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Re: [ferret_users] after scat2gridlaplace some values are obsolote (data origins of lambert grid)

Hi All,
All of this shows that it's important to do what Peter did when he looked closely at his results to see if they were reasonable. That's the way to determine which methods are best for the given problem.  Thanks for bringing this up, Peter.

I just found an interesting page, which shows the value and the limitations of spline interpolation:


The intial picture shows a nice smooth curve between some scattered points. Keep clicking on "add more points" and you'll see the spurious peaks and valleys that can show up between the scattered points which are being fit with the curve. Below is a screen shot of one combination, showing how the curve has to go way up and down to fit a polynomial through the given points. In our Ferret function, when argument 6 is large, we're doing a spline interpolation in 2 dimensions. If we've chosen to use spline interpolation, and if the destination grid happens to have coordinate points at places where the spline interpolation has gone way up or down, that's where the spurious peaks come from. This isn't a bug, but just a fat of life when using the particular method, which is good for some data and some choices of parameters, and not so good for other combinations.

spline fit


Ansley Manke wrote:
Hi Peter,
The Laplacian gridding algorithm fits a surface function to the scattered points and then interpolates to the grid from that surface.  This can result in the function values going above or below the original data values. Have you tried different values for the function arguments? Here is the documentation for SCAT2GRIDLAPLACE_XY about the value of argument 6

CAY   Amount of spline eqation (between 0 and inf.) vs Laplace interpolation:

If CAY=0.0, Laplacian interpolation is used. The resulting surface tends to have rather sharp peaks and dips at the data points (like a tent with poles pushed up into it). There is no chance of spurious peaks appearing. As CAY is increased, Spline interpolation predominates over the Laplacian, and the surface passes through the data points more smoothly. The possibility of spurious peaks increases with CAY. CAY= infinity is pure Spline interpolation. An over relaxation process in used to perform the interpolation. A value of CAY=5 often gives a good surface.

In particular, "The possibility of spurious peaks increases with CAY."  The interpolating function may well dip below zero as it is fit between points; the higher value gives extra wiggles in the function. I can't say for sure, but this may well be what's happening.

Compare the results if you use, say 5 and 5 for the last two arguments to your call to SCAT2GRIDLAPLACE_XY.  Is it better?

Because you have the 2-D longitude and latitude fields that define your grid, another option for you is the CURV_TO_RECT functions. You might want to check into that.


Peter Szabo wrote:
Dear Users,

I have a daily precipitation data set on a lambert grid stored in ASCII file.
I wanted to put this on a lat-lon grid with functions scat2gridlaplace and/or scat2gridlaplace. (After ferret cant deal with Lambertian data sets  and I want to make some computations thats why i change its grid)
Somehow after the scat2gridlaplace my data contains truly negative values. Does anyone know what mistake could i make? Or is it the function thats not working properly?

Here is my script:

DEFINE AXIS/x=12.42:24.6/np=97 lons
DEFINE AXIS/y=44.9:49.92/np=61 lats
DEFINE AXIS/t="1-JAN-1961 12:00":"31-DEC-1990 12:00":1/t0="31-DEC-1960 12:00"/units=days time

DEFINE GRID/t=time/x=lons/y=lats gridxyt
DEFINE GRID/x=lons/y=lats gridxy

SET DATA/EZ/VARIABLES="lon,lat"/GRID=gridxy "ASCII_koord.txt" !->i need the coordinate values from this file
let xx1D = XSEQUENCE(lon[d=1])
let yy1D = XSEQUENCE(lat[d=1])

SET DATA/EZ/VARIABLES="pre"/GRID=gridxyt "predaily.txt"

fill pre[l=@sum],lon[d=1],lat[d=1]  !->I attach the picture of the original data (AA.lambert.gif) created with similarly to this command

let precipG=scat2gridgauss_xy(xx1d,yy1d,pre,x[gx=lons],y[gy=lats],0.01,0.01,10,0)
fill precipG[l=@sum] !-> the data looks like this after the gaussian weightening (AA.gauss.gif)

let precipL=scat2gridlaplace_xy(xx1D,yy1D,pre,x[gx=lons],y[gy=lats],100,100)
fill precipG[l=@sum] !-> the data looks like this after the laplace interpolation (AA.laplace.gif)

Now the data is on a lat-lon grid and both looks pretty the same, but if i count the minimum of the daily data the actual values are negative in the case of scat2gridlaplace. (i attach also the minimum value of the "laplace" data set. the two others dont have negative values larger than 0.05).
I know i should use the gaussian weightening and interpolation, but this bug/my fault still troubles me.

Thanks in  advance,
Peter Szabo

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