1. Atmospheric Cooling in the Far-Infrared
Daniel Feldman1
Kuo-Nan Liou2, Yuk Yung3, Xianglei Huang4,
2011 Workshop on Far-Infrared Remote Sensing
November 8, 2011
1 Lawrence Berkeley National Laboratory, Earth Sciences Division
2 UCLA, Department of Atmospheric and Oceanic Sciences
3 Caltech, Department of Geological and Planetary Science
4 University of Michigan, Department of Atmospheric, Oceanic, and Space Sciences

2. Outline
Importance of atmospheric cooling and the role of the far-infrared.
How measurements impart information on cooling rates (either directly or indirectly).
Comparison of distinct methods for determining cooling rates from measurements.
How the current measurements from AIRS and CERES may be used to gauge processes that affect far-IR cooling.

3. Cooling Rate Profiles Background
Cooling arises from net radiative flux divergence from absorption by gases including H2O, CO2, and O3 and condensed species.
Models perform band radiation calculations to calculate heating/cooling rates to integrate the primitive equations.
Radiation can account for 30% of computational expense.
Radiation impacts circulation, especially vertical velocity, controls TTL and convection
From Clough, et al., 1995
Background

4. Heating/Cooling Rates Matter
Iacono, et al., [2000] investigated the results of an RTM change in CCM3.
Significant cooling rate changes from revised H2O continuum model.
A comparison of model integrations shows changes in T, H2O profiles due to altered latent, radiative energy distribution.
To illustrate the importance of the cooling rates, in particular, to model performance, I would like to take a few brief moments to discuss the results of changing the cooling rate profile calculation scheme in a climate model. Iacono et al introduced an updated RTM into the NCAR CCM3 that contained many improvements over previous models, most notably in the treatment of the water vapor continuum. The updates were consistent with a comprehensive measurement set. The figure on the upper right indicates the initial forcing as measured in zonal mean clear-sky cooling rates associated with the change in radiative transfer model and the lower two figures show the resulting changes in zonal-mean temperature and water vapor after a 5-year model integration. The changes are rather significant, especially in water vapor concentration, and indicate that indeed the specifics of radiative transfer in a model do matter. Also, it is reasonable to conclude that improper cooling rate profile values arising from other sources of uncertainty and bias will degrade model performance.
All figs. from Iacono, et al., 2000
Background

5. Remote Sensing Measurements
Artist’s rendition of the A-Train courtesy of NASA
There is a critical need for having accurate, computationally-inexpensive cooling rate data and remote sensing systems may be able to provide this.
The polar-orbiting EOS A-Train flotilla presents a voluminous dataset describing the earth’s lower atmosphere including T, H2O, O3, and clouds
AIRS has been operational for 9+ years.
CloudSat and CALIPSO platforms operational for 5+ years.

6. Information in AIRS measurements
Synthetic Tropical Atm AIRS Spectrum
Wavenumber (cm-1)
Radiance (mW/m^2/sr/cm-1)
Passive IR spectra provide information on the T, H2O, and O3 profiles through differential absorption.
2378 channels
3.7 to 15.4 μm ( cm-1)
No far-IR coverage mostly due to detector limitations.
From JPL AIRS website

7. Deriving Information from Retrieval Flow Chart
Measurement+uncertainty
A priori Atmospheric State
RTM
Retrieval algorithm
A priori spectrum
In order to understand how this instrument compares to other instruments such as AIRS, we can use a retrieval sensitivity test in which we start with a model atmosphere, make several perturbations consistent with our understanding of the variability of the atmospheric state which yields the “a priori” state, plug the results into a radiative transfer model (in this case LBLRTM and CHARTS), perform a retrieval, and then examine retrieval performance relative to the known atmospheric state either in measurement or model space.
A priori
uncertainty
T(z); H2O(z); O3(z); CWC(z); CER(z) …
Analyze retrieved state, spectra, and associated statistics
From Rodgers, 2000

8. Cooling Rate Profile Uncertainty
Perturbations in T, H2O, O3 profiles lead to θ’ changes that propagate across layers.
Calculation of θ’ uncertainty requires formal error propagation analysis.
Covariance counts!
It is important to be able to compare how different retrieval techniques constrain cooling rate profiles. Since retrievals from instruments such as AIRS produce imperfect estimates of temperature, water vapor, and ozone profiles, we can address how these uncertainties in these retrievals propagate ultimately into cooling rate uncertainty. In doing this, it is necessary to recognize that changes in the T, H2O, or O3 value in one layer of the atmosphere will have an impact on the total IR cooling in that layer and in other layers. If a layer increases in temperature, it will be emitting more and that layer’s cooling rate will increase whereas the cooling in other layers will decrease. However, an increase in ozone in the troposphere will lead to increase heating (decreased cooling) in that layer and increased cooling in upper layers. Increases in water vapor in the upper trop, on the other hand, lead to increased cooling in the layer and inhibit the cooling-to-space of vapor of lower layers. All of those details can be combined through formal error propagation analysis for Gaussian distributed variables. As such, the uncertainty in the cooling rate for a layer depends on the sensitivity to changes in each atmospheric state parameter and on the covariance between that parameter and other parameters.
From Feldman, et al., 2008.

9. Cooling Rate Error Propagationab
T, H2O, O3 profile covariance matrix derived from kernel spread.
Exclusion of off-diagonal elements leads to underestimation of uncertainty.
To expand upon the previous slide, here are retrieval covariance matrices for temperature, water vapor, and ozone. Formal error propagation of these covariance matrices again leads to cooling rate covariance matrices. Here, I’ve shown the square-root of the diagonal of the covariance matrices for each IR band which gives you a sense for which spectral regions are contributing to the total cooling rate uncertainty. Also, it is important to note that the off-diagonal components of the T, H2O, and O3 covariance matrices lead to increased cooling rate uncertainty and conversely that not taking into account the off-diagonal components of atmospheric state covariance matrices will lead to an underestimation of the uncertainty in the cooling rate profile.
From Feldman, et al., 2008

10. Cooling Rate Covariance Matrix
Covariance matrices assess how prior and posterior errors are correlated
Information content of a measurement vis-avis the cooling rate profile can be assessed.
The retrieval of profiles of T, H2O and O3 leads to uncertainties and associated covariance matrices of these profile quantities. These retrieval covariance matrices can be utilized along with the cooling rate profile Jacobian to make an estimate of the cooling rate covariance matrix, given the assumption of Gaussian statistics. I have shown an estimate of a priori and a posteriori total IR cooling rate covariance matrices associated with an AIRS measurement and retrieval. We can compare these two matrices unidimensionally with the information content which is similar to the notion of a signal-to-noise ratio but is useful when comparing a set of correlated quantities.
From Feldman, et al., 2008

11. Cooling Rate Information Content
Information content is related to the change in understanding of a set of correlated variables as a result of the measurement.
From Feldman, et al. 2008
Instrument
Time period
Spectral range (cm- 1)
NeDT (K)
Spectral resolution (cm-1)
hTRP (bits)
hMLS (bits)
hSAW (bits)
IRIS-D
2-4
2.8
9.8
8.4
6.4
AIRS
2002-Present ,
1-2
17.1
11.5
12.6
TES
2004-Present ,
1-4
0.12
13.2
10.5
8.0
IASI
2006-Present
0.5
21.8
19.9
18.3
Far-IR
Proposed
1.1
0.6
17.5
11.4
The notion of information content allows us to compare unidimensionally the performance of several different instruments in their abilities to constrain cooling rate profiles. In particular, we can see that heritage instruments such as IRIS-D do not do as well as the current generation. AIRS and TES have similar spectral coverage though the former instrument has inferior spectral resolution and superior instrumental noise. This analysis shows that the instrumental noise is more important than high spectral resolution. Recently, the ESA implemented the IASI instrument and indications suggest that it will outperform AIRS and TES in terms of describing cooling rates. Finally, the FIRST instrument is a prototype but measures in the far-IR in addition to the mid-IR and it is possible to compare the extra information introduced by making measurements at wavelengths longer than 15 um.

12. Retrieval of Cooling Rates
Many products derived from the satellite instrument measurements through retrievals.
Many different approaches to retrieving quantities from measurements.
Cooling rates retrieval proposed by Liou and Xue [1988] and Feldman et al [2006]
Currently, NASA missions such as AIRS produce a hierarchy of retrieval products that can be utilized as inputs to a radiative transfer model to calculate cooling rate profiles. It may also be possible to perform a more direct retrieval of the cooling rates from radiance measurements, especially considering that a host of assumptions is necessary to retrieve atmospheric state profile quantities and that similar spectra can be produced with different underlying atmospheric states.

13. Inversion for Infrared Cooling Rate Profile
Conventionally use T, H2O, O3, CH4, and N2O profiles
Remote sensing measurements can be inverted for atmospheric state  calculate cooling rates.
TOA radiance closely related to TOA flux which is a function of net flux divergence
Monotonic kernel but a priori constraint guarantees measurement information imparted uniformly across profile
Measurement
Kernel
TOA Flux
Flux interpretation
Background

14. In the absence of TOA far-IR measurements
Extensive datasets of mid-IR measurements and also information from CloudSat and CALIPSO.
Standard retrieval products can (and should) be used to gauge estimate far-IR cooling
These require covariance matrix estimates!
In the absence of far-IR measurements, measurements from other sources must be extrapolated
Critical requirement for accurate spectroscopy, cloud optical properties, and an appropriate mapping from mid-IR clouds to far-IR clouds.
The data is out there!
Routine calculations are performed by weather models, in climate models and for satellite products. Comparison required.

15. Using AIRS + CERES to understand far-IR
AIRS radiance spectra has been converted to spectrally-resolved fluxes collocated with Aqua CERES LW fluxes [Huang et al, 2010].
A comparison of the principal components AIRS mid-IR flux ( cm-1) to CERES broadband flux ( cm-1) will indicate the extra information in the far-IR.
Process studies are likely required to understand how the discrepancies between mid-IR and broadband flux map onto far-IR cooling.
Data courtesy of Xianglei Huang

16. Discussion
Radiative cooling rates are important to atmospheric circulation and far-IR cooling from water vapor and clouds represent a significant component of this cooling.
Remote sensing measurements provide information, either directly or indirectly, about spectral and broadband cooling rates
The incorporation of this information requires careful attention to retrieval theory.
Ongoing efforts to compare mid- and broadband IR measurements from AIRS and CERES respectively may yield extra information about far-IR flux and ultimately far-IR cooling.

17. Acknowledgements
Collaborators Marty Mlynczak and Dave Johnson of LaRC.
NASA Earth Systems Science Fellowship, grant number NNG05GP90H.
NASA Grant NNX08AT80G, NAS , NNX10AK27G and NNX11AE65G.
Yuk Yung Radiation Group: Jack Margolis, Vijay Natraj, King-Fai Li, & Kuai Le
AER, Inc. including Eli Mlawer, Mark Shepard, and Tony Clough for tech support
Xianglei Huang from University of Michigan
Yi Huang from (recently) McGill University