| Re: Interpolation routines [message #92659 is a reply to message #92657] |
Tue, 02 February 2016 14:01   |
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Paul Van Delst[1]
Messages: 1157
Registered: April 2002
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On 02/02/16 16:31, laura.hike@gmail.com wrote:
> On Tuesday, February 2, 2016 at 12:17:06 PM UTC-8, wlandsman wrote:
>
>> I don't believe this is true anymore. INTERPOL() used to be
>> biggest problem but since IDL 7.0, it is a professional level
>> interpolation routine (and certainly more powerful than QUADTERP).
>>
>> I do agree that you best bet is to probably remove the NAN values
>> (using WHERE and FINITE() ). I would use INTERPOL() without the
>> /NAN keyword.
>>
>> g = where(finite(y)) result = interpol( y[g], x[g], xinterp,
>> /spline)
>
> Thanks for the comment, wlandsman. I tried the "finite" method and
> got the same result as when I left the NaNs in and included the /NaN
> keyword. The interpolation works correctly (except when there are
> fewer than 4 valid points left, so I would have to write a trap for
> this in any case), but it continues beyond the end of the input
> range, becoming extrapolation instead of interpolation. This is
> completely invalid, so I specifically want to prevent it.
Umm, don't you specify the output interpolated pressures? So shouldn't
you just truncate them based on the inputs? That is, the maximum
output/interpolated pressure is the first value that is less than the
maximum finite input pressure. (Does that sound right?)
I interpolate lots of atmospheric temperature and absorber (e.g. H2O,
O3, etc) profiles and that's what I do. I agree with you that
extrapolation is completely invalid (in general), and in my case for
T(p) and H2O(p)/etc profiles it gets non-physical real fast.
Also, I don't know what the "SW" data is but, for atmospheric profiles,
shouldn't you be interpolating in ln(P) space rather than P?
> I show an
> example below in order to be clear. Yes, this is a vertical profile
> in pressure coordinates, for anyone who cares:
>
> Input abscissa Pin:
>
> 0.187500 0.362500 0.675000 1.26250 2.02500
> 2.98750 4.47500 6.75000 8.40000 8.98750 9.62500
> 10.2875 11.0000 11.7750 12.6000 13.4875
> 14.4500 15.4750 16.5750 17.7625 19.0250
> 20.3875 21.8625 23.4375 25.1250 26.9375
> 28.8875 30.9750 33.2125 35.6125 38.1875
> 40.9750 43.9750 46.3375 48.0000 49.7250
> 51.5125 53.3625 55.2875 57.2875 59.3500
> 61.4875 63.7000 66.0000 68.3875 70.8625
> 73.4250 76.0750 78.8250 81.6875 84.6500
> 87.7125 90.9000 94.2000 97.6125 101.150
> 104.825 108.637 112.587 116.688 120.938
> 125.337 129.900 134.638 139.538 144.625
> 149.913 155.388 161.062 166.938 173.025
> 179.350 185.913 192.700 199.737 207.038
> 214.663 222.625 230.888 239.513 248.513 257.913
> 267.725 277.925 288.575 299.688 311.237
> 323.100 335.288 347.938 361.050 374.463
> 388.188 402.400 417.025 432.087 447.612
> 463.550 479.925 496.812 514.300 532.287
> 550.725 569.738 589.312 609.463 630.287
> 651.825 NaN NaN NaN NaN NaN
> NaN NaN NaN NaN NaN NaN
> NaN NaN NaN NaN NaN NaN
> NaN NaN NaN NaN NaN NaN
> NaN NaN NaN NaN NaN NaN
> NaN
>
> Output abscissa Pout:
>
> 0.100000 0.300000 0.400000 0.500000 0.700000
> 1.00000 2.00000 3.00000 4.00000 5.00000 7.00000
> 10.0000 20.0000 30.0000 40.0000 50.0000
> 70.0000 100.000 150.000 200.000 250.000
> 300.000 350.000 400.000 450.000 500.000
> 550.000 600.000 650.000 700.000 725.000 750.000
> 775.000 800.000 825.000 850.000 875.000
> 900.000 925.000 950.000 975.000 1000.00
>
> Values obviously occur in Pout that are beyond the range of Pin.
>
> Ordinate in SWin:
>
> 0.000156151 0.000173488 0.000207377 0.000210915 0.000169155
> 0.000110047 7.45450e-05 5.23441e-05 3.99181e-05 3.90353e-05
> 3.75340e-05 3.97617e-05 3.25255e-05 3.04963e-05 3.44416e-05
> 2.90153e-05 2.68362e-05 3.02042e-05 2.54594e-05 2.58893e-05
> 2.62765e-05 2.39674e-05 2.39971e-05 2.40214e-05 2.37010e-05
> 2.34202e-05 2.16869e-05 2.26950e-05 1.99376e-05 2.16858e-05
> 1.91526e-05 1.85088e-05 1.88882e-05 1.80156e-05 1.72226e-05
> 1.67287e-05 1.73794e-05 1.56135e-05 1.48229e-05 1.44584e-05
> 1.51021e-05 1.45813e-05 1.19285e-05 1.34967e-05 1.10665e-05
> 1.15942e-05 1.21990e-05 1.08427e-05 9.58437e-06 1.00086e-05
> 8.94639e-06 9.36905e-06 8.25729e-06 8.73890e-06 7.72265e-06
> 7.45533e-06 6.50589e-06 6.92547e-06 6.66663e-06 6.42854e-06
> 6.20490e-06 5.99692e-06 5.77185e-06 5.05578e-06 4.90454e-06
> 4.69174e-06 4.99278e-06 4.37616e-06 3.80173e-06 3.67547e-06
> 3.93453e-06 3.40434e-06 3.28958e-06 3.18232e-06 3.06034e-06
> 2.62840e-06 2.80613e-06 2.71086e-06 2.02691e-06 2.48816e-06
> 1.59571e-06 2.53445e-06 2.43971e-06 3.04975e-06 4.47653e-06
> 4.95492e-06 6.00842e-06 7.14583e-06 7.06873e-06 7.76889e-06
> 7.85854e-06 8.32823e-06 8.90338e-06 9.45487e-06 9.72611e-06
> 9.55187e-06 9.46401e-06 8.91291e-06 9.40596e-06 8.94922e-06
> 9.59435e-06 9.93338e-06 9.91535e-06 1.02259e-05 1.02142e-05
> 1.00091e-05 8.75643e-06 8.13227e-06 NaN NaN NaN
> NaN NaN NaN NaN NaN NaN
> NaN NaN NaN NaN NaN NaN
> NaN NaN NaN NaN NaN NaN
> NaN NaN NaN NaN NaN NaN
> NaN NaN NaN
>
> Ordinate out:
>
> 0.000147821 0.000166955 0.000177699 0.000189441 0.000209155
> 0.000217363 0.000170853 0.000109465 8.07843e-05 6.65560e-05
> 4.99181e-05 3.92060e-05 2.45898e-05 2.22732e-05 1.85323e-05
> 1.68197e-05 1.12288e-05 7.54906e-06 4.98966e-06 3.04681e-06
> 1.66306e-06 4.97638e-06 7.80974e-06 9.37925e-06 9.38277e-06
> 9.00669e-06 9.91276e-06 1.01958e-05 8.16361e-06 4.44220e-06
> -3.16524e-06 -1.78092e-05 -4.18935e-05 -7.78224e-05 -0.000128000
> -0.000194829 -0.000280715 -0.000388062 -0.000519273 -0.000676752
> -0.000862904 -0.00108013
>
> Values are returned for every Pout, whether it's off the end of Pin
> or not. If you plot these, they form an arc in the negative going to
> magnitudes higher than any of the input values. Is there any way to
> get rid of these short of searching for the max and min values of Pin
> and excluding Pouts outside this range? How does interpol come up
> with values out there anyway, given that inputs on either side of the
> output should be required for the spline function? Adding all these
> searches and exclusions would make using this function impractical,
> given that I have to apply it thousands of times. Note that Pin
> varies over time while Pout is fixed.
>
>
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