A study of polarimetric error induced by satellite motion: application to the 3MI and similar sensors
<p>This study investigates the magnitude of the error introduced by the co-registration and interpolation in computing Stokes vector elements from observations by the Multi-viewing, Multi-channel, Multi-polarisation Imager (3MI). The Stokes parameter derivation from the 3MI measurements requir...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Copernicus Publications
2021-03-01
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| Series: | Atmospheric Measurement Techniques |
| Online Access: | https://amt.copernicus.org/articles/14/1801/2021/amt-14-1801-2021.pdf |
| Summary: | <p>This study investigates the magnitude of the error
introduced by the co-registration and interpolation in computing Stokes
vector elements from observations by the Multi-viewing, Multi-channel,
Multi-polarisation Imager (3MI). The Stokes parameter derivation from the
3MI measurements requires the syntheses of three wide-field-of-view images
taken by the instrument at 0.25 s interval with polarizers at different
angles. Even though the synthesis of spatially or temporally inhomogeneous
data is inevitable for a number of polarimetric instruments, it is
particularly challenging for 3MI because of the instrument design, which prioritizes
the stability during a long life cycle and enables the
wide-field-of-view and multiwavelength capabilities. This study therefore
focuses on 3MI's motion-induced error brought in by the co-registration
and interpolation that are necessary for the synthesis of three images. The
2-D polarimetric measurements from the Second-generation Global Imager
(SGLI) are weighted and averaged to produce two proxy datasets of the 3MI
measurements, with and without considering the effect of the satellite
motion along the orbit. The comparison of these two datasets shows that the
motion-induced error is not symmetric about zero and not negligible when the
intensity variability of the observed scene is large. The results are
analyzed in five categories of pixels: (1) cloud over water, (2) clear sky over water, (3) coastlines, (4) cloud over
land, and (5) clear sky over land. The
most spread distribution of normalized polarized radiance (<span class="inline-formula"><i>L</i><sub>p</sub></span>)
difference is in the cloud-over-water class, and the most spread
distribution of degree of linear polarization (DOLP) difference is in the
clear-sky-over-water class. The 5th to 95th percentile ranges of <span class="inline-formula"><i>L</i><sub>p</sub></span> difference for
each class are (1) [<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M3" display="inline" overflow="scroll" dspmath="mathml"><mrow><mo>-</mo><mn mathvariant="normal">0.0051</mn><mo>,</mo><mn mathvariant="normal">0.012</mn></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="75pt" height="11pt" class="svg-formula" dspmath="mathimg" md5hash="f4f90a041038d7e407c0708f7af9ff8a"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="amt-14-1801-2021-ie00001.svg" width="75pt" height="11pt" src="amt-14-1801-2021-ie00001.png"/></svg:svg></span></span>], (2) [<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M4" display="inline" overflow="scroll" dspmath="mathml"><mrow><mo>-</mo><mn mathvariant="normal">0.0040</mn><mo>,</mo><mn mathvariant="normal">0.0088</mn></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="81pt" height="11pt" class="svg-formula" dspmath="mathimg" md5hash="38e8b3627963758ebfc7bcd95eff4135"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="amt-14-1801-2021-ie00002.svg" width="81pt" height="11pt" src="amt-14-1801-2021-ie00002.png"/></svg:svg></span></span>], (3)
[<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M5" display="inline" overflow="scroll" dspmath="mathml"><mrow><mo>-</mo><mn mathvariant="normal">0.0033</mn><mo>,</mo><mn mathvariant="normal">0.012</mn></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="75pt" height="11pt" class="svg-formula" dspmath="mathimg" md5hash="66bfb3d9094539fdad0eeec2d214d483"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="amt-14-1801-2021-ie00003.svg" width="75pt" height="11pt" src="amt-14-1801-2021-ie00003.png"/></svg:svg></span></span>], (4) [<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M6" display="inline" overflow="scroll" dspmath="mathml"><mrow><mo>-</mo><mn mathvariant="normal">0.0033</mn><mo>,</mo><mn mathvariant="normal">0.0062</mn></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="81pt" height="11pt" class="svg-formula" dspmath="mathimg" md5hash="9e02cee55d292f6b4f56b49131f3f727"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="amt-14-1801-2021-ie00004.svg" width="81pt" height="11pt" src="amt-14-1801-2021-ie00004.png"/></svg:svg></span></span>], and (5) [<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M7" display="inline" overflow="scroll" dspmath="mathml"><mrow><mo>-</mo><mn mathvariant="normal">0.0023</mn><mo>,</mo><mn mathvariant="normal">0.0032</mn></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="81pt" height="11pt" class="svg-formula" dspmath="mathimg" md5hash="bdaafe7b48e967755bd17e974687372f"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="amt-14-1801-2021-ie00005.svg" width="81pt" height="11pt" src="amt-14-1801-2021-ie00005.png"/></svg:svg></span></span>]. The same
percentile range of DOLP difference for each class are (1) [<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M8" display="inline" overflow="scroll" dspmath="mathml"><mrow><mo>-</mo><mn mathvariant="normal">0.023</mn><mo>,</mo><mn mathvariant="normal">0.060</mn></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="69pt" height="11pt" class="svg-formula" dspmath="mathimg" md5hash="f0398b31bef0ffb3cb6f41350819e8b8"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="amt-14-1801-2021-ie00006.svg" width="69pt" height="11pt" src="amt-14-1801-2021-ie00006.png"/></svg:svg></span></span>],
(2) [<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M9" display="inline" overflow="scroll" dspmath="mathml"><mrow><mo>-</mo><mn mathvariant="normal">0.043</mn><mo>,</mo><mn mathvariant="normal">0.093</mn></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="69pt" height="11pt" class="svg-formula" dspmath="mathimg" md5hash="a53be921cf5868f00fb554d118cb8a40"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="amt-14-1801-2021-ie00007.svg" width="69pt" height="11pt" src="amt-14-1801-2021-ie00007.png"/></svg:svg></span></span>], (3) [<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M10" display="inline" overflow="scroll" dspmath="mathml"><mrow><mo>-</mo><mn mathvariant="normal">0.019</mn><mo>,</mo><mn mathvariant="normal">0.082</mn></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="69pt" height="11pt" class="svg-formula" dspmath="mathimg" md5hash="3c77071906e97bc03f3462143a91cf35"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="amt-14-1801-2021-ie00008.svg" width="69pt" height="11pt" src="amt-14-1801-2021-ie00008.png"/></svg:svg></span></span>], (4) [<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M11" display="inline" overflow="scroll" dspmath="mathml"><mrow><mo>-</mo><mn mathvariant="normal">0.0075</mn><mo>,</mo><mn mathvariant="normal">0.014</mn></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="75pt" height="11pt" class="svg-formula" dspmath="mathimg" md5hash="56b27af29fcc25c3e018f26d1ba40674"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="amt-14-1801-2021-ie00009.svg" width="75pt" height="11pt" src="amt-14-1801-2021-ie00009.png"/></svg:svg></span></span>], and (5)
[<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M12" display="inline" overflow="scroll" dspmath="mathml"><mrow><mo>-</mo><mn mathvariant="normal">0.011</mn><mo>,</mo><mn mathvariant="normal">0.016</mn></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="69pt" height="11pt" class="svg-formula" dspmath="mathimg" md5hash="6abcabbbfb4827f96fa136d3c9aa2230"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="amt-14-1801-2021-ie00010.svg" width="69pt" height="11pt" src="amt-14-1801-2021-ie00010.png"/></svg:svg></span></span>]. The medians of the <span class="inline-formula"><i>L</i><sub>p</sub></span> difference are (1) 0.00035, (2)
0.000049, (3) 0.00031, (4), 0.000089, and (5) 0.000037, whereas the medians
of the DOLP difference are (1) 0.0014, (2) 0.0015, (3) 0.0025, (4) 0.00027,
and (5) 0.00014. A model using Monte Carlo simulation confirms that the
magnitude of these errors over clouds are closely related to the spatial
correlation in the horizontal cloud structure. For the cloud-over-water
category, it is shown that the error model developed in this study can
statistically simulate the magnitude and trends of the 3MI's motion-induced
error estimated from SGLI data. The obtained statistics and the simulation
technique can be utilized to provide pixel-level quality information for 3MI
Level 1B products. In addition, the simulation method can be applied to the
past, current, and future spaceborne instruments with a similar design.</p> |
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| ISSN: | 1867-1381 1867-8548 |