1. Introduction
Radiative transfer is a critical part of the climate system. About 30% of the incoming solar energy is reflected by the Earth–atmosphere system (Ellingson and Fels 1991), while the remaining part is absorbed. To maintain an equilibrium energy state, the thermal infrared radiation is emitted by Earth and the atmosphere. Most greenhouse gases in the atmosphere allow the solar rays to pass through and warm the Earth–atmosphere system but generally prevent infrared radiation from escaping the atmosphere into space (Donohoe et al. 2014). Modeling of infrared radiative processes in climate models have improved over time, including the use of the correlated-k distribution technique (Mlawer et al. 1997; Li and Barker 2005) and treatment of clouds and their subgrid variability (Raisanen et al. 2004; Shonk et al. 2010; Hill et al. 2011; Li and Barker 2018) resulting in simulations that are closer to observations (von Salzen et al. 2013). However, there is still room to improve the infrared radiation process in climate models.
The Canadian Atmospheric Model version 4.3 (CanAM4.3) and its radiative transfer scheme are used to examine changes to three parameterizations important to modeling infrared radiation, including treatment of incident solar radiation beyond 4 μm, the scattering of infrared radiation by clouds, and the emissivity of the ocean.
According to Planck’s formula, the solar spectra incident at the top of atmosphere (TOA) should extend well beyond 4 μm (the wavelength often used to demarcate solar and infrared radiation). Calculations using MODTRAN version 3.7 (Anderson et al. 1995) indicate that between 4 and 100 μm the solar irradiance at TOA is roughly 11.78 W m−2. How to account for the interaction between the solar and infrared radiation is an essential issue for climate models. A widely used method (Morcrette 1989; Scinocca et al. 2008) includes roughly 12 W m−2 of solar energy beyond 4 μm with the solar radiative fluxes. Doing so can be problematic since most of the solar energy will be transmitted through the atmosphere when in fact it should be interacting with the more strongly absorbing gases at infrared wavelengths. To address this issue, two approaches have been suggested. RRTMG (Mlawer et al. 1997) uses an additional wavelength interval (4–10 μm) in its solar radiative transfer model to account for the optical properties at the longer wavelengths. Li et al. (2010) has proposed another method by directly using the incident solar radiation as an upper boundary condition for infrared radiative transfer calculation. In this method, the solar and longwave radiation utilize the same parameterization of gaseous transmission. Comparison of these two schemes to handle the overlapping of solar and infrared spectra is the first focus of this work.
For the infrared, the method of absorption approximation, neglecting the multiscattering effect, is widely used in current climate models (Mlawer et al. 1997; Chou and Suarez 1999; Oreopoulos et al. 2012; Chen et al. 2014) due to the assumed weak scattering effect in the infrared. However, it has been shown in theoretical studies that neglecting scattering in the infrared can cause an overestimation of the outgoing longwave radiation (OLR) by a few watts per square meter (Li and Fu 2000; Li 2002; Schmidt et al. 2006; Costa and Shine 2006; Zhang et al. 2016; Kuo et al. 2017). Based on observed clouds, Joseph and Min (2003) demonstrated that OLR in the thin cirrus cloud regions could be overestimated by up to 6–8 W m−2 (depending on cloud optical depth and particle size) due to the exclusion of the reflection of upwelling longwave radiation (LW) at the cloud base resulting in heating rate errors of as much as 0.2 K day−1.
Although there are several studies on the cloud LW scattering, most of them are offline and instantaneous. The sensitivity of simulated climate to the inclusion or neglect of cloud scattering is studied using CanAM4.3 is the primary focus of this study.
Surface emissivity has a direct impact on the interaction of infrared radiation with the surface. Modeling surface emissivity is complicated, as it depends on surface geometry, surface reflections, and microscopic heterogeneity (Hanssen et al. 2004). In the last century, surface emissivity in climate models was often simply set to 1, or some value close to 1. However, observations (Mironova 1973) show that emissivity is about 0.95–1.0 at about 5–12.5 μm and decreases with wavelength over 12.5 μm. Hansen et al. (1983) proposed a scheme for broadband ocean surface emissivity, which is characterized by solar zenith angle, and surface wind speed but independent of the spectral wavelength. This scheme is widely used in GCMs (Scinocca et al. 2008; Hanssen et al. 2004; Oreopoulos et al. 2012; von Salzen et al. 2013). Recently, Huang et al. (2016) developed a global surface emissivity database that accounts for variation with the wavelength that is suitable for use in climate and weather models. It was based on both radiative transfer calculations and satellite observations that were validated against independent satellite observations. Differing from the broadband surface emissivity of Hansen et al. (1983), the oceanic surface emissivity is a function of wavelength, changing from 0.95 near 10 μm to 0.85 near 50 μm. Also, Huang et al. (2016) argued that the wind dependence of ocean surface emissivity is relatively small. By calculating the hemispherical-mean spectral emissivity of the calm water surface and the wind-roughed ocean surface (Wu and Smith 1997), Huang et al. (2016) found that the difference in oceanic surface emissivity is bounded to 0.02 in the entire longwave spectrum even for a surface wind speed as large as 15 m s−1. Therefore it is acceptable to use the emissivity of a calm water surface in GCMs. A recent study by Huang et al. (2018) incorporated the global surface emissivity dataset described in Huang et al. (2016) into the NCAR CESM 1.1.1 and evaluated its impact on the simulated climatology as well as simulated climate change scenarios. The slab-ocean runs show that the incorporation of surface emissivity can reduce the cold biases in the polar surface climatology and alleviate the excessive freezing of sea ice in both poles. The impact on the simulated climate change, on the other hand, is negligible. Besides, the solar zenith angle can affect the oceanic surface reflection but has little influence on the thermal emission. Comparison of the two different ocean emissivity schemes is the third focus of this study.
In the following section 2, the climate model used in this study and two radiative transfer schemes are introduced. The discussion about the overlapping of solar and infrared spectra is in section 3. In section 4, the climate effects caused by scattering process in infrared radiation are discussed. Section 5 compares the two oceanic emissivity schemes in climate models. Finally, conclusions are given in section 6.
2. Methods and model
a. Model description
Version 4.3 of the Canadian Atmospheric Model (CanAM4.3) has several improvements relative to its predecessor, CanAM4 (von Salzen et al. 2013), including improvements to parameterizations of radiation and land surface processes. CanAM4.3 uses a hybrid vertical coordinate system with 49 levels between the surface and 1 hPa, with a resolution of about 100 m near the surface. The triangular spectral truncation of the model dynamical core is T63, with an approximate horizontal resolution of 2.8° latitude/longitude (von Salzen et al. 2013). The correlated-k distribution (CKD) method of Li and Barker (2005) is used for gaseous transmission, including most of greenhouse gases H2O, O3, CH4, CO2, N2O, CO, and O2. Nine infrared bands are adopted in the wavenumber ranges 2200–2500, 1900–2200, 1400–1900, 1100–1400, 980–1100, 800–980, 540–800, 340–540, 0–340 cm−1. Optical properties of aerosols and cloud particles vary relatively slowly with wavenumber so they are parameterized as appropriately weighted mean values over each of the wavenumber intervals with liquid and ice cloud optical properties parameterized following Lindner and Li (2000) and Yang et al. (2015) respectively.
CanAM4.3 was used in this study to perform two kinds of numerical experiments. One is an experiment where CanAM4.3 is run over the period 2004–08 (or 1991–2010) and the radiative transfer is called twice, once to compute the radiative fluxes and heating rates that interact with the model and a second time to compute diagnostic fluxes in which some input to the radiative transfer code is modified. This is referred to as an “instantaneous” simulation and is used to illustrate the radiative perturbation of the change in the absence of feedback.
The second type of experiment is referred to as “interactive” simulations in which the modification to the input for the radiative transfer model and the resulting radiative fluxes interact with other physics in CanAM4.3. Thus, the impact of the change and its feedback in the simulated climate can be examined using a pair of simulations. To average over climate variability, these interactive experiments are each simulated for 20 years (1991–2010) using the AMIP configuration from phase 5 of the Coupled Model Intercomparison Project (CMIP5) (Hurrell et al. 2011), including transient specified sea surface temperatures, sea ice extent averaged, and forcings over the period 1991–2010.
b. Infrared radiative transfer with and without the cloud scattering effect
3. Overlapping of solar and infrared spectra
For wavelengths where solar and infrared radiation overlap, incoming solar energy at TOA is inserted into the longwave radiative transfer process of (5) as an upper boundary condition (Li et al. 2010). When there is no incoming solar energy at TOA, the upper boundary condition at level 1 is 
In this section, we compare two methods used to account for incident solar radiation at TOA for wavelengths greater than 4 μm, using a single band in the solar radiative transfer model (as is the case for RRTMG) and treating it as a upper boundary conditions for the infrared radiative transfer (as is the case in the CanAM4.3 model). The use of a single extra band in the solar radiative transfer code has two potential problems. First, using average cloud optical properties for a large wavelength interval in the infrared can introduce an error since the cloud longwave optical properties are sensitive to wavelength (Yang et al. 2015; Zhao et al. 2018) and second, the k-distribution of gaseous transmission in the extra band is very rough, as the k number of the extra band is only about one-tenth of that in LW bands covering 4–10 μm in RRTMG. The simplified gaseous transmission can introduce substantial errors as well. In the following, we treat the k-distribution of the extra band the same as that of the infrared bands 1–5 (4–10.2 μm) since the radiation algorithm we used contains no extra band and we do not know how to properly simplify the gaseous transmission for such band property. Therefore, we only analyze error caused by using averaged cloud optical properties. We call this method AA_SBN, which is the sum of the result from AA_SCA with zero upper boundary input and the result from the extra band through solar radiative transfer, based on the linearity of the radiative transfer equation. Because we use the same gaseous transmission in the extra band as that in AA_SCA, the clear-sky results are the same for AA_SBN and AA_SCA, and we only examine the cloudy-sky results.
The top two rows of Fig. 1 present the errors of the two methods for sky containing an ice cloud located between 9 and 11 km with an ice water content 0.0048 g m−3. The U.S. standard atmosphere profile (McClatchey et al. 1972) is used. The benchmark results are from the discrete ordinates numerical model (DISORT) (Stamnes et al. 1988) with 128 streams (D128S). Since AA_SCA is a two-stream approximation, there is a relatively large error in the downward flux, mostly in the atmospheric window region. However, AA_SCA is very accurate for wavelengths less than 8 μm, indicating that the method of direct input solar energy is accurate because more than 90% of the total incident solar energy in the infrared (>4 μm) is within 4–8 μm. In contrast, AA_SBN produces a much larger error for wavelengths less than 8 μm because the optical properties of the high cloud are wavelength dependent and cannot be modeled well by broadband mean. The second column shows the errors of the upward flux. Also, AA_SCA produces relatively large error close to the spectral 10 μm, due to the two-stream approximation. The broadband errors of AA_SCA were shown in Li and Fu (2000), with the relative errors less than 1%. Also, the AA_SBN produces a larger error between 4 and 6 μm compared to AA_SCA. The third column shows the cooling rate for the high cloud. AA_SBN produces relatively large error at the cloud top, while the result of AA_SCA is much more accurate.
The errors in (left) longwave downward flux, (center) upward flux, and (right) heating rate for the (top two rows) high cloud and (bottom two rows) low cloud for (first and third rows) AA_SCA and (second and fourth rows) AA_SBN; the dotted area indicates the location of the prescribed cloud cases. The benchmark results are from D128S, and the solar zenith angle is 60°.
Citation: Journal of Climate 32, 15; 10.1175/JCLI-D-18-0648.1
The bottom two rows show the results of the water cloud located between 1 and 2 km with a liquid water content of 0.22 g m−3. In contrast to the high cloud, the difference between the two schemes is much smaller because the water cloud optical properties are less dependent on wavelength (Lindner and Li 2000). Besides, the downward solar flux, including that beyond 4 μm, is strongly attenuated by the atmosphere when it reaches the top of the low cloud, reducing the solar radiance incident on the top of the cloud. This means that the downward flux below the low cloud mostly comes from the thermal emission by the cloud, which is primarily dependent on local temperature. All these factors make the difference between the two schemes less in comparison with the high cloud case.
Note that the error of AA_SBN would be much larger than that shown in Fig. 1 if the gaseous transmission were treated in a single wavelength interval as done in RRTMG.
Overall, the superiority of AA_SCA is clear, as it requires no extra calculation but produces more accurate results compared to AA_SBN. RRTMG uses a LW radiative transfer equation similar to (5) (Mlawer et al. 1997), and thus it is straightforward to account for the incoming solar energy through an upper boundary condition at TOA.
Instantaneous experiments with CanAM4.3 are performed to investigate the impact of the different treatment for the overlapped incoming solar energy in the infrared (AA_SCA and AA_SBN). Figures 2a and 2b show the net flux differences at TOA between AA_SCA and AA_SBN. Since the downward solar flux at TOA is the same for both schemes, the net flux is the difference in OLR between AA_SCA and AA_SBN. It is found that AA_SCA always produces a lower OLR, which is consistent with Fig. 1. Differences between the two schemes are generally small, less than 0.01 W m−2 in the boreal winter and austral winter with relatively larger differences occurring in the Pacific warm pool region, where the warm surface temperature produces more high clouds. The distribution of the difference in OLR is consistent with that of the high cloud (see Fig. 4), as it is shown in Fig. 1 that AA_SBN causes a larger reflection for high clouds.
Instantaneous run: the differences in the longwave net flux (a),(b) at TOA and (c),(d) at the surface between AA_SCA and AA_SBN for (left) JJA and (right) DJF. Contour lines are the results simulated by the 5-yr (2004–08) CanAM4.3 standard run of AA_SCA.
Citation: Journal of Climate 32, 15; 10.1175/JCLI-D-18-0648.1
Figures 2c and 2d show the net flux at the surface between AA_SCA and AA_SBN. Since the upward LW flux at the surface is the same for both schemes, the results refer to the difference in downward flux at the surface between AA_SBN and AA_SCA. It is found that AA_SBN always produces a lower downward flux at the surface; however, the differences between the two schemes are small in most areas, with the value generally less than 0.1 W m−2 although larger differences, up to 0.7 W m−2, occur over Antarctica during austral summer (Fig. 2d). Again, this larger difference in the downward flux is consistent with the existence of high cloud (Fig. 4) since during austral summer over Antarctica the diurnal mean solar zenith angle is large and the difference between the two schemes is larger (see Fig. 1 for μ0 = 0.5). Because the difference is generally very small in the instantaneous experiments, interactive experiments are not shown.
4. Cloud LW scattering
In this section, we examine the effect of scattering of LW radiation by clouds in CanAM4.3. An instantaneous experiment with CanAM4.3 is used to show the effect of scattering (AA_SCA minus AA) in the absence of feedbacks (Figs. 3a,b). More than −3 W m−2 difference in OLR between AA_SCA and AA occurs in the Asian summer monsoon region, central Africa, and Central America due to the cloud LW scattering and the relatively large cloud fraction in these regions (Fig. 4). Downward scattering of LW radiation by clouds enhances the downward flux at the surface shown (Figs. 3c,d). This means that scattering of LW radiation by clouds reduces the LW radiation emitted to space. For regions with smaller cloud fraction, such as North Africa, central Asia, South America, and central Australia, the differences between AA_SCA and AA in OLR are smaller, bounded to 1.2 W m−2. Globally averaged reduction in OLR is 1.63 W m−2 during JJA and 1.64 W m−2 during DJF while the globally averaged difference in downward LW flux at the surface is much smaller, 0.4 W m−2 during JJA and 0.43 W m−2 during DJF.
Instantaneous run: the differences in (a),(b) the longwave upward flux at TOA and (c),(d) the downward flux at the surface between AA_SCA and AA for (left) JJA and (right) DJF. The global mean value is given in the top-right corner of each panel. Contour lines are results simulated by the 20-yr (1991–2010) CanAM4.3 standard run of AA_SCA.
Citation: Journal of Climate 32, 15; 10.1175/JCLI-D-18-0648.1
(a),(b) Total cloud fraction and (e),(f) high cloud fraction based on the 20-yr (1991–2010) CanAM4.3 standard run of AA_SCA; the differences (AA_SCA − AA) in the (c),(d) total and (g),(h) high cloud fractions.
Citation: Journal of Climate 32, 15; 10.1175/JCLI-D-18-0648.1
To evaluate the effect of cloud LW scattering on climate two interactive experiments based on AA and AA_SCA are performed with CanAM4.3. Since CanAM4.3 uses the AA SCA configuration and it has already been adjusted to balance a TOA energy budget consistent with observations (von Salzen et al. 2013). In the AA experiment, the model was readjusted to rebalance the net flux at TOA because of enhanced OLR (see details in the appendix). Figures 4a and 4b show the seasonal mean total cloud fractions of AA_SCA, and Figs. 4c and 4d show the difference in cloud fraction between AA_SCA and AA. Cloud LW scattering reduces the OLR (Fig. 3), which is beneficial as it generates more water vapor and cloud in the atmosphere, which in turn can induce a stronger LW scattering effect and positive climate feedback. Usually, ice clouds are more crucial to LW scattering because of the large temperature differences relative to the surface compared to water cloud (Hong and Liu 2015). High cloud fraction simulated by CanAM4.3 mainly occurs in boreal and austral summers (Figs. 4e–h) with a different pattern similar to that of the total cloud fraction, especially in regions between 30°S and 30°N, indicating that high cloud dominates the change in the total cloud.
The interactive runs have a distribution of OLR (Figs. 5a,b) that differs from the instantaneous experiment (Fig. 3) but both have a peak difference over the Asian monsoon region. Substantial changes due to cloud LW scattering also occur over central Africa and northern Latin America during JJA, and the Pacific warm pool region, southern Africa, and southern Latin America during DJF. The global and seasonal mean OLR differences are −2.02 W m−2 during JJA and −2.12 W m−2 during DJF, about 30% higher than for the instantaneous simulations. Therefore, we posit that positive climate feedback occurs that considerably enhances the cloud LW scattering effects and the result is more reduction of OLR, given that regions of large OLR reduction roughly match regions with obviously increased cloud fraction (Fig. 4).
Interactive run: the difference in (a),(b) the LW upward flux at TOA, (c),(d) the downward flux at the surface, and (e),(f) LW cloud forcing between AA_SCA and AA for (left) JJA and (right) DJF. The global mean value of the difference is shown at the top-right corner of each panel. The dots are the locations passing the 90% confidence level. Contour lines are results simulated by the 20-yr (1991–2010) CanAM4.3 standard run of AA_SCA.
Citation: Journal of Climate 32, 15; 10.1175/JCLI-D-18-0648.1
For the downward LW flux at the surface, the differences between the AA_SCA and AA configurations (Figs. 5c,d) in the interactive simulations are also found to be larger than in the instantaneous simulations. The global and seasonal mean difference of the downward LW flux at the surface is +0.92 W m−2 during JJA and +0.86 W m−2 during DJF, double the difference found in the instantaneous experiment. Comparing Figs. 3 and 5, the cloud LW scattering effects at the surface show very different patterns between instantaneous and interactive runs, with the difference pattern for the interactive runs being much more inhomogeneous than for the instantaneous run. This seems to be caused by changes in temperature structure within the interactive runs (Figs. 6c,d).
Interactive run: the difference in (a),(b) the zonal mean longwave heating rate, (c),(d) the zonal mean temperature, and (e),(f) the zonal mean specific humidity between AA_SCA and AA for (left) JJA and (right) DJF. The dots are the locations passing the 90% confidence level. Contour lines are results simulated by the 20-yr (1991–2010) CanAM4.3 standard run of AA_SCA.
Citation: Journal of Climate 32, 15; 10.1175/JCLI-D-18-0648.1
Longwave cloud radiative forcing (LWCF) at TOA is shown in Figs. 5e and 5f. The physics of LWCF indicates the locally trapped LW energy by clouds. Scattering of LW radiation by clouds always increases LWCF because more infrared radiation is scattered back to the lower atmosphere and surface. Patterns of change in LWCF closely follow patterns of change in OLR with global and seasonal mean enhancements of LWCF due to the cloud LW scattering effect of +1.80 W m−2 during JJA and +1.76 W m−2 during DJF. The increase in LWCF can exceed 10 W m−2 in the summer Asian monsoon region where the local LWCF is only about 60 W m−2; thus, the cloud LW scattering effect can cause a considerable enhancement warming effect in such area.
Figures 6a and 6b show the zonal mean distribution of the longwave heating rate due to the cloud LW scattering. The longwave cooling is strengthened near the tropopause, which is up to about −0.18 K day−1 at 0°–20°N during JJA and about −0.12 K day−1 at 0°–20°S during DJF, as less infrared energy is transmitted through the high clouds due to the energy trap effect by the LW scattering. In contrast, below the tropopause, the warming can reach 0.18 K day−1 during JJA and 0.16 K day−1 during DJF, which is caused by the cloud LW scattering and the positive climate feedback.
Cloud LW scattering decreases the zonal mean temperature (Figs. 6c,d) above the tropopause, similar to the cooling effect shown in Figs. 6a and 6b. In the troposphere, temperature generally increases with the largest increase (up to 10°C) occurring in the upper tropical troposphere. The temperature change is not completely consistent with the change in heating rate since temperature is also affected by thermodynamic heating. Generally, atmospheric water vapor amount increases with temperature since a warmer environment can hold more water vapor. Figures 6e and 6f show the change in specific humidity due to the cloud LW scattering effect. The large increases of specific humidity happen in the troposphere, mostly at 10°S–30°N during JJA and 20°–20°N during DJF. Water vapor is the strongest greenhouse gas in the trapping of longwave radiation energy, and such positive feedback can further enhance the water vapor in the atmosphere (Ceppi and Shepherd 2017).
The change in the strength of the Hadley circulation is characterized by the meridional streamfunction (Figs. 7a,b). During JJA, the temperature gradient in the Southern Hemisphere is increased toward the polar region (Fig. 6c), which can strengthen the Hadley circulation in the Southern Hemisphere (Cook 2003; Lu et al. 2007; Adam et al. 2014). Because the streamfunction in the Southern Hemisphere is a negative value, a negative difference between the AA_SCA and AA indicates a strengthening of the Hadley circulation. The ascending branch of the Hadley circulation is significantly strengthened, as the difference in the streamfunction reaches −0.8 × 1010 kg s−1. A stronger ascending branch can enhance the northward shifting of the intertropical convergence zone (ITCZ) (Dargan and Hwang 2011), which is beneficial to the enhancement of Asian summer monsoons (Gadgil 2003; Fleitmann et al. 2007). Figure 7c shows the distribution of zonal wind during JJA. A strong westerly wind, known as the high-level jet stream, occurs in the upper half of the troposphere (up to 12–15 km). The westerly wind is weakened near the descending branch of the Hadley circulation because the stronger descending branch can weaken the westerly due to the Coriolis force. The strengthening and the northward shift of the ITCZ are shown in the zonal wind distribution. During DJF, the Hadley circulation becomes stronger in the Northern Hemisphere. Also the ascending and descending regions of the Hadley circulation strengthen, and the westerly wind weakens near the descending branch of the Hadley circulation.
Interactive run: the difference in (a),(b) the zonal mean of the meridional streamfunction, (c),(d) the zonal mean wind speed, and (e),(f) the distributions of precipitation and the zonal mean results between AA_SCA and AA for (left) JJA and (right) DJF. The dots are the locations passing the 90% confidence level. Contour lines are results simulated by the 20-yr (1991–2010) CanAM4.3 standard run of AA_SCA.
Citation: Journal of Climate 32, 15; 10.1175/JCLI-D-18-0648.1
The enhanced rising motion in the Hadley circulation and the shift of ITCZ can cause changes in precipitation (Z̆agar et al. 2011), as shown in Figs. 7e and 7f. During JJA, a significant increase of precipitation happens near the equator at about 15°N, within the ascending branch of the Hadley circulation. In the descending branch of the Hadley circulation, around 20°–30°S, the reduction of precipitation is apparent. Near the equator, precipitation increases in several regions, which could relate to the enhancement of water vapor and cloud fractions there (Holton 2004). During DJF, precipitation is reduced in the winter Asian monsoon region and North Australia between 0° and 20°S where the Hadley circulation is weakened. Precipitation near 20°S increases, corresponding to increased southward cross-equatorial airflow and a southward shift of the ITCZ. On the other hand, warming in the midtroposphere near the equator caused by cloud LW scattering effect may inhibit the convergence of moist air, leading to less latent heat release and reduced precipitation near the equator.
5. Surface emissivity
In Huang et al. (2016), the oceanic surface emissivity is instead only dependent on spectral bands. For the nine infrared wavelength intervals used in the CanAM4.3 radiative transfer model, the values of ocean emissivity are 0.962, 0.963, 0.963, 0.967, 0.975, 0.976, 0.926, 0.908, and 0.868, showing that the emissivity decreases as in the far infrared. This section compares the surface emissivity schemes by Hansen et al. (1983) and by Huang et al. (2016) (referred to simply as the Hansen scheme and as the Huang scheme).
a. Offline results
Offline radiative transfer calculations used a midlatitude summer atmospheric profile. Because the Hansen scheme depends on the surface wind speed and solar zenith angle, wind speeds varying from 0 to 35 m s−1 and three values of the cosine of solar zenith angle 
Figure 8 shows the band-to-band upward flux at the surface between the Hansen and Huang schemes (Hansen minus Huang) for a clear sky, a low cloud, and a high cloud case. The definitions of low and high clouds are the same as those in Fig. 1. Compared to the Huang scheme, generally the Hansen scheme produces a larger upward flux at a smaller solar zenith angle but a smaller upward flux at a larger solar zenith angle, especially in bands 4–7. The differences in upward flux between the clear and cloudy skies are small. The Hansen scheme also depends on the surface wind speed. At a smaller zenith angle of 30°, the difference between the two schemes increases with an increasing surface wind speed; at a larger zenith angle of 75°, the result becomes opposite.
The difference (Hansen scheme minus Huang scheme) of the upward flux at the surface for (left) clear sky, (center) cloudy sky of a low cloud, and (right) cloudy sky of a high cloud for three solar zenith angles of (top) 30°, (middle) 60°, and (bottom) 75°. In each plot, the x axis varies with the infrared bands and the y axis varies with the surface wind speeds.
Citation: Journal of Climate 32, 15; 10.1175/JCLI-D-18-0648.1
b. Radiative effects in climate model
Experiments with CanAM4.3 include LW scattering by clouds (AA_SCA), which is the default configuration. Instantaneous seasonal mean differences (Hansen minus Huang) in upward flux at the surface and TOA between the two schemes is shown in Fig. 9. Since only ocean emissivity was changed, sea ice and land emissivities were kept the same, and we just focus on instantaneous differences over open ocean. During DJF, the Hansen scheme produces larger values of upward surface flux in the tropics and lower latitudes but smaller values at higher latitudes compared to the Huang scheme (Fig. 9). This is consistent with the offline results because the diurnal mean solar zenith angle is smaller for lower latitudes and the Hansen scheme produces a lower upward surface flux at a smaller solar zenith angle. The maximum difference in the upward fluxes occurs in the eastern Asia Kuroshio region and Labrador Sea, with values over 1.0 W m−2 for JJA and 1.4 W m−2 for DJF. According to Monahan (2006), these two regions have strong sea surface winds that affect the Hansen scheme emissivity. During JJA, large differences (over 2 W m−2) between the two schemes occur in the Southern Hemisphere jet stream region due to the strong surface winds there.
Instantaneous run: the differences (Hansen scheme minus Huang scheme) of the LW upward flux (a),(b) at the surface and (c),(d) at TOA for (left) JJA and (right) DJF.
Citation: Journal of Climate 32, 15; 10.1175/JCLI-D-18-0648.1
Figures 9c and 9d show the differences in upward flux at TOA (up to 0.6 W m−2), which is much smaller than differences in the surface fluxes. From (4), the upward radiance through a layer is determined by two factors, the transmission of radiance from the layer bottom and emission inside the layer. At TOA, a large portion of the radiance from the surface has been attenuated by the atmosphere, so differences in emissivity are reduced. In the instantaneous experiments, the temperature is kept the same for all radiative transfer calculations so the atmospheric emission is similar. Therefore, the differences in upward flux between the two schemes become much smaller at TOA compared to the surface.
The difference in the upward surface flux for a pair of interactive simulations (one using the Huang scheme and the other the Hansen scheme) is shown in Figs. 10a and 10b. To some extent, the different patterns are similar to those of the instantaneous experiments with the Hansen scheme producing larger values of upward surface flux in the tropics and lower latitudes but smaller values at the higher latitudes. However, the magnitude of the differences between the two schemes is much smaller. Because of climate feedback, the temperature structure inside the atmosphere changes (see Figs. 10g,h), which influences the downward flux and further changes the surface emissivity as discussed in (7). Since the difference between the two schemes in an interactive simulation becomes smaller compared to that in an instantaneous simulation, the climate feedback is negative. This is opposite to the effect of LW scattering, which results in positive climate feedback.
Interactive run: the difference (Hansen scheme minus Huang scheme) of (a),(b) the LW upward flux at the surface, (c),(d) the upward flux at TOA, and (e),(f) cloud fraction between the Hansen scheme and Huang scheme for JJA and DJF. (g),(h) The zonal mean temperature difference between the two schemes. Contour lines are results simulated by the 20-yr (1991–2010) CanAM4.3 standard run of Hansen scheme.
Citation: Journal of Climate 32, 15; 10.1175/JCLI-D-18-0648.1
Figures 10c and 10d show differences in OLR between the two schemes. As for the surface fluxes, climate feedbacks reduce differences between the two schemes compared to the instantaneous experiment. In Fig. 9, the Hansen scheme always produces a higher OLR in lower latitudes but such a different pattern is not seen in the interactive experiments, which we attribute to changes in cloud fraction. Since cloud top re-emitted upward flux is generally much lower than that from the surface emission, cloud distribution, especially high clouds, can strongly influence OLR. Figures 10e and 10f show the differences in cloud fraction between the two interactive simulations, showing that changes in cloud fraction are mostly anticorrelated to change in OLR (i.e., an increase in cloud fraction corresponds to a decrease in OLR).
In the tropics and lower-latitude regions, the Hansen scheme produces larger upward surface fluxes causing the atmosphere to warm (Figs. 10g,h), while at higher latitudes the Hansen scheme reduces the energy into the atmosphere but the response in temperature is not as straightforward. In the northern polar region, although the Hansen scheme produces a lower temperature compared to the Huang scheme, the result cannot pass the t test. Over Antarctica during DJF, the surface emissivity is the same for both simulations since it is snow covered but there is a relatively large increase in temperature for the simulation using the Hansen scheme. This is largely due to the change of atmospheric circulation, which transports more energy into the polar region. Generally, the climate impact from the different oceanic surface emissivity is much smaller than that from the cloud LW scattering.
6. Conclusions
In this study, we have discussed three issues that can affect infrared radiation in climate models, including the treatment of incident solar radiation beyond 4 μm, cloud longwave scattering, and the ocean surface emissivity.
For the treatment of solar radiation beyond 4 μm two approaches were compared, using a single additional band in the solar radiative transfer model and using the incident solar radiation as an upper boundary condition for infrared radiative transfer calculation. Offline calculations with a high cloud show that the extra band approach can overestimate the downward flux and overestimate heating rate at cloud top while the method of direct input solar energy yield very accurate results in the range of 4–10 μm, where most of the solar energy beyond 4 μm, up to 12 W m−2, occurs. The difference between the two schemes is minimal in the low cloud case. Instantaneous simulations with CanAM4.3 show that differences in the net radiative flux at TOA and surface are generally very small, with the values less than 0.1 W m−2 for most of the regions.
Cloud LW scattering causes more infrared energy to be trapped in the atmosphere, which reduces OLR and enhances the downward flux and cloud longwave radiation forcing. The longwave cooling rate is enhanced above the tropopause and reduced inside the troposphere. Consequently, the temperature increases in almost the whole troposphere with the largest increase (up to 1°C) occurring in the tropical upper troposphere. This causes the temperature gradient to increase toward the polar region, which in turn causes strengthens the Hadley circulation and shifts the ITCZ. The water vapor in the lower troposphere is increased due to the increased of tropospheric temperature. Simulated precipitation was also impacted by changes in the Hadley circulation, ITCZ and water vapor inside the atmosphere.
Two oceanic surface emissivity schemes are compared. It is found that the broadband Hansen scheme is very sensitive to the surface wind speed and solar zenith angle while the Huang scheme depends only on the spectral band. CanAM4.3 instantaneous simulations show that the Huang scheme produces larger values of upward surface flux in the tropics and lower-latitude regions but smaller values at high latitudes. The seasonal mean difference between the two schemes can be over 1 W m−2. Opposite to the cloud LW scattering effect, the climate feedback to the surface emissivity is negative.
Overall, the cloud LW scattering causes much larger climate impact compared to the other two physical processes discussed in this study. Although the choice of the two schemes on the overlapping of solar and LW spectra causes the minimum different climate responses, the method of direct input solar incident energy is much more efficient than the method of an extra band. The physics in climate models will be more accurately processed if these issues are correctly addressed.
Acknowledgments
The authors thank two anonymous reviewers for their constructive comment, and Professor Norris for his editorial effort. Kun Wu acknowledges funding support by the Postgraduate Research and Practice Innovation Program of Jiangsu Province (KYCX17_0873).
APPENDIX
The LW Scattering and the Tuning of the GCM for Energy Balance in the AA Scheme
This appendix contains two parts: the LW scattering and the tuning of GCM for energy balance in AA scheme.
a. LW scattering
b. GCM tuning
CanAM4.3 with the AA_SCA scheme has reached the energy balance at TOA. When the AA scheme is used in the interactive runs, the energy balance at TOA is broken since OLR is enhanced due to no LW scattering effect. For a longer time scale, the global averaged net solar flux at TOA should be very close to the global averaged OLR. To obtain the energy balance, we have to boost the reflected solar flux to space, which can be achieved by tuning cloud microphysical and microphysical parameters. For example, a slight increase of low cloud fraction is an efficient way for such a tune. Figures A1a and A1b show the differences in net solar and infrared fluxes between the tuned AA and AA_SCA (AA minus AA_SCA). AA has a larger OLR compared to AA_SCA (global mean value of 1.52 W m−2) but smaller solar reflection (global mean value of −1.47 W m−2). Most areas of large values of OLR correspond to large solar reflections, as both runs of CanAM4.3 with AA and AA_SCA schemes are well balanced. Since most current GCMs do not contain the effect of LW scattering, when LW scattering is introduced, the tuning to energy rebalance at TOA is necessary. However, the tuning direction is opposite, as they need to enhance the cloud solar reflection to balance the reduced OLR due to the inclusion of LW scattering.
Interactive run: the differences (AA minus AA_SCA) of (a) net solar flux at TOA and (b) net infrared flux at TOA. The annual global mean value is given in the top-left corner of each panel. Contour lines are results simulated by the 20-yr (1991–2010) CanAM4.3 standard run of AA_SCA.
Citation: Journal of Climate 32, 15; 10.1175/JCLI-D-18-0648.1
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