# TIGR-like atmospheric-profile databases for accurate radiative-flux computation

F. Chevallier, A. Chédin, F. Cheruy, J.-J. Morcrette

► To cite this version:

F. Chevallier, A. Chédin, F. Cheruy, J.-J. Morcrette. TIGR-like atmospheric-profile databases for accurate radiative-flux computation. Quarterly Journal of the Royal Meteorological Society, 2000, 126 (563), pp.777-785. 10.1002/QJ.49712656319. hal-02946854

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# TIGR-like atmospheric-profile databases for accurate radiative-flux computation

By F. CHEVALLIER¹*, A. CHÉDIN², F. CHÉRUY² and J.-J. MORCRETTE¹

¹European Centre for Medium-Range Weather Forecasts, UK

²Laboratoire de Météorologie Dynamique, France

(Received 12 March 1999; revised 8 July 1999)

## SUMMARY

This note summarizes the characteristics of different topological methods for sampling vertical profiles of heterogeneous variables, like atmospheric temperature and water-vapour concentration. The methods presented follow the approach developed for the successive Thermodynamic Initial Guess Retrieval (TIGR) databases at Laboratoire de Météorologie Dynamique. The most recent one is applied to select limited numbers of profiles (some thousands) by the sampling of a much larger dataset (more than one million profiles) from the European Centre for Medium-Range Weather Forecasts short-range forecasts. The sampled datasets are then used for training a neural-network-based radiative-flux profile computation model (NeuroFlux).

**KEYWORDS:** Artificial neural networks Long-wave radiative transfer Sampling methods

## 1. INTRODUCTION

The importance of the role played by radiation in climate research, results in a growing interest in accurate modelling of forward or inverse radiative-transfer problems. A key for increased accuracy is an improved use of pertinent and representative (adequately sampled) a priori information on the systems considered. A major attempt to sample this kind of a priori information on global scales has been the construction of successive versions of the Thermodynamic Initial Guess Retrieval database (TIGR) (Chédin et al. 1985; Achard 1991; Escobar-Munoz 1993; Chevallier et al. 1998b) by the Laboratoire de Météorologie Dynamique (LMD). Each version groups together hundreds of soundings sampled from larger data banks of observations of the atmosphere: radiosonde reports and, for the latest version (TIGR-3) only, satellite-retrieved atmospheric profiles. Providing initial-guess solutions and a priori information (covariance matrices) for the weakly nonlinear problem of the retrieval of atmospheric temperature profiles, from observations of TIROS-N Operational Vertical Sounder (TOVS) on board the National Oceanic and Atmospheric Administration (NOAA) polar-orbiting satellites, has been the main purpose of the TIGR databases. This approach has been developed in the framework of the Improved Initialization Inversion (3I) (Chédin et al. 1985; Scott et al. 1999). For stronger nonlinear problems, like the retrieval of water vapour from TOVS or the design of fast forward radiative-transfer models, TIGR has been used for training artificial neural networks (e.g. Escobar-Munoz et al. 1993; Chéruy et al. 1996; Rieu et al. 1996; Chaboureau et al. 1998).

In practice, the high dimensionality of the atmospheric-variable space makes the sampling problem delicate. From one TIGR version to the next, important choices have been made and improvements introduced, so as to fit with the applications of the database. New applications of the neural-network-based techniques, like the computation of long-wave (LW) flux profiles in general-circulation models (GCMs) have led to further improvements of the sampling strategy.

This paper summarizes the characteristics of the TIGR sampling methods, and discusses these prospects. Section 2 describes the TIGR database and reviews its three versions. Section 3 analyses the characteristics of the TIGR sampling methods on the basis of a simple but representative problem. An extension of the most recent TIGR sampling method is presented. Its application for the sampling of atmospheric situations from the European Centre for Medium-Range Weather Forecasts (ECMWF) short-range forecasts is shown in section 4.

## 2. THE TIGR DATABASE

### (a) General description

The TIGR database consists of several subgroups, to serve as a database upon which several direct and inverse radiative-transfer models rely. Each subgroup describes a particular aspect of the archived atmospheric soundings.

<footnote>* Corresponding author: European Centre for Medium-Range Weather Forecasts, Shinfield Park, Reading, Berkshire RG2 9AX, UK. e-mail: chevallier@ecmwf.int</footnote>
The subgroup of the geophysical parameters is the kernel of the database. To each sounding are associated a vertical temperature profile, a vertical water-vapour concentration profile and a vertical ozone concentration profile. The vertical discretization refers to 40 levels between 0.05 and 1013 hPa. It has been chosen in the context of TOVS retrievals: for instance, the relatively coarse resolution in the lower troposphere is consistent with the instrument specifications. All soundings come from observations; the geographic location and the date of these are also archived. Unlike the temperature and water-vapour profiles, the ozone profiles come from climatologies.

Various radiative characteristics of these soundings have been computed. Initially, only TOVS-related quantities were archived: the theoretical radiances for different satellite viewing angles and surface pressures, together with the corresponding atmospheric transmission profiles. With the new generation of vertical sounders, similar quantities have also been computed with reference to the Special Sensor Microwave/Temperature (SSM/T) (Rieu *et al.* 1996), to the Advanced Microwave Sounding Unit (AMSU) (Cabrera-Mercader and Staelin 1995), and to the Infrared Atmospheric Sounder Interferometer (IASI) (Aires *et al.* 1998). LW radiative-flux profiles have also been added to the database for its use in a fast model for the computation of atmospheric LW-flux profiles (NeuroFlux) (Chevallier *et al.* 1998b).

For practical use, the database is currently divided into five statistically homogeneous air-mass classes: tropical, mid-latitude 1, mid-latitude 2, polar 1 and polar 2 (Achard 1991).

### (b) *Three successive versions*

Up to now, there have been three different versions of the TIGR database. The first one, TIGR-1, groups together 1207 soundings (Moulinier 1983). The initial database from which they were sampled was limited to 6600 radiosoundings, which was shown not to be enough for the use of TIGR in the framework of the 31 scheme (Flobert *et al.* 1991). It has been followed by TIGR-2: the updated database contains 1761 situations sampled from a much larger set of 80 000 radiosoundings (Achard 1991; Escobar-Munoz 1993). The sampling methods for TIGR-1 and TIGR-2 are similar and rely on a temperature criterion. They are described in section 3(b). The necessity of an improved representativity of water-vapour concentration led to the improvement of the method, and to the second update of the database (TIGR-3) (Chevallier *et al.* 1998b). The method is described in section 3(b). TIGR-3 gathers 2311 soundings and has been successfully used within the frame of the NOAA/National Aeronautics and Space Administration (NASA) Pathfinder programme, for the re-analysis of the 20 years of TOVS observations (Scott *et al.* 1999).

### (c) *Application to the computation of LW-flux profiles*

TIGR-3 has been used as a training database for the neural-network-based LW radiative-transfer model NeuroFlux. NeuroFlux is a highly parametrized scheme that has been designed for computing LW-flux profiles significantly more rapidly than the presently existing wide-band models. It relies on a series of artificial neural networks, as defined by Rumelhart *et al.* (1986) (Multi-Layer Perceptrons). For a complete description of NeuroFlux, the reader is referred to Chevallier *et al.* (1998b).

For the application of NeuroFlux in GCMs (Chevallier *et al.* 1998a), difficulties arose mainly because of the insufficient description of the boundary layer in the vertical pressure grid on which the soundings are archived in TIGR-3. These induced systematic errors by NeuroFlux in the lower troposphere and, therefore, non-negligible uncertainties in the GCM simulations using NeuroFlux to compute the LW radiative budget. As a consequence, it appeared that for that kind of application the training database of NeuroFlux had to be redefined. The next section focuses on the TIGR sampling technique, in order to define an updated methodology for sampling the earth's atmospheric profiles.

## 3. CHOICE OF A SAMPLING TECHNIQUE

### (a) *The TIGR approaches*

The successive TIGR databases were set up with similar two-step methods. The first step consists in filtering the infinity of possible profiles in the atmosphere, by gathering a much reduced but representative sample of them; for example, 80 000 radiosonde reports have been used for TIGR-2. Let us call *S* this initial database. The sampling of *S* with a topological approach is the second step of the method. It relies on an index, *I*, that measures the dissimilarity between two atmospheric situations. The process is iterative. At step one, a first atmospheric situation from *S* is randomly drawn and archived in a new set, *E*. At step *n*, an *n*th atmospheric situation is randomly drawn and archived in *E* if it is different enough from the already selected situations, relatively to index *I*. With that approach, the distribution of *E* over the space of the various atmospheric variables is more uniform than that of *S*. In practice, restriction to some variables had to be made: for TIGR-1 and TIGR-2, index *I* only takes into account the information about vertical
temperature profiles, whereas the improvements in TIGR-3 mostly came from the combined use of vertical temperature and water-vapour concentration profiles.

(b) *Tests on a two-dimensional problem*

Assessing the quality of a sampling technique is rather difficult when dealing with a high-dimensional space. In order to visualize the qualities of the TIGR sampling methods, a simplified problem has been studied. For the initial set S, 450 000 tropical soundings have been used: they had been gathered originally for the setting up of TIGR-3. Instead of processing all the geophysical variables, only the mean temperature and the water-vapour content of the layer 850–1013 hPa have been kept. Let us call x the first variable and y the second one; x goes from 265 to 310 K, and y from very low values up to 4.5 cm.

Three sampling experiments are carried out on this reduced set, using three different topological sampling methods. The results are evaluated with regard to the histograms of the sampled datasets. Indeed, with the aim of gathering a data bank for regression parameter estimation, the histograms should be as regular as possible. Other applications of the sampling may need a different criterion, but this is not discussed here.

The first experiment reproduces the approach used for TIGR-1 and TIGR-2: only the information about temperature is taken into account. It will be referred to as A1. A1 uses the simple distance

$$D_1(s_i, s_j) = (x_i - x_j)^2, \quad (1)$$

where $s_i$ and $s_j$ represent two soundings i and j of the database S.

The A1 dissimilarity index is the following: to be archived in E, a situation (different from the initial one) has to satisfy:

$$\min_{s_j \in E} D_1(s_i, s_j) > d, \quad (2)$$

where d is an arbitrary parameter. Choosing d is equivalent to choosing n, the number of situations in the final database. In the following, n = 100.

Figure 1 shows the 100-class histograms of x and y in E after the sampling. An ideal method would have led to regular histograms: every class among the 100 would contain one and only one situation. This is nearly the case for x: 12 classes only are empty. Variable y is far more irregularly distributed with 55 empty classes, and includes no situation with layer water-vapour content in excess of 3 cm.

The second experiment, A2, is inspired by the unsuccessful attempt of Escobar-Munoz (1993) to introduce information about the water-vapour concentration into the selection. The algorithm is the same as in A1, but $D_1$ is replaced by $D_2$:

$$D_2(s_i, s_j) = \left\{ \left( \frac{x_i - x_j}{\sigma_x} \right)^2 + \left( \frac{y_i - y_j}{\sigma_y} \right)^2 \right\}^{1/2}, \quad (3)$$

where $\sigma_x$ ($\sigma_y$) is the standard deviation of the variable x (y), computed in the TIGR-2 database. With this normalization, the quantities of Eq. (3) are of the same order of magnitude.

Figure 2 shows the resulting histograms for x and y corresponding to the 100 selected situations. Compared to A1, A2 improves the partitioning of y, with only 37 empty classes and a coverage of the highest values, but clearly degrades that of x with 37 empty classes also. Although the two quantities $|(x_i - x_j)/\sigma_x|$ and $|(y_i - y_j)/\sigma_y|$ are normalized, their respective variability is too different to allow a satisfactory dissimilarity index to be obtained from their sum.

Thus, in a third approach, A3, the proximity recognition in the x space is separated from the one in the y space. This is the method used for TIGR-3 (Chevallier 1998). For each situation $s_i$ in selection phase, the two non-Euclidian distances are defined:

$$D_x^m(s_i, E) = \min_{s_j \in E} \left\{ \left( \frac{x_i - x_j}{\sigma_x} \right)^2 \right\}^{1/2}, \quad (4)$$

$$D_y^m(s_i, E) = \min_{s_j \in E} \left\{ \left( \frac{y_i - y_j}{\sigma_y} \right)^2 \right\}^{1/2}. \quad (5)$$

In each space, this algorithm looks for the nearest neighbour, by computing the minimum distance of the considered situation to the ones already archived in E, $D_x^m$ and $D_y^m$. Then the two minimum distances,
<figure><img src="image_2.png" /><figcaption>Figure 1. Histograms (100 classes) of x and y after the A1 sampling (see text).</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>Figure 2. Histograms (100 classes) of x and y after the A2 sampling (see text).</figcaption></figure>
<figure><img src="image_4.png" /><figcaption>Figure 3. Histograms (100 classes) of x and y after the A3 sampling (see text).</figcaption></figure>

separately computed, are added and the criterion of the minimum distance is applied to the sum

$$D_x^m(s_i, E) + D_y^m(s_i, E) > d. \quad (6)$$

This criterion enables a situation $s_i$ to be selected in three cases: if $x_i$ is different enough from the $x_j$'s already archived; or if $y_i$ is different enough from the $y_j$'s already archived; or if $x_i$ and $y_i$ are different enough from those already archived, even though none of the two differences is outstanding.

A hundred situations have been selected with A3. The histograms are shown in Fig. 3. Twenty-two classes are empty for x and 27 for y. This shows improvements compared to A2, with a more regular spread of the two variables.

There is no unique satisfactory sampling method. Different approaches yield results similar to those of A3 (Chevallier 1998). A good approach results in a compromise between the regular spread of x and that of y. Thus, the highest peak of the x histogram in Fig. 3 appears in the highest values of x, corresponding to the highest variability of y. Similarly, A3 tends to select the situations in the low values of the layer water vapour y, corresponding to the highest variability of the temperature x.

### (c) Update of the TIGR-3 sampling technique

In the previous example, only tropical-type situations have been considered. A wider range of soundings would not significantly change the conclusions, although it is obvious that the peaks of the histograms would be more pronounced: for instance, adding polar-type situations would increase the temperature variability in the low values of the water vapour. In order to smooth out the asymmetries, the initial heterogeneous database S can be divided into subgroups that are more homogeneous, and each subgroup is then sampled separately from the others. This approach is called 'stratified sampling' (e.g. Cochran 1977). The values of the $\sigma_x$'s and of the $\sigma_y$'s in Eqs. (4) and (5) have to be adapted for each subset. For TIGR-3, the initial database was divided into tropical and non-tropical situations. The classification relied on a statistical analysis performed on TIGR-2 (Achard 1991). Instead, as the natural variability of water vapour is much more heterogeneous than that of the temperature, and increases with the total water-vapour content, the initial database can be divided into subgroups, with respect to water-vapour contents only. For instance, one subset may contain the lowest values of the layer water vapour, a second one the highest values, and a third one the intermediate values. Then the final sampled database E results from
the merging of the three sampled subgroups. Such a division enables clear separation to be made between different ranges of variability of the water vapour.

Extrapolating results from the former two-dimensional problem to a 2 × N-dimensional problem, if N is the number of vertical layers in the soundings, is not trivial. Extending the A3 approach to vertical profiles, one can replace the distances given by Eqs. (4) and (5) by

$$D_{\theta}^{m}(s_i, E) = \min_{s_j \in E} \left\{ \sum_{k=1}^{N} \left( \frac{\theta_i(k) - \theta_j(k)}{\sigma_{\theta}(k)} \right)^2 \right\}^{1/2}, \quad (7)$$

$$D_{w}^{m}(s_i, E) = \min_{s_j \in E} \left\{ \sum_{k=1}^{N} \left( \frac{w_i(k) - w_j(k)}{\sigma_{w}(k)} \right)^2 \right\}^{1/2}, \quad (8)$$

where $\theta(k)$ and $w(k)$ are the mean temperature and mean water-vapour concentration, respectively, in layer k. They correspond to variables x and y of Eqs. (4) and (5).

The criterion of the minimum distance of Eq. (6) can be rewritten

$$D_{\theta}^{m}(s_i, E) + \mu D_{w}^{m}(s_i, E) > d, \quad (9)$$

where $\mu$ is a weight.

The standard deviations $\sigma_{\theta}(k)$ and $\sigma_{w}(k)$ in Eqs. (7) and (8) deal with the different ranges of the variables, whereas $\mu$ is introduced as a weight that takes into account the difference in the vertical variability of temperature on the one hand, and of water vapour on the other. In the following $\mu = 1/9$. Tests have shown that the characteristics of the sampled database do not depend critically on the precise value of $\mu$: for example, $\mu = 1/8$ gives results comparable to $\mu = 1/9$.

This technique is similar to the TIGR-3 approach, except that the TIGR-3 sampling took layer water-vapour contents into account, rather than water-vapour mixing ratios. This choice was influenced by the previous definition of a water-vapour distance by Flobert *et al.* (1986) for pattern recognition, but induced an arbitrary reduction of the information about the water-vapour profiles.

## 4. APPLICATION: NEW DATABASES FROM THE ECMWF MODEL OUTPUTS

Given a large database of samples S, covering a wide range of atmospheric water-vapour and temperature profiles, the approach described above enables the selection of a smaller sample E, the size of which is determined by the factor d. It has been used for the sampling of profiles generated from the ECMWF atmospheric model. Two databases have been gathered in this way. The first one corresponds to the 31-layer vertical grid (from the top of the atmosphere to the surface) that has been used at ECMWF between 1991 and 1999. The second one uses the 50-layer vertical grid, with increased resolution in the stratosphere, that was introduced into operation at ECMWF in March 1999.

In this application, S (either $S_{31}$ or $S_{50}$) mainly results from the aggregation of twelve days of profiles from the ECMWF short-range forecasts. Each day is selected from a different month's worth of data. The database includes a complete description of the atmosphere on the corresponding vertical grid (31 or 50 levels) and on a horizontal 1.125° × 1.125° grid for the four synoptic times (00, 06, 12 and 18 UTC). Both $S_{31}$ and $S_{50}$ consist of about 1500 000 profiles. They are divided into seven subgroups differing by the total precipitable water-vapour content of the profiles: the first group ranges from 0 to 0.5 cm, the second from 0.5 to 1.5 cm, the third from 1.5 to 2.5 cm, and so on, until the seventh one that goes from 5.5 cm up to the highest values. In each group and for each vertical resolution, the standard deviations, i.e. the $\sigma_{\theta}$'s and the $\sigma_{w}$'s of Eqs. (7) and (8), are directly computed.

The sampling approach described in section 3(c) is used for the extraction of about the same number (n) of samples from each class, except for the first one, where twice as many (2 × n) profiles are extracted, in consideration of the higher temperature variability: this class includes all types of situations from polar to tropical. The density of the sampled database is determined by n. For the 31-level database, n = 750 was chosen. For the 50-level database, n = 1700 was chosen. The whole sampled databases include respectively about 6000 and 13 500 profiles. It should be noted that the sampling is performed on the ECMWF model vertical layers and not on fixed pressure layers. As a consequence, the sampled databases gather profiles corresponding to various ocean conditions as well as to land conditions, including high elevated ground.

Figure 4 shows the histograms of the 31-level sampled database in layer 6, characterized by a mean pressure of about 800 hPa when the surface pressure equals 1000 hPa. Two symmetric peaks appear as in Fig. 3. As explained in section 3(b), the wing in the temperature (water-vapour) histogram, between 220 and 270 K (0.002 and 0.012 g g⁻¹), illustrates the weak variability of water vapour (temperature) in the
<figure><img src="image_5.png" /><figcaption>Figure 4. Histograms (100 classes) of (a) temperature (K) and (b) water-vapour concentration (g g⁻¹) in the database sampled using criterion A3 (section 3(b)) from ECMWF generated profiles, on a 31-level vertical grid in layer 6 (see text).</figcaption></figure>

temperature (water-vapour) range in the initial set S. Since the stratified sampling forced the representation of high water-vapour contents (see section 3(c)), the wing in the water-vapour histogram is more regular than that in the temperature histogram.

The qualities of these new sampled database have been estimated in the framework of NeuroFlux, the neural-network-based LW radiative-flux profile computation model. The various results are presented in Chevallier *et al.* (2000).

## 5. CONCLUSION

Collecting pertinent, i.e. properly sampled, a priori information about the atmosphere is an essential need for atmospheric modelling. An important step has been the construction of the TIGR database. In this paper, the characteristics of successive versions developed at LMD since 1983 were summarized. A flexible sampling method was defined, based on the approach used in the latest TIGR database, TIGR-3. It is being applied to the development of TIGR-type databases adapted to applications involving a higher vertical variability than TIGR-3. In addition to the 31-level and 50-level ECMWF databases presented here, ongoing work concerns the forthcoming 60-level ECMWF model, with increased vertical resolution in the boundary layer. As shown in a companion paper (Chevallier *et al.* 2000), these databases are applied to NeuroFlux, a neural-network-based long-wave radiative-transfer model (Chéruy *et al.* 1996; Chevallier *et al.* 1998b). In the same way, other databases are needed for application to the retrieval of thermodynamic variables from the IASI and Advanced Infrared Radiometric Sounder (AIRS) instruments. They could simply be derived by interpolating the 50-level ECMWF database, or the 60-level one once it is available, to a coarser grid.
ACKNOWLEDGEMENTS

The authors are grateful to N. A. Scott for very fruitful discussions and to R. Armante for substantial help in the design of the TIGR-3 database at LMD. They also wish to thank M. Miller for careful review of the manuscript.

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