</mi> </msub> <mo>)</mo> </mrow> <mi>u</mi> <mo>-</mo> <mover> <mi>f</mi> <mo>&amp;OverBar;</mo> </mover> <mi>w</mi> <mo>-</mo> <msup> <mi>vwa</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>&amp;rsqb;</mo> <mo>+</mo> <msqrt> <mi>G</mi> </msqrt> <msub> <mi>D</mi> <mi>v</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced>
Wherein can be disturbed time tendency item beRepresent the v variables of time grid turbulence parameterized procedure output when Between be inclined to, in the prognostic equation of v exceptIt is every cannot be disturbed, it is impossible to disturbed item includes the complete of v variables Time is inclined to (ρ * v)t, pressure gradient-force itemAdvective term-ADV (v) and geostrophic deviating force item
The prognostic equation of w is:
<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mrow> <mo>(</mo> <mi>&amp;rho;</mi> <mo>*</mo> <mi>w</mi> <mo>)</mo> </mrow> <mi>t</mi> </msub> <mo>+</mo> <mi>m</mi> <mover> <mi>&amp;rho;</mi> <mo>&amp;OverBar;</mo> </mover> <msup> <mi>&amp;rho;</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>{</mo> <msub> <mrow> <mo>&amp;lsqb;</mo> <msub> <mi>J</mi> <mn>3</mn> </msub> <mrow> <mo>(</mo> <msup> <mi>p</mi> <mo>&amp;prime;</mo> </msup> <mo>-</mo> <msub> <mi>&amp;alpha;</mi> <mi>&amp;xi;</mi> </msub> <mi>D</mi> <mi>i</mi> <mi>v</mi> <mo>*</mo> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mi>&amp;xi;</mi> </msub> <mo>+</mo> <msub> <mrow> <mo>&amp;lsqb;</mo> <msub> <mi>J</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <msup> <mi>p</mi> <mo>&amp;prime;</mo> </msup> <mo>-</mo> <msub> <mi>&amp;alpha;</mi> <mi>&amp;xi;</mi> </msub> <mi>D</mi> <mi>i</mi> <mi>v</mi> <mo>*</mo> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mi>&amp;zeta;</mi> </msub> <mo>}</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mo>-</mo> <mi>A</mi> <mi>D</mi> <mi>V</mi> <mrow> <mo>(</mo> <mi>w</mi> <mo>)</mo> </mrow> <mo>+</mo> <mi>&amp;rho;</mi> <mo>*</mo> <mo>&amp;lsqb;</mo> <mrow> <mo>(</mo> <mi>f</mi> <mo>+</mo> <msub> <mi>f</mi> <mi>m</mi> </msub> <mo>)</mo> </mrow> <mi>w</mi> <mo>-</mo> <mover> <mi>f</mi> <mo>&amp;OverBar;</mo> </mover> <mi>u</mi> <mo>-</mo> <msup> <mi>vwa</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>&amp;rsqb;</mo> <mo>+</mo> <msqrt> <mi>G</mi> </msqrt> <msub> <mi>D</mi> <mi>w</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced>
Wherein can be disturbed time tendency item beRepresent the w variables of time grid turbulence parameterized procedure output when Between be inclined to, in the prognostic equation of w exceptIt is every cannot be disturbed, it is impossible to disturbed item includes the complete of w variables The whole time is inclined to (ρ * w)t, pressure gradient-force itemAdvective term- ADV (w), and geostrophic deviating force item
The prognostic equation of the T is:
<mrow> <msub> <mrow> <mo>(</mo> <mi>&amp;rho;</mi> <mo>*</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> <mi>t</mi> </msub> <mo>+</mo> <mi>&amp;rho;</mi> <mo>*</mo> <mi>w</mi> <msub> <mover> <mi>&amp;theta;</mi> <mo>&amp;OverBar;</mo> </mover> <mi>x</mi> </msub> <mo>=</mo> <mo>-</mo> <mi>A</mi> <mi>D</mi> <mi>V</mi> <mrow> <mo>(</mo> <msup> <mi>&amp;theta;</mi> <mo>&amp;prime;</mo> </msup> <mo>)</mo> </mrow> <mo>+</mo> <msqrt> <mi>G</mi> </msqrt> <msub> <mi>D</mi> <mi>&amp;theta;</mi> </msub> <mo>+</mo> <msqrt> <mi>G</mi> </msqrt> <msub> <mi>S</mi> <mi>&amp;theta;</mi> </msub> <mo>,</mo> </mrow>
The tendency item for including time grid turbulence parameterized procedure that can be disturbed in formulaWith Microphysical scheme and radiation The tendency item of the nonadiabatic process of schemeWhereinIncluding the temperature tendency item of Microphysical scheme output and radiation The temperature tendency item of scheme output;Removed in the prognostic equation of TWithOuter items cannot be disturbed, it is impossible to is disturbed Dynamic item includes the full time tendency item (ρ * θ) of position temperaturet, convective termAnd advective term-the ADV (θ ') of position temperature;
The prognostic equation of the qv is:
<mrow> <msub> <mrow> <mo>(</mo> <mi>&amp;rho;</mi> <mo>*</mo> <mi>q</mi> <mo>)</mo> </mrow> <mi>t</mi> </msub> <mo>=</mo> <mo>-</mo> <mi>A</mi> <mi>D</mi> <mi>V</mi> <mrow> <mo>(</mo> <mi>q</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mrow> <mo>(</mo> <mi>&amp;rho;</mi> <mo>*</mo> <msub> <mi>V</mi> <mi>q</mi> </msub> <mi>q</mi> <mo>/</mo> <msub> <mi>z</mi> <mi>&amp;zeta;</mi> </msub> <mo>)</mo> </mrow> <mi>&amp;zeta;</mi> </msub> <mo>+</mo> <msqrt> <mi>G</mi> </msqrt> <msub> <mi>D</mi> <mi>q</mi> </msub> <mo>+</mo> <msqrt> <mi>G</mi> </msqrt> <msub> <mi>S</mi> <mi>q</mi> </msub> </mrow>
The tendency item for including time grid turbulence parameterized procedure that can be disturbed in formulaCaused by Microphysical scheme The tendency item of steam changeIn the prognostic equation of qv exceptItems cannot be disturbed, it is impossible to disturbed item Full time tendency item (ρ * q) including steamt, the advective term-ADV (q) of steam, flux term (the ρ * V of steamqq/zζ)ζ
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