Long-wave spectral cloud forcing is computed for realistic clouds of various optical thickness embedded in the tropical and subarctic winter standard atmospheres. The strict connections between the integrated long-wave cloud forcing (LCF) and cloud's altitude and transmissivity are shown. LCF, especially in presence of ice clouds, grows almost linearly with cloud transmissivity, and largest values are found in presence of high and opaque cirri. We have also considered the effect of incomplete spectral coverage in broadband long-wave radiometry when estimating LCF. The error has been computed as a function of edge cutoff (two different filters are used) and cloud's transmissivity and top altitude. Uncorrected measurements from sensors with incomplete spectral coverage generally underestimate the real LCF, especially for the highest cirrus clouds in the tropics. A correction is possible since the percentage error is practically constant with cloud's transmissivity.
 Clouds are recognized as one of the most important elements of the atmospheric energy balance and of the general circulation. The influence they exert on radiative fluxes is sensible at all atmospheric levels, especially within and below the clouds themselves, and is fundamental when computing the amount of energy reaching the surface. The clear sky radiative heating or cooling within the atmospheric fluid [Clough et al., 1992; Clough and Iacono, 1995] is abruptly changed by the presence of a cloud, thus producing strong effects also in the dynamics on both small and large scales and on the release of latent heat [Slingo and Slingo, 1988]. Maestri and Rizzi  show that flux convergence for ice clouds is strongly dependent on cloud altitude. Tenuous ice clouds experience long-wave heating at all cloud levels when placed at high altitude and cooling at all levels when they occupy lower layers. Opaque clouds at all levels show long-wave cooling at the top layer and heating at the base. Upon integration of flux convergence over the whole cloud depth, two well defined spectral regions are revealed, both for tenuous and opaque clouds: a region where gaseous absorption is low (essentially the atmospheric window) where cloud are net absorbers of radiation, and a region where gaseous absorption is high where clouds are net emitters of radiation. Because of the range of typical atmospheric temperatures the latter interval is mostly long-wave of 16 μm, a spectral interval too often neglected or taken into insufficient consideration. Changes in ice water path do not significantly shift the wave number which separates the net absorption and emission ranges. Thus the radiative effects of ice clouds in the tropical atmosphere depend critically on the balance between radiative cooling in the far infrared and radiative heating in the window.
 One of the most common parameter used in determining the influence of clouds upon radiation is the cloud radiative forcing (CF) [Ramanathan, 1987; Hartmann et al., 1986]. By using radiation budget data it is possible to estimate the effects of actual cloudiness on the top of atmosphere (TOA) heat balance and the dependence of these effects on location and season [Hartmann et al., 1986]. CF is especially useful in quantifying the interactions between clouds, radiation and climate at the TOA [Stuhlmann, 1995] since it provides an immediate picture of how much emitted radiation is trapped and of how much solar radiation is reflected by clouds with respect to clear sky conditions. A positive CF indicates that the clouds cause a warming of the overall Earth-atmosphere system [Doelling et al., 2001]. The major limitation of this parameter is that the vertical distribution of the cooling and warming is not dealt with. Nevertheless CF is a fundamental quantity needed to constrain the effects of clouds within short or long-term climate models and should be determined as accurately as possible [Doelling et al., 2001]. By means of this parameter it was immediately recognized by Ramanathan  that the long-wave effects of clouds is to enhance the meridional heating gradient in the Troposphere while the albedo or solar effect of clouds is largely to reduce the available solar energy at the surface. Tian and Ramanathan  show that CF provide the major energy source for balancing the divergence of moist static energy transport (from the intertropical convergence zone, the South Pacific convergence zone, and the warm pool to the Sub Tropics and the cold tongue) by the large-scale atmospheric circulation. Despite its theoretical simplicity the calculation of the CF is a very delicate task [Hartmann et al., 1986; Stuhlmann, 1995; Tian and Ramanathan, 2002] since, for example, in many tropical convective regions the large long-wave and short-wave cloud forcing more or less compensate each other. That is why it is fundamental to correctly and precisely measure the two contrasting terms constituting the total CF. In general it is not easily retrieved from satellite measurements since many uncertainties may affect its determination [Ramanathan, 1987; Harrison et al., 1990; Doelling et al., 2001; Tian and Ramanathan, 2002].
 We study long-wave cloud forcing in presence of realistic clouds and we focus our attention on the tropical (TRO) and the subarctic winter (SAW) standard atmospheres [Anderson, 1986; McClatchey, 1972]. The first is chosen for its energetic importance and its high cloudiness and the second one since CF in the Arctic is an uncertain quantity because of similarities between clouds and snow covered surfaces, at both solar and infrared wavelengths [Doelling et al., 2001] and for its extreme conditions.
 The simulation technique adopted, the atmospheric profiles and properties of the cloud types used in the computations are discussed first. In the third paragraph we describe the results in different cloudy scenarios. In the fourth paragraph we address a potential problem arising when estimating long-wave cloud forcing (LCF) using broadband radiometers with incomplete long-wave spectral coverage.
2. Simulation Technique
 The computation of high spectral resolution (HR) radiances in presence of clouds requires the integration of three steps: computation of a database of high-resolution optical depths for the major gas absorbers; computation of a database of single scattering properties for the cloud layers present in the line of sight; and computation of upward and downward radiances and fluxes at all levels for each resolution interval.
 Line-by-line (LBL) computations of layer optical depths are made using the high-resolution atmospheric radiative transfer code HARTCODE [Miskolczi et al., 1989, 1990]. A detailed description of the code mechanics, that includes the standards adopted for continuum gaseous properties, is given by Rizzi et al. . The layer total gaseous optical depth is obtained by integration of the monochromatic optical depths over intervals of width 0.05 cm−1 which is the sampling rate of the final product (layer optical depth). The optical depths are computed from 10 to 2910 cm−1, an interval that practically corresponds to the total emission to space. Two databases of layer spectral optical depth are generated for the TRO and SAW standard atmospheric profiles. Both profiles are relayered to 55 levels and top of atmosphere is placed at 60 km. The lower surface is taken as a lambertian surface with unit emissivity.
 Water and ice cloud layers, as defined in Table 1, are inserted into the SAW and TRO atmosphere. These cloudy layers are made of a number of atmospheric sublayers as shown in last column of Table 1. Although there is experimental evidence that temperature is the predominant factor controlling ice crystal size distribution and volumetric ice content (IWC) [Liou, 1992], we have chosen a fixed particle size distribution with given effective radius (Reff) and effective variance (Veff) and use the ice/water content as the modulator of the opacity of the cloud. Other choices could have been, for example, changing cloud thickness or Reff: we have studied these cases but results are not discussed here. The microphysical parameters for ice and water clouds used for our computations are summarized in Table 2.
Table 1. Symbolic Names and Geometric Characteristics of the Clouds Used in the Computations
Bottom Level, km
Top Level, km
Number of Sublayers
High tropical cirrus
Medium tropical cirrus
Low tropical cirrus
Table 2. Microphysical Parameters of the Ice and Water Clouds Used in the Computations
Effective Radius Reff, micrometers
Radius Range, micrometers
 The problem of evaluating the single scattering properties of particles with various shapes and aspects is being given great attention, but currently there is no database of coherent radiative properties covering most of the infrared spectral range with the exception of the parameterization published by Fu  and Fu et al.  (denoted in the following as FYS). It is based on a composite scheme that employs a linear combination of single scattering properties from the Mie theory, anomalous diffraction theory, geometrical optics and finite difference time domain methods, applied to a large set of measured ice crystal size distributions to derive averaged single scattering properties of cirrus clouds. Maestri and Rizzi  compared spectral fluxes obtained using Mie theory and FYS and found that differences in the TOA spectral fluxes between the two methods appear fairly small when compared to the effects of current uncertainties of the main properties of clouds, such as ice amount and effective radius. Maestri et al.  show that interferometric measurements of upwelling spectral radiance emerging above a thin cirrus cloud layer can be correctly simulated in the whole infrared range taking ice particles to be spherical. Moreover, the percentage error between Mie and FYS results is even smaller for TOA spectrally integrated radiances (and fluxes) because of (spectrally) compensating effects. On the basis of these considerations the general results presented in this paper involve the use of Mie theory. The methodology adopted is same as by Rizzi et al. .
 Transmissivity τ (at 900 cm−1) is used as a measure of the opacity of a cloud in presence of absorption processes alone
where kabs is the spectral absorption coefficient (m2/g) at 900 cm−1 and Δz is the thickness of the cloud. Table 3 provides some examples of trasmissivity as a function of IWC (or liquid water content, LWC) for the high tropical cirrus and for the tropical stratus. In case of cirrus cloud, typical values of IWC are found between 0.001 and 0.5 g/m3 [Liou, 1992].
Table 3. Transmission of Selected Cloud Layers
IWC or LWC, g/m3
Transmission at 900 cm−1
 The integration of the radiative transfer equation in clear and cloudy conditions, including multiple scattering, is based on the code RT3 [Evans and Stephens, 1991]. The whole simulation scheme has been compared to infrared interferometric measurements in clear and cloudy conditions [Rizzi et al., 2001].
3. Long-Wave Cloud Forcing
 LCF can be derived from nearby measurements taken by same broadband sensor under the assumption that the two separate scenes are spatially close enough so that the surface and atmospheric conditions are nearly the same, except for the presence of cloudiness in one scene. In general the problem is to infer the clear sky estimate from available data. The goal of this paper is not to discuss the problem of how this task can be fulfilled but nevertheless it is important to underline that the methodology to derive LCF is somewhat different from an experiment to another.
 Long-wave cloud forcing expressed in terms of radiance, Lt (W/m2 sr), is:
where the asterisk indicates always the cloudy scene and the subscript t denotes a perfect measurement, extending to the whole long-wave emission spectrum. Although cloud forcing is normally expressed in terms of fluxes, we prefer in this context to use radiance instead since the accuracy and sensitivity for the basic unfiltered radiance measured by a broadband radiometer can be more readily estimated, while the process to convert the basic measurement to a flux estimate involves many approximations and in some instances the use of data taken from different platforms. Thus the resulting flux error estimates are dependent on mission, not only sensor characteristics [Wielicki, 1995]. Furthermore it has been immediately recognized [Ramanathan, 1987] that the uncertainty in the models that convert the measured radiance to fluxes is one of the principal causes of the uncertainty estimates in the cloud forcing parameter.
 Cloud altitude (that is temperature) and optical thickness are most important factors that affect the LCF. In Figures 1 and 2, LCF is plotted for several cloud types in TRO and SAW atmospheres respectively. The figures show that Ft is almost linear with transmissivity, with slopes depending mainly on cloud altitude. The positive change seen for very thick clouds can be explained by the decrease in the layer source function with cloud opacity in presence of a temperature gradient within the cloud layer. Largest cloud forcing is seen for TRO and CS_h which effectively traps 67% of the TOA upward radiance in clear sky. Ft for the more opaque CS_l is 42% of the TOA clear radiance. It is worth noting that the cloud forcing by a completely opaque AS_t cloud is matched by a CS_h with a transmissivity of about 0.80 or by the CS_l with a transmissivity of about 0.65.
 Lower absolute values are seen in the SAW atmosphere. The subarctic cirrus CS_a, when completely opaque, traps 35% of the clear radiance at TOA. Ft reaches significant values in presence of an arctic cirrus and only very low values for low subarctic clouds. Since no short-wave radiative forcing can occur during the winter season [Doelling et al., 2001], the total cloud forcing practically equals the LCF. In winter the LCF over the Arctic is positive since the clouds are generally colder than the surface. An exception is the ST_a since the stratus is placed in a layer at higher temperature than surface.
 Even if in some cases the LCF at the TOA is small, there might be a strong effect of clouds on the weather and climate processes which is felt through the changes in radiative interaction at the surface and in the atmosphere separately [Stuhlmann, 1995]. For example, very interesting is the case of the thin cirrus and midlevel cloud outflows surrounding the strongest convective areas in the tropics. For this situation the total CF is positive since without optically thick low clouds beneath cirrus there is insufficient reflection to compensate for the cirrus greenhouse effect [Harrison et al., 1990].
4. A Problem in Estimating Long-Wave Cloud Forcing
 Broadband radiometers sense a large portion of the infrared spectrum. We are interested in the energy falling in the far infrared part that is not measured and its effect on the long-wave cloud forcing estimate. The total energy channel of the various instruments flying on the three satellites collecting data for the Earth Radiation Budget Experiment (ERBE), that is ERBS, deployed from space shuttle Challenger in 1984, NOAA 9 and NOAA 10 satellites, measured for more than eight years radiation short-wave of 200 cm−1 (http://asd-www.larc.nasa.gov/). In some references describing the ERBE instrumentations [Barkstrom et al., 1989] a different value of the covered spectrum is reported (from 0,2 to more than 200 microns, that is up to 50 cm−1), but more recent works make use of data in the long-wave region up to a maximum of 50 microns (200 cm−1) as by Harrison et al. . The study of the Earth Radiation Budget has been followed by the Scanner for Radiation Budget (ScaRaB) instrument [Kandel et al., 1994], on board the Meteor 3 satellite, scanning exactly the same spectral band, from 0.2 to 50 microns, of the ERBS satellites. The NASA instrument Clouds and Earth Radiant Energy System (CERES) is collecting data in a wide spectral range: 0.3–100 microns. The total energy channel of the Geostationary Earth Radiation Budget (GERB) on board Meteosat Second Generation (MSG) measures radiance shortwave of 333 cm−1 (http://www.ssd.rl.ac.uk/gerb/inst_chr.htm) even if technical project documentation [Caldwell and Delderfield, 2002] defines a normalized long-wave response decreasing from 25 microns and reaching zero at 70 microns. The same authors compute the error due to nonmeasured portion beyond 70 microns.
 A study of how the unmeasured portion influences the derivation of long-wave cloud forcing has never been published. The aim of this paragraph is to provide an evaluation of the effect. In analogy to equation (2) the LCF derived from a sensor which is not sensitive to the complete emission spectrum is:
where the measured radiances (denoted by subscript m) can be written as functions of the total and the unmeasured (subscript u) portion:
The error in cloud forcing due to incomplete spectral coverage is
defines the percentage fraction of unmeasured energy weighted against the real LCF. In order to simulate D we have assumed that the measurement is taken with sensors that have a box instrument filter function except long-wave of a cutoff value (expressed in cm−1) where the filter function is assumed Gaussian with a specified value for the standard deviation σ. We call T filter the one with σ = 0.7 cm−1 and S filter when σ = 35 cm−1. The two filters do not reflect any specific instrument and are chosen to simulate diverse spectral response functions.
D is plotted in Figure 3 versus cloud top height for the TRO and SAW profiles and the clouds defined in Table 1, using values of IWC that make them completely opaque. The T filter is used with cutoff at 350 cm−1, which filters out all incoming radiance at wave numbers smaller than 347.9 cm−1.
 It is seen that D is always positive (except possibly in some subarctic winter conditions when stratus clouds are embedded into the temperature inversion). Therefore uncorrected measurements from sensors with incomplete spectral coverage produce a systematic underestimation of the real cloud forcing. The value of D becomes important only in presence of cirrus clouds, especially for the highest cirrus cloud (CS_h), not an uncommon situation in the tropics. Remarkably important however is the value of D in case of the SAW cirrus. Even if the absolute error in the long-wave cloud forcing evaluation of this case (CS_a in Table 1) is smaller than that concerning the CS_m (0.860 Wm−2 sr−1 vice 1.672 Wm−2 sr−1) the value of D is larger since the LCF is smaller for the arctic cirrus.
Figure 4 shows the results obtained with both filters and various cutoffs from 100 to 350 cm−1 for an opaque CS_h. The magnitude of D exceeds 1% for the S filter with cutoff at 250 cm−1 and for the T filter with cutoff at about 210 cm−1.
D is plotted in Figure 5 as a function of cloud trasmissivity at 900 cm−1 for the three tropical cirri and the subarctic one. The T filter is used with cutoff at 350 cm−1. For a given cloud type D can be considered nearly constant with transmissivity (that is for various IWC) and this same result (albeit with different numerical values) is obtained with the S filter and different cutoff values (results are not presented here). We have not included in Figure 5, for simplicity, all the results we have obtained for different cloud types and optical depths. However, these show that the error D is always quite independent of cloud transmissivity.
 The nearly constant behavior is obtained since the error (Lu–L*u) due to a particular type of cloud increases almost linearly with decreasing transmissivity and the rate of increase is almost the same of the rate of increase of real long-wave cloud forcing (Lt–L*t) with transmissivity of same cloud (see Figure1). The increase seen for very thick clouds for transmittances less than 0.1 is linked to rapid decrease in the layer source function with cloud opacity mentioned above. As opacity grows the level of effective blackbody emission moves higher and both Ft and Fm decrease because of the lower emitting temperature. However, the decrease of Fm is larger because the maximum emission shifts to lower wave number with decreasing temperature.
 The combined results of Figures 4 and 5 show that once filter type and cutoff are defined for a specific instrument, the systematic error affecting the estimate of cloud forcing can be computed for a given cloud altitude. For example a T filter with cutoff at 210 cm−1 produces (see Figure 4) a D of about 1% in the tropical atmosphere for a cirrus with top at 15.42 km (quite independently of transmissivity).
 Clearly, in real conditions, the temperature profile must be known, the scene must be detected as cloudy and the cloud top height derived from the measurements; the task is not trivial at all, especially if broadband measurements are the only data source, and can be tackled best in case some collocated imagery and spectral information is available.
 The Cloud radiative Forcing (CF) is a much used parameter in the study of the radiative balance of the atmosphere. Its definition relates the role of clouds to the energy absorbed and reflected by the Earth system atmosphere. Recent insights have shown its relations with the energy budget, general circulation, latent heat release and of course with local and regional climate. Because of its importance in climate science it is fundamental to get an exhaustive comprehension and a precise determination of the CF considering that it is the balance of two large terms (short-wave and long-wave cloud forcing) whose determination is affected by various errors and uncertainties.
 We have performed a detailed analysis of the long-wave cloud forcing (LCF), considering the presence of realistic clouds. The impact of different cloudiness has been evaluated in tropical (TRO) and subarctic winter (SAW) conditions. The LCF appears to be linear if plotted versus cloud's transmissivity, with the slope strictly dependent on the cloud's altitude (i.e., temperature).
 In the tropical atmosphere the most opaque stratus and altostratus clouds produce LCF values that are similar to those obtained by very transmissive cirri. The upward radiance that is trapped into the atmosphere can be more than the 67% of the total for the densest and highest cirrus considered. This percentage decreases very fast when lowering the top of the cloud. The SAW cirrus is very efficient, but the energy involved is lesser than the TRO case.
 We have also considered the error introduced in the estimate of LCF when broadband radiometers have an incomplete long-wave spectral coverage and no correction is applied to account for it. The error D (percentage fraction of unmeasured energy weighted against the real LCF) is evaluated for two idealized instrument filter functions (T filter and S filter) with various cutoffs from 100 to 350 cm−1, for the TRO and SAW profiles with different clouds. The error may reach 5% for high opaque tropical cirrus clouds for a T filter cutoff at 350 cm−1, while the error associated with stratus or altostratus clouds is practically zero. High opaque tropical cirrus clouds produce an error that is already higher than 1% for T filter at 200 cm−1 and S filter at 250 cm−1, while the absolute error is around 0.3 W/m2sr for the S filter with cutoff at 200 cm−1 and it doubles with the T filter. Overall these results show that an imperfect long-wave coverage produces a systematic error in the determination of LCF for some cloud conditions. It is found that D varies only slightly with cloud transmissivity, for a given cloud type and height, which indicates the possibility of a correction if the temperature profile and the cloud top height can be derived from the measurements.
transmissivity of the cloud layer.
absorption coefficient, m2/g.
ice water content, g/m3.
liquid water content, g/m3.
effective radius, micron.
radiance, W/m2sr (*cloudy; t total long-wave spectrum; m measured; u unmeasured).
long-wave cloud forcing, W/m2sr (t total long-wave spectrum; m measured).
percentage error in long-wave cloud forcing due to an incomplete spectral coverage.