**To**:**ferret_users@xxxxxxxx****Subject**:**Re: [ferret_users] velocity projected onto isotherm?****From**:**Ryo Furue <furue@xxxxxxxxxx>**- Date: Mon, 21 Sep 2009 20:47:41 -1000 (HST)
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Hi Yangxing, | I recently encounter a difficult problem. Suppose I have | ocean currents (u,v) and temperature (temp), how can I calculate the | cross-isotherm of component of currents in ferret? If your flow field is steady, cross-isothermal volume flux can be relatively easily computed from the horizontal velocity field: U = [integration from bottom to Z(x,y)] u(x,y,z) dz V = [integration from bottom to Z(x,y)] v(x,y,z) dz where z = Z(x,y) is the depth of the target isotherm. Then, vertical volume flux (per unit horizontal area) across the isotherm is w* = div(U,V) . When the field is not steady, w* is the sum of the cross-isotherm velocity and the vertical migration speed of the isotherm. It think it's difficult to separate the two at each timestep. If you are interested in mean values, then compute w* at each timestep and take a time average, which will give you the mean cross-isothermal flux, if the mean migration of the isotherm is zero over the averaging period. I included a derivation of these results in an Appendix of Furue, McCreary, and Yu. 2009. J. Phys. Oceanogr. 39(9): 2024--2051. To do this in Ferret, take the vertical indefinite integral (z=@IIN) of the horizontal velocity components, 2) project (regrid) the result onto temperature coordinates, and 3) take the horizontal divergence. I'm not sure whether or z=@IIN gives you exact results. (I'd have to read the documentation.) Hope this helps, Ryo

**References**:**[ferret_users] velocity projected onto isotherm?***From:*yangxing zheng

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