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I would like to ask about horizontal wind shear. In most cases, we frequently talk about vertical wind shear (VWS), which is the change in wind speed and direction with height or within a given layer/depth of the atmosphere. I understand that VWS is calculated typically as a vector difference between wind velocities at different levels in the atmosphere, say between the 850 hPa and 200 hPa pressure levels.

What I'm wondering about is: how can I calculate horizontal wind shear (HWS)? I'm interested in calculating and visualizing how wind velocities change along the horizontal or parallel to the Earth's surface, preferably via Python given gridded data (esp. reanalysis), especially in phenomena where there are sharp changes in wind velocity (esp. shear lines, but also in true fronts). Since we calculate VWS along an axis (i.e. along the vertical axis), I assume that HWS should also be calculated along an axis, but which axis exactly? Would it be North-South (meridional) or East-West (zonal), or both (like components being combined into a vector)? And how do I calculate the vector differences? Would it be in between points, or in between lines or latitude/longitude?

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    $\begingroup$ Are you asking how to visualize a vector field, or solving an equation to obtain a sheared wind vector field, or do you want real data on wind velocities and obtain your shear from this data? Very unclear question at the moment. $\endgroup$ Commented Nov 13, 2024 at 0:54
  • $\begingroup$ I mean you'd calculate it the same way vertical wind shear is calculated... you'd have a horizontal (or pseudo-horizontal if aloft) grid of winds. You could calculate the difference in vectors between neighboring "x" gridpoints and neighboring "y" gridpoints (and probably diagonally too, to x+1, y+1, to get the fullest field). I'm sure there are basic functions/packages available to do vector calculations. $\endgroup$ Commented Nov 13, 2024 at 7:24
  • $\begingroup$ But I'd think in typical meteorological data, you'll get a horizontal shear that is poorly representative of the values needed for like aviation. Because the resolution of global and even mesoscale models are quite a few miles/km. And the biggest issues are much more localized (convective downbursts and such). For things like planes, or situations that like do damage or such, you need the change over like 100 meters or less. Whereas the models will be the difference averaged over 3 km or much more. Plus the coarser gridscale means the peak values will be blurred out in each grid point too $\endgroup$ Commented Nov 13, 2024 at 7:30
  • $\begingroup$ Reanalysis is often even worse (I see NCAR has a 2.5° field! A degree is 111 km/69 miles. So where you're typically looking for sharp differences over a tiny distance, you're instead only seeing the gradual synoptic differences between states/countries). If you want an estimate of true potential horizontal shear from reanalysis/global/mesoscale models, I'd believe the only option would be developing analysis equations upon key widescale factors to estimate the possibility of certain shear levels. Think that's how turbulence, microburst, etc forecasting is typically done regionally. $\endgroup$ Commented Nov 13, 2024 at 7:42
  • $\begingroup$ You can take a look at the equation for the horizontal shear here - math.stackexchange.com/questions/1196427/what-does-shear-mean $\endgroup$ Commented Nov 15, 2024 at 15:14

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