The radiative infrared cooling of CO

Carbon dioxide is the major infrared cooler of the atmosphere from the lower stratosphere up to the lower thermosphere, where emission by nitric oxide becomes important

The most used parameterization of the CO

The paper is structured as follows. A very basic description of the parameterization is presented in Sect.

As discussed above, this parameterization is essentially based on that of

Input data used in the reference calculations.

The parameterization computes cooling rates for given inputs of temperature and concentrations of CO

Further, the collisional (de)activation of CO

We used the same six pressure–temperature reference atmospheres as in

We should also mention that the envelope of these reference atmospheres does not fully cover the predicted temperatures for the end of this century for projections with high CO

The valid range of the parameterization of

As discussed above, the parameterization requires the N

We describe in this section the non-LTE cooling rates used as a reference. To compute the coefficients of the parameterization and the boundaries of the different layers, they also require the calculations of the cooling rates in LTE, which are also described in this section. Further, we have assessed the accuracy of the LTE cooling rates by comparing them with those calculated by an independent code, the Reference Forward Model

LTE cooling rates for the US standard temperature profile and the CO

The LTE cooling rates have been computed using a modified Curtis matrix formulation

In order to ensure the accuracy of these LTE cooling rates, we have compared them with those obtained with another very well-tested and widely used radiative transfer code, RFM

The same formulation has been used to calculate the Curtis matrices of all the CO

The reference line-by-line non-LTE cooling rates have been computed by using the GRANADA non-LTE code. The details of the method for solving the system of equations for CO

For this case of non-LTE cooling rates, each ro-vibrational band contributes according to the non-LTE populations of their upper and lower levels. The non-LTE cooling rates calculated here comprise 16

The main collisional processes affecting the CO

For the calculations of the non-LTE cooling rates, a collisional scheme and collisional rates are required. Although the collisional rates affecting the CO

The cooling rates near 15

The non-LTE cooling rates for four reference atmospheres shown for altitudes up to the lower thermosphere. The cooling rates extended to the thermosphere are shown in Fig. S5. Note the different

Contributions of the different CO

The results for the accurate, line-by-line non-LTE cooling rates computed for the six reference

Non-LTE–LTE cooling rate differences for four

The dependence of the non-LTE cooling rates on the CO

Effect of the

A comparison of the non-LTE and LTE cooling rates for the six

For completeness, Fig.

The atomic oxygen concentration is an input to the parameterization and plays a crucial role in determining the CO

Atmospheric regions considered in the parameterization.

Essentially, here we follow the parameterization developed by

The atmosphere is divided into five different regions (see Fig.

The lowermost (LTE) and uppermost (NLTE4) regions are the most straightforward and also the regions where the errors are in general smaller. The most difficult parts are the transition regions from LTE to non-LTE, where (i) several bands contribute to the cooling with different source functions and their relative contributions depend very much on the actual temperature profiles (see Fig.

The parameterization in the LTE region is based on the Curtis matrix method. The cooling rate

In the parameterization, the Curtis matrix is expressed with an explicit temperature dependence by

Next, we define global

In that way, we have parameterized the cooling rates as a function of temperature. The cooling rates also depend on the CO

This region is difficult to parameterize because we have several bands contributing to the cooling (see Fig.

The lower boundary of this region, i.e. the LTE–NLTE1 transition, occurs, depending on the temperature profile, at altitudes from

The upper limit of this region was set up in the previous parameterization at the pressure levels where collisions with O(

In this region we followed, as in

The parameterization in the NLTE2, NLTE3 and NLTE4 regions is based on the recurrence formula proposed by

The lower boundary of the NLTE2 region is set up in the layer where the cooling rate obtained by the corrected recurrence formula is more accurate than that given by the non-LTE-corrected Curtis matrix approach (used in NLTE1). This has been set up at

Thus, the cooling rates in the NLTE2 and NLTE3 regions are calculated by

Note that this constant has been changed from its value of

The

The

In the NLTE3 region, we used the same method as in region NLTE2, except that no correction for the

The recurrence formula described above is also valid in the uppermost NLTE4 region, but, as the CO

The parameterization has been tested against the reference cooling rates calculated for the reference atmospheres (the six

Comparison of the cooling rates of the current and previous parameterizations with respect to reference non-LTE cooling rates for the present-day CO

In this section, we discuss the accuracy of the current parameterization for the assumed reference atmospheres. The non-LTE models used in the original

Mean of the cooling rate differences of the current and previous parameterizations with respect to the reference cooling rates for the four lowest CO

The differences are more clearly illustrated in Figs.

For the very high CO

That increase in the differences of the new parameterization with respect to the reference calculations for the very high CO

The aim of the parameterization is to be used for any CO

Mean of the cooling rate differences of the current parameterization with respect to the reference cooling rates for the intermediate CO

Figure

As the CO

Mean of the cooling rate differences of the current parameterization with respect to the reference cooling rates for the results in Fig.

In Table

Performance of the parameterization.

Zonal mean of the differences in the cooling rates of the old parameterization

We have compared the cooling rates estimated by the parameterization with the reference ones for realistic, e.g. measured, temperature profiles that present a large variability and very variable vertical structure (see e.g. Fig.

Mean (solid lines) and rms (dash lines) of the differences in the cooling rates of the old parameterization (blue) and the new one (red) with respect to the reference accurate cooling rates obtained for MIPAS temperatures for 14 January and 13 June 2010 (solstice,

The results are presented in Fig.

Overall, the errors in the mean profiles of the cooling rates of the new parameterization for 1 d of measurements are below 0.5 K d

As in Fig.

Mean (solid) and rms (dash) of the differences in the cooling rates of the old parameterization (in blue) and the new one (red) with respect to the reference cooling rates obtained for MIPAS temperatures for 15 February 2009 for latitudes north of 50° N.

The comparison of the cooling rates estimated by the old and new parameterizations with respect to the reference calculations for 15 February 2009, a day with a pronounced and unusual elevated stratopause event (see the zonal mean temperatures in Fig.

It seems clear that part of this underestimation is caused by the fact that such atypical temperature profiles (see Sect.

In addition to the tests above, we have also tested the parameterizations for the temperature structure obtained with a high-resolution version of the WACCM-X model

We recall that the

The parameterization has been tested for a total of 225 temperature profiles. They have been selected from the model output for January conditions at four latitudes, 20, 40, 60 and 70° N of the northern winter hemisphere, and two additional latitudes, 60 and 70° S of the southern summer hemisphere. For each latitude, 36 profiles corresponding to longitudes from 0 to 360° every 10° were selected. A few

Comparison of cooling rates of the parameterization and the reference calculations for high-resolution WACCM-X temperature profiles. The left column shows the panels for the pressure–temperature profiles, with two profiles (black and red) in each panel. The middle column shows the reference cooling rates (solid) and the cooling rate from the parameterization (dotted) for the corresponding

Mean and rms of the differences in the cooling rates of the parameterization with respect to the reference cooling rates obtained for the WACCM-X high-resolution temperature profiles.

Solar NIR heating rates for the tropical atmosphere and a SZA of 44.5° computed by the solar NIR heating parameterization of

The results for a few representative

To have a global perspective, we have plotted in Fig.

Some of the GCM models use the parameterization of the CO

The results of the comparison are shown in Fig.

An improved and extended parameterization of the CO

Other improvements or updates are as follows. They have an extended and finer vertical grid, increasing the number of levels from 8 to 83. The CO

The new parameterization has been thoroughly tested against line-by-line LTE and non-LTE cooling rates for (i) the six

For the reference temperature profiles, the errors of the new parameterization (mean of the differences in the cooling rates with respect to the reference calculations for the six

From the testing of the parameterization for realistic current temperature fields of the middle atmosphere as measured by MIPAS, we found that, in general, the new parameterization is slightly more accurate. In particular, in the 105–115 km range, the previous parameterization overestimates the cooling rate by 1.5 K d

In addition, we have tested the parameterization for the temperature structure obtained by a high-resolution version of WACCM-X, with the temperatures showing a large variability and pronounced vertical wave structure. The mean (bias) error of the parameterization is very small, smaller than 0.5 K d

As has been shown, this parameterization has some limitations (see Sects.

The routine source code is written in Fortran 90 and is available at

The code is organized in a library (in the directory source/modules/) that can be included in a more complex GCM model. The subroutine to be called is

The following inputs are required (in order) by

Atmospheric profiles as a function of pressure for temperature and four VMRs of CO

The values are the temperature (K), pressure (hPa), VMRs (mol mol

Input profiles can run either from the ground to the top of the atmosphere (decreasing pressures) or reverse (top to ground with increasing pressures). The pressure grid can be irregular.

Important notes: calculations in the LTE region.

Pressure levels should include the surface pressure (near 10

If 15

To compile the routine, follow these steps.

Edit

From this folder, run

A test program,

First input at line 9:

Start from line 12.

Six atmospheric profiles are read (

The output heating rates are written in the

Check that the results in

The same procedure can be done for test 2.

The rates are defined in the form

for CO

for CO

for CO

Although the parameterization is specifically developed for the CO

Contributions of the different CO

Altitude

Non-LTE–LTE cooling rate differences for the six

Comparison of the cooling rates of the current and previous parameterizations with respect to accurate cooling rates for the intermediate CO

Testing the effect of the CO

An example of the MIPAS nighttime temperature profiles (15 February 2009) used for verifying the parameterization accuracy. Note the large variability of the temperature profiles.

MIPAS zonal mean nighttime temperatures for 14 January 2010 (northern winter hemisphere,

Zonal mean of the differences in the cooling rates of the old parameterization

The MIPAS nighttime temperature zonal mean for 15 February 2009 (see also Fig.

The code is available at

The supplement related to this article is available online at:

MLP performed the LTE and non-LTE reference calculations, participated in the adaptation of the original parameterization, wrote the manuscript and had the final editorial responsibility for this paper. FF led (together with BF) the adaptation of the original parameterization of

The authors declare that they have no conflict of interest.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors.

The IAA team acknowledges financial support from the Agencia Estatal de Investigación, MCIN/AEI/10.13039/501100011033, through grant nos. PID2019-110689RB-I00, PID2022-141216NB-I00 and CEX2021-001131-S. We thank two anonymous referees for their very valuable suggestions leading to an improvement of this work.

This research has been supported by the Agencia Estatal de Investigación (grant nos. PID2019-110689RB-I00, PID2022-141216NB-I00 and CEX2021-001131-S).The article processing charges for this open-access publication were covered by the CSIC Open Access Publication Support Initiative through its Unit of Information Resources for Research (URICI).

This paper was edited by Tatiana Egorova and reviewed by two anonymous referees.