Uncertainty of AMSU-A derived temperature trends in relationship with clouds and precipitation over ocean


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

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Correspondence to X. Zou.

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

$$y(t_{i} ) = \beta x(t_{i} ) + \varepsilon (t_{i} )$$

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

$$\hat{\beta } = \frac{{\sum_{i = 1}^{N} {\left[ {y(t_{i} ) - \bar{y}} \right]\left[ {x(t_{i} ) - \bar{x}} \right]} }}{{\sum\nolimits_{i = 1}^{N} {\left[ {x(t_{i} ) - \bar{x}} \right]^{2} } }}$$

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

$$\hat{\beta } = \frac{{\frac{1}{N}\sum_{i = 1}^{N} {\left[ {y(t_{i} ) - \bar{y}} \right]\left[ {x(t_{i} ) - \bar{x}} \right]} }}{{\sigma_{x} }} ,$$

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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  • Climate trend
  • Satellite
  • Cloud