| Re: Interpolation routines [message #92661 is a reply to message #92660] |
Wed, 03 February 2016 01:34  |
lecacheux.alain
Messages: 325
Registered: January 2008
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Senior Member |
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Le mardi 2 février 2016 23:38:18 UTC+1, laura...@gmail.com a écrit :
> On Tuesday, February 2, 2016 at 2:01:35 PM UTC-8, Paul van Delst wrote:
>
> Yes, this is the only solution that I've found. It seems ridiculous to have to do this manually -- surely the interpolation function should handle this, or at least have it as an option. Cutting the range does have the drawback of not assigning a value to a point that is barely outside the input range. Could throw in a little margin for that, I suppose.
>
> SWin is related to density, which is linear in P.
>
>
>
Spline is well known for extrapolating badly (even extremely badly !).
In your case, assuming some stationarity of your data, an autoregressive model (e.g. TS_FCAST in IDL) might give better result (of course after truncating your series by using some where(finite(...)).
alx.
>>
>> 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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