## Abstract

Microwave Sounding Unit (MSU) and Advanced Microwave Sounding Unit-A (AMSU-A) observations from a series of National Oceanic and Atmospheric Administration satellites have been extensively utilized for estimating the atmospheric temperature trend. For a given atmospheric temperature condition, the emission and scattering of clouds and precipitation modulate MSU and AMSU-A brightness temperatures. In this study, the effects of the radiation from clouds and precipitation on AMSU-A derived atmospheric temperature trend are assessed using the information from AMSU-A window channels. It is shown that the global mean temperature in the low and middle troposphere has a larger warming rate (about 20–30 % higher) when the cloud-affected radiances are removed from AMSU-A data. It is also shown that the inclusion of cloud-affected radiances in the trend analysis can significantly offset the stratospheric cooling represented by AMSU-A channel 9 over the middle and high latitudes of Northern Hemisphere.

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## Acknowledgments

This work was supported by Chinese Ministry of Science and Technology under 973 project 2010CB951600.

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## Appendix 1

### Appendix 1

Regional contributions to the global trends are obtained using the linear regression method. Suppose there are two time series of \(x(t_{i} )\) and \(y(t_{i} )\), \(i = 1, \ldots ,N\), where *N* is the length of the two time series. The linear regression of \(y(t_{i} )\) onto \(x(t_{i} )\) can be written as

where \(\varepsilon (t_{i} )\) is the part of \(y(t_{i} )\) that cannot be explained by \(x(t_{i} )\) and \(\beta x(t_{i} )\) is the part of \(y(t_{i} )\) that explained by \(x(t_{i} )\), with \(\beta\) being the regression coefficient of which the estimated value is

where notation “bar” represents the temporal mean.

Since the regression coefficient \(\beta\) is inversely proportional to the standard deviation of \(x(t_{i} )\) and the actual variation of \(y(t_{i} )\) associated with \(x(t_{i} )\) is \(\beta x(t_{i} )\), the regression coefficient \(\beta\) is often obtained using a normalized \(x(t_{i} )\). In the latter case, the estimated \(\hat{\beta }\) is expressed as

where \(\sigma_{x}\) is the standard deviation of \(x(t_{i} )\).

In this study, the monthly mean brightness temperature at a set of longitude \(\lambda\) and latitude \(\phi\) gridpoints, \(T_{b} \left( {\lambda ,\phi ,t_{i} } \right)\) (\(i = 1, \ldots ,N\)), is regressed onto the linear trend of the global mean brightness temperature \(T_{b}^{LR,global}\). In Eq. (1), \(R\left( {\lambda ,\phi } \right)\) corresponds to \(\hat{\beta }\) in Eq. (4); \(T_{b}^{LR,global}\)to *x*; and \(T_{b} \left( {\lambda ,\phi ,t_{i} } \right)\) to *y*.

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Weng, F., Zou, X. & Qin, Z. Uncertainty of AMSU-A derived temperature trends in relationship with clouds and precipitation over ocean.
*Clim Dyn* **43, **1439–1448 (2014). https://doi.org/10.1007/s00382-013-1958-7

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### Keywords

- Climate trend
- Satellite
- Cloud