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  • View in gallery

    MSU channel 2 instantaneous weighting functions at nadir. MSU channel 2 weighting functions are average values over land and ocean. UAH weighting functions were generated from mean static weighting functions for 5-hPa layers provided by J. Christy, UAH (dashed). RSS weighting functions were calculated from instantaneous weighting functions of height provided by RSS (solid), in which the COESA (1976) profiles, a surface relative humidity of 70%, and a PV scale height of 1500 m were used.

  • View in gallery

    Time series of global MSU T2 anomalies for multimodel ensemble simulations (blue solid), ERA-Interim (black dashes), UAH v5.4 (red dashes), STAR v2.0 (green dotted), and RSS v3.3 (purple dashes). All the models’ and ERA-Interim T2 are calculated by RTTOV v11.

  • View in gallery

    (a) Vertical distribution of trends of air temperature for 16 models’ historical simulations at global scales during the period of 1979–2005. Only the first realization is plotted from each model. (b) MSU T2 weighting functions for UAH (blue solid), RSS (black dashes), ERA Interim (red dashes) and climate models (colored dashes) averaged at global scales. The MSU T2 weighting functions for the climate models and ERA-Interim are calculated using RTTOV v11. The simulated weighting functions are yearly averaged for the period of 1979–2005. (c) Vertical distribution of trends of air temperature for multimodel mean and ERA-Interim at global scales during the period of 1979–2005. (d) As for (b), but for weighting functions calculated from climate models and ERA-Interim using RTTOV v11 without CLW considered as the input.

  • View in gallery

    Scatter diagram of comparisons of global-mean trends for MSU T2 from 16 climate models’ simulations and ERA-Interim between those calculated by RTTOV v11 directly (x axis) and those using climate models’ weighting functions derived by RTTOV v11 (y axis). All trends are statistically significant (). The analysis period is from January 1979 to December 2005, the period of maximum overlap between the observations and CMIP5 historical simulations. The diagonal line in the plot is a y = x line.

  • View in gallery

    As in Fig. 4, except calculated by RTTOV v11 directly between with CLW effect considered (x axis) and without CLW effect considered (y axis).

  • View in gallery

    (a) MSU T2 weighting functions for ERA-Interim with (solid line) and without (dashed line) the effect of CLW, and climate models with the effect of CLW (dotted line for BNU-ESM, centerline for FGOALS-s2, phantom line for GFDL-ESM2M) averaged at global scales. The weighting functions of climate models without the effect of CLW are all identical to the weighting function of ERA-Interim without the effect of CLW. The MSU T2 weighting functions for climate models and ERA-Interim are calculated using RTTOV v11. The simulated weighting functions are yearly averaged for the period of 1979–2005. (b) Vertical distribution of monthly CLW simulated by climate models (BNU-ESM, FGOALS-s2, GFDL-ESM2M) and ERA-Interim averaged at global scales from 1979 to 2005.

  • View in gallery

    The difference fields of monthly mean MSU T2 simulated by RTTOV using the 6-hourly ERA-Interim data as the input to obtain 6-hourly MSU T2 and using the monthly averaged ERA-Interim data as the input are calculated for (left) January and (right) July in (top) 1979 and (bottom) 2006.

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Trends of MSU Brightness Temperature in the Middle Troposphere Simulated by CMIP5 Models and Their Sensitivity to Cloud Liquid Water

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  • 1 College of Global Change and Earth System Science, Beijing Normal University, Beijing, China
  • 2 Centre for Australian Weather and Climate Research, Bureau of Meteorology, Victoria, Melbourne, Australia
  • 3 College of Global Change and Earth System Science, Beijing Normal University, Beijing, China
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Abstract

Only a climate model that is able to simulate well the historical atmospheric temperature trend can be used for estimating the future atmospheric temperature trends on different emission scenarios. Satellite-based Microwave Sounding Unit (MSU) brightness temperature in the middle troposphere (T2) is an important analog of midtropospheric atmospheric temperature. So, there is the need to compare the atmospheric temperature trend simulated by the fifth phase of the Coupled Model Intercomparison Project (CMIP5) historical realizations and the observed MSU T2. There are two approaches for estimating modeled MSU T2: apply a global-mean static weighting function to generate the weighted average of the modeled temperature at all atmospheric layers and simulate satellite-view MSU T2 using the model’s output as input into a radiative transfer model (RTM).

In this paper, the two approaches for estimating modeled MSU T2 are evaluated. For each CMIP5, it is shown that there exists a model-simulated static weighting function, such that the MSU T2 trend using the weighting function is equivalent to that calculated by RTM. The effect of modeled cloud liquid water on MSU T2 trends in CMIP5 simulations is investigated by comparing the modeled cloud liquid water vertical profile and the weighting function. Moreover, it is found that warming trends of MSU T2 for CMIP5 simulations calculated by the RTM are about 15% less than those using the two traditional static weighting functions. By comparing the model-derived weighting function with the two traditional weighting functions, the reason for the systematical biases is revealed.

Corresponding author address: Xiaogu Zheng, College of Global Change and Earth System Science, Beijing Normal University, No. 19, XinJieKouWai St., HaiDian District, Beijing 100875, China. E-mail: x.zheng@bnu.edu.cn

Abstract

Only a climate model that is able to simulate well the historical atmospheric temperature trend can be used for estimating the future atmospheric temperature trends on different emission scenarios. Satellite-based Microwave Sounding Unit (MSU) brightness temperature in the middle troposphere (T2) is an important analog of midtropospheric atmospheric temperature. So, there is the need to compare the atmospheric temperature trend simulated by the fifth phase of the Coupled Model Intercomparison Project (CMIP5) historical realizations and the observed MSU T2. There are two approaches for estimating modeled MSU T2: apply a global-mean static weighting function to generate the weighted average of the modeled temperature at all atmospheric layers and simulate satellite-view MSU T2 using the model’s output as input into a radiative transfer model (RTM).

In this paper, the two approaches for estimating modeled MSU T2 are evaluated. For each CMIP5, it is shown that there exists a model-simulated static weighting function, such that the MSU T2 trend using the weighting function is equivalent to that calculated by RTM. The effect of modeled cloud liquid water on MSU T2 trends in CMIP5 simulations is investigated by comparing the modeled cloud liquid water vertical profile and the weighting function. Moreover, it is found that warming trends of MSU T2 for CMIP5 simulations calculated by the RTM are about 15% less than those using the two traditional static weighting functions. By comparing the model-derived weighting function with the two traditional weighting functions, the reason for the systematical biases is revealed.

Corresponding author address: Xiaogu Zheng, College of Global Change and Earth System Science, Beijing Normal University, No. 19, XinJieKouWai St., HaiDian District, Beijing 100875, China. E-mail: x.zheng@bnu.edu.cn

1. Introduction

The amount of scientific evidence indicates that the global climate is influenced by natural forcing (such as volcanoes and solar irradiance) and anthropogenic forcing (such as increases in well-mixed greenhouse gases, depletion of stratospheric ozone, and changes in atmospheric burdens of various aerosol particles) (e.g., Tett et al. 2002; Hegerl GC et al. 2007; IPCC 2007; Karl et al. 2006; Forster et al. 2007; Wigley and Santer 2013; Santer et al. 2003a, 2005, 2013). Atmospheric temperature variability is a very important component for monitoring global climate change. Studies on atmospheric temperature variability help us better understand the anthropogenic influence on climate change (Santer et al. 1996).

Study of the future atmospheric temperature trend is an important component of climate change. Using atmosphere–ocean global climate models (AOGCMs) to simulate the trends under different emission scenarios for future world developments is a feasible way to achieve this goal. The modeled temperature trends can be evaluated using that from satellite measurements. Global satellite observational brightness temperatures (Tb) from the Microwave Sounding Unit (MSU) and the Advanced Microwave Sounding Unit (AMSU) can provide continuous and wide coverage records of atmospheric temperatures, and they have been used in many climatic studies and major scientific assessments (e.g., Karl et al. 2006; Solomon et al. 2007; Santer et al. 2005; Thorne et al. 2005, 2011).

To study the models’ simulations, observations are required. However, the MSU Tb is not a standard variable in any climate model outputs and has to be determined using the models’ output variables, such as temperature, pressure, humidity, clouds, etc. Two methods can be used to generate equivalent MSU Tb from the AOGCMs’ simulations. One is known as the weighting function method. In this application, a global-mean static weighting function is used to generate a weighted average temperature of the atmospheric layer for each MSU channel (Spencer and Christy 1992a,b; Santer et al. 1999, 2000, 2005, 2008; Steiner et al. 2007; Douglass et al. 2008; McKitrick et al. 2010). This approach is computationally cheaper and easier to apply, but the effects of clouds on MSU Tb are ignored. Another approach is to simulate MSU Tb by a radiative transfer model (RTM) using the climate models’ output variables (e.g., Spencer and Christy 1990; Santer et al. 1999; Steiner et al. 2007; Zhang et al. 2013). In this case, the effects of the clouds on MSU Tb can be considered. Although two methods have been used by many researchers, there is a lack of cross comparison between the two methods. Since the modeled temperature trends are strongly dependent on the weighting function, it is necessary to investigate if the temperature trends determined by these two methods are consistent.

Two static weighting functions provided by Remote Sensing Systems (RSS; Mears and Wentz 2009a,b) and the University of Alabama in Huntsville (UAH; Spencer and Christy 1990), and the latest version of the fast radiative transfer model RTTOV, version 11 (v11), are used in this study to calculate MSU Tb using the AOGCMs’ historical simulations from the fifth phase of the Coupled Model Intercomparison Project (CMIP5) (Taylor et al. 2012). The MSU Tb in the middle troposphere (T2) trends determined by the RTTOV are compared with those estimated using the static weighting functions. The results from both methods show similar warming trends in the middle troposphere, but the trends using the weighting function method are warmer than that using RTTOV. We also found that the effect of cloud liquid water on the MSU T2 trend cannot be ignored. The paper is organized as follows. Section 2 briefly introduces the CMIP5 historical experiments, AMSU/MSU observations, and ERA-Interim. Section 3 describes the two methods for the computation of MSU-equivalent T2 and a method for estimating T2 linear trend. Section 4 gives results of a comparison of the simulated and observed T2 trends. Section 5 discusses causes that make differences among simulated trends using the weighting function method and calculated by RTTOV.

2. Data

a. CMIP5 historical output

In this study, a subset of 42 historical realizations simulated by 16 climate models from CMIP5, which is an important scientific resource for the Fifth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC), was used for comparative calculation with the satellite-based observational MSU T2. Each climate model has several realizations that are initialized from different times of a control run or from different initial conditions with observations using different methods or different observational datasets. Forcings for historical (from 1850 to at least 2005) simulations of CMIP5 may include the following: atmospheric composition (including CO2) due to both anthropogenic and volcanic influences, solar forcing, land use, emissions or concentrations of short-lived species, and natural and anthropogenic aerosols (Taylor et al. 2012). In this study, monthly outputs of CMIP5 modeled atmospheric profiles (such as pressure, temperature, specific humidity, and cloud liquid water content) and of surface properties (i.e., surface pressure, surface wind at 10 m, surface temperature at 2 m, skin temperature, surface sea temperature, elevation, cloud cover, etc.) were used as the input of RTTOV v11. Some more detailed information about the climate models (i.e., resolution, realization) used in this study is shown in Table 1.

Table 1.

16 AOGCMs’ historical (1850–2005) experiments of CMIP5. The detailed information for abbreviated “Forcings” can be found in Appendix 1.2 at http://cmip-pcmdi.llnl.gov/cmip5/docs/cmip5_data_reference_syntax.pdf.

Table 1.

b. MSU/AMSU observations

To date, the instruments MSU/AMSU carried by the TIROS-N series satellites have provided more than 30 years of atmospheric-layer temperature records since late 1978. MSU has three oxygen absorption band channels (channels 2, 3, and 4) with center frequencies at 53.74, 54.96, and 57.95 GHz, corresponding to the layer temperature in the middle troposphere, the troposphere/stratosphere, and the lower stratosphere, respectively. Beginning in 1998, AMSU became the successor of MSU on board (the NOAA K, L, M, N series; and MetOp-A, MetOp-B). AMSU consists of more channels than MSU, and its channels 5, 7, 9 (corresponding to the middle troposphere, the upper troposphere, and the lower stratosphere, respectively) have similar frequencies to channels 2–4 of the MSU sensor (Christy et al. 2003).

The records from AMSU were merged into MSU channels to form three independent long-term MSU Tb series, by research groups at UAH (Spencer and Christy 1990; Christy et al. 2007); RSS in Santa Rosa, California (Wentz and Schabel 1998; Mears et al. 2003; Mears and Wentz 2005); and the Center for Satellite Applications and Research (STAR) in Maryland (Zou et al. 2006, 2009). The latest versions of the three groups of datasets, which are denoted as RSS v3.3, STAR v2.0, and UAH v5.4, have been used in this study. The major differences among their AMSU/MSU Tb datasets come from different data adjustment schemes that are made for instrument calibration and diurnal corrections for the NOAA satellite series (Grody et al. 2004; Weng and Zou 2014; Lu and Bell 2014). The detailed discussions on differences among the three groups of datasets are beyond the scope of this paper. Their results are used to compare with those from the CMIP5 models’ simulations.

c. ERA-Interim

ERA-Interim is the latest global atmospheric reanalysis produced by the European Centre for Medium-Range Weather Forecasts (ECMWF). ERA-Interim was conceived in part to prepare for a future, more ambitious reanalysis project to replace ERA-40 at ECMWF that will span the entire twentieth century. It was derived using a 4D variational data assimilation (4DVAR) system based on the forecasting system, Integrated Forecasting System (IFS) Cy29r1, and a new variational bias-correction scheme (VarBC) for radiance data. To date, ERA-Interim has prepared gridded-data products from 1979 to the present, including a large variety of 6-hourly surface parameters, describing weather as well as ocean-wave and land surface conditions, and 6-hourly upper-air parameters covering the troposphere and stratosphere (Dee et al. 2011b; Berrisford et al. 2009; Simons et al. 2007). Information about ERA-Interim production, availability of data online, and near-real-time updates of various climate products derived from ERA-Interim data can be found online (at http://apps.ecmwf.int/datasets/).

In this study, ERA-Interim full-resolution (1.0° latitude × 1.0° longitude) monthly means data were used to produce MSU-equivalent Tb as a benchmark to compare with satellite-observed and climate model–simulated datasets (Dee et al. 2011a, 2014; Thorne and Vose 2010; Xu and Powell 2010). The 6-hourly ERA-Interim data were also used to investigate if monthly mean data can be used as input of radiative transfer models for estimating MSU-equivalent Tb trend.

3. Methodology

To facilitate comparisons of simulated atmospheric temperature and the actual observed MSU Tb in the middle troposphere, two methods were used to generate equivalent MSU T2 from gridded monthly mean output of CMIP5 simulations. One approach is to use a global-mean static MSU weighting function that has been used in previous studies (e.g., Mears and Wentz 2009a,b); another is to simulate MSU Tb by RTTOV v11. For the static weighting function method, MSU-equivalent Tb is estimated as a weighted average of simulated temperature at all model levels.

a. MSU weighting functions

In this study, two static weighting functions (provided by RSS and UAH) are used for generating equivalent MSU T2 of climate model simulations. Their vertical distributions at nadir are shown in Fig. 1. RSS weighting functions (Mears and Wentz 2009a,b) were determined from the U.S. Standard Atmosphere, 1976, using a radiative transfer model based on Rosenkranz (1993, 1998) and a model of the ocean surface (Wentz and Meissner 2000). UAH weighting functions were derived from the U.S. Standard Atmosphere, 1976, using Rosenkranz’s (1975) oxygen absorption model and Liebe et al.’s (1977) line width parameters (Spencer and Christy 1990, 1992a; Grody 1983). The peaks of MSU T2 weighting functions are located at about the 300-hPa level. In addition, the RSS weighting function has a term representing the contribution from the land surface emission, while the UAH weighting function does not.

Fig. 1.
Fig. 1.

MSU channel 2 instantaneous weighting functions at nadir. MSU channel 2 weighting functions are average values over land and ocean. UAH weighting functions were generated from mean static weighting functions for 5-hPa layers provided by J. Christy, UAH (dashed). RSS weighting functions were calculated from instantaneous weighting functions of height provided by RSS (solid), in which the COESA (1976) profiles, a surface relative humidity of 70%, and a PV scale height of 1500 m were used.

Citation: Journal of Atmospheric and Oceanic Technology 32, 5; 10.1175/JTECH-D-13-00250.1

Since weight values of the UAH T2 weighting function are larger than that of the RSS weighting function at above the peak level, the estimated MSU T2 trends could be different if these weighting functions are applied. Since the levels of static weighting functions are different from the models’ atmosphere vertical levels, the static weighting functions have to be interpolated onto the vertical levels of the models. The method to obtain the RSS (or UAH) static weighting function at all model pressure levels has been described by Zhang et al. (2013) and Santer et al. (1999) (see appendix A for the more details). The model-level RSS (UAH) static weighting functions are denoted as WF-RSS (WF-UAH).

b. Radiative transfer model RTTOV v11

The fast radiative transfer model RTTOV v11 is used to calculate MSU Tb from CMIP5 simulations. RTTOV v11 is the latest development version for the TIROS Operational Vertical Sounder, as a project of the European Organisation for the Exploitation of Meteorological Satellites (EUMETSAT) Satellite Application Facility for Numerical Weather Prediction (NWP SAF) (Saunders et al. 1999; Matricardi et al. 2001, 2004). MSU (include channels 1–4) of the satellite platform NOAA-14 and its corresponding coefficient files in RTTOV v11 were used in this study.

The primary role of RTTOV v11 is as an observational operator that is used in a data assimilation scheme by connecting the model states with radiances (i.e., Tb) observed by the satellite monitoring system. Given profiles of atmospheric variables such as pressure, temperature, water vapor, various gas concentrations, cloud liquid/ice water content, and surface properties (referred to as the model states), RTTOV allows rapid simulations of radiances for satellite-based MSU microwave nadir scanning radiometers. The microwave radiance for the MSU channels consists of upwelling components from surface microwave emission and atmospheric-layer emission. In the atmospheric layer, the molecular oxygen (O2), as well as cloud liquid water, can absorb and emit microwave radiation. The radiance from oxygen molecules is affected by profiles of the pressure and temperature. The atmospheric transmittance could be affected by the cloud liquid water content due to its absorption. It has a negative exponent relationship with the absorption optical depth that reduces radiance as seen by satellites.

The brightness temperature at microwave frequency can be defined as (Liou 2002)
e1
where represents the surface emissivity, is the skin temperature, is the transmittance from surface to the top of the atmosphere (TOA), is the transmittance from pressure level to the TOA, and is a temperature profile. The first terms describe the contribution of the surface emission. The second terms present the contribution of the surface-reflected emission from the atmosphere. The third terms account for the contribution of atmospheric emission.
The second terms and the third terms of (1) represent the total contribution from direct and reflected atmospheric emissions. They can be rewritten as
e2
where is the transmittance from the surface to the TOA, represents the transmittance from the specific pressure level to the TOA at the frequency . Therefore, the weighting function for MSU T2 derived from RTTOV v11 at the lpth level can be written as
e3
Since is dominated by temperature at the specific pressure level and affected by cloud liquid water, then the weighting function for MSU T2 may be affected by the cloud liquid water content. From (1), the weight for the contribution from the surface emission can be written as
e4
Finally, the value of the integrated weights [(3) and (4)] using RTTOV is . For blackbody emission at the surface, , the integrated weighting function is 1. Since and are in orders of 0.05 and 0.9 (0.5 for the ocean), respectively, is very close to 1.

RTTOV v11 was originally designed to transfer instantaneous atmospheric state variables into instantaneous brightness temperature. However, the outputs of the CMIP5 climate models are monthly mean in general. In this case, monthly state variables have to be used as the inputs to RTTOV. In fact, this approach has been adopted in earlier research for estimation of T2 (e.g., Santer et al. 1999; Spencer and Christy 1990). Since the radiative transfer processes are highly nonlinear, the validity of using average quantities will be questionable. Therefore, it is necessary to investigate whether the MSU T2 trend simulated in this way is equivalent to that simulated using the instantaneous state variable. Here, we use the 6-hourly ERA-Interim data to investigate this question (see appendix B for the more details). The result suggests that although using monthly data as input can lead to systematic negatively biased estimations of MSU T2, it may not significantly affect the estimated trends.

4. Results

In this section, we focus on a comparison among the MSU T2 trends in 16 CMIP5 climate model simulations and in observations. The MSU Tb monthly anomalies from satellite-based observations (i.e., RSS v3.3, STAR v2.0, and UAH v5.4) and those calculated using static weighting functions (WF-RSS and WF-UAH) and by RTTOV v11 are used to obtain linear trends in 27 years over 1979–2005. We consider the residual of annual MSU T2 series as a red noise series, aiming to remove its temporal correlation (Jones 1989; Zheng and Basher 1999).

The time series of global MSU T2 anomalies for the multimodel ensemble simulations and ERA-Interim calculated by RTTOV v11, and satellite observations are shown in Fig. 2. It shows that the agreement among the three groups’ results and the reanalysis data is reasonable. They all pick up the signals in the T2 time series as the response to El Niño–Southern Oscillation events. The operational data of MSU/AMSU have been assimilated in ERA-Interim with its own method to deal with observational biases that consist of a variational bias-correction scheme (Dee et al. 2011b). Therefore, the good agreement reflects the influence of MSU/AMSU data and its bias-correction scheme on ERA-Interim. It is a very good sign to see that two very different approaches give similar results. However, this is not the case for the AOGCMs’ ensemble simulations because no such constraint applies to any model, and SSTs are not forced by observations in AOGCMs (Santer et al. 2003b). On the other hand, the less warming signals of the two volcanic eruptions (i.e., El Chichón in 1983 and Mount Pinatubo in 1991) are well captured by the ensemble mean of the AOGCMs. But for the three satellite observations and the reanalysis data, only the less warming signal of the Mount Pinatubo eruption in 1991 is captured. The less warming signal of the eruption of El Chichón in 1983 is masked by the warming signal of the 1983 El Niño event.

Fig. 2.
Fig. 2.

Time series of global MSU T2 anomalies for multimodel ensemble simulations (blue solid), ERA-Interim (black dashes), UAH v5.4 (red dashes), STAR v2.0 (green dotted), and RSS v3.3 (purple dashes). All the models’ and ERA-Interim T2 are calculated by RTTOV v11.

Citation: Journal of Atmospheric and Oceanic Technology 32, 5; 10.1175/JTECH-D-13-00250.1

The climate model–simulated trends of T2 at global scales using the WF-RSS and WF-UAH weighting functions, and calculated by RTTOV v11 are listed in Table 2. It shows that the T2 trend using the WF-RSS weighting function is larger than that using the WF-UAH weighting function. This could be due to the fact that the WF-RSS weighting function has a contribution term from the surface emission, whereas the WF-UAH weighting function does not. The climate models’ MSU-equivalent T2 trends calculated using the two static weighting functions are warmer than that calculated by RTTOV.

Table 2.

Multimodel averaged trends for MSU T2 using weighting functions and those calculated by RTTOV v11 (Cal_RTTOV) and satellite-based observational trends provided by groups UAH, RSS, and STAR (K decade−1). The analysis period is January 1979–December 2005.

Table 2.

To investigate the impacts of the static weighting function method and RTTOV method on T2 trends on the regional scale, the T2 trends over the tropics, the northern extratropics, and southern extratropics are estimated using the two methods and the results are also shown in Table 2. The T2 trend calculated using the two weighting functions constitutes about 0.02 K decade−1 more warming over the tropics and less warming in the northern extratropics than the T2 trend calculated by RTTOV. However, in the southern extratropics, the T2 trend calculated using the two weighting functions constitutes about 0.045 K decade−1 more warming than the T2 trend calculated by RTTOV.

The T2 trends of the three MSU/AMSU observations are also listed in Table 2. It shows that the T2 trends calculated using RTTOV are the closest to those observed in all regions, except for the northern extratropics, where all simulated T2 trends are within the range of the observed T2 trends.

5. Discussions

a. T2 trends using weighting functions

In section 4, we have demonstrated that the global T2 trend using the WF-RSS weighting function shows a larger warming than that using the WF-UAH weighting function. To investigate the causes of this difference, the vertical global trends of air temperature for multimodel historical simulations from 1979 to 2005 are shown in Figs. 3a and 3c. As seen the trends are unevenly distributed at the vertical levels: from the surface to 300 hPa, the warming trends are almost stable; from 300 to 150 hPa , the warming trends are not as significant as those from the surface to 300 hPa; and from 150 hPa to the top of the model atmosphere, the trends show systematically cooling.

Fig. 3.
Fig. 3.

(a) Vertical distribution of trends of air temperature for 16 models’ historical simulations at global scales during the period of 1979–2005. Only the first realization is plotted from each model. (b) MSU T2 weighting functions for UAH (blue solid), RSS (black dashes), ERA Interim (red dashes) and climate models (colored dashes) averaged at global scales. The MSU T2 weighting functions for the climate models and ERA-Interim are calculated using RTTOV v11. The simulated weighting functions are yearly averaged for the period of 1979–2005. (c) Vertical distribution of trends of air temperature for multimodel mean and ERA-Interim at global scales during the period of 1979–2005. (d) As for (b), but for weighting functions calculated from climate models and ERA-Interim using RTTOV v11 without CLW considered as the input.

Citation: Journal of Atmospheric and Oceanic Technology 32, 5; 10.1175/JTECH-D-13-00250.1

Figure 1 shows that from 300 hPa to the top of the model atmosphere, the WF-RSS weighting function is systematically smaller than the WF-UAH weighting function. The larger the weight at a vertical level, the more significant the contribution of the temperature trend at that level is made to the T2 trend. Since the temperature trends above 300 hPa are less warming than those below 300 hPa, and the WF-RSS weighting function has less (more) weight above (below) 300 hPa, the T2 trend calculated using the WF-RSS weighting function is more warming than that calculated using the WF-UAH weighting function (Table 2).

b. T2 trends using RTTOV v11

In section 4, we have also demonstrated that the MSU T2 trends simulated by RTTOV v11 show less warming than those calculated using the WF-UAH and WF-RSS weighting functions. The causes of the difference are investigated below.

To simplify the T2 trend calculations, we calculate a globally averaged model weighting function derived using RTTOV and name it WF-RTTOV. We first test if the T2 trends determined by WF-RTTOV are consistent with those calculated directly by the RTTOV model. Then we compare WF-RTTOV with WF-UAH and WF-RSS.

For each model at each grid and at each time step, weighting function for the atmospheric component can be calculated using (3). The simulated weighting functions are yearly averaged for the period of 1979 –2005. The spatial- and temporal-averaged weighting function for each model is presented in Fig. 3b. The scatterplot of climate model–simulated MSU T2 trends calculated by RTTOV v11 and those using climate model weighting functions derived by RTTOV v11 is shown in Fig. 4. It shows that both methods produce results in a fairly good agreement. Therefore, the models’ weighting function WF-RTTOV can be used to determine MSU T2 trends from climate model simulations.

Fig. 4.
Fig. 4.

Scatter diagram of comparisons of global-mean trends for MSU T2 from 16 climate models’ simulations and ERA-Interim between those calculated by RTTOV v11 directly (x axis) and those using climate models’ weighting functions derived by RTTOV v11 (y axis). All trends are statistically significant (). The analysis period is from January 1979 to December 2005, the period of maximum overlap between the observations and CMIP5 historical simulations. The diagonal line in the plot is a y = x line.

Citation: Journal of Atmospheric and Oceanic Technology 32, 5; 10.1175/JTECH-D-13-00250.1

As seen in Fig. 3b the weights from WF-RTTOV are systematically larger than those from WF-UAH and WF-RSS for the pressure levels above 150 hPa. This is equivalent to the contributions to T2 from the atmospheric layers below 150 hPa by WF-UAH/RSS, which are higher than that by WF-RTTOV because the total value of weighting function is conservative. This is the reason why the simulated T2 trends using the WF-UAH/RSS weighting functions are warmer than that calculated by RTTOV v11 because there are more contributions from warmer atmospheric layers to the T2 calculations.

c. Impact of cloud liquid water on T2 trends

As is well known, microwave radiation sounded by the satellite-based instrument MSU channel 2 has a good ability to penetrate through clouds in the sky over most regions. Nevertheless, it is still sensitive to cloud liquid water. The effects of cloud particles on transmittance of microwave radiation cannot be neglected. The weighting function for MSU T2 is calculated from transmittance at the corresponding microwave frequency at all discrete pressure levels, and the transmittance has a negatively exponential relationship with the absorption optical depth of the corresponding layer. Since the optical depth is related to cloud liquid water (Saunders et al. 1999), the effect of cloud liquid water on MSU T2 plays an important role in changing the vertical structure of weighting function for MSU T2.

For investigating the sensitivity of modeled T2 trend calculated by RTTOV v11 to model cloud liquid water, the vertical structure of weighting functions for MSU T2 generated by RTTOV without including cloud liquid water content for multimodel simulations and ERA-Interim are shown in Fig. 3d. It shows that these weighting functions are almost identical. Comparing with the results in Fig. 3b, where the effects of cloud liquid water content are included, it is seen that the shapes of the weighting function change significantly due to the effect of cloud liquid water content. The presence of clouds leads to increasing the peak values of the weighting function and shifting the peak levels upward, which results in a less warming in the T2 trend.

Figure 5 shows a scatterplot of the T2 trends determined using RTTOV v11 with and without the effects of cloud liquid water from 16 climate models and ERA-Interim. For ERA-Interim, whether considering the effects of cloud liquid water or not, the T2 trends calculated by RTTOV v11 are almost identical. This is indeed true for some of CMIP5 models, such as GFDL-ESM2M, MRI-CGCM3, HadGEM2-AO, etc. (Fig. 5). However, for some other CMIP5 models, such as FGOALS-s2 and BNU-ESM, the T2 trends calculated by RTTOV v11 without including the cloud liquid water effect are significantly warmer than that with the cloud liquid water effect considered.

Fig. 5.
Fig. 5.

As in Fig. 4, except calculated by RTTOV v11 directly between with CLW effect considered (x axis) and without CLW effect considered (y axis).

Citation: Journal of Atmospheric and Oceanic Technology 32, 5; 10.1175/JTECH-D-13-00250.1

For further investigating the sensitivity of MSU T2 trends to cloud liquid water, we focus our analysis on the weighting functions from three CMIP5 models (BNU-ESM, FGOALS-s2, GFDL-ESM2M) and ERA-Interim. The T2 from the first two models is more sensitive to cloud liquid water, while the last two models are not. The weighting functions from these four models with the cloud liquid water are shown in Fig. 6a. Note the result from ERA-Interim without cloud water is also plotted in this figure for comparison. It is suggested that the larger difference between the weighting functions with and without cloud liquid water considered within the range of 150–300 hPa is, the less warming of the MSU T2 trend with cloud liquid water considered than that without cloud liquid water. For example, the derived weighting functions for ERA-Interim with or without the cloud liquid water considered within the range of 150–300 hPa are almost identical (Fig. 6a), then the T2 trends of ERA-Interim with or without the cloud liquid water are also almost identical (Fig. 5). For model GFDL-EM2M, the derived weighting function with cloud liquid water effect is slightly larger than that without cloud liquid water effect, then the responding T2 trend with cloud liquid water effect is slightly less warming. For BNU-ESM, the derived weighting function with cloud liquid water effect is much larger than that without cloud liquid water effect, then the responding T2 trend with cloud liquid water effect is much less warming. For FGOALS-s2, the difference between the derived weighting functions with and without cloud liquid water effect is the largest; therefore, the difference between the derived T2 trends is the largest.

Fig. 6.
Fig. 6.

(a) MSU T2 weighting functions for ERA-Interim with (solid line) and without (dashed line) the effect of CLW, and climate models with the effect of CLW (dotted line for BNU-ESM, centerline for FGOALS-s2, phantom line for GFDL-ESM2M) averaged at global scales. The weighting functions of climate models without the effect of CLW are all identical to the weighting function of ERA-Interim without the effect of CLW. The MSU T2 weighting functions for climate models and ERA-Interim are calculated using RTTOV v11. The simulated weighting functions are yearly averaged for the period of 1979–2005. (b) Vertical distribution of monthly CLW simulated by climate models (BNU-ESM, FGOALS-s2, GFDL-ESM2M) and ERA-Interim averaged at global scales from 1979 to 2005.

Citation: Journal of Atmospheric and Oceanic Technology 32, 5; 10.1175/JTECH-D-13-00250.1

Figures 3b and 3d show that the weighting functions of all the climate models and ERA-Interim above the 150-hPa level are almost identical due to very little clouds there. Thus, the differences between the trends with and without clouds are mainly due to the differences of the weighting functions below 150 hPa. Because the accumulated value of an individual weighting function profile is one, the larger weight within the range of 150–300 hPa corresponds to less weight below the 300-hPa level. Since the simulated air temperature trends for models and ERA-Interim between 150 and 300 hPa are less warming than that below 300 hPa, the derived differences between MSU T2 with and without the cloud liquid water effect are mainly due to the differences between values of the weighting functions within the range of 150–300 hPa with and without the cloud liquid water effect.

For further investigating of the sensitivity of the weighting functions for CMIP5 models to cloud liquid water, the vertical profiles of monthly mean cloud liquid water averaged at global scale from 1979 to 2005 of three CMIP5 models (BNU-ESM, FGOALS-s2, GFDL-ESM2M) and ERA-Interim are shown in Fig. 6b. Generally speaking, the larger the accumulated values of the cloud liquid water (such as BNU-ESM, FGOALS-s2) below the 300-hPa height, the smaller the accumulated value of the weighting functions below the 300-hPa height. This leads to the larger accumulated value of the weighting functions within the range of 150–300 hPa and therefore to the less warming MSU T2 trends with the cloud liquid water effect.

6. Conclusions

In this paper, the weighting function WF-RTTOV for each CMIP5 climate model has been derived using the radiative transfer code RTTOV v11. The trends of MSU T2 derived by applying the WF-RTTOV weighting functions to the CMIP5 model–simulated atmospheric temperatures at all pressure levels are consistent with those calculated directly using the RTTOV v11 with the CMIP5 model outputs. The WF-RTTOV weighting functions successfully explained the systematic differences between the MSU T2 trends calculated by RTTOV v11 and those using traditional static WF-UAH/RSS weighting functions. The WF-RTTOV weighting functions also explained the effect of the cloud liquid water content on MSU T2 trends in the model simulations. It has been found that the higher values of cloud liquid water below the 300-hPa level lead to less warming trends of the simulated MSU T2 series.

These results could help improve the understanding of MSU T2 trends derived from different methodologies and therefore better assess the air temperature trends in the middle troposphere under different future emission scenarios. Finally, we will apply our methodology to assess air temperature trends simulated by more CMIP climate models.

Acknowledgments

This work was supported by the National Program on Key Basic Research Projects of China (Grants 2010CB951604 and 2012CB956203), the Key Technologies Research and Development Program of China (Grant 2013BAC05B04), the Research and Development Special Fund for Non-profit Industry (Meteorology, GYHY201206008), and the Joint Center for Global Change Studies. We acknowledge the World Climate Research Programme’s Working Group on Coupled Modelling, which is responsible for CMIP, and we thank the climate modeling groups (listed in Table 1) for producing and making available their model output.

APPENDIX A

Model-Level Static Weighting Functions

Since the vertical levels of models and the levels (about 300 levels) of weighting functions are different, the weighting functions have to be assigned at the vertical levels of the climate models. Assuming that model-simulated air temperature T can be represented by a four-dimensional array (lon, lat, lp, t), where the variables lon and lat run over longitude and latitude grid points, the lp index (lp = 1, nlp) runs over the number of pressure levels of the model, and t is an index over months (1979–2005). From the top to the bottom of the climate model atmosphere, the weight for the lpth model level can be given by
eq1
where is the value of a static weighting function at the ith pressure level, is the responding pressure at the ith pressure level, and N(lp) [M(lp)] is the pressure level of the weighting function that is closest to the (lp+1)th [(lp−1)th] pressure level of the model (Zhang et al. 2013).

APPENDIX B

Validity of Using Monthly Dataset to Calculate MSU T2

To investigate whether the MSU T2 trend simulated using monthly mean data is equivalent to the monthly averaged T2 that is simulated using the instantaneous state variables. Here, we use 6-hourly ERA-Interim data to perform such an investigation to answer this question. We use the RTTOV and ERA-Interim data to calculate the monthly mean brightness temperature for MSU channel 2 using two methods. The first method calculates 6-hourly T2 using 6-hourly ERA-Interim data [grid individual profiles of pressure, temperature, specific humidity, cloud liquid water (CLW) content, and surface properties] for years 1979 and 2006, and the results are averaged for each month to form monthly mean values of T2. The second method calculates monthly mean T2 directly using the monthly averaged ERA-Interim data. The brightness temperature differences from these two calculations provide a measure of validity in the second method. The comparison results (the second method minus the first method) for January and July in 1979 and 2006 are shown in Fig. B1. As seen the results obtained from these two methods are different, but the differences are all within ±0.3°C, which is not significant compared with the brightness temperature itself. The differences are negative in most areas. This systematic signature implies that the use of the monthly mean dataset to calculate the T2 will not affect its trend. The difference between the annual global-averaged difference fields in 2006 and the annual global-averaged difference fields in 1979 is only 0.003 252 18 K (i.e., 0.000 116 K yr−1). Given the estimated T2 trends of larger than 0.015 K yr−1 (Table 2), 0.000 116 K yr−1 is less than 1% of the estimated trends and therefore can be ignored in the trend analysis.

Fig. B1.
Fig. B1.

The difference fields of monthly mean MSU T2 simulated by RTTOV using the 6-hourly ERA-Interim data as the input to obtain 6-hourly MSU T2 and using the monthly averaged ERA-Interim data as the input are calculated for (left) January and (right) July in (top) 1979 and (bottom) 2006.

Citation: Journal of Atmospheric and Oceanic Technology 32, 5; 10.1175/JTECH-D-13-00250.1

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