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Rigorous determination of stratospheric water vapor trends from MIPAS observations

Simone Ceccherini, Bruno Carli, Piera Raspollini, and Marco Ridolfi

Open Access Open Access

Abstract

The trend of stratospheric water vapor as a function of latitude is estimated by the MIPAS measurements by means of a new method that uses the measurement space solution. The method uses all the information provided by the observations avoiding the artifacts introduced by the a priori information and by the interpolation to different vertical grids. The analysis provides very precise values of the trends that, however, are limited by a relatively large systematic error induced by the radiometric calibration error of the instrument. The results show in the five years from 2005 to 2009 a dependence on latitude of the stratospheric (from 37 to 53 km) water vapor trend with a positive value of (0.41 ± 0.16)%yr−1 in the northern hemisphere and less than 0.16%yr−1 in the southern hemisphere.

©2011 Optical Society of America

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Figures (9)
Fig. 1
Fig. 1 Vector w as a function of pressure.

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Fig. 2
Fig. 2 Histogram of the percentage incompleteness errors obtained from the 265448 analyzed measurements with a bin width of 0.05%. The mean and the standard deviation of the distribution are reported.

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Fig. 3
Fig. 3 Standard deviations σc (lat,t) as a function of time for different latitude bands. In the x-axis 1 corresponds to January 2005 and 60 to December 2009. Missing data points correspond to periods for which either nominal MIPAS measurements are not available or the measurements are filtered out due to large errors (see subsection 3.2).

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Fig. 4
Fig. 4 Standard deviations σc (lat,t) as a function of time for different latitude bands and globally. In the x-axis 1 corresponds to January 2005 and 60 to December 2009. Missing data points correspond to periods for which either nominal MIPAS measurements are not available or the measurements are filtered out due to large errors (see subsection 3.2).

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Fig. 5
Fig. 5 Constant part plus seasonal variability for different latitude bands. In the x-axis 1 corresponds to January 2005 and 60 to December 2009.

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Fig. 6
Fig. 6 Constant part plus seasonal variability for different latitude bands and globally. In the x-axis 1 corresponds to January 2005 and 60 to December 2009.

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Fig. 7
Fig. 7 Trend a(lat)t in percentage for different latitude bands with the best linear fit (red line). In the x-axis 1 corresponds to January 2005 and 60 to December 2009. Missing data points correspond to periods for which either nominal MIPAS measurements are not available or the measurements are filtered out due to large errors (see subsection 3.2).

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Fig. 8
Fig. 8 Trend a(lat)t in percentage for different latitude bands and globally with the best linear fit (red line). In the x-axis 1 corresponds to January 2005 and 60 to December 2009. Missing data points correspond to periods for which either nominal MIPAS measurements are not available or the measurements are filtered out due to large errors (see subsection 3.2).

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Fig. 9
Fig. 9 Fitted annual trend 12a(lat) in percentage as a function of latitude (black solid line) with the corresponding errors. Results of the sensitivity test performed simulating a drift of the gain error for June (blue solid line) and December (red solid line) 2009. The bias due to the instrumental errors is represented by the gray area centered around 0.76%yr−1, the mean value of the red and blue lines.

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Equations (20)

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c ( t )   =   w T   x ( t ) ,
∑ i = 1 n w i   = 1.
x ^ ( t )   =   x ^ 0 ( t )   +   A [ x ( t )   −   x 0 ( t ) ]   +   ɛ ( t ) ,
c ^ ( t )   =   w T H x ^ ( t )   =   w T HAx ( t )   +   w T   ( I   −   HA ) x 0 ( t )   +   w T [ H x ^ 0 ( t )   −   x 0 ( t ) ]   +   w T H ɛ ( t ) .
c ^ ( t )   −   c ( t )   =   w T ( H A   −   I ) [ x ( t )   −   x 0 ( t ) ]   +   w T [ H x ^ 0 ( t )   −   x 0 ( t ) ]   +   w T H ɛ ( t ) .
c ^ ( t )   =   v T x ^ ( t ) .
c ^ ( t )   −   c ( t )   =   v T   A   −   w T ) [ x ( t )   −   x 0 ( t ) ]   +   v T x ^ 0 ( t )   −   w T x 0 ( t )   +   v T   ɛ ( t ) .
w   =   w A   +   w A ⊥ .
| ( A T v   −   w ) | 2   =   ( A T   v   −   w A   −   w A ⊥ ) T   ( A T   v   −   w A   −   w A ⊥ )   =   | A T   v   −   w A | 2   +   | w A ⊥ | 2 .
| ( A T   v min   −   w ) |   =   | w A ⊥ | .
A   =   GK ,
x ( t )   =   x K ( t )   +   x K ⊥ ( t )
x K ( t )   =   Va ( t ) ,
x K ⊥ ( t )   =   Wb ( t ) ,
a ( t )   =   V T x ( t ) ,
b ( t )   =   W T x ( t ) .
c ( t )   =   ( w K   +   w K ⊥ ) T   ( x K ( t )   +   x K ⊥ ( t ) )   = w K T x K ( t )   +   w K ⊥ T x K ⊥ ( t ) .
w i   =   N ⋅ exp [ − ( log ( p i )   −   log ( p ¯ ) ) 2 2 σ 2 ] ,
c ¯ ( l a t , t )   =   k ( l a t )   +   s ( l a t , t )   +   a ( l a t ) t ,
1 2 [ sin ( φ max )   −   sin ( φ min ) ] ,
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