Patrick, thank you very much for your reply. I will proceed to share what I did. I implemented the first of your suggestions. So,
Se = Sn + Kt*St*Kt^T + Kh2o*Sh2o*Kh2o^T (I changed the nomenclature with respect to the previous email to not confuse with the nomenclature of Matlab functions) where: Sn: covariance related with noise (in Matlab function, Sn=Y.TNOISE^2.*Q.TNOISE_C) Kt: jacobian temperature St: covariance matrix of temperature Kh2o: jacobian of water vapour Sh2o: covariance matrix of water vapour I implemented it inside of a function called qp2_y2Q, which is inside of qpack2.m. qp2_y2Q is implemented as: [Q,Se] = qp2_y2Q( Q, Y, m); where the output Se is now the quantity in the equation of the covariance matrix as above (Se = Sn + Kt*St*Kt^T + Kh2o*Sh2o*Kh2o^T). Therefore, the retrieval error will consider the error due to noise, temperature and H2O without any other modification in Qpack because the calculation of other retrieval parameters (such as cost, G, etc.) in oem.m takes into account the covariance matrix Se. Is it correct? Thanks in advance Best regards Facundo 2015-11-01 18:17 GMT-03:00 Patrick Eriksson <[email protected]>: > Facundo, > > You were not unclear, I tried to answer exactly what you wrote in your > last email. > > First of all, if you want to sum up uncertainties you should not use > matrix inverses. You do it as: > > S = Se + Kb*Sb*Kb^T > > > (What you want to do was better supported in Qpack1, but I had a hard time > to find a general way to cover all possible combinations that could be of > interest. For Qpack2 you need to do some tricks.) > > Let us use T as example. If you want to get out the Kb matching T, you can > e.g. deactivate all present retrieval variables, and just set T as > retrieval variable, and Q.T.L2 = true. Then make a linear inversion and Kb > = L2.J. (You can do the same thing for H2O. The uncertainty associated with > O2 should be negligible.) > > With this Kb, the retrieval error due to T is calculated as > > Sr = G*Kb*St*Kb^T*G^T > > where St is the temperature covariance matrix. > > The above should answer your direct question. However, if the error due to > T is significant, you can do better. This simple by retrieving T in > parallel to O3. The extra calculation cost is quite small, and I would > recommend you to do this as the error related to T will then be smaller. If > you don't care about the result for T, you just set Q.T.L2=false. > > If you still want to calculate the error due to T, you can do as above, or > use L2.jq and L2.ji to extract the part of L2.J that matches T, as I tried > to describe in my last answer. > > If H2O should also be retrieved depends on your exact set-up. > > Bye, > > Patrick > > > > > > > On 10/29/15 14:19, Facundo Orte wrote: > >> Dear Patrick, >> Thank you so much for the reply and I am sorry for not be clear. >> I set Qpack to retrieve only ozone. Other gases and T (H2O, O2 and T) I >> set as Q.ABS_SPECIES.RETRIEVE=false, because I am not interesting in >> water vapor, oxygen, and T, but I include NCEP profiles of >> these gases and temperature in Q.DEFINITIONS.m for ARTS calculation and >> to model the spectrum. O2 is included because the frequency range of >> measurement is 110.83GHz and this gas also absorb the signal. These >> profiles have some uncertainties and I want to introduce these >> uncertainties in the covariance matrix for the cost calculation and so >> on. What I need is to include these uncertainties in the covariance >> matrix. >> >> I think that I can include it in the covariance matrix doing: >> >> S^(-1)=Se^(-1) + Kb^T*Sb^(-1)*Kb >> >> where Kb is the jacobian of non-retrieval parameters (in my case H2O, T, >> and O2), Sb is the covariance matrix related with the non-retrieval >> parameters and Se is the covariance matrix related with noise. S is the >> covariance matrix used to calculate the cost as following. >> >> cost=[y-F(x,b)]^T * *S*^(-1) * [y-F(x,b)] + [x-xa]^T * Sx^(-1) * [x-xa] >> >> At this time, I introduce the covariance matrix only related with noise >> (S=Se) and I not include the uncertainties for water vapor, T and O2 >> profiles. >> >> I think that the Jacobians of non-retrieval parameters are similar for >> different measurements. So, my idea is to calculate these jacobians one >> time and use it then for the calculation of different measurements. It >> will avoid the calculation of these jacobians in each measurement. >> >> My problem is that I do not know how to include the uncertainties for >> non-retrieval parameters profiles in the covariance matrix S. >> >> Thanks in advance >> Best regards >> >> 2015-10-27 16:55 GMT-03:00 Patrick Eriksson >> <[email protected] <mailto:[email protected]>>: >> >> >> Dear Facundo, >> >> As I understand your question, the answer is no. Or at least, this >> can not be done automatically. >> >> However, if you think that H2O and temperature can give substantial >> errors (I can not see how O2 should give rise to an error), you >> should retrieve H2O and T in parallel to O3. That will decrease the >> impact of H2O and T. In short, OEM will then adjust as far as >> possible to H2O and T uncertainties. The impact of H2O and T will >> then be included in the standard error estimate. >> >> You have seen that Qpack can give you the error covariance matrix? >> >> If you retrieve H2O and T, what you call df/dH2O and df/dT are part >> of the (total) Jacobian matrix, that you can trigger Qpack to >> output, i.e. L2.J. The fields L2.jq and L2.ji give you information >> about what part of J that belong to H2O and T etc. That should give >> you a way to calculate separate errors. >> >> Bye, >> >> Patrick >> >> >> >> >> On 10/27/15 20:15, Facundo Orte wrote: >> >> Dear all, >> I am very new using Qpack. I am setting Qpack to retrieve ozone >> profiles >> using ARTS. At this moment, I am able to retrieve coherent ozone >> profiles, but to calculate covariance matrix I am trying to get >> the >> jacobian for water vapor (df/dH2O), oxygen(df/dO2) and temperature >> (df/dT) (to include the uncertainties of these gases and >> temperature), >> due to these gases absorb radiation in the frequency range of >> measurement. Is it possible to get these jacobians at the same >> time as >> the retrieval species (O3)? >> Thanks in advance >> >> Regards >> Facundo >> >> >> _______________________________________________ >> qpack mailing list >> [email protected] <mailto:[email protected]> >> https://www.sat.ltu.se/mailman/listinfo/qpack >> >> >>
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