Such as in:
Triple collocation
Jur Vogelzang and Ad Stoffelen
Document NWPSAF-KN-TR-021
http://research.metoffice.gov.uk/research/interproj/nwpsaf/scatterometer/TripleCollocation_NWPSAF_TR_KN_021_v1_0.pdf
Here you can find a freely available python Toolbox for the Evaluation of Soil Moisture Observations: http://rs.geo.tuwien.ac.at/validation_tool/pytesmo/docs/index.html
The function "pytesmo.metrics" performs triple collocation: http://rs.geo.tuwien.ac.at/validation_tool/pytesmo/docs/pytesmo.html#module-pytesmo.metrics
See: pytesmo.metrics.tcol_error(x, y, z)
Could you pleas make your question more accurate. I have a tool for identifying several point source from a set of concentration measurements simultaneously influencing the detectors.
I am looking for an implementation of the triple collocation analysis that includes a quality control step and a calibration step with a neutral regresion code (or similar).
My question is if someone else has already integrated the steps and is willing to share the code (the triple collocation step itself is in the code mentioned by Luca Brocca). It is not too complex to do since there is a good flow diagram in Table 4.1 (p. 18) of Vogelzang and Ad Stoffelen, and also there is a good discusion of the steps to take in
Janssen, P.A.E.M., S. Abdalla, H. Hersbach, and J.-R.Bidlot, 2007,
Error estimates of buoy, satellite, and model wave height data.
J. Atm. Ocean. Tech. 24, 1665-1677
It can be done, but if it has already been done, it would be easier to use...
Following multiple requests I added my original Fortran code, library and Linux script as supplementary resource to https://www.researchgate.net/publication/248798881_Toward_the_true_near-surface_wind_speed_Error_modeling_and_calibration_using_triple_collocation
Although it includes QC and linear and higher order (PDF matching) calibration (=regression), it is specifically written for the wind domain. I added a small README section in the program to discuss the main caveats. The program has been further tested by Jur Vogelzang et al. (2011).
Article Error Modeling and Calibration; Towards the true surface wind speed
A simple version of TC and ETC results, based on :
McColl, K. A., J. Vogelzang, A. G. Konings,
D. Entekhabi, M. Piles, and A. Stoffelen
(2014), Extended triple collocation:
Estimating errors and correlation
coefficients with respect to an unknown
target, Geophys. Res. Lett., 41,
6229–6236, doi:10.1002/2014GL061322.
c=cov(x);
q=[];
q(1)=sqrt(c(1,1)-c(1,2).*c(1,3)/c(2,3));
q(2)=sqrt(c(2,2)-c(1,2).*c(2,3)/c(1,3));
q(3)=sqrt(c(3,3)-c(1,3).*c(2,3)/c(1,2));
p=[];
p(1)=sqrt((c(1,2)*c(1,3))/(c(1,1)*c(2,3)));
p(2)=sqrt((c(1,2)*c(2,3))/(c(2,2)*c(1,3)));
p(3)=sqrt((c(1,3)*c(2,3))/(c(3,3)*c(1,2)));
Just wondering if anyone has compared the value of beta(y) obtained from equation (6) of Janssen et. al 2007 and beta(2) obtained from equation (13) of Abdalla and Chiara (2017) entitled: Estimating random errors of scatterometer, altimeter and model wind speed data.
I have tried to compared them but I could not get the same result. I probably missed something.
As mentioned in Abdalla and Chiara (2017) paper, they found the value of beta to be the same up to five digits.
Thanks,
Agustinus
You can find a Python code with user guide on https://github.com/knmiscat/triple_collocation
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