Please explain it

[vishal]

I was analyzing SST fields during a La-nina event. My friend asked me a question that is,whether it is SST or the gradient which is prominent? I am really confused about the question itself. He smiled and ran a way.Can anybody explain me regarding the same?

[vinu]

Hi Vishal,

The question you asked is interesting. I think more answers will be
adding to this.

I think:
First of all, Temperature (T) gradient is purely a local measurement.
It tells "how much of T will change with unit distance (unit is
degree-C/meter). The following figure shows an example field of
Temperature and its gradient in x-direction. Look at the phase of the
T and dT/dx. They are different. (axis units are in meters).

http://wwwoa.ees.hokudai.ac.jp/people/vinu/share_pal/gradient.gif

The term dT/dx gives the regions where maximum/minimum change in
temperature with distance occur. Physically, a gradient plot may be
meaningful if the analysis is interested on terms involving dT/dx.

Gradient and Advection

If we multiply the dT/dx with velocity (U), then U.dT/dx is called
the temperature advection flux. Virtually, any dT/dx can be
interpreted in the following way,

dT/dx = 1.dT/dx, suppose U = 1 m/s.

Thus a gradient plot can tell (at least), the amount of temperature change, in
unit time and in unit distance, which might occur if there exist a flow
of magnitude 1 m/s. This is equivalent to the amount of temperature
advected to that region. Since the time component involves in the
flux expression, the pattern begins to advect from one region to
another. The more complete form is, dT/dt + U.dT/dx = 0, is
called the advection-equation.

However, the gradient-plots are meaningful in some analysis. For
example, Liu et al. (2000) suggested the phase relation with SST
gradient and surface winds, namely, the surface wind convergence
is in phase with the SST gradient and a 90-degree phase shift with
the SST itself. However please note that the physical reason for this
phase relationship is nothing to explain with the gradient of SST (refer
the paper).

In conclusion, in your analysis, if you are concerned with terms
involving dT/dx, then a gradient-plot will be meaningful. Also, from
the above example figure, you can find the phase of a "field" and
its "gradient" are different. Therefore care must be taken while
interpreting the gradient fields.

Liu W. et al., 2000: Atmospheric manifestation of Tropical instability
wave observed by QuikSCAT and Tropical Rain Measuring Mission,
Geophysical Research Letters, Vol.27, No.16, 2545-2548.


-Thanks

-

[vishal]

Thanks vinu for your explanation. To compute the gradient of sst, I should measure dt/dx or dt/dy or ?