# Use of a neural-network-based long-wave radiative-transfer scheme in the ECMWF atmospheric model

F. Chevallier, J.-J. Morcrette, F. Chéruy, N. Scott

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F. Chevallier, J.-J. Morcrette, F. Chéruy, N. Scott. Use of a neural-network-based long-wave radiative-transfer scheme in the ECMWF atmospheric model. Quarterly Journal of the Royal Meteorological Society, 2000, 126 (563), pp.761-776. 10.1002/QJ.49712656318. hal-02947766

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# Use of a neural-network-based long-wave radiative-transfer scheme in the ECMWF atmospheric model

By F. CHEVALLIER¹*, J.-J. MORCRETTE¹, F. CHÉRUY² and N. A. SCOTT²

¹European Centre for Medium-Range Weather Forecasts, UK

²Laboratoire de Météorologie Dynamique, France

(Received 12 March 1999; revised 8 July 1999)

## SUMMARY

The definition of an approach for radiative-transfer modelling that would enable computation times suitable for climate studies and a satisfactory accuracy, has proved to be a challenge for modellers. A fast radiative-transfer model is tested at ECMWF: NeuroFlux. It is based on an artificial neural-network technique used in conjunction with a classical cloud approximation (the multilayer grey-body model). The accuracy of the method is assessed through code-by-code comparisons, climate simulations and ten-day forecasts with the ECMWF model. The accuracy of NeuroFlux appears to be comparable to the accuracy of the ECMWF operational scheme, with a negligible impact on the simulations, while its computing time is seven times faster.

KEYWORDS: Artificial neural networks General-circulation models Long-wave radiative transfer

## 1. INTRODUCTION

Parametric representation, or parametrization, is used in the numerical modelling of various atmospheric processes. It usually involves a statistical analysis that enables the representation of the true processes by simpler parametric relations. Three purposes may motivate such an analysis: (i) getting a better understanding of the system (e.g. Bretherton et al. 1992); (ii) allowing a computation of the processes that is faster than the exact formulation (as in numerous radiative-transfer models—Goody and Yung 1989); (iii) obtaining a simpler system without having to deal with the complicated details (as in precipitation schemes; e.g. Sundqvist 1981).

The most accurate as well as the fastest long-wave (LW) radiative-transfer schemes include parametrized components. For instance, the current line-by-line computations take into account every absorption line from every absorbing gas, but usually do not exactly resolve the contribution of the line wings after a few tens of $cm^{-1}$ off the centre of the lines. The absorption coefficients outside this interval are parametrized under the form of structureless continua, whose contribution to the radiation variations is essential (e.g. Clough et al. 1992; Sinha and Harries 1997). The high computational burden of the line-by-line codes prevents their use for most climatic studies and leads to the use of more heavily parametrized schemes. However, because a minimum accuracy is required, the resulting gain in computing time is still not sufficient, and therefore many general-circulation models (GCMs) reduce the frequency of radiation computations, compared to the other diabatic computations. This degrades the quality of the climate simulations (Wilson and Mitchell 1986; Morcrette 2000).

The interactions between LW radiation on the one hand and solid and liquid water on the other hand, add further difficulties to the atmospheric modelling. Indeed, the computational burden of the most accurate approaches limits their applicability, and furthermore, it is seldom that all the required input variables are available. This is obvious in GCMs, where the subgrid processes, like the distribution of the cloud particles in a vertical layer, are crudely treated. Some approximations are necessary to deal with this lack of knowledge.

<footnote>* Corresponding author: European Centre for Medium-Range Weather Forecasts, Shinfield Park, Reading, Berkshire RG2 9AX, UK. e-mail: chevallier@ecmwf.int</footnote>
The parametrizations, the temporal sampling and the approximations lead to significant uncertainties in climate studies and in weather forecasts. Therefore, improvement of the LW radiative codes is a key objective for atmospheric modelling. An original approach has been initiated at Laboratoire de Météorologie Dynamique (LMD) (Chéruy *et al.* 1996; Chevallier *et al.* 1998b). It makes use of an artificial neural-network technique: the multilayer perceptron (MLP) as defined by Rumelhart *et al.* (1986). It has been carried out in a highly parameterized scheme called NeuroFlux, that combines the MLP with a classical cloud approximation (the multilayer grey-body model) (Washington and Williamson 1977). All the parameters in NeuroFlux, several tens of thousands, are inferred from a series of learning data banks during supervised learning phases (Chevallier *et al.* 1998b). The neural-network-based method enables fast computing times: on a 19 vertical-layer grid, a gain in computation time of at least one order of magnitude compared to the operational code at the European Centre for Medium-Range Weather Forecasts (ECMWF) has been recorded. Concerning the accuracy, satisfactory results of code-by-code comparisons between NeuroFlux and other radiative-transfer models, were obtained (Chevallier *et al.* 1998b). Preliminary tests of NeuroFlux in the LMD GCM (Sadourny and Laval 1984) led to further developments of the method (Chevallier *et al.* 1998a; Chevallier *et al.* 2000).

This paper presents the results of the testing of NeuroFlux in the ECMWF GCM in its 31 vertical-layer configuration. It is structured as follows. Section 2 describes the neural-network-based radiative-transfer model. Section 3 presents its instantaneous error through code-by-code comparisons with the ECMWF operational scheme (Morcrette 1991; Zhong and Haigh 1995). The impact of NeuroFlux on climate simulation is evaluated in section 4. Comparisons of the simulations with ECMWF analyses of the atmosphere and with observations are used in section 5 to give a quantitative estimation of the uncertainty introduced. Section 6 contains the conclusions.

## 2. PRINCIPLES OF NEUROFLUX

### (a) *The multilayer perceptron*

An MLP (Rumelhart *et al.* 1986) is an artificial neural network that realizes a nonlinear application from an input space to an output space. The information is propagated from its inputs to its outputs by nonlinear projections on successive spaces, that transform and filter it. Each variable of the various spaces is computed by a nonlinear (sigmoidal) transformation of a weighted sum of the variables from the previous space. The weights of the sums are the parameters of the MLP. They are inferred once and for all during a supervised learning. A nonlinear regression, based on a gradient descent, iteratively adapts the parameters of the projections, so that together they achieve an optimal transformation from the inputs of the learning dataset to its outputs. It should be noted that, because of this statistical technique, the choice of the learning dataset is of crucial importance for the accuracy of the multilayer perceptron parametrization. The gradient descent technique requires the sigmoidal function to be differentiable. Furthermore, the existence of horizontal asymptotes are important to avoid the propagation of high values in the MLP. In the following, the sigmoidal functions are the widely used hyperbolic tangent.

The simple structure of the MLP enables fast computing time for the MLP relative to its number of parameters; therefore, the MLP is an interesting tool for parametrization. The MLP could be used at various stages in parametrized radiative computations, for example for the computation of transmissions or for the whole flux computations.
(d) *The learning datasets*

The choice of the learning datasets has been the most involved part in the develop-
ment of the neural-network-based radiative-transfer model. Indeed, because of the high
level of parametrization in NeuroFlux, the accuracy of the scheme dramatically depends
on their statistical characteristics. In the results presented here, the learning datasets are
based on a 6000 profile set: this comes from the sampling of 1 350 000 atmospheric
situations from the ECMWF short-range forecasts. The method is detailed in Chevallier
et al. (2000). The 6000 soundings are represented by temperature and water-vapour
profiles. Among the variables that are necessary for the radiative computations, some are
not archived in the set: the ozone and cloudiness profiles, the mean CO2 concentration
and the surface temperature and emissivity. The ozone profiles have been added from a
climatology dependent on season and latitude (Fortuin and Langematz 1994). The mean
CO2 concentration, the surface temperature and LW emissivity in the window region
have been introduced by random sampling between selected boundaries, ensuring regu-
lar partitions desirable for the MLP learning. For instance, the CO2 concentrations range
between 200 and 900 parts per million by volume, so that NeuroFlux can be applied to
CO2-doubling experiments (Chevallier et al. 1998b). As the NN-Clr's and the NN-Cld's
differ altogether in the position of the cloud layer among the 31 possible, the cloudiness
simply derives from the learning dataset considered: the learning dataset of the NN-
Clr's include the 6000 soundings without any cloud, whereas the other learning datasets
include the same 6000 soundings, associated with the systematic presence of a black
body in a particular layer. Due to these techniques, the learning sets contain atmospheric
situations that may never be observed in the atmosphere: they are not compilations of
real atmospheric situations, but are derived to teach the networks the computation of
LW radiative fluxes from thermodynamic profiles. For this purpose, it is appropriate
that a physical phenomenon, like the presence of a cloud in the atmospheric layers, has
a regular rather than a realistic distribution in the learning datasets.

In the present study, the ECMWF operational LW code (Morcrette 1991; Zhong and Haigh 1995) was used to compute the radiative characteristics of these soundings (the $F_k^\uparrow$ s and the $F_k^\downarrow$ s, $k \ge 0$). In the following, it will be referred to as 'EC-OPE'. Any other LW radiative-transfer model can be chosen, including a line-by-line code: the learning phases are the most time-consuming step of NeuroFlux, but they are run only once. The routine utilization of NeuroFlux is computationally cheap.

(e) *Validation method*

A new version of NeuroFlux has been set up with these learning datasets. Compared to EC-OPE, it is seven times faster (mean computing time recorded on a Fujitsu VPP700 in the framework of a ten-day forecast). If NeuroFlux was a perfect simulator, the result of its computations would be identical to the result of EC-OPE computations. In fact, the neural-network parametrization introduces a small uncertainty in the fluxes and cooling rates. This has been studied from three points of view: in terms of errors in cooling rates and fluxes, in terms of long-term (four months) climate simulations, and in terms of forecast accuracy. For the last two points, the methodology follows the approach of Morcrette *et al.* (1998) who studied the impact of the change of radiative-transfer model to Rapid Radiative Transfer Model (RRTM) (Mlawer *et al.* 1997) in the ECMWF GCM.

3. VALIDATION OF NEUROFLUX THROUGH CODE-BY-CODE COMPARISONS

The code-by-code comparisons are based on the ECMWF forecast archive of
profiles. A series of comparisons has been performed, in which radiative fluxes obtained
<figure><img src="image_2.png" /></figure>

<figure><img src="image_3.png" /></figure>

<figure><img src="image_4.png" /><figcaption>Figure 1. Comparison between the computations of NeuroFlux and those of EC-OPE: cooling rates from NeuroFlux minus cooling rates from EC-OPE (K d⁻¹). ECMWF six-hour forecasts, L31 T319; 00, 06, 12 and 18 UTC 1 June 1998. Results are shown in three latitude classes. (a) The biases and (b) the standard deviations, in each latitude class. (c) The maximum absolute differences. Model-layer 1 is the highest layer and model-layer 31 is the lowest.</figcaption></figure>

by using NeuroFlux and by using EC-OPE have been compared for the whole globe. They differ in the characteristics of the ECMWF forecast model used to produce the archived profiles (assimilation scheme, horizontal resolution, physical and dynamical parametrizations) and in the corresponding dates (year as well as month). Because all comparisons yield similar results, only one example is presented here. It corresponds to the global archives from 1 June 1998 for the four synoptic times (00, 06, 12 and 18 UTC) and at operational resolution 0.5625° × 0.5625°: 800 000 atmospheric situations. Results are presented in three latitude classes. The tropical class covers the 30°N–30°S region; the mid-latitude class covers the 60°N–30°N region and the symmetrical band in the southern hemisphere; the polar class covers the 30° bands surrounding the two poles. For the three latitude classes, the biases and standard deviations of the differences between the radiative calculations of NeuroFlux and those of EC-OPE were computed, as well as the maximum absolute differences. Results for LW cooling rates are shown in Fig. 1.

The standard deviations and the absolute biases are less than 0.4 K d⁻¹ and 0.2 K d⁻¹, respectively, except in the lower layer where the standard deviation is around 1.4 K d⁻¹ and the bias around 0.3 K d⁻¹. The maximum instantaneous error reaches
<table><caption>TABLE 1. MEAN (M), STANDARD DEVIATION (σ) AND ABSOLUTE MAXIMUM DIFFERENCE (MD) OF THE COMPARISONS BETWEEN NEUROFLUX AND EC-OPE FOR THE COMPUTATION OF THE OLR, AND THE NET FLUX AT THE SURFACE (NFS; NEUROFLUX MINUS EC-OPE). ECMWF SIX-HOUR FORECASTS, L31 T319, 00, 06, 12 AND 18 UTC 1 JUNE 1998. RESULTS ARE SHOWN IN THREE LATITUDE CLASSES.</caption><thead><tr><th rowspan="2"></th><th colspan="3">Polar</th><th colspan="3">Mid-latitude</th><th colspan="3">Tropical</th></tr><tr><th>M</th><th>σ</th><th>MD</th><th>M</th><th>σ</th><th>MD</th><th>M</th><th>σ</th><th>MD</th></tr></thead><tbody><tr><td>OLR</td><td>0.28</td><td>0.85</td><td>4.84</td><td>-0.06</td><td>0.77</td><td>4.85</td><td>-0.16</td><td>0.89</td><td>7.17</td></tr><tr><td>NFS</td><td>0.76</td><td>1.72</td><td>8.07</td><td>0.16</td><td>1.06</td><td>6.83</td><td>-0.12</td><td>0.88</td><td>9.34</td></tr></tbody></table>

Fluxes are in W m⁻².

See text for further explanation.

10 K d⁻¹. The higher standard deviation for the cooling rates in the lowest layer also exists when the test is performed on the training database (result not shown). Sensitivity tests have shown that it originates from the correlation between surface temperature and surface air temperature. Such a problem could be reduced with more complex neural networks, but the code would then be computationally less efficient. Its impact on atmosphere simulation is examined in the following. Similar statistics are presented for the outgoing long-wave radiation (OLR) and the surface net flux in Table 1. Standard deviations and absolute biases are less than 1.7 W m⁻² and 0.8 W m⁻², respectively. Maximum values reach 7 W m⁻² for the OLR and 9 W m⁻² for the surface net flux. The results of the validation are similar when the clouds are not taken into account in the radiative computations (not shown).

The most erroneous cases for NeuroFlux obviously correspond to situation types that are less represented in the initial 1 350 000 sounding database, from which the learning datasets have been taken (see section 2(d)), in particular some cases of high elevation. Further reduction of the error maxima will follow from the extension of the initial database.

To the authors' knowledge, no radiative transfer has been validated with reference computations on such a high number of soundings. In particular, the maximum errors produced by EC-OPE, with reference to the real values, are not known. They are expected to be larger in a cloudy sky, because of the weakness of the cloud radiative-transfer parametrization, shared by most of today's radiative-transfer codes. As a consequence, the errors of NeuroFlux come in addition to those of EC-OPE that are not known. Nevertheless, the availability of such an exhaustive documentation of the errors of NeuroFlux compared to EC-OPE leads one to wonder about their impact on GCM simulations. This is explored in details in the following sections.

# 4. VALIDATION OF NEUROFLUX THROUGH CLIMATE SIMULATIONS

## (a) Methodology

The assessment of the impact of NeuroFlux in climate simulations has been performed as follows. An ensemble of ten members of four-month forecasts were run with initial dates between 21 and 30 April 87. Cycle 18r5 of the ECMWF model has been used, with a T63 truncation, equivalent to a 1.875° × 1.875° horizontal resolution. T63 is the usual configuration at ECMWF for extended-range studies, even though operational forecasts use a finer grid (0.5625° × 0.5625°). Indeed, Tibaldi *et al.* (1990) showed that T63 was sufficiently fine for climate studies. The short-wave radiation transfer in the GCM is based on Fouquart and Bonnel (1980) (Morcrette 1991). Since the atmosphere has a strong chaotic behaviour, the simulations have been studied as means
<figure><img src="image_5.png" /><figcaption>Figure 2. (a) The difference between the clear-sky outgoing long-wave radiation (OLR) averaged over ten simulations and over three months, with the ECMWF GCM using NeuroFlux or EC-OPE (simulations using NeuroFlux minus simulations using EC-OPE). The OLR is in W m⁻². Contours every 2 W m⁻². Negative values less than -2 W m⁻² are dark-shaded, positive values greater than 2 W m⁻² are light-shaded. (b) The result of a Student's t-test of statistical significance: values greater than 0.95 are shaded. (c) The OLR values for EC-OPE, with contours every 20 W m⁻².</figcaption></figure>

over the three-month period between 1 June and 30 August 87 and over the ten-member ensemble.

(b) *LW fluxes at the boundaries and cloudiness*

For the three-month average, the impact of NeuroFlux on the clear-sky OLR (Fig. 2) is mostly under 2 W m⁻², which is comparable to the uncertainty in the instantaneous OLRs from NeuroFlux (1 W m⁻², see Table 1). Limited areas display stronger impact, but still under 5 W m⁻². The Student's t-test performed on the data shows that in most of the regions where the differences are statistically significant, these are under
(a)

<figure><img src="image_6.png" /></figure>

(b)

<figure><img src="image_7.png" /></figure>

(c)

<figure><img src="image_8.png" /><figcaption>Figure 3. As in Fig. 2, but for the full-sky OLR, in W m⁻².</figcaption></figure>

2 W m⁻² (Fig. 2(b)). By comparison, the recent change of the surface emissivity in the LW window region (800–1250 cm⁻¹) from 0.99 to 0.93 for the desert regions in the ECMWF GCM (Gregory *et al.* 1998) affected the clear-sky OLR by more than 5 W m⁻² over the corresponding regions in the same conditions of experiment.

The differences are stronger when the clouds are taken into account in the OLR (Fig. 3), though remaining under 14 W m⁻². This is not surprising since cloud models use step functions: small differences in temperature or water vapour can make clouds appear or disappear. Indeed, as shown in Fig. 4, the simulations using NeuroFlux are marked by a small decrease (between 0.01 and 0.03 on an average) of high-level cloud cover in the Inter-Tropical Convergence Zone (ITCZ). This is associated with the increase in full-sky OLR in the same region on an average (Fig. 3). As far as the other latitudes are concerned, the impact of NeuroFlux on cloud cover appears to be
<figure><img src="image_9.png" /><figcaption>Figure 4. (a) The difference between the vertical distribution of the zonally averaged cloud cover, averaged over ten simulations and over three months, with the ECMWF GCM using NeuroFlux or EC-OPE (simulations using NeuroFlux minus simulations using EC-OPE). The cloud cover is in %. Contours every 2%; negative values less than -1% are dark-shaded, positive values greater than 1% are light-shaded. In the shaded areas, only the differences in the Tropics are statistically significant at the 95% confidence level. (b) The cloud cover values for EC-OPE with contours every 5%.</figcaption></figure>

rather limited, to 0.01, with a maximum at 0.06. The differences for the surface net flux, shown in Fig. 5, corroborates the results concerning the OLR.

(c) *Impact of the temporal resolution of the radiative computations*

One of the main motivations in the development of NeuroFlux has been the interest in fast codes that could resolve the diurnal cycle better than existing codes. As an example, in the ECMWF model the full radiation code is called every three hours whereas the ‘time-step’ for the rest of the model varies from 20 minutes for the operational model to one hour for the seasonal simulations. Morcrette (2000) showed that the main impact of this reduced computation frequency is a decrease in the convection and therefore of the high-level cloudiness in the Tropics. Climate simulations, however, incorporate this artificial signal, even though this missing cloudiness tends to warm the stratosphere and cool the troposphere, and therefore degrades the climate-sensitivity studies.

The question arises as to whether the accuracy of NeuroFlux is enough to restore the right climatic signal if NeuroFlux is called more often in the simulations. In order to answer this question, the following experiment has been conducted. The ensemble simulations using either NeuroFlux or EC-OPE have been repeated with a time-step of 60 minutes for the radiation instead of three hours. Because NeuroFlux is seven times faster than EC-OPE, even this configuration using NeuroFlux is cheaper than the current configuration with EC-OPE and a three-hour time-step. Figure 6 shows some of the differences when the time-step is changed, with either NeuroFlux (Fig. 6(a)) or
<figure><img src="image_10.png" /></figure>

<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /><figcaption>Figure 5. As in Fig. 2, but for the net flux at the surface, in W m⁻².</figcaption></figure>

EC-OPE (Fig. 6(b)). As stated earlier, the main signal induced by the full radiation time-step change is the high-level cloudiness in the ITCZ. This signal is correctly captured by NeuroFlux. Even though differences in the detailed structures can be noted for smaller parts of the signal, the uncertainty introduced by NeuroFlux in the cloud-cover simulations appears to be far smaller than the one induced by the reduced frequency of radiative computation in the climate simulations.

## 5. IMPACT OF NEUROFLUX ON FORECAST ACCURACY

The quality of the simulations using NeuroFlux has also been evaluated by comparison with analyses of the atmosphere, expressed in objective scores. Two ensembles of twelve ten-day forecasts, starting on the 15th of each month from 15 April 1997 to 15 March 1998, have been gathered. The LW model, either NeuroFlux or EC-OPE, is
<figure><img src="image_13.png" /><figcaption>Figure 6. Difference between the vertical distribution of the zonally averaged cloud cover, in %, with the ECMWF GCM using (a) NeuroFlux or (b) EC-OPE, and a radiation time-step of either three hours or one hour (version with three hours minus version with one hour). Contours every 1%; negative values less than -0.5% are dark-shaded, positive values greater than 0.5% are light-shaded. In the shaded areas, only the differences shown at latitudes 0° and 35°N are statistically significant at the 95% confidence level.</figcaption></figure>

the only difference between the sets. The radiative 'time-step' is set to three hours in both sets, as in the operational model. The horizontal resolution corresponds to a T213 truncation. Figure 7 presents the scores for the northern hemisphere, defined as the region between 20°N and 90°N. Similar results have been obtained for the tropical band, and for the southern hemisphere. The impact of NeuroFlux appears to be negligible on the 500 hPa and 1000 hPa geopotentials, as well as on the temperature at 850 hPa, 500 hPa, 200 hPa and 50 hPa. For instance, the mean differences for the temperature are of the order of a hundredth of a degree without exhibiting any significant trend.

Because the instantaneous error of NeuroFlux is higher in the lower layer (Fig. 1), special attention has been paid to the quality of the 2 m temperature forecast. We illustrate this study with the ten-day forecast for the 25 January 1998. Figures 8 and 9 display the difference between the two forecasts and the corresponding observations over Europe at 12 UTC. Biases, around 1.4 K, and standard deviation, around 3.5 K, are similar for the two forecasts. In this particular case, NeuroFlux even performs slightly better. This result illustrates that the uncertainty introduced by NeuroFlux in the GCM simulation, of the order of 1 K or less for the ten-day forecast of the 2 m temperature, does not make the simulation diverge from the real atmosphere, as far as the 2 m temperature is concerned. It corroborates, from a different point of view, the study of the scores that relies on zonal means and on a statistical ensemble.
<figure><img src="image_14.png" /></figure>

<figure><img src="image_15.png" /></figure>

<figure><img src="image_16.png" /></figure>

<figure><img src="image_17.png" /></figure>

<figure><img src="image_18.png" /></figure>

<figure><img src="image_19.png" /><figcaption>Figure 7. T213 L31 simulations. Forecast verification for northern hemisphere: (a) and (b) geopotential, and (c)–(f) temperature. The geopotential verification is expressed in terms of anomaly correlations, and the temperature verification in terms of temperature biases. Mean over 12 cases.</figcaption></figure>

## 6. CONCLUSIONS

The structure of the ECMWF operational LW radiative-transfer code, based on the work of Morcrette (1984, 1991), has proved to be suitable for incorporating recent important developments in radiative transfer, such as those on water-vapour continuum (Zhong and Haigh 1995) and cloudiness (Raïsänen 1998). However, as with other radiative-transfer models used in GCMs, because of computational costs, it is still necessary to apply both a spatial and a temporal sampling in the usual climate simulations. This code has been parametrized through the neural-network-based approach developed by Chéruy *et al.* (1996) and Chevallier *et al.* (1998b). This new radiative-transfer code, called NeuroFlux, was shown to be seven times faster than the original code. The evaluation of the error introduced in the climate simulations by this approach, compared to the original code, is painstaking work because of the numerous possible points of view for its validation. This paper illustrates the chosen validation methodology. Firstly, code-by-code comparisons have quantified the instantaneous error of NeuroFlux. Then the impact of this error on climate simulation has been estimated through four-month simulations, with emphasis on long-wave boundary fluxes and cloudiness. Finally, the qualitative estimation of this error has been made by comparisons of ten-day forecasts
<figure><img src="image_20.png" /><figcaption>Figure 8. Ten-day forecast for 12 UTC 25 January 98, using EC-OPE. Validation of the 2 m temperature forecast with observations. The difference between the forecast 2 m temperature and the observed one (K) is printed for each station. The mean of the differences is 1.53 K, and the standard deviation is 3.55 K.</figcaption></figure>

with ECMWF analyses of geopotential and atmospheric temperature on the one hand, and surface observations of 2 m temperature on the other. Through these various studies, the accuracy of NeuroFlux appears to be comparable to the accuracy of the original scheme, with a negligible impact on the simulations. The use of NeuroFlux in a six-day forecast-assimilation process has confirmed the various results reported here: the departure of the background forecasts as well as of the analyses from the observations appear to be the same with NeuroFlux as with the operational configuration (result not shown). All the results presented here concern the ECMWF 31-level model. The adaptation of NeuroFlux to the ECMWF 50-level model with increased vertical resolution in the stratosphere shows similar results compared to EC-OPE, both in terms of accuracy and in terms of computing time (results not shown).
<figure><img src="image_21.png" /><figcaption>Figure 9. As in Fig. 8, but with NeuroFlux. The mean difference with the observations is 1.38 K, and the standard deviation is 3.51 K.</figcaption></figure>

These satisfactory results rely on the high representativity of the NeuroFlux training sets. In particular, the variability of these databases is far larger than the expected changes of the atmospheric variables during the next century (e.g. Houghton *et al.* 1990). This enables NeuroFlux to be used for climate studies, as already stressed by Chevallier *et al.* (1998b).

The potential of the neural-network-based approach has not yet been fully used at ECMWF. In particular, as shown by Chevallier *et al.* (1998b), the use of a more accurate radiative-transfer code in the learning phase, like a line-by-line model or RRTM for instance (Mlawer *et al.* 1997), would reduce the current biases of EC-OPE in the clear-sky contribution to the fluxes, while keeping the same reduced computational burden. The various tests that we performed tend to show that the standard deviations of NeuroFlux compared to the original code, whatever it is, can not be further reduced,
though they do not appear to affect the simulations. The cloud parametrization, that is classically formulated in NeuroFlux (Washington and Williamson 1977) obviously brings much more uncertainty to the code, although quantifying this is rather difficult, because of the lack of observations of radiative-cooling rates.

Even without any further improvement, NeuroFlux appears to be suitable for two main applications in atmospheric studies. The first one is the reduction of the cost of the radiative computations in atmospheric models, like those used in ensemble predictions, coupled atmosphere-ocean simulations, or four-dimensional variational assimilation, for extended use of these models. The second application is the improvement of the climate simulations if the computational savings are used to increase the radiative computation frequency in the GCMs. Indeed, we showed that the uncertainty introduced in the simulations by NeuroFlux is negligible compared to the effect in an increase of the radiation time-step in the GCMs, as studied by Wilson and Mitchell (1986) and Morcrette (2000).

ACKNOWLEDGEMENTS

The authors wish to thank M. Miller and A. Beljaars for careful review of the manuscript.

REFERENCES

<table><tbody><tr><td>Bretherton, C. S., Smith, C. and Wallace, J. M.</td><td>1992</td><td>An intercomparison of methods for finding coupled patterns in climate data. J. Climate, 5, 541-560</td></tr><tr><td>Chéruy, F., Chevallier, F., Morcrette, J.-J., Scott, N. A. and Chédin, A.</td><td>1996</td><td>Une méthode utilisant les techniques neuronales pour le calcul rapide de la distribution verticale du bilan radiatif thermique terrestre. C. R. Acad. Sci. Paris, 322, 665-672</td></tr><tr><td>Chevallier, F., Chéruy, F., Li, Z. X. and Scott, N. A.</td><td>1998a</td><td>'A fast and accurate neural network-based computation of long-wave radiative budget: Application in a GCM'. Pp. 690-693 in Proceedings of the Sixth conference on satellite meteorology and oceanography. 25-29 May 1998, Paris. American Meteorological Society</td></tr><tr><td>Chevallier, F., Chéruy, F., Scott, N. A. and Chédin, A.</td><td>1998b</td><td>A neural network approach for a fast and accurate computation of longwave radiative budget. J. Appl. Meteorol., 37, 1385-1397</td></tr><tr><td>Chevallier, F., Chédin A., Chéruy, F. and Morcrette, J.-J.</td><td>2000</td><td>TIGR-like atmospheric-profile databases for accurate radiative-flux computation. Q. J. R. Meteorol. Soc., 126, 777-785</td></tr><tr><td>Clough, S. A., Iacono, M. J. and Moncet, J.-L.</td><td>1992</td><td>Line-by-line calculations of atmospheric fluxes and cooling rates: application to water vapor. J. Geophys. Res., 97, 15761-15785</td></tr><tr><td>Ebert, E. E. and Curry, J. A.</td><td>1992</td><td>A parametrisation of ice cloud optical properties for climate models. J. Geophys. Res., 97, 3831-3836</td></tr><tr><td>Fortuin, J. P. F. and Langematz, U.</td><td>1994</td><td>An update on the global ozone climatology and on concurrent ozone and temperature trends. Proceedings SPIE, 2311, 207-216</td></tr><tr><td>Fouquart, Y. and Bonnel, B.</td><td>1980</td><td>Computation of solar heating of the Earth's atmosphere: A new parameterization. Beitr. Phys. Atmos., 53, 35-62</td></tr><tr><td>Geleyn, J.-F. and Hollingsworth, T.</td><td>1979</td><td>An economical and analytical method for the computation of the interaction between scattering and line absorption of radiation. Beitr. Phys. Atmos., 52, 1-16</td></tr><tr><td>Goody, R. M. and Yung, Y. L.</td><td>1989</td><td>Atmospheric radiation. Theoretical basis. Oxford University Press</td></tr><tr><td>Gregory, D., Morcrette, J.-J., Jakob, C. and Beljaars, A.</td><td>1998</td><td>Introduction of revised radiation, convection, cloud and vertical diffusion schemes into Cy18r3 of the ECMWF integrated forecasting system. ECMWF Technical Memorandum No. 254 (available from ECMWF, Shinfield Park, Reading, Berks RG2 9AX, UK)</td></tr><tr><td>Houghton, J. T., Jenkins, G. J. and Ephraums, J. J.</td><td>1990</td><td>Climate change. The IPCC scientific assessment. Cambridge University Press</td></tr></tbody></table>
<table>
  <tbody>
    <tr>
      <td>Mlawer, E. J., Taubman, S. J., Brown, P. D., Iacono, M. J. and Clough, S. A. Morcrette, J.-J.</td>
      <td>1997</td>
      <td>Radiative transfer for inhomogeneous atmospheres: RRTM, a validated correlated-k model for the longwave. J. Geophys. Res., 102, 16663-16682</td>
    </tr>
    <tr>
      <td></td>
      <td>1984</td>
      <td>'Sur la paramétrisation du rayonnement dans les modèles de circulation générale atmosphérique'. PhD thesis, University of Lille</td>
    </tr>
    <tr>
      <td></td>
      <td>1991</td>
      <td>Radiation and cloud radiative properties in the European Centre for Medium-Range Weather Forecasts forecasting system. J. Geophys. Res., 96, 9121-9132</td>
    </tr>
    <tr>
      <td></td>
      <td>2000</td>
      <td>On the effects of the temporal and spatial sampling of radiation fields on the ECMWF forecasts and analyses. Mon. Weather Rev. (in press)</td>
    </tr>
    <tr>
      <td>Morcrette, J.-J., Clough, S. A., Mlawer, E. J. and Iacono, M. J.</td>
      <td>1998</td>
      <td>Impact of a validated radiative transfer scheme, RRTM, on the ECMWF model climate and 10-day forecasts. ECMWF Technical Memorandum No. 252. (Available from ECMWF, Shinfield Park, Reading, Berks RG2 9AX, UK)</td>
    </tr>
    <tr>
      <td>Räisänen, P.</td>
      <td>1998</td>
      <td>Effective longwave cloud fraction and maximum-random overlap clouds—a problem and a solution. Mon. Weather Rev., 126, 3336-3340</td>
    </tr>
    <tr>
      <td>Rumelhart, D. E., Hinton, G. E. and Williams, R. J.</td>
      <td>1986</td>
      <td>Learning internal representations by error propagation. Pp. 318-362 in Parallel distributed processing: Explorations in the macrostructure of cognition 1. Eds. Rumelhart and McClelland. MIT Press</td>
    </tr>
    <tr>
      <td>Sadourny, R. and Laval, K.</td>
      <td>1984</td>
      <td>January and July performances of the LMD general circulation model. Pp. 173-198 in New perspectives in climate mod-elling. Eds. Berger and Nicolis. Elsevier, Amsterdam</td>
    </tr>
    <tr>
      <td>Sinha, A. and Harries, J. E.</td>
      <td>1997</td>
      <td>The Earth's clear-sky radiation budget and water vapor absorption in the far infrared. J. Clim., 10, 1601-1614</td>
    </tr>
    <tr>
      <td>Sundqvist, H.</td>
      <td>1981</td>
      <td>Parameterization of condensation and associated clouds in models for weather prediction and general circulation simulation. Tellus, 33, 344-355</td>
    </tr>
    <tr>
      <td>Tibaldi, S., Palmer, T. N., Branković, Č. and Cubasch, U.</td>
      <td>1990</td>
      <td>Extended-range predictions with ECMWF models: Influence of horizontal resolution on systematic errors and forecast skill. Q. J. R. Meteorol. Soc., 116, 835-866</td>
    </tr>
    <tr>
      <td>Washington, W. M. and Williamson, D. L.</td>
      <td>1977</td>
      <td>A description of the NCAR GCMs in general circulation models of the atmosphere. Pp. 111-172 in Method in computational physics. Ed. J. Chang. Academic Press, New York</td>
    </tr>
    <tr>
      <td>Wilson, C. A. and Mitchell, J. F. B.</td>
      <td>1986</td>
      <td>Diurnal variation and cloud in general circulation model. Q. J. R. Meteorol. Soc., 112, 347-369</td>
    </tr>
    <tr>
      <td>Zhong, W. and Haigh, J. D.</td>
      <td>1995</td>
      <td>Improved broadband emisivity parameterization for water vapor cooling rate calculations. J. Atmos. Sci., 52, 124-138</td>
    </tr>
  </tbody>
</table>