[gradsusr] Advection term in the moisture convergence equation

[Jeff Duda]

Your plot looks correct to me the way you defined it. Whether or not you
include the '-1' is up to you so long as you understand which sign refers
to "divergence" and which to "convergence". Traditionally, divergence is
calculated without the negative sign - in that case convergence has a
negative value (i.e., convergence is negative divergence). I think the
choice of whether to use the -1 is a matter of personal preference and/or
ease of plotting negative contours.

Jeff

On Sat, Jan 28, 2017 at 12:30 AM, Lyndon Mark Olaguera <
olagueralyndonmark429 at gmail.com> wrote:

> Dear Sir Jeff,
>
> Thank you for this wonderful explanation. You are a genius!
>
> I have one last question regarding the sign of the output attached in this
> email.
>
> Here's the script that I am using.
>
> 'sdfopen pentad_ensmean_shum_1981-2010.nc'
> 'sdfopen ../uwind/pentad/pentad_ensmean_uwind_1981-2010.nc'
> 'sdfopen ../vwind/pentad/pentad_ensmean_vwind_1981-2010.nc'
> 'set dfile 1'
> 'define q=shum(z=3)'
> 'set dfile 2'
> 'define u=uwnd(z=3)'
> 'set dfile 3'
> 'define v=vwnd(z=3)'
> 'color -0.2 0.2 0.02 -kind blue->white->red'
>
> *'define mconv=(-1)*hdivg(u*q,v*q)*1e6'*
>
>
> 'set lat -5 45'
> 'set lon 80 180'
> 'd mconv'
> 'xcbar -fs 2'
>
> *overlay 850mb winds
> 'set gxout vector'
> 'set arrscl 0.3 10'
> 'd u;v'
>
>
> Question:
>
> 1. I overlayed the 850 mb winds over the calculated MFC, but the results
> do not match. I'm not sure if I understand this correctly.
> From the defined mconv equation, negative values should correspond to
> "convergence", while positive values should correspond to "divergence".
> But in the attached image, positive values are seen over areas of
> convergence. Is the correct equation for the MFC above should contain -1 or
> this depends on the situation?
>
>
> *Lyndon Mark P. Olaguera*
>
>
> On Sat, Jan 28, 2017 at 2:53 PM, Jeff Duda <jeffduda319 at gmail.com> wrote:
>
>> Lyndon,
>> Absolutely. I calclulate MFC frequently. Use cdiff. But before I give the
>> full explanation, I should note that your formula already gives the full
>> MFC field. hdivg(q*u,q*v) should include the advection term. You can verify
>> this by comparing that formula to those below that I will give you.
>>
>> The trick with this is to define your grid spacing before doing anything
>> else. While your model integration may use a fixed grid spacing (whether in
>> degrees or linear distance or otherwise), if you use a control file to
>> display the data, and if it includes XDEF and YDEF entries, then the grid
>> on which your data are calculated may differ from that on which the model
>> was integrated, so you can't use your scalar grid spacing value in that
>> case. You can define your data grid spacing using trigonometry. The
>> equations to calculate that are
>>
>> dx = Re * cos(lat) * cdiff(lon,x)
>> dy = Re * cdiff(lat,y)
>>
>> In the above equations, Re is the radius of the earth, and you need to
>> make sure to convert between radians and degrees. Grads functions assume
>> inputs are in radians and also output in radians. However, the lat and lon
>> fields are in degrees, so convert. Both formulas are also instances of the
>> arc length formula for a circle, which assumes the angle is in radians. So
>> basically, convert everything to radians in those equations.
>>
>> Once you have those terms, you have all the fields you need (assuming you
>> have mixing ratio and wind components defined on the same grid already):
>>
>> advection term = -u * cdiff(q,x) / dx - v * cdiff(q,y) / dy
>> convergence term = q*hdivg(u,v)
>>
>> To verify that the advection term is already contained in hdivg(q*u,q*v),
>> it should suffice to display
>> hdivg(q*u,q*v) - q * hdivg(u,v)
>> This field should match the advection term field above. You can also
>> display
>> hdivg(q*u,q*v) - q * hdivg(u,v) - [ -u * cdiff(q,x) / dx - v * cdiff(q,y)
>> / dy] and it should be 0.
>>
>> I might be wrong about this since the divergence operator in spherical
>> coordinates includes an additional term to represent convergence for purely
>> meridional wind, so you may want to crack open a dynamics textbook and find
>> what that term is and include it in here somewhere. Either way, I hope this
>> helps.
>>
>> Jeff Duda
>>
>> On Fri, Jan 27, 2017 at 11:35 PM, Lyndon Mark Olaguera <
>> olagueralyndonmark429 at gmail.com> wrote:
>>
>>> Dear All,
>>>
>>> I'm trying to calculate the moisture flux convergence using the
>>> following commands:
>>>
>>> *At 850 mb
>>>
>>> 'set dfile 1'
>>> 'define q=shum(z=3)'
>>>
>>> 'set dfile 2'
>>> 'define u=uwnd(z=3)'
>>>
>>> 'set dfile 3'
>>> 'define v=vwnd(z=3)'
>>>
>>> 'color -0.2 0.2 0.02 -kind blue->white->red'
>>> 'define mconv=(1)*hdivg(u*q,v*q)*1e6'
>>>
>>> According to this link, I have to add the advection term.
>>>
>>> http://www.spc.noaa.gov/publications/banacos/mfc-sls.pdf
>>>
>>> [image: Inline image 1]
>>>
>>> Question:
>>>
>>> 1. Is there a way to do this in grads?
>>> 2. Or is there a function in GRADS that can calculate partial
>>> derivatives?
>>>
>>> I'll appreciate any help.
>>>
>>> Best,
>>>
>>> *Lyndon Mark P. Olaguera*
>>>
>>>
>>> _______________________________________________
>>> gradsusr mailing list
>>> gradsusr at gradsusr.org
>>> http://gradsusr.org/mailman/listinfo/gradsusr
>>>
>>>
>>
>>
>> --
>> Jeff Duda
>> Post-doctoral research fellow
>> University of Oklahoma School of Meteorology
>>
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>>
>
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-- 
Jeff Duda
Post-doctoral research fellow
University of Oklahoma School of Meteorology
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