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We provide a complete classification of the radial solutions to a class of reaction diffusion equations arising in the study of thermal structures such as plasmas with thermal equilibrium or no flux at the boundary. In particular, our study includes

The Southern Ocean is a critical region for global climate, yet large cloud and solar radiation biases over the Southern Ocean are a long-standing problem in climate models and are poorly understood, leading to biases in simulated sea surface temperatures. This study shows that supercooled liquid clouds are central to understanding and simulating the Southern Ocean environment. A combination of satellite observational data and detailed radiative transfer calculations is used to quantify the impact of cloud phase and cloud vertical structure on the reflected solar radiation in the Southern Hemisphere summer. It is found that clouds with supercooled liquid tops dominate the population of liquid clouds. The observations show that clouds with supercooled liquid tops contribute between 27% and 38% to the total reflected solar radiation between 40° and 70°S, and climate models are found to poorly simulate these clouds. The results quantify the importance of supercooled liquid clouds in the Southern Ocean environment and highlight the need to improve understanding of the physical processes that control these clouds in order to improve their simulation in numerical models. This is not only important for improving the simulation of present-day climate and climate variability, but also relevant for increasing confidence in climate feedback processes and future climate projections.

Climate models and observations robustly agree that Earth’s clear-sky longwave feedback has a value of about −2 W m −2 K −1 , suggesting that this feedback can be estimated from first principles. In this study, we derive an analytic model for Earth’s clear-sky longwave feedback. Our approach uses a novel spectral decomposition that splits the feedback into four components: a surface Planck feedback and three atmospheric feedbacks from CO 2 , H 2 O, and the H 2 O continuum. We obtain analytic expressions for each of these terms, and the model can also be framed in terms of Simpson’s law and deviations therefrom. We validate the model by comparing it against line-by-line radiative transfer calculations across a wide range of climates. Additionally, the model qualitatively matches the spatial feedback maps of a comprehensive climate model. For present-day Earth, our analysis shows that the clear-sky longwave feedback is dominated by the surface in the global mean and in the dry subtropics; meanwhile, atmospheric feedbacks from CO 2 and H 2 O become important in the inner tropics. Together, these results show that a spectral view of Earth’s clear-sky longwave feedback elucidates not only its global-mean magnitude, but also its spatial pattern and its state dependence across past and future climates.

This paper gives an update of the RTTOV (Radiative Transfer for TOVS) fast radiative transfer model, which is widely used in the satellite retrieval and data assimilation communities. RTTOV is a fast radiative transfer model for simulating top-of-atmosphere radiances from passive visible, infrared and microwave downward-viewing satellite radiometers. In addition to the forward model, it also optionally computes the tangent linear, adjoint and Jacobian matrix providing changes in radiances for profile variable perturbations assuming a linear relationship about a given atmospheric state. This makes it a useful tool for developing physical retrievals from satellite radiances, for direct radiance assimilation in NWP models, for simulating future instruments, and for training or teaching with a graphical user interface. An overview of the RTTOV model is given, highlighting the updates and increased capability of the latest versions, and it gives some examples of its current performance when compared with more accurate line-by-line radiative transfer models and a few selected observations. The improvement over the original version of the model released in 1999 is demonstrated.

Solar flares are efficient particle accelerators, with a substantial fraction of the energy released manifesting as nonthermal particles. While the role that nonthermal electrons play in transporting flare energy is well studied, the properties and importance of nonthermal protons are rather less well understood. This is in large part due to the paucity of diagnostics, particularly at the lower-energy (deka-keV) range of nonthermal proton distributions in flares. One means to identify the presence of deka-keV protons is by an effect originally described by Orrall & Zirker. In the Orrall–Zirker effect, nonthermal protons interact with ambient neutral hydrogen, and via charge exchange produce a population of energetic neutral atoms (ENAs) in the chromosphere. These ENAs subsequently produce an extremely redshifted photon in the red wings of hydrogen spectral lines. We revisit predictions of the strength of this effect using modern interaction cross sections, and numerical models capable of self-consistently simulating the flaring nonequilibrium ionization stratification, and the nonthermal proton distribution (and, crucially, their feedback on each other). We synthesize both the thermal and nonthermal emission from Ly α and Ly β, the most promising lines that may exhibit a detectable signal. These new predictions are weaker and more transient than prior estimates, but the effects should be detectable in fortuitous circumstances. We degrade the Ly β emission to the resolution of the Spectral Imaging of the Coronal Environment (SPICE) instrument on board Solar Orbiter, demonstrating that though likely difficult, it should be possible to detect the presence of nonthermal protons in flares observed by SPICE.

The physical characteristics and atmospheric chemical composition of newly discovered exoplanets are often inferred from their transit spectra, which are obtained from complex numerical models of radiative transfer. Alternatively, simple analytical expressions provide insightful physical intuition into the relevant atmospheric processes. The deep-learning revolution has opened the door for deriving such analytical results directly with a computer algorithm fitting to the data. As a proof of concept, we successfully demonstrate the use of symbolic regression on synthetic data for the transit radii of generic hot-Jupiter exoplanets to derive a corresponding analytical formula. As a preprocessing step, we use dimensional analysis to identify the relevant dimensionless combinations of variables and reduce the number of independent inputs, which improves the performance of the symbolic regression. The dimensional analysis also allowed us to mathematically derive and properly parameterize the most general family of degeneracies among the input atmospheric parameters that affect the characterization of an exoplanet atmosphere through transit spectroscopy.

The estimate of surface irradiance on a global scale is possible through radiative transfer calculations using satellite-retrieved surface, cloud, and aerosol properties as input. Computed top-of-atmosphere (TOA) irradiances, however, do not necessarily agree with observation-based values, for example, from the Clouds and the Earth’s Radiant Energy System (CERES). This paper presents a method to determine surface irradiances using observational constraints of TOA irradiance from CERES. A Lagrange multiplier procedure is used to objectively adjust inputs based on their uncertainties such that the computed TOA irradiance is consistent with CERES-derived irradiance to within the uncertainty. These input adjustments are then used to determine surface irradiance adjustments. Observations by the Atmospheric Infrared Sounder (AIRS),Cloud–Aerosol Lidar and Infrared Pathfinder Satellite Observations(CALIPSO),CloudSat, and Moderate Resolution Imaging Spectroradiometer (MODIS) that are a part of the NASA A-Train constellation provide the uncertainty estimates. A comparison with surface observations from a number of sites shows that the bias [root-mean-square (RMS) difference] between computed and observed monthly mean irradiances calculated with 10 years of data is 4.7 (13.3) W m−2for downward shortwave and −2.5 (7.1) W m−2for downward longwave irradiances over ocean and −1.7 (7.8) W m−2for downward shortwave and −1.0 (7.6) W m−2for downward longwave irradiances over land. The bias and RMS error for the downward longwave and shortwave irradiances over ocean are decreased from those without constraint. Similarly, the bias and RMS error for downward longwave over land improves, although the constraint does not improve downward shortwave over land. This study demonstrates how synergetic use of multiple instruments (CERES, MODIS,CALIPSO, CloudSat, AIRS, and geostationary satellites) improves the accuracy of surface irradiance computations.

An unprecedented spectroscopic data stream will soon become available with forthcoming Earth-observing satellite missions equipped with imaging spectroradiometers. This data stream will open up a vast array of opportunities to quantify a diversity of biochemical and structural vegetation properties. The processing requirements for such large data streams require reliable retrieval techniques enabling the spatiotemporally explicit quantification of biophysical variables. With the aim of preparing for this new era of Earth observation, this review summarizes the state-of-the-art retrieval methods that have been applied in experimental imaging spectroscopy studies inferring all kinds of vegetation biophysical variables. Identified retrieval methods are categorized into: (1) parametric regression, including vegetation indices, shape indices and spectral transformations; (2) nonparametric regression, including linear and nonlinear machine learning regression algorithms; (3) physically based, including inversion of radiative transfer models (RTMs) using numerical optimization and look-up table approaches; and (4) hybrid regression methods, which combine RTM simulations with machine learning regression methods. For each of these categories, an overview of widely applied methods with application to mapping vegetation properties is given. In view of processing imaging spectroscopy data, a critical aspect involves the challenge of dealing with spectral multicollinearity. The ability to provide robust estimates, retrieval uncertainties and acceptable retrieval processing speed are other important aspects in view of operational processing. Recommendations towards new-generation spectroscopy-based processing chains for operational production of biophysical variables are given.

Recent observations have indicated significant modulation of the Madden–Julian oscillation (MJO) by the phase of the stratospheric quasi-biennial oscillation (QBO) during boreal winter. Composites of the MJO show that upper-tropospheric ice cloud fraction and water vapor anomalies are generally collocated, and that an eastward tilt with height in cloud fraction exists. Through radiative transfer calculations, it is shown that ice clouds have a stronger tropospheric radiative forcing than do water vapor anomalies, highlighting the importance of incorporating upper-tropospheric–lower-stratospheric processes into simple models of the MJO. The coupled troposphere–stratosphere linear model previously developed by the authors is extended by including a mean wind in the stratosphere and a prognostic equation for cirrus clouds, which are forced dynamically and allowed to modulate tropospheric radiative cooling, similar to the effect of tropospheric water vapor in previous formulations. Under these modifications, the model still produces a slow, eastward-propagating mode that resembles the MJO. The sign of zonal mean wind in the stratosphere is shown to control both the upward wave propagation and tropospheric vertical structure of the mode. Under varying stratospheric wind and interactive cirrus cloud radiation, the MJO-like mode has weaker growth rates under stratospheric westerlies than easterlies, consistent with the observed MJO–QBO relationship. These results are directly attributable to an enhanced barotropic mode under QBO easterlies. It is also shown that differential zonal advection of cirrus clouds leads to weaker growth rates under stratospheric westerlies than easterlies. Implications and limitations of the linear theory are discussed.

The objective of this paper is to investigate whether estimates of the cloud frequency of occurrence and associated cloud radiative forcing as derived from ground-based and satellite active remote sensing and radiative transfer calculations can be reconciled over a well-instrumented active remote sensing site located in Darwin, Australia, despite the very different viewing geometry and instrument characteristics. It is found that the ground-based radar–lidar combination at Darwin does not detect most of the cirrus clouds above 10km (because of limited lidar detection capability and signal obscuration by low-level clouds) and that theCloudSatradar–Cloud–Aerosol Lidar with Orthogonal Polarization (CALIOP) combination underreports the hydrometeor frequency of occurrence below 2-km height because of instrument limitations at these heights. The radiative impact associated with these differences in cloud frequency of occurrence is large on the surface downwelling shortwave fluxes (ground and satellite) and the top-of-atmosphere upwelling shortwave and longwave fluxes (ground). Good agreement is found for other radiative fluxes. Large differences in radiative heating rate as derived from ground and satellite radar–lidar instruments and radiative transfer calculations are also found above 10km (up to 0.35Kday−1for the shortwave and 0.8Kday−1for the longwave). Given that the ground-based and satellite estimates of cloud frequency of occurrence and radiative impact cannot be fully reconciled over Darwin, caution should be exercised when evaluating the representation of clouds and cloud–radiation interactions in large-scale models, and limitations of each set of instrumentation should be considered when interpreting model–observation differences.