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A New Approach to MTP Retrievals

MJ Mahoney

TemplateRAOBs Introduction

Retrieving temperature profiles during the arctic winter is extremely challenging on an airborne platform. This is because there can be very large variations in the shape of the actual temperature profile over the course of a campaign, which is illustrated in the figure to the right. It displays 40 radiosonde soundings located near the DC-8 flight track during the one-month long SOLVE-2 campaign based in Kiruna, Sweden. Stratospheric temperatures can vary by as much as 50 K at some altitudes. Such a large temperature variation would lead to large formal retrieval errors if hundreds of such soundings were used to calculate a single set of retrieval coefficients.

During the first SOLVE campaign in the winter of 1999-2000, we attempted to overcome this limitation by binning radiosondes into different temperature ranges or shape regimes. This was significantly better than putting all the radiosondes into a single bin, but a retrieval quality metric indicated that on some flights the retrievals were not as good as we would have liked.

This led us to consider a new approach, which in hindsite is rather obvious but computationally intensive: use radiosondes from launch sites which the aircraft flew near as templates to select  other soundings for calculating retrieval coefficients. This is done by simply requiring that the other soundings needed to calculate retrieval coefficients be within some specified bias and variance of the template sonde. To calculate robust retrieval coefficients (RCs) at least 100 soundings are required, and preferably several hundred. Using a data base of >25,000 arctic winter radiosondes, it was generally possible to find enough similar looking sounding, but in some extreme cases it was only possible to find a handfull of soundings that matched the template sonde. In this case other strategies had to be adopted to come up with enough sondes.

The New Retrieval Algorithm

In order to capture the conditions near the aircraft flight track 40 sets of retrieval coefficients were calculated. But other changes were made in the retrieval process. First some nomenclature. Brightness temperatures measured by the MTP at different elevation angles and frequencies are referred to as observables. Retrieval coefficients for a given set of radiosondes are calculated  by first doing the forward radiative transfer. That is, for each radiosonde the expected brightness temperature is calculated for each MTP viewing angle and frequency, and for a number of selected flight levels. These calculated observables arethen  regressed against the actual radiosonde temperature profiles to determine a set of retrieval coefficients which define the statistical relationship between observables and actual physical temperatures. The average brightness temperatures for a set of radiosondes is referred to as the archive average (AA) observables.

When a retrieval is performed, the MTP observables are compared to the archive average observables for each set of RCs to determine their bias and standard deviation. Using a priori measurment errors that are a combination of radiometric noise and measurement errors, an information theory metric, which we call the MRI, is calculated to determine which set of archive average observables best matches the measurements. It turns out that the standard deviation is much more important than the bias in determining which set of RCs to use in a retrieval. This is because the standard deviation represents shape differences between measurements and archive average observables. The bias, or average temperature difference between the observables and AA observables, does matter, but it is a second order effect because absorption coefficients don't depend as strongly on temperature as they do on pressure. We do however correct for it by calculating a temperature sensitivity matrix. This is done by adding and subtracting 20 K to AA radiosonde temperature profile and noting the change in the AA observables. The change is not linear with temperature bias and so a quadratic fit is done to obtain first and second order coefficients which comprise the sensitivity matrix. The measured observables corrected by the senstivity matrix and the bias is also subracted from all the observables. This has the effect of making measurements look like what the would have been if there had not been an observable bias. A retrieval is then performed and a bias added to compensate for the bias removed from the observables.

Another consideration in deciding which set of RCs to use is to compare the temporally interpolated radiosonde profiles along the flight track to the AA temperature profile for each set of retrieval coefficients. This establishes the best RC set for each radiosonde launch site, and this step is needed because RCs are not calculated for every possible launch site encounter and flight day. During the course of a flight, a check is made of the great circle distance to all radiosonde launch sites in the flight region. If  the nearest site is < 2 great circle degrees (222 km, 120 nm) and the RCs associated with that site has one of the three best MRIs, then that set is used for the retrieval. The three best RC sets are considered because it is possible that there can be small differences between the best RC sets, and we want to be sure not to get the correct one because of noise on the observables. If this is not done, there can be large changes in the temperature profile >6 km from flight level, the practical limit of the MTP measurements. Put another way, the portion of the temperature profile > 6 km from the aircraft does not contribute to the measurements, and so very different profiles in this region produce the same measurements. What we are doing near radiosonde launch sites is the same thing that is done in DAO re-analysis, we are simply forcing the profile >6 km from the aircraft to look like temporally interpolated temperature profile.The information is available and we use it even though we can't measure it. If the nearest radiosonde launch site is between 2 and 4 great circle degrees and the RCs associated with that site has one of the two best MRIs, then that set is used for the retrieval. Beyond 4 great circle degrees, the RCs associated with a site is used only if it has the best MRI.





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