用户Brendan Wallace -地球科学江南体育网页版堆栈交换江南电子竞技平台 最近30个来自www.hoelymoley.com 2023 - 03 - 25 - t04:29:14z //www.hoelymoley.com/feeds/user/28638 https://creativecommons.org/licenses/by-sa/4.0/rdf //www.hoelymoley.com/q/24989 4 从WRF输出的三维场估计大气垂直运动 布伦丹·华莱士 //www.hoelymoley.com/users/28638 2023 - 03 - 03 - t19:21:30z 2023 - 03 - 09 - t17:36:18z 我有等压水平的WRF数据,不幸的是,在输出中不包含z风或ω场,我想对天气尺度垂直运动的大小进行一些估计。< / p >

Upon reviewing the three main methods of estimating vertical motion in prior papers (kinematic, thermodynamic, and QG-omega), I've decided that implementing the kinematic method might be the most straightforward method to understand and also seems to be best suited to my needs. I initially tried solving for the traditional QG-Omega equation, but I am really struggling with "inverting" the laplacian on the left-hand side of the equation, and so have now opted to approach this problem using the kinematic method. However, I'm running into some trouble working out the logic of using this method in my head.

Its derivation seems easy enough. Starting with the continuity equation in pressure coordinates: $$ \frac{dw}{dp} + \frac{du}{dx} + \frac{dv}{dy} = 0 $$

we can rearrange and integrate to yield:

$$ w_{p} = w_{p+\Delta p} + \int_{p}^{p+\Delta p} ( \frac{du}{dx} + \frac{dv}{dy})dp $$

where w is vertical velocity, p is some reference pressure, u is zonal wind, and v is meridional wind.

Now the problem I'm running into is that much of the literature recommends against using the kinematic method for acquiring a realistic estimate of vertical motion. This seems mainly due to the fact that the geostrophic wind is non-divergent, and errors in the ageostrophic wind are large enough to significantly affect horizontal divergence. This makes sense to me for instances where one is using observations, since the goal is to match reality as closely as possible, and observational readings are prone to error both due to instrumentation and error that likely arises from the interpolation process from discrete observations onto a grid.

However, for model data, would this drawback still apply? There are no "errors" since the fields are continuous and the model is simulating everything based on its own assumptions. In that sense, I'm not looking to match reality, but rather match whatever the model's reality is. It seems to me like this is how the WRF model already calculates omega (indicated within the comments of the calc_ww_cp subroutine in the WRF code, although my Fortran is a bit too rusty to actually make sense of it). Basically, I'm looking for the most efficient way of obtaining a realistic quantity representing vertical motion within the model output.

In that sense, is the integration of the continuity equation the best way of accomplishing this for numerical model output? Or is it worthwhile to pursue a different method?

Thanks in advance, and I look forward to any fruitful discussions that can come out of this!

//www.hoelymoley.com/questions/24989/estimating-atmospheric-vertical-motion-from-3d-fields-in-wrf-output/25014#25014 2 Brendan Wallace关于从WRF输出中的3D场估计大气垂直运动的回答 布伦丹·华莱士 //www.hoelymoley.com/users/28638 2023 - 03 - 09 - t17:36:02z 2023 - 03 - 09 - t17:36:02z 经过深入研究,似乎在压力坐标中垂直积分连续性方程(如上所示)是估计数值模型输出中垂直运动的合理方法<强>在天气尺度。我说天气尺度,是因为在将高度坐标中的初始连续性方程转换为压力坐标时,使用了流体静力近似。在这种情况下,水平网格间距足够细,可以解决深对流和/或地形中的急剧梯度(<~10km),流体静力近似不再有效,因此您可能会遇到一些问题。我的模型网格间距非常精细(4公里),所以我通过在x&y方向上对运动学$\omega$字段应用~150公里的运行平均平滑滤波器来解决这个问题。这样就过滤掉了小尺度噪声,保留了大尺度信号。对再分析数据使用这种方法的一些初始测试产生了可接受的结果,因此我相信这种实现是合理的。< / p >

The major drawback of the kinematic method (errors in the ageostrophic wind propagating into estimates of $\omega$) does not apply to model data where the accuracy in horizontal wind is approximated to several orders of digits. In observational data, where this order of accuracy does not exist, it's recommended to avoid the kinematic method. In some personal tests, I found that integrating divergence on isobaric levels in reanalysis data (ERA5) successfully reproduces the $\omega$ field within the reanalysis itself. Digging through the ECMWF technical notes confirms that continuity is used for their purpose of estimating $\omega$ in gridded data (specifically, they refer to Simmons & Burridge (1980) - An Energy and Angular-Momentum Conserving Vertical Finite-Difference Scheme and Hybrid Vertical Coordinates [Specifically eqn (2.5). This is the approach ECMWF uses to solve for omega on hybrid vertical levels]).

Speaking subjectively, this method seems to be the easiest to implement and the most intuitive. In instances where $\omega$ is not available for your data and the phenomena you wish to study satisfies the hydrostatic approximation (such as in most GCMs or studies examining synoptic-scale features), the kinematic approach is justifiable.

//www.hoelymoley.com/questions/24989/estimating-atmospheric-vertical-motion-from-3d-fields-in-wrf-output?cid=58539 Brendan Wallace关于从WRF输出的3D场估计大气垂直运动的评论 布伦丹·华莱士 //www.hoelymoley.com/users/28638 2023 - 03 - 09 - t17:36:57z 2023 - 03 - 09 - t17:36:57z @JoschaFregin感谢提示-更新了这篇文章的答案!
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