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Microwave Integrated Retrieval System (MIRS)
Advantages/Drawbacks of Simultaneous Retrieval

As stated above, MIRS nominally retrieves the state vector in one single vector. The resulting solution is consistent in its fitting of all radiances used for the retrieval. Here simultaneous retrieval refer to both geophysical (all parameters retrieved together) and radiometric (all available channels used in the retrieval) simultaneous retrieval. The following is a general discussion about the advantages/drawbacks of following this approach. Note that the MIRS system is capable of retrieving the whole geophysical vector X or a subset of it and is capable of using the whole radiometric vector Y or just a subset of it.

1. Channel Purity

Some algorithms prefer to make use of specific channels for the retrieval of specific parameters. The temperature profile sounding for instance is often done using channels that are sensitive only to the temperature profile and nothing else. Channels that are 'contaminated' by other parameters are disregarded. The drawback with this approach is that we are missing significant information contained in other channels that are sensitive to the lower part of the atmosphere (where most atmospheric phenomenology occurs) but which are also sensitive to other parameters such as water vapor, cloud and surface emissivity. Moreover, it is unlikely to have a channel that is purely sensitive to one parameter alone and is instead a varied mixture of signatures from different parameters. The rate of this mixture varies with the channel itself and with the geophysical situation. The tropospheric temperature sounding channels are in some instances sensitive to high thick clouds as well. The water vapor channels are in some dry cases sensitive to the surface emissivity as well because of the low opacity due to atmospheric dryness. This multi-signatures nature of the measurements is a significant argument for taking the approach of the simultaneous retrieval, both at the geophysical level (whole vector X retrieved), and at the radiometric level (all channels used simultaneously to benefit from all information content available).

2. Natural Correlation

An additional benefit in retrieving the geophysical vector together is the possibility to account for the natural correlation that exists between the different parameters. This correlation refers to cause- effect type of relationships between parameters (highly humid profiles are likely over warm ocean surface temperatures for instance). The correlation refers also to inter-correlation between different layers of the same parameter (due to natural constraints on the temperature atmospheric gradient, layers of the temperature profile are naturally correlated). By performing a physical retrieval, these natural correlations are accounted for and therefore introduce an additional piece of information, especially useful in under-determined problems.

3. Unwanted Errors?

(if a channel that has no information is used) It is sometimes assumed that if a channel does not contain any information about a specific parameter and if this channel is included in the retrieval, then this will introduce unwanted errors. However, if no signal is present in a measurement, then its Jacobian is null. Therefore, the solution in equation 20 would result in a value that would not move from the background value (worst case scenario). However, if there is any signal under specific conditions (tskin signal in a water vapor channel under dry conditions for instance), then the Jacobian would not be null and therefore the retrieval would benefit from including this seemingly non-useful channel. The physical approach is therefore assessing dynamically, if a channel is used or not in a particular retrieval. The mere fact that the channel is put in the list of channels to be used does not mean that it is effectively used in the estimation of the optimal solution (it is in fact not used if its Jacobian is zero).

In practice however, the Jacobian is not necessarily null when it depends on the assumed state vector (like at the first guess stage).

4. Added noisiness? (if a noisy channel is used in the retrieval)

It is generally assumed that a noisy channel is better left out of the retrieval system, otherwise it will introduce unwanted noise in the retrieved state vector. This is only true if we do not know the amount of noise impacting the channel measurement. If we wrongly underestimate the noise level, then the retrieval process will tend to overfit the measurements producing therefore noisy retrievals (see section below about the importance of the knowledge of the noise level). Note that if we on the contrary, overestimate the noise level impacting the radiances, then the restrieval process will tend to smooth out the retrievals.

If on the other hand, the noise level is known (even if it is high), then the inclusion of the 'noisy' channel in the physical retrieval should not introduce any error in theory. The reason is that the channel is used effectively in the physical process only if its signal-to-noise ratio is high enough. See first item of the right side of equation (19). The term could become zero (or close) if the noise is much higher than the signal, resulting in no departure from the background, similar to the case where a channel has no signal for the parameter to retrieve, cited above. In other words, if the signal (Jacobian) of a parameter present in the measurement of a channel is less than the noise level known, then the retrieval won't move that parameter. It is only when the signal is higher than the noise level, that the parameter is modified in the course of the retrieval. Of course, in practice, the guessed signal would depend on the geophysical situation itself and on the parameter in question. Examples include a channel that might be sensitive just a little to water vapor but strongly to precipitation, or a channel like the water vapor sounding 183 GHz that might not see any cloud because of the water vapor screening but could become very sensitive to the same cloud in a dry atmosphere situation. So the ratio between the signal and the noise impacting the channel used in the physical retrieval, will decide dynamically on the usefulness of including the noisy channel or not in the retrieval. This tends to advocate using all channels in the retrieval procedure but at the condition of knowing quite well the noise level impacting the measurements.