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Tropospheric temperatures (T2) monitored by channel 2 of the satellite-based Microwave Sounding Unit (MSU) include a contribution from temperatures in the cooling stratosphere1,2 (T4). Using radiosonde data, Fu et al.2 apply a regression method to quantify the relative influences of T4 and T2 on the mean temperature of the 850–300-hPa layer (T850–300). We apply the Fu et al. regression method to simulated 1958–97 monthly-mean global-mean T4, T2 and T850–300 from a four-member ensemble of a climate-change experiment that was performed with the National Center for Atmospheric Research Parallel Climate Model (PCM)3,4 with combined anthropogenic and natural forcing.

The model-derived regression coefficients of T850–300 against T2 and T4 are a2=1.106±0.026 and a4=−0.157±0.019, with 5–95% uncertainty ranges derived from intra-ensemble variability. Results are in close agreement with the coefficients estimated by Fu et al.2 from radiosonde data (a2=1.156, a4=−0.153). To assess the contribution to these coefficients of the overlap between the T2 and T4 weighting functions, we derive a weighting function for T850–300 and regress this directly against the mass-based weighting functions5 of T2 and T4. This yields a2=1.089 and a4=−0.129, implying that the regression relation derived by Fu et al. arises largely from the overlap of the weighting functions, rather than from physical coupling between tropospheric and stratospheric temperatures.

Because we know the actual T850–300 trends over 1979–99 in PCM, we can evaluate the reliability of the statistical method of Fu et al.2 for reconstructing these trends. For each ensemble member, trend reconstructions were produced with the Fu et al. and PCM-derived regression coefficients. Reconstructed trends agree with the actual PCM T850–300 trends to within 0.016 K per decade on average (Fig. 1). We find a similar level of agreement between PCM's reconstructed and actual T850–300 trends for the Northern and Southern Hemispheres and the tropics. Note that although simulated trends in T2LT (where T2LT is a synthetic channel for lower-middle troposphere) and T850–300 are in close correspondence, PCM's T2LT trends are not subject to problems that affect the observed T2LT product, such as changes in surface emissivity, intersatellite calibration biases, and noise amplification2.

Figure 1: Simulated trends in global-mean free-tropospheric temperature.
figure 1

Black crosses, trends in T850–300 over the period 1979–99, as simulated by the National Center for Atmospheric Research Parallel Climate Model (PCM) in each of four realizations of an experiment with anthropogenic and natural forcing3,4. Asterisks indicate free-tropospheric temperature trends reconstructed from synthetic T2 and T4 trends using the method of Fu et al.2. These are calculated using three different sets of regression coefficients, which are derived from radiosonde observations by Fu et al.2 (pink asterisks), estimated from the PCM experiments (dark blue asterisks), and obtained directly from the T2 and T4 weighting functions (light blue asterisks). Red crosses, simulated trends in T2; green crosses, simulated trends in T2LT. The simulated trend in T4 is −0.36±0.03 K per decade. The model's surface warming over 1890–1999 (0.62 °C) is consistent with that observed.

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Our model-based T850–300 trends shown in Fig. 1 are consistent with the free tropospheric temperature trends that Fu et al. reconstructed from MSU observations for the period 1979–2001 (refs 2, 6; 0.09 and 0.18 K per decade for the UAH (University of Alabama at Huntsville) and RSS (Remote Sensing Systems) reconstructions, respectively). Overall, we find that the analysis method of Fu et al.2 is robust, and that their radiosonde-based regression relationships between T4, T2 and T850–300 are in good agreement with those independently derived from climate-model output.