Abstract

The aspect ratio (AR) of a nonspherical ice particle is identified as the key microphysical parameter to determine its asymmetry factor for solar radiation. The mean effective AR is defined for cirrus clouds containing various nonspherical ice particles. A new parameterization of the asymmetry factor of cirrus clouds in terms of AR and mean effective size, D_ge, is developed for solar radiation. It is based on geometric ray-tracing calculations for hexagonal ice crystals with a simple representation of particle surface roughness. The present parameterization well reproduces the asymmetry factors of complicated ice particles such as bullet rosettes, aggregates with rough surfaces, and fractal crystals and agrees well with observations. It thus can be properly applied to cirrus clouds containing various nonspherical ice particles. The asymmetry factor from this parameterization in the visible spectrum ranges from about 0.73 to more than 0.85.

Radiative transfer calculations show that for a cirrus cloud with an optical depth of 4 and a solar zenith angle of 60°, changes in AR from 1.0 to 0.5 or from 1.0 to 0.1 result in differences in reflected solar fluxes of about −30 or −70 W m⁻², respectively. For the same cloudy conditions, the effect of ice particle surface roughness on the reflected solar flux is found to be about 20 W m⁻².

Abstract

An accurate parameterization of the solar radiative properties of cirrus clouds is developed based on improved light scattering calculations. Here 28 ice crystal size distributions from in situ aircraft observations in both tropical and midlatitude regions are employed. In the single scattering calculations, the most recent measurements of the imaginary refractive indices of ice are used, thereby eliminating a large existing uncertainty. The single scattering properties of hexagonal ice crystals are calculated by using an improved geometric ray-tracing program that can produce accurate results for size parameters larger than 15.

A generalized effective size, D_ge is defined to account for the ice crystal size distribution in the radiative calculations. Based on physical principles, the single scattering properties have been parameterized in terms of ice water content (IWC) and D_ge . This allows the cirrus cloud single scattering properties to respond independently to changes in IWC or D_ge . The generalized effective size can be related to the total cross-sectional area of ice particles per unit volume, a quantity directly measured by the 2D optical probe in in situ microphysical observations of cirrus clouds. The present parameterization of the extinction coefficient and the single scattering albedo in terms of IWC and D_ge can be properly applied to cirrus clouds that contain various nonspherical particles, such as plates, columns, bullet rosettes, and aggregates, etc.

The present parameterization of the single scattering properties of cirrus clouds is evaluated by examining the bulk radiative properties for a wide range of atmospheric conditions. Compared with reference results, the typical relative errors due to the parameterization are ∼1.2%, ∼0.3%, and ∼2.9% in reflectance, transmittance, and absorptance, respectively. The accuracy of this parameterization guarantees its reliability in applications to climate models.

Cloud absorption plays an important role in cloud-radiation interactions and therefore in climate systems. Because of the large variation in the co-albedo of ice near the wavelength of 1.41 μm sum, one of the spectral divisions is chosen at 1.41 μm to predict cloud absorption properly. Furthermore, the averaging technique for single scattering albedo in spectral intervals associated with absorption bands is important for the parameterization of radiative properties of ice clouds.

Abstract

A scheme that can handle cloud infrared scattering based on the absorption approximation is developed. In a two-stream mode, the new scheme produces more accurate results than those from the modified two-stream discrete ordinate method. For low and middle clouds, the two-stream version of the scheme produces a flux error less than 1 W m⁻² and a heating rate error less than 0.5 K day⁻¹. With high clouds, the errors in calculated fluxes and heating rates are less than 1.4 W m⁻² and 1.5 K day⁻¹, respectively. The four-stream version of the proposed scheme is slightly inferior to the four-stream discrete ordinate method. However, as opposed to the discrete ordinate technique, this scheme treats cloud-free layers the same as the absorption approximation. Therefore, numerically, it is much more efficient. Considering the radiative transfer module only, in a two-stream mode, the new scheme, which considers multiple scattering, uses only about 50% more CPU time than the absorption approximation method for a 100-layer column atmosphere with 20 cloudy layers.

Abstract

The parameterization of in-cloud water vapor pressure below 0°C is examined using in situ aircraft observations from Canadian National Research Council (NRC) Convair-580 flights during the Surface Heat Budget of the Arctic Ocean (SHEBA)/First International Satellite Cloud Climatology Project (ISCCP) Regional Experiment– Arctic Cloud Experiment (FIRE–ACE) campaign. The accuracy of in-cloud water vapor measurements is evaluated against the saturated water vapor pressure in liquid water clouds as derived from measured temperatures, which have a mean bias of about −1%. This study reveals that the parameterization used in the ECMWF cloud scheme, which employs a temperature-weighted average of the values with respect to ice and liquid water underestimates the saturated water vapor by ∼9% when applied to all in-cloud data from the campaign. It is found that a parameterization that relates the weighting to the cloud liquid and ice water contents agrees well with the observations. This study also reveals that it is incorrect to assume that water vapor is in equilibrium with liquid water in mixed-phase clouds.

Abstract

One pronounced feature in observed latitudinal dependence of lower-stratospheric temperature trends is the enhanced cooling near 30° latitude in both hemispheres. The observed phenomenon has not, to date, been explained in the literature. This study shows that the enhanced cooling is a direct response of the lower-stratospheric temperature to the poleward shift of subtropical jets. Furthermore, this enhanced lower-stratospheric cooling can be used to quantify the poleward shift of subtropical jets. Using the lower-stratospheric temperatures observed by satellite-borne microwave sounding units, it is shown that the subtropical jets have shifted poleward by 0.6° ± 0.1° and 1.0° ± 0.3° latitude in the Southern and Northern Hemispheres, respectively, in last 30 years since 1979, indicating a widening of tropical belt by 1.6° ± 0.4° latitude.

Abstract

The correlated k-distribution method for radiative transfer in nonhomogeneous atmospheres is discussed in terms of the physical and mathematical conditions under which this method is valid. Two correlated conditions are necessary and sufficient for the exact transformation of the wavenumber integration to an integration over the cumulative probability (g), a monotonically increasing and smooth function in the absorption coefficient space. These conditions involve the use of a reference condition to define the absorption coefficient and an assumption concerning the ordering of the absorption coefficient. The correlated conditions are exact in the context of a single line, periodic lines, and the strong- and weak-line limits. In realistic atmospheres, these assumptions are best for adjacent levels but produce increasing blurring or deviations for distant levels.

We investigate the blurring of the correlated assumptions on the computations of fluxes and heating rates based on “exact” line-by-line results, using a variety of atmospheric profiles and spectral intervals containing principal absorbing gases. In the thermal infrared, errors in fluxes are less than 0.2% for H₂O, CO₂, CH₄, and N₂O, and ∼2% for O₃. Errors in heating rates are less than 0.01 K day⁻¹ for these gases below ∼30 km. Larger errors of ∼0.1 K day⁻¹ can occur at some levels above this height. For H₂O lines in the solar region, errors in fluxes and heating rates are within 0.05% and 0.01 K day⁻¹, respectively. Based on numerical experimentation, we find that the number of g values ranging from 1 (for weak bands) to ∼10 (for strong bands) are usually sufficient to achieve acceptable accuracy for flux and heating rate calculations.

The correlated k-distribution method differs fundamentally from the traditional approach that employs scaling approximations and band models to separate height and wavenumber integrations for transmittance calculations. The equivalent k values for various gases computed from this approach can be directly incorporated in the multiple-scattering program involving cloud and aerosol particles.

Abstract

A new approach for parameterization of the broadband solar and infrared radiative properties of ice clouds has been developed. This parameterization scheme integrates in a coherent manner the δ-four-stream approximation for radiative transfer, the correlated k-distribution method for nongray gaseous absorption, and the scattering and absorption properties of hexagonal ice crystals. A mean effective size is used, representing an area-weighted mean crystal width, to account for the ice crystal size distribution with respect to radiative calculation. Based on physical principles, the basic single-scattering properties of ice crystals, including the extinction coefficient divided by ice water content single-scattering albedo, and expansion coefficients of the phase function, can be parameterized using third-degree polynomials in terms of the mean effective size. In the development of this parameterization the results computed from a light scattering program that includes a Geometric ray-tracing program for size parameters larger than 30 and the exact spheroid solution for size parameters less than 30 are used. The computations are carried out for 11 observed ice crystal size distributions and cover the entire solar and thermal infrared spectra. Parameterization of the single-scattering properties is shown to provide an accuracy within about 1%. Comparisons have been carried out between results computed from the model and those obtained during the 1986 cirrus FIRE IFO. It is shown that the model results can be used to reasonably interpret the observed IR emissivities and solar albedo involving cirrus clouds. The newly developed scheme has been employed to investigate the radiative effects of ice crystal size distributions. For a given ice water path, cirrus clouds with smaller mean effective sizes reflect more solar radiation, trap more infrared radiation, and product stronger cloud-top cooling and cloud-base beating. The latter effect would enhance the in-cloud heating rate gradients. Further, the effects of ice crystal size distribution in the context of IR greenhouse versus solar albedo effects involving cirrus clouds are presented with the aid of the upward flux at the top of the atmosphere. In most cirrus cases, the IR greenhouse effect outweigh the solar albedo effect. One exception occurs when a significant number of small ice crystals are present. The present scheme for radiative transfer in the atmosphere involving cirrus clouds is well suited for incorporation in numerical models to study the climatic effects of cirrus clouds, as well as to investigate interactions and feedbacks between cloud microphysics and radiation.

Abstract

An observationally based global climatology of the temperature diurnal cycle in the lower stratosphere is derived from 11 different satellites with global positioning system–radio occultation (GPS-RO) measurements from 2006 to 2020. Methods used in our analysis allow for accurate characterization of global stratospheric temperature diurnal cycles, even in the high latitudes where the diurnal signal is small but longer time-scale variability is large. A climatology of the synthetic Microwave Sounding Unit (MSU) and Advanced MSU (AMSU) Temperature in the Lower Stratosphere (TLS) is presented to assess the accuracy of diurnal cycle climatologies for the MSU and AMSU TLS observations, which have traditionally been generated by model data. The TLS diurnal ranges are typically less than 0.4 K in all latitude bands and seasons investigated. It is shown that the diurnal range (maximum minus minimum temperature) of TLS is largest over Southern Hemisphere tropical land in the boreal winter season, indicating the important role of deep convection. The range, phase, and seasonality of the TLS diurnal cycle are generally well captured by the WACCM6 simulation and ERA5 dataset. We also present an observationally based diurnal cycle climatology of temperature profiles from 300 to 10 hPa for various latitude bands and seasons and compare the ERA5 data with the observations.

Abstract

The main finding by Po-Chedley and Fu was that the University of Alabama in Huntsville (UAH) microwave sounding unit (MSU) product has a bias in its NOAA-9 midtropospheric channel (TMT) warm target factor, which leads to a cold bias in the TMT trend. This reply demonstrates that the central arguments by Christy and Spencer to challenge Po-Chedley and Fu do not stand. This reply establishes that 1) Christy and Spencer found a similar, but insignificant, bias in the UAH target factor because their radiosonde data lack adequate sampling and measurement errors were considered twice; 2) the UAH individual satellite TMT difference between NOAA-9 and NOAA-6 reveals a bias of 0.082 ± 0.011 in the UAH NOAA-9 target factor; 3) comparing the periods before and after NOAA-9 is not an adequate method to draw conclusions about NOAA-9 because of the influence of other satellites; 4) using the Christy and Spencer trend sensitivity value, UAH TMT has a cold bias of 0.035 K decade⁻¹ given a target factor bias of 0.082; 5) similar trends from UAH and Remote Sensing Systems (RSS) for the lower tropospheric temperature product (TLT) do not indicate that the UAH TMT and TLT NOAA-9 target factor is unbiased; and 6) the NOAA-9 warm target temperature signal in UAH TMT indicates a problem with the UAH empirical algorithm to derive the target factor.

Abstract

The two primary foci of this note are to assess the ability of the multilayer gamma-weighted two-stream approximation (GWTSA) to compute domain-averaged solar radiative fluxes and to demonstrate how its execution time can be reduced with negligible impact on performance. In addition to the usual parameters needed by a 1D solar code, the GWTSA requires ν ∈ R⁺, which depends on both the horizontal mean and mean logarithm of cloud water content. Reduced central processing unit (CPU) time is realized by simply rounding ν to the nearest whole number, denoted as [ν]. The experiment reported on here uses 120 fields generated by a 2D cloud-resolving model simulation of an evolving tropical mesoscale convective cloud system. Benchmark calculations are provided by the independent column approximation (ICA), and results are also shown for the conventional two-stream model.

The full GWTSA yields time- and domain-averaged broadband top-of-atmosphere albedo and surface absorptance values of 0.32 and 0.49, which are very close to the ICA values of 0.32 and 0.47. Correspondingly, the GWTSA using [ν] produces 0.34 and 0.46. In contrast, the conventional two-stream’s estimates are 0.56 and 0.20. While mean heating rate errors for the conventional two-stream average about −0.5 K day⁻¹ near the surface and almost +2 K day⁻¹ at 10 km, they are diminished at both altitudes to ∼0.25 K day⁻¹ for the GWTSA regardless of whether ν or [ν] is used. For this simulation, the GWTSA using [ν] requires just ∼25% more CPU time than the conventional two-stream approximation.