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  • View in gallery

    Zonally averaged, nonsaturated, latitude–height distributions of RH for (left) January and (right) July in (top to bottom) 2003, 2007, and 2011. The colored RH (%) shadings of 10, 30, 60, 80, 90, 100 are displayed and RH is only plotted for good-quality data (QC = 0, 1). White areas indicate that there are no retrievals of this quality or the RH < 10%.

  • View in gallery

    Height vs latitude RH climatologies of (left) January and (right) July from AIRS 11 yr of measurements (1 Sep 2002–31 Aug 2013).

  • View in gallery

    January minus July RH differences in (top to bottom) 2003, 2007, and 2011. The light contours mark positive differences, and the dark contours mark negative differences.

  • View in gallery

    The RH profiles in the tropics for (left) January and (right) July in (top to bottom) 2003, 2007, and 2011. In all cases, with a slight exception of January 2011, the minimum RH is reached at 300 hPa.

  • View in gallery

    Pdfs of RH at (top to bottom) 200–925 hPa for (left) January and (right) July 2003 in the ascending branch of the Hadley circulation (10°N–10°S). Solid curves in this figure and Figs. 6 and 7 correspond to daytime spacecraft orbits and the dashed curves correspond to nighttime orbits to show changes in pdfs due to the diurnal cycle, which is mainly seen below 500 hPa. The bimodal distributions at 500 hPa in January and July, and at 700 hPa in July are statistically significant at the 95% level, as found using the pdf smoothing method illustrated in Fig. 8.

  • View in gallery

    As in Fig. 5, but for the descending branch of the Hadley circulation. The additional dry peak at 925 hPa reflects the contribution of the Sahara Desert.

  • View in gallery

    As in Fig. 5, but for the middle northern latitudes (30°–60°N) where air is well mixed by turbulent eddies. The bimodal distributions at 300 hPa in January and July are statistically significant at the 95% level.

  • View in gallery

    As in Fig. 5, but for the high northern latitudes (60°–90°N). Note the appearance of bimodality at 300 hPa. (top) Extremely dry air is present in the polar stratosphere at 200 hPa.

  • View in gallery

    (top) The family of pdfs of RH smoothed with progressively increased widths of the Gaussian kernel. The data are for 500 hPa during January 2003 in the 10°S–10°N area. The thick curve corresponds to the optimal selection of the kernel width used in the pdf shown in the third panel on the left in Fig. 4. (bottom) The map of the signs of derivatives (slopes) of the curves shown in the top panel. The thin line corresponds to the “optimal” selection of the kernel width whose pdf can be seen in Fig. 3. The black and light gray colors show the statistically significant signs of the derivatives at the 95% level, indicating that only two large peaks are statistically significant at this level. The dark gray color marks insignificant areas.

  • View in gallery

    Clear-sky OLR (crosses) and all-sky OLR (solid line) as functions of surface temperature percentiles (Tsurf pts). We use 20 percentiles equally spaced between the 0th and 100th percentiles. The numbers along the x axis mark the values of the percentiles in kelvins. (left) January and (right) July (top to bottom) 2003, 2007, and 2011. The top number in each panel refers to the sensitivity for clear-sky OLR and the lower number refers to the sensitivity for all-sky OLR. The sensitivities are determined by fitting a line to linear parts of the curves. The errors of the slopes are given at the 1σ level of significance. The starting nonlinear parts of the curves refer mostly to frozen areas.

  • View in gallery

    Clear-sky OLR in the tropics as a function of RH for (left) January and (right) July 2003 (top to bottom) from 60°N–90°N to 10°S–10°N. Note that the vertical axes in a given latitudinal range are the same for January and July but change with the latitude band.

  • View in gallery

    Contoured shading (W m−2) of clear-sky OLR in the tropics as a function of the percentiles of the surface temperature and RH. The slope of contour lines is changing with the decrease of RH, reaching the highest values at low relative humidities.

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Relative Humidity in the Troposphere with AIRS

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Abstract

New global satellite data from the Atmospheric Infrared Sounder (AIRS) are applied to study the tropospheric relative humidity (RH) distribution and its influence on outgoing longwave radiation (OLR) for January and July in 2003, 2007, and 2011. RH has the largest maxima over 90% in the equatorial tropopause layer in January. Maxima in July do not arise above 60%. Seasonal variations of about 20% in zonally averaged RH are observed in the equatorial region of the low troposphere, in the equatorial tropopause layer, and in the polar regions. The seasonal variability in the recent decade has increased by about 5% relative to that in 1973–88, indicating a positive trend. The observed RH profiles indicate a moist bias in the tropical and subtropical regions typically produced by the general circulation models. The new data and method of evaluating the statistical significance of bimodality confirm bimodal probability distributions of RH at large tropospheric scales, notably in the ascending branch of the Hadley circulation. Bimodality is also seen at 500–300 hPa in mid- and high latitudes. Since the drying time of the air is short compared with the mixing time of moist and dry air, the bimodality reflects the large-scale distribution of sources of moisture and the atmospheric circulation. Analysis of OLR dependence on surface temperature shows a 0.2 W m−2 K−1 difference in sensitivities between clear-sky and all-sky OLR, indicating a positive longwave cloud radiative forcing. Diagrams of the clear-sky OLR as functions of percentiles of surface temperature and relative humidity in the tropics are designed to provide a new measure of the supergreenhouse effect.

Corresponding author address: Alexander Ruzmaikin, MS 169-506, Jet Propulsion Laboratory, 4800 Oak Grove Dr., Pasadena, CA 91109. E-mail: alexander.ruzmaikin@jpl.nasa.gov

Abstract

New global satellite data from the Atmospheric Infrared Sounder (AIRS) are applied to study the tropospheric relative humidity (RH) distribution and its influence on outgoing longwave radiation (OLR) for January and July in 2003, 2007, and 2011. RH has the largest maxima over 90% in the equatorial tropopause layer in January. Maxima in July do not arise above 60%. Seasonal variations of about 20% in zonally averaged RH are observed in the equatorial region of the low troposphere, in the equatorial tropopause layer, and in the polar regions. The seasonal variability in the recent decade has increased by about 5% relative to that in 1973–88, indicating a positive trend. The observed RH profiles indicate a moist bias in the tropical and subtropical regions typically produced by the general circulation models. The new data and method of evaluating the statistical significance of bimodality confirm bimodal probability distributions of RH at large tropospheric scales, notably in the ascending branch of the Hadley circulation. Bimodality is also seen at 500–300 hPa in mid- and high latitudes. Since the drying time of the air is short compared with the mixing time of moist and dry air, the bimodality reflects the large-scale distribution of sources of moisture and the atmospheric circulation. Analysis of OLR dependence on surface temperature shows a 0.2 W m−2 K−1 difference in sensitivities between clear-sky and all-sky OLR, indicating a positive longwave cloud radiative forcing. Diagrams of the clear-sky OLR as functions of percentiles of surface temperature and relative humidity in the tropics are designed to provide a new measure of the supergreenhouse effect.

Corresponding author address: Alexander Ruzmaikin, MS 169-506, Jet Propulsion Laboratory, 4800 Oak Grove Dr., Pasadena, CA 91109. E-mail: alexander.ruzmaikin@jpl.nasa.gov

1. Introduction

In accord with the Gibbs’s phase rule (Gibbs 1876), which allows us to identify the number of independent variables in a multicomponent, multiphase thermodynamic system as C + 2 − P, where C is the number of components and P is the number of phases, the dry air and water in Earth’s atmosphere in a nonsaturated (one phase) state can be characterized by three independent variables. These variables are usually selected as the pressure, temperature, and a water-substance characteristic. The relative humidity (RH) is perhaps the best state variable to characterize the water substance (Manabe and Wetherald 1967; Peixoto and Ort 1996; Held and Shell 2012). It depends on the amount of water in the atmosphere and on the holding capacity of air for moisture and is an indicator of possible phase changes such as cloud formation and precipitation. It is related to convection, subsidence, and horizontal air advection; and it offers a better description of water vapor and cloud feedbacks compared with specific humidity. RH is defined as the ratio of water vapor pressure to the saturation vapor pressure, which is an exponential function of temperature given by the Clausius–Clapeyron equation (cf. Peixoto and Ort 1996). In their outstanding work, Peixoto and Ort (1996) advocated the importance of using relative humidity in weather and climate studies and the need for global satellite observations to provide global space–time coverage of it.

Our paper, which uses new retrievals of relative humidity from the Atmospheric Infrared Sounder (AIRS) global satellite data, addresses three well-known but not fully resolved problems: 1) the time invariance of the global relative humidity that is critically important for determination of the water vapor climate feedback (Manabe and Wetherald 1967; Held and Soden 2000; Sherwood et al. 2010); 2) simultaneous occurrence of separated moist and dry air, which was seen in the bimodality of the relative humidity probability distributions and reported to be common by Zhang et al. (2003) but disputed by Sherwood et al. (2006); and 3) humidity dependence of the outgoing longwave radiation (OLR) in the tropics, the so-called the supergreenhouse effect (Raval and Ramanathan 1989).

Satellite data involving the water vapor and relative humidity have widely been used, for example, for investigating the relationship between water vapor and sea surface temperature (Stephens 1990), studying the upper-tropospheric humidity (Soden and Bretherton 1993; Schmetz and van de Berg 1994), studying the climatology of upper-tropospheric air (Gettelman et al. 2006), for comparison of RH in clear-sky and cloudy areas (Kahn et al. 2009), for testing the time invariance of global RH (Du et al. 2012), and for the assessment of climate feedback processes (Chung et al. 2010). The validation of general circulation models (GCMs) demonstrated that the GCMs that have relative humidity consistent with the RH observed by satellites in the tropics (in boreal summer) predict the highest rise of global temperature in the global warming runs (Fasullo and Trenberth 2012).

Numerous studies (see references below) have also been carried out to investigate the influence of the relative humidity on the basic longwave cooling agent of Earth and its atmosphere, the OLR. It is common to investigate both OLR for clear-sky conditions and the total OLR that includes the effects of clouds. Although the OLR critically depends on the surface temperature (Ts), the relative humidity influences the transmittance of the radiation via the atmosphere (Allan et al. 1999). It has been found that in some tropical regions the clear-sky OLR decreases with the increase of Ts, the so-called supergreenhouse effect (Raval and Ramanathan 1989; Minschwaner and McElroy 1992; Inamdar and Ramanathan 1994; Raval et al. 1994; Bony et al. 1997; Allan et al. 1999). When the tropical sea surface temperature is confined to the range 27.5°–29.5°C (Waliser et al. 1993), the moisture of the upper troposphere and cloud-ice increase, driven by tropical deep convection. This effect greatly enhances the water vapor feedback (Su et al. 2006), although no specific measure of its dependence on the surface temperature and humidity has been suggested. Clear-sky OLR data from the Earth Radiation Budget Experiment (ERBE) in 1985–88 were compared with outputs of the Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (AR4) Atmospheric Model Intercomparison Project for assessing climate feedbacks processes (Chung et al. 2010). The OLR anomalies are strongly correlated with El Niño (Dessler 2010; Susskind et al. 2012). Dessler et al. (2008) analyzed the clear-sky top-of-atmosphere OLR measured by the Clouds and the Earth’s Radiant Energy System (CERES) in March 2005. They found excellent agreement between the models’ predictions of OLR, sensitivity of OLR to the changing surface, and atmospheric temperature–water vapor and observations.

Newly retrieved data from more than a decade (2002–present) by AIRS on board the Aqua satellite give an opportunity to provide new observational tests of the above problems related to the relative humidity in the troposphere. The AIRS L2 products have spatial resolution of about 50 km with data produced twice per day at 0130 and 1330 equator crossing times. For our data analysis we selected daily data for winter (January) and summer (July) months in the three years 2003, 2007, and 2011. The full description of the AIRS products is available from the Goddard Earth Sciences (GES) Data and Information Services Center (DISC) (DISC 2013). The new AIRS L2 and L3 version 6 retrievals produce improved climate variables such as the temperature and specific humidity and now for the first time include the relative humidity, retrievals of OLR, and the cloud-top characteristics at the infrared footprint resolution. The retrievals use a neural network start-up state trained on the reanalysis from the European Centre for Medium-Range Weather Forecasts (ECMWF), allowing accurate retrievals in cases of more severe cloud conditions. They also implement improved quality-control methodology and the OLR radiative transfer algorithm. The retrievals do not provide direct statistical errors and use instead a quality control index (QC). Our estimated accuracy of RH is 10%–15% of its mean value. It is at the high end in the cold regions, since the RH is defined as the ratio of specific humidity and the value of the specific humidity at the saturation level, which is exponentially dependent on the temperature. Version 6 is a significant improvement over AIRS version 5 level-2 products in terms of greater stability, yield, and quality. The AIRS OLR and clear-sky OLR (OLRclear) products are calculated from the retrieved profiles and radiance spectrum. At a given location, OLR depends on Earth’s skin surface temperature, skin surface spectral emissivity, and spectral emissivities of multiple layers of cloud cover, atmospheric vertical temperature profile, water vapor profile, and on the vertical distributions of trace gases (mainly CO2) (Susskind et al. 2012). In the OLRclear case, radiation to space is calculated assuming cloud-free conditions for all footprints that have successfully retrieved temperature and water vapor profiles. Thus, OLRclear does not only use clear footprints but includes what the OLR values would have been if the atmosphere had been cloud free, but everything else was the same.

In section 2, we present zonally averaged global patterns of the RH obtained with the new AIRS data to demonstrate their seasonal change and global stability, thus providing a new observational test for the time invariance of the global RH. In section 3, we show that bimodal RH distribution does appear in some areas of the free troposphere. In section 4, using the new AIRS data, we construct the 2D patterns of the clear-sky OLR as functions of percentiles of the surface temperature and relative humidity that clearly show where the clear-sky OLR depends on the RH and how stable this dependence is. Section 5 summarizes the results.

2. Global distribution of relative humidity in the troposphere

In their classic paper, Manabe and Wetherald (1967) presented a radiative–convective model in which the atmosphere maintains a specified, vertical distribution of relative humidity. The model was designed to investigate the issue of climate sensitivity to external forcing. The surface equilibrium temperature and the vertical temperature structure in that model were extremely sensitive to changes in the solar irradiance and the concentrations of carbon dioxide. Later, the GCM studies, which did not impose the time-constant RH, confirmed that globally the water vapor–climate feedbacks are generally consistent with the approximation of a time-invariant global relative humidity (Held and Soden 2000). This means that the specific humidity should change in accord with atmospheric temperature, following the Clausius–Clapeyron law. The resulting exponential increase in water vapor with increasing temperature traps more and more longwave radiation causing further increases in surface temperature and thus leading to the largest positive feedback in the climate system.

However, the changes in the RH patterns that may not be sufficient to substantially affect the global radiative feedback of water vapor could still affect processes such as cloud formation or precipitation efficiency (Sherwood et al. 2010). Thus, the analysis based on a single-column, radiative, convective model (Minschwaner and Dessler 2004) showed that as the surface warms, changes in the vertical distribution and temperature of detraining air from tropical convection lead to higher water vapor mixing ratios in the upper troposphere. The increase in mixing ratio is not as large as the increase in the saturation mixing ratio due to warmer environmental temperatures, so that the relative humidity decreases. This analysis was supported by the Microwave Limb Sounder (MLS) measurements in the upper troposphere (Su et al. 2006). Du et al. (2012) tested the time invariance of RH subjected to averaging. They used the AIRS version 5 data scaled to 1° × 1 latitude–longitude grid in the free troposphere (700–300 hPa) in a multiple linear regression of RH on the seasonal cycles, trend, and an El Niño index. The complex patterns of the regression modes presented by Du et al. (2012) showed that a mean annual variability is dependent on atmospheric height, with a peak-to-peak amplitude of about 4% RH at 300 hPa, decreasing to less than 2% RH at 700 hPa, and almost no trend and no dependence on El Niño.

To simplify the analysis and make the results more visual, we construct here the patterns of zonally averaged RH using the new AIRS L2 version 6 data in the extended altitude range of 1000–50 hPa. For this purpose, we first put RH on a 1° × 1° latitude–longitude grid and then averaged over longitude. The latitude–height distributions of the zonally averaged relative humidity for January and July in 2003, 2007, and 2011 are shown in Fig. 1 for good-quality data (marked as QC = 0, 1 in the AIRS data archive). White areas indicate that there are no retrievals of this quality or its values are less than 10%. Using the L2 data allows us to have some flexibility in using the quality control parameter QC, but similar maps can be constructed with the AIRS L3 data, which now become available for the users. We limit our presentation to the three cited years that sufficiently well characterize the January–July differences in RH. The January and July climatologies for a more extended time period from September 2002 to September 2013 are shown in Fig. 2.

Fig. 1.
Fig. 1.

Zonally averaged, nonsaturated, latitude–height distributions of RH for (left) January and (right) July in (top to bottom) 2003, 2007, and 2011. The colored RH (%) shadings of 10, 30, 60, 80, 90, 100 are displayed and RH is only plotted for good-quality data (QC = 0, 1). White areas indicate that there are no retrievals of this quality or the RH < 10%.

Citation: Journal of the Atmospheric Sciences 71, 7; 10.1175/JAS-D-13-0363.1

Fig. 2.
Fig. 2.

Height vs latitude RH climatologies of (left) January and (right) July from AIRS 11 yr of measurements (1 Sep 2002–31 Aug 2013).

Citation: Journal of the Atmospheric Sciences 71, 7; 10.1175/JAS-D-13-0363.1

Actual spatial patterns of the relative humidity are not zonally symmetric, so that zonally averaged global patterns serve only as an approximation to the more detailed longitude–latitude–height patterns. The monthly patterns presented in Fig. 1 confirm the finding from the early AIRS version 4 data that the relative humidity has high values in the upper and lower troposphere and low values in the middle troposphere (Gettelman et al. 2006). The RH data used in that analysis were limited to atmospheric heights below 200 hPa. The new version 6 data of RH extend to higher altitudes, covering the tropopause layer and low stratosphere up to 50 hPa. We find that the January relative humidity has the largest maxima over 90% in the equatorial tropopause layer (see left panels in Fig. 1). The corresponding maxima in July patterns have a smaller spatial extent and do not rise above 60%.

Comparison of the left and right panels in Fig. 1 shows the seasonal changes in the patterns of the relative humidity (Fig. 3). Relative humidity in the tropical equatorial region of the lower troposphere changes up to 20% from winter to summer. Larger seasonal changes (exceeding 30%) are recorded in the equatorial tropopause layer and in the polar regions. The major changes that take place near the equatorial troposphere are similar but about 5% larger than the seasonal variations of RH found earlier by Peixoto and Ort (1996) from radiosonde observations in 1973–88 (see their Fig. 4). This indicates a small positive trend in seasonal variation in the low equatorial troposphere. The strong seasonal variations are also seen near the equatorial tropopause and in the upper Antarctic region of the atmosphere.

Fig. 3.
Fig. 3.

January minus July RH differences in (top to bottom) 2003, 2007, and 2011. The light contours mark positive differences, and the dark contours mark negative differences.

Citation: Journal of the Atmospheric Sciences 71, 7; 10.1175/JAS-D-13-0363.1

The interannual variability of the winter and summer zonal patterns taken separately is weaker than the seasonal variability. The 2007–03 and 2011–07 difference patterns (not shown) have localized values typically not exceeding 10%, with the largest differences near the equatorial tropopause at 100 hPa and in the polar areas. The change in the winter patterns of the RH between 2003 and 2011 may be caused by a transition from a strong El Niño in 2003 (with the January SST anomaly 1.19 K) to a relatively strong La Niña in 2011 (with the January SST anomaly −1.64 K). The July anomalies for 2003 and 2011 were weaker, 0.21 and −0.26 K, correspondingly (http://www.cpc.ncep.noaa.gov/data/indices).

Evaluating the processes controlling tropospheric relative humidity in atmospheric GCMs is crucial for assessment of the credibility of predicted climate changes. In particular, GCMs typically exhibit a moist bias in the tropical and subtropical mid- and upper troposphere, which could be due to the misrepresentation of cloud processes or of the large-scale circulation or to excessive diffusion during water vapor transport; see Risi et al. (2012) and references in that paper. The cited paper compares the relative humidity profiles averaged over the tropics with the early version of the AIRS data (see Fig. 3a in that paper). In Fig. 4, we generated the RH profiles in the tropics (30°S–30°N) for winter and summer seasons in 3 yr using the new AIRS data. The profiles have minima near 300 hPa; the profile showed in Risi et al. (2012) have similar extrema but at about 450 hPa. Thus, the observed profiles are slightly more shifted toward the lower RH, and thus even more emphasizing the moist bias in GCMs.

Fig. 4.
Fig. 4.

The RH profiles in the tropics for (left) January and (right) July in (top to bottom) 2003, 2007, and 2011. In all cases, with a slight exception of January 2011, the minimum RH is reached at 300 hPa.

Citation: Journal of the Atmospheric Sciences 71, 7; 10.1175/JAS-D-13-0363.1

3. On the bimodality of the relative humidity distributions

The form of the RH probability distribution functions (pdfs) carries information that can be used in the evaluation of dynamics of moist and dry air and in the radiative balance calculations. The importance of using pdfs was emphasized by Yang and Pierrehumbert (1994), who studied the transport of relative humidity along the 315-hPa isentropic surface using a simple advection–condensation model. This surface dips into a moist reservoir at low altitudes in the tropics and spreads to the midlatitude upper troposphere and the polar low stratosphere at high latitudes. The modeling showed that the pdfs of the relative humidity on this surface are bimodal in the midlatitudes, with one peak representing near-saturated air parcels that originated in the tropics, while the other peak represents dry air parcels subsiding along isentropic surfaces from higher latitudes. Spencer and Braswell (1997) used the RH pdfs in their study of the tropical relative humidity that revealed that a substantial part of the tropics has a very low RH.

Data analyses of in situ soundings and some remote sensing observations indicated that the pdfs of tropospheric water vapor in the tropics are commonly bimodal on multiple space–time scales, implying sharp gradients between dry and moist regimes in space and time and slow mixing between high- and low-humidity air masses compared to the time scales involved in their production and indicating that spatial separation of moist and dry air reflects the distribution of regions with and without deep convective moisture sources (Zhang et al. 2003). In contrast, Sherwood et al. (2006) found no evidence of bimodality and suggested that the bimodality reported by Zhang et al. (2003) could have been an artifact of sampling biases since many of the field programs providing their data were specifically designed to observe across sharp gradients in atmospheric conditions. Sherwood et al. (2006) modeled the distribution of RH as a Poisson process in which the air dries due to uniform subsidence and remoistens through random events. The corresponding pdf has a form of a monotonically decreasing function ∝ RH−1+r, diverging at small RH. The cumulative distribution of the RH, cumulative distribution function (cdf) ∝ RHr, where r is the ratio of the characteristic drying and remoistening times have been fitted to the values 0.40–0.67 using the global positioning system (GPS) and Microwave Limb Sounding [Upper Atmosphere Research Satellite (UARS)] satellite data. However, the MLS data obtained later from the Aura satellite did not show a diverging dry bias leading to monotonically decreasing pdfs (see Read et al. 2007, their Fig. 20). The difference between conclusions by Zhang et al. (2003) and Sherwood et al. (2006) concerning the presence of bimodality may also be produced by data analysis, because Sherwood et al. (2006) arranged their data into latitude–height bins, that is, effectively zonally averaged RH, thus mixing longitudinally separated moist and dry air. Ryoo et al. (2009) suggested a generalization form of the pdf (still Poissonian) by adding an extra parameter, characterizing the rate of the air moistening. They showed that the two-parameter pdf provides a much better fit to the satellite data, including the AIRS data, in different regions with a unimodal distribution of RH and suggested that the observed bimodal distribution can be explained by the sum of the pdfs from high RH and low RH regions. Since in this paper no statistical significance of the observed visually bimodal pdfs has been carried out and these pdfs were fit by the same two-parametric distribution, it is essential to further investigate the presence of the bimodality of the RH distributions.

Here we extend the observational part of this research by investigating the probability distribution functions of relative humidity on large spatial scales at a monthly time scale using the newly retrieved AIRS version 6 data. For this purpose, we take all good-quality daily retrievals of the RH defined by the parameter QC = 0, 1 in each AIRS L2 pixel (about 50 × 50 km in size) and sampled them over a month in the selected area and atmospheric height, for example, over 10°S–10°N tropical area for all heights, without any averaging. Since a characteristic drying time of moist air is about a day (Mapes 2001) and eddy mixing results in air diffusion with a diffusion coefficient D ≈ 20 km2 s−1 (υ = 10 m s−1, l = 2000 km) (Zhang et al. 2003), the scale of dry areas L must exceed 8000 km (L2/D > 30 days) to persist on a monthly time scale.

Figures 58 show examples of pdfs in the tropics and northern mid- and polar latitudes in 2003. Similar pdfs are seen in 2007 and 2011. The pdfs are calculated using kernel density estimation (cf. the ksdensity function in Matlab), a nonparametric way to calculate the probability distribution function with an optimal selection of the bin widths. This way of pdf calculating is superior to the use of standard histograms, which could show multiple peaks dependent on the size and shifts of bin widths. From these figures we see that some pdfs are bimodal or multimodal, that is, some have more than one peak. To test whether or not the bimodality is statistically significant, the previous researchers (cf. Zhang et al. 2003) applied the test of unimodality, which uses the maximum difference between the empirical distribution function and the unimodal distribution function that minimizes that maximum difference (Hartigan and Hartigan 1985). It does not test explicitly for bimodality but for unimodality. If one can show that the distribution is not unimodal, bimodality is the logical, though not explicit, alternative. This test also does not distinguish between bimodal and multimodal distributions.

Fig. 5.
Fig. 5.

Pdfs of RH at (top to bottom) 200–925 hPa for (left) January and (right) July 2003 in the ascending branch of the Hadley circulation (10°N–10°S). Solid curves in this figure and Figs. 6 and 7 correspond to daytime spacecraft orbits and the dashed curves correspond to nighttime orbits to show changes in pdfs due to the diurnal cycle, which is mainly seen below 500 hPa. The bimodal distributions at 500 hPa in January and July, and at 700 hPa in July are statistically significant at the 95% level, as found using the pdf smoothing method illustrated in Fig. 8.

Citation: Journal of the Atmospheric Sciences 71, 7; 10.1175/JAS-D-13-0363.1

Fig. 6.
Fig. 6.

As in Fig. 5, but for the descending branch of the Hadley circulation. The additional dry peak at 925 hPa reflects the contribution of the Sahara Desert.

Citation: Journal of the Atmospheric Sciences 71, 7; 10.1175/JAS-D-13-0363.1

Fig. 7.
Fig. 7.

As in Fig. 5, but for the middle northern latitudes (30°–60°N) where air is well mixed by turbulent eddies. The bimodal distributions at 300 hPa in January and July are statistically significant at the 95% level.

Citation: Journal of the Atmospheric Sciences 71, 7; 10.1175/JAS-D-13-0363.1

Fig. 8.
Fig. 8.

As in Fig. 5, but for the high northern latitudes (60°–90°N). Note the appearance of bimodality at 300 hPa. (top) Extremely dry air is present in the polar stratosphere at 200 hPa.

Citation: Journal of the Atmospheric Sciences 71, 7; 10.1175/JAS-D-13-0363.1

Here we adopt a different, simple, and visually clear test of statistical significance of multimodality based on the smoothing method introduced in Chaudhuri and Marron (1999). The idea of this method is to construct a family of smooth pdfs using a range of widths of the smoothing kernel (the kernel widths are similar to optimally weighted bin widths in histograms) and investigate the slopes around each peak to determine which ones are real. We illustrate the method by applying it to the sample of the RH data at 500 hPa in the tropics (Fig. 9). We see that the number of peaks depends on the level of smoothing. A peak is simply characterized by a local maximum; that is, when the smooth pdf goes up on one side and comes down on the other. A statistical significance is attached to these ups and downs, that is, to the left and right slopes of a suspected peak. For each peak, there is a zero crossing in the slope (derivative) of the smooth pdf. The peak is considered to be statistically significant when that zero crossing is significant. At each kernel width, a confidence interval for the derivative is constructed. When that confidence interval is above zero (a statistically significant increase), that location on the surface is shaded black. When the confidence interval is below zero (a significant decrease), the light gray color is used. When the confidence interval for the derivative contains zero, the dark gray color is used. This coloring scheme allows us to find significant peaks, which are black on the left side (where the curve increases) and white on the right side (as it decreases). Peaks that are spurious sampling artifacts will be completely dark gray. The bottom panel in Fig. 9 shows that the derivative of the smooth pdf is significant at the level of 95%. The results of the statistical significance tests for other figures are cited in the figure captions.

Fig. 9.
Fig. 9.

(top) The family of pdfs of RH smoothed with progressively increased widths of the Gaussian kernel. The data are for 500 hPa during January 2003 in the 10°S–10°N area. The thick curve corresponds to the optimal selection of the kernel width used in the pdf shown in the third panel on the left in Fig. 4. (bottom) The map of the signs of derivatives (slopes) of the curves shown in the top panel. The thin line corresponds to the “optimal” selection of the kernel width whose pdf can be seen in Fig. 3. The black and light gray colors show the statistically significant signs of the derivatives at the 95% level, indicating that only two large peaks are statistically significant at this level. The dark gray color marks insignificant areas.

Citation: Journal of the Atmospheric Sciences 71, 7; 10.1175/JAS-D-13-0363.1

In the tropics, the probability distributions show that the relative humidity is high and unimodal in the boundary layer near the equator in area of the ascending branch of the Hadley circulation (10°S–10°N; Fig. 5). In January (Fig. 5, left panels), the pdf develops a dry knee above the boundary layer at 700 hPa, becomes markedly bimodal at 500 hPa, and shifts to a dry unimodal distribution at 300 hPa. An additional investigation, in which we used daily, 10-, and 20-day samples instead of monthly averages, shows that these pdfs form within about 20 days. The 700-hPa atmospheric height is close to the 315-K isentropic surface in the tropics, allowing us to compare the probability distributions constructed from the AIRS data with the model distributions presented by Yang and Pierrehumbert (1994) in their Fig. 6. The observed distribution and the modeled one both have peaks at about RH = 50%–60% and a minimum at 20%. But our data do not show a sharp increase of pdfs seen in the model near the saturation end.

The observed pdfs are strikingly different in the latitudinal range of the descending branch of the Hadley circulation (10°–30°N; Fig. 6). Because of the dominance of the descending dry air, all winter pdfs here are unimodal with the exception of the boundary layer pdf. An inspection of the RH maps shows that the dry peak in the 10°–30°N area is caused mostly by the Sahara Desert. The July pdfs are more complicated and somewhat resemble the pdfs for the ascending branch due to the seasonal shift of the Hadley circulation.

The AIRS pdfs are consistent with the presence of a critical height of 8 km (350 hPa) that has been identified as a transition of the temperature structure from the moist adiabatic to the dry adiabatic (Mapes 2001). The relative humidity increases in the upper troposphere above the critical height in accord with the upward transport of humidity there.

The bimodality in mid- and polar latitudes shifts to higher altitudes (500–300 hPa; see Figs. 7 and 8), which cross the 315-K isentropic surface studied by Yang and Pierrehumbert (1994). Since the drying times of air are short (1–2 days) (Zhang et al. 2003), the bimodality observed at large scales cannot arise at random but could only be due to the spatial separation of moist and dry areas, that is, it reflects the large-scale structure of distribution of sources of deep convection such as the Pacific warm pool.

4. Relative humidity and outgoing longwave radiation

Here we use the OLR from the new AIRS version 6 data to investigate its relationship with the surface temperature Ts and RH. First, we determine how OLR depends on its main driver, the surface temperature using good-quality data (QC = 0, 1).

Figure 10 shows the clear-sky and all-sky OLR as functions of surface temperature percentiles for winter and summer in three selected years of AIRS measurements. We see a statistically significant seasonal variation of the sensitivity (defined as a slope of quasi-linear parts of the curves) and its interannual changes. The sensitivity is positive, indicating that an increase in temperature increases the clear-sky OLR. It is substantially smaller than the rate of Planck radiative damping (3.6 W m−2 K−1) but larger than that anticipated from a uniform warming with time-invariant relative humidity (2.0 W m−2 K−1) (Chung et al. 2010). The AIRS clear-sky sensitivities are comparable with but slightly smaller than those found from ERBE data for the time period 1985–88 by Chung et al. (2010). Note the regime change at about 300 K earlier found in analysis of the 1985–88 ERBE data (Raval et al. 1994) and in scatterplots of clouds versus sea surface temperature (Su et al. 2006). An important feature of these dependences is a strong deviation from linearity at high temperatures, especially for the all-sky OLR, indicating the influence of humidity on the outgoing longwave radiation.

Fig. 10.
Fig. 10.

Clear-sky OLR (crosses) and all-sky OLR (solid line) as functions of surface temperature percentiles (Tsurf pts). We use 20 percentiles equally spaced between the 0th and 100th percentiles. The numbers along the x axis mark the values of the percentiles in kelvins. (left) January and (right) July (top to bottom) 2003, 2007, and 2011. The top number in each panel refers to the sensitivity for clear-sky OLR and the lower number refers to the sensitivity for all-sky OLR. The sensitivities are determined by fitting a line to linear parts of the curves. The errors of the slopes are given at the 1σ level of significance. The starting nonlinear parts of the curves refer mostly to frozen areas.

Citation: Journal of the Atmospheric Sciences 71, 7; 10.1175/JAS-D-13-0363.1

The magnitudes of the all-sky OLR and clear-sky OLR are obviously different. But more interesting is the change of the slope from clear-sky to all-sky OLR. It indicates a positive cloud radiative forcing of about 0.2 W m−2 K−1 with error varying from 0.01 to 0.05 W m−2 K−1 (with the exception of the summer of 2003 when we find no clear linear fit). Could this sensitivity difference be caused by the cloud-clearing related issues involved in the retrievals? If we use only the highest-quality retrievals (defined by QC = 0), then this small difference in the sensitivities becomes insignificant because this restriction leads to selection of data in the clear-sky pixels in which the surface temperatures has higher values and all-sky OLR is hardly distinguishable from clear-sky OLR in the whole sample. Inclusion of OLR data with QC = 1 makes the result statistically significant. However, the sensitivity difference still have to be considered as a low limit because not all clouds are cleared in the AIRS retrievals marked by QC = 0 and 1. The independent analysis by Aumann et al. (2012), who used the OLR and the clear-sky OLR derived directly from AIRS L1b spectral radiances, that is, with no retrievals involved, resulted in a higher value of the longwave cloud forcing of 0.5 ± 0.2 W m−2 K−1.

The dependence of clear-sky OLR on the relative humidity is shown in Fig. 11 for the 2003 data in the same latitudinal zones as in Figs. 58. We see a substantial seasonal dependence (except near the equator) and the decrease of clear-sky OLR from the equator to high latitudes. The dependence is in general nonlinear except in the near-equatorial region in winter. The top panels show that the clear-sky OLR does not significantly depend on RH in the polar latitudes.

Fig. 11.
Fig. 11.

Clear-sky OLR in the tropics as a function of RH for (left) January and (right) July 2003 (top to bottom) from 60°N–90°N to 10°S–10°N. Note that the vertical axes in a given latitudinal range are the same for January and July but change with the latitude band.

Citation: Journal of the Atmospheric Sciences 71, 7; 10.1175/JAS-D-13-0363.1

Since the OLR is driven by the surface temperature and depends on the relative humidity in the atmosphere, it is imperative to consider these variables at the same time over the same region. To show the clear-sky OLR as a function of the surface temperature and the relative humidity taken at the same spatial spots, we construct 2D probability distributions. To avoid the inaccuracy that comes with using uniform bins (a technique often employed in the construction of histograms), we plot the clear OLR as a function of the Ts and RH percentiles taken in equal steps from the 0th percentile to the 100th percentile. Instead of selecting the RH at a particular atmospheric level, we average the relative humidity over the column confined between 850 and 200 hPa, since in this atmospheric column the clear-sky OLR is mostly sensitive to relative humidity (Allan et al. 1999). Figure 12 shows the clear-sky OLR for the tropics for January and July in 2003, 2007, and 2011. The slopes of the clear-sky OLR contours quantify its dependence on the RH, giving some measure of the so-called supergreenhouse effect. If the contour lines were vertical, there would be no dependence on relative humidity. We see that at high RH the slope is almost horizontal, that is, the clear-sky OLR is substantially suppressed no matter how large the surface temperature is. The highest clear-sky OLR at high surface temperatures is obviously emitted where RH is very low (bottom-right corners in the diagrams). Figure 12 also shows that the contours of the clear-sky OLR for each season remain approximately stable over the decade of the AIRS observations [for a comprehensive discussion of stabilizing mechanisms balancing radiative budget against a runaway greenhouse effect see for comparison Waliser (1996)], although the July 2011 contours are slightly disturbed by a relatively strong La Niña that occurred in 2011.

Fig. 12.
Fig. 12.

Contoured shading (W m−2) of clear-sky OLR in the tropics as a function of the percentiles of the surface temperature and RH. The slope of contour lines is changing with the decrease of RH, reaching the highest values at low relative humidities.

Citation: Journal of the Atmospheric Sciences 71, 7; 10.1175/JAS-D-13-0363.1

5. Conclusions

Using the newly retrieved AIRS data in the atmosphere from 1000 to 50 hPa, we find that zonally averaged patterns of relative humidity have maxima over 90% in the equatorial tropopause layer in January. The corresponding maxima of RH in July patterns have a smaller spatial extent and do not rise above 60%. These results put an observational constraint on the assumption of a fixed relative humidity in the upper troposphere (above 250 hPa).

Relative humidity in the tropical equatorial region of the lower troposphere changes up to 20% from winter to summer. Larger seasonal changes (exceeding 30%) are recorded in the equatorial tropopause layer and in the polar regions. Larger seasonal variability is seen near the tropical tropopause and near the polar regions. However, the winter and summer global patterns of RH taken separately were changing slower in time (not exceeding 10%). The amplitude of the seasonal variability of RH in the currently past decade is increased relative to the amplitude of seasonal variability found in the 1973–88 time period by Peixoto and Ort (1996), indicating a positive trend. The climate models that diagnose the change in zonal-mean relative humidity indicate that the doubling of CO2 results in a trend that depends on the height and latitude but does not exceed 10% (Wright et al. 2010).

We confirmed the finding reported in Zhang et al. (2003) and Ryoo et al. (2009) that bimodal distributions of the relative humidity exist at large scales in the free troposphere, and we support this finding with the analysis of statistical significance. The presence of bimodality is consistent with the distribution of sources of the moist air and patterns of the atmospheric circulation. Thus, relative humidity in the equatorial zone is markedly bimodal above the boundary layer in the ascending branch of the Hadley circulation. The pdfs of the relative humidity in the free troposphere are unimodal in the descending branch of the Hadley circulation and show bimodality near the surface due to the contribution of deserts. Bimodality is also seen at 500–300-hPa heights in mid- and high latitudes.

We find a 0.2 ± 0.05 W m−2 K−1 difference in sensitivities of clear-sky and all-sky OLR to surface temperature. This difference indicates a positive cloud forcing.

We constructed 2D diagrams of the clear-sky OLR as functions of percentiles of the surface temperature and relative humidity in the free tropical troposphere as a measure of the relative humidity influence on the clear-sky OLR. These diagrams of the clear-sky OLR are found to be stable over the decade of the AIRS observations, thus supporting the notion of the stability of the so-called supergreenhouse effect.

Acknowledgments

We thank Joan Feynman, Eric Fetzer, Brian Kahn, and Hui Su for expert advice. We are grateful to two reviewers for helpful critical comments. This work was supported in part by the Jet Propulsion Laboratory of the California Institute of Technology, under a contract with the National Aeronautics and Space Administration.

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