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

F. Weng; X. Zou; Z. Qin

doi:10.1007/s00382-013-1958-7

Climate Dynamics

September 2014, Volume 43, Issue 5–6, pp 1439–1448 | Cite as

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

Authors
Authors and affiliations

F. Weng
X. ZouEmail author
Z. Qin

Article

First Online: 06 October 2013

Received: 16 July 2013

Accepted: 26 September 2013

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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.

Keywords

Climate trend Satellite Cloud

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Notes

Acknowledgments

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

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

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

(2)

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

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

(3)

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

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

(4)

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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Authors and Affiliations

F. Weng
- 1
X. Zou
- 2
Email author
Z. Qin
- 3

1.NOAA/NESDIS/Center for Satellite Applications and ResearchCollege ParkUSA
2.Department of Earth, Ocean and Atmospheric ScienceFlorida State UniversityTallahasseeUSA
3.NUIST/Center of Data Assimilation for Research and ApplicationNanjingChina

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

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