University:
Widener University
Course:
ESSC 103 | Intriduction To Earth Science
Academic year:

2023
Views:

26

Pages:

1
Author:

zdrowotno8ct

Rossby Waves — Ocean data Purpose Examine the temperature and salinity data from the Local Dynamics Experiment to see if the motions correspond even approximately to the Rossby Wave dispersion relationship. Data Copy ~glenn/oceanwave/*.mto your directory. This gives you three routines, load ctdwhich brings in the data and reports the starting and ending dates, mapctdwhich will map a particular ﬁeld, and barnes.mwhich is the analysis routine for taking data from an irregular set of stations and putting it on a regular grid. Note — this routine is also available in GEMPAK. The data has been preselected to give four levels in the vertical. You will want to look at the diﬀerent levels and probably the diﬀerent ﬁelds as well. For looking at salinity, you may want to modify the mapctd.mﬁle to subtract oﬀ 35 o/oo in order to get readable contour labels. Comments on the Barnes scheme This is a successive iteration routine. The values on the grid are ﬁrst set to the average, and the initial residuals at the data points are then the measured values minus the average. We then calculate a new estimateon the grid by � residi × W (xi − x, yi − y) new(x, y) = old(x, y) + �i i W (xi − x, yi − y) + ehalf where (x, y) are the grid point locations and (xi , yi ) are the data locations. The weighting function is chosen to fall oﬀ as a gaussian with distance (30 km is a reasonable scale at ﬁrst). Corrections are applied for diﬀerences in distance of a 1o latitude or longitude displacement. The scheme then interpolates back (with linear interpolation) to get the values estimated at the data positions given the current grid values. This then gives a new estimate of the residual and of the error. These steps are repeated until the residual is suﬃciently low. Usually at some point, the scale of the Gaussian is reduced (so that grid values will mirror the nearby points more closely); however, it then becomes important to introduce an “ehalf” value which is � non–zero, so that points for which W (xi − x, yi − y) is very small will not be altered by the algorithm. You can try various sequences of (radius, ehalf ) and see how the maps are altered. To do: From a sequence of maps, try to estimate the dominant wavenumber(s) and propagation speed. Compare with the Rossby wave dispersion relationship. The ﬁrst mode deformation radius is about 47 km.