A Spatio-Temporal Model for Arctic Sea Ice

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<br><br><br>
## A Spatio-Temporal Model for Arctic Sea Ice
### Joint Statistical Meetings, August 2022
#### Alison Kleffner, Susan VanderPlas, Yawen Guan
#### Department of Statistics, University of Nebraska - Lincoln
##### <svg aria-hidden="true" role="img" viewBox="0 0 512 512" style="height:1em;width:1em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:black;overflow:visible;position:relative;"><path d="M502.3 190.8c3.9-3.1 9.7-.2 9.7 4.7V400c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V195.6c0-5 5.7-7.8 9.7-4.7 22.4 17.4 52.1 39.5 154.1 113.6 21.1 15.4 56.7 47.8 92.2 47.6 35.7.3 72-32.8 92.3-47.6 102-74.1 131.6-96.3 154-113.7zM256 320c23.2.4 56.6-29.2 73.4-41.4 132.7-96.3 142.8-104.7 173.4-128.7 5.8-4.5 9.2-11.5 9.2-18.9v-19c0-26.5-21.5-48-48-48H48C21.5 64 0 85.5 0 112v19c0 7.4 3.4 14.3 9.2 18.9 30.6 23.9 40.7 32.4 173.4 128.7 16.8 12.2 50.2 41.8 73.4 41.4z"/></svg> [akleffner@huskers.unl.edu](akleffner@huskers.unl.edu)
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<br><br>
.medium[*Slides: https://alisonkleffner.github.io/presentations/JSM_2022/index.html#1]

---
class: primary
# Goal: Sea Ice Crack Detection

+ Sea ice is frozen sea water that can occur as an ice pack which drifts over the oceans surface
+ Cracks, or leads, may form in the ice pack due to dynamic processes
  - Allows for heat from the ocean to be transferred to the atmosphere (Schreyer, Sulsky, Munday, et al., 2006). 
+ Other Ice Crack Detection Methods
  - Involve the use of thermal images or deformation calculations found through satellite images (Key, Stone, Maslanik, et al., 1993; Peterson and Sulsky, 2011).
    + Satellite images can be low in resolution and are affected by atmospheric conditions (Willmes and Heinemann, 2015)

---
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# Method Motivation: Trajectory Plot

---
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# Our Proposed Methods: Overview

+ Clustering Method: Bounding Box - Find Cracks:
  - Uses movement features of trajectory to group similar trajectories
  - Boundaries of clusters - location of potential ice cracks
- Spatio-Temporal Interpolation Method: Intersections
  - Due to data collection method, data tends to be missing in chunks
  - Uses spatio-temporal neighbors of missing data 
      + Found using the clusters
<div class="figure" style="text-align: center">
<img src="images/bounding-box.png" alt="Picture of different features of our Bounding Box" width="291" />
<p class="caption">Picture of different features of our Bounding Box</p>
</div>

---
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# References
<font size="2">
<p><cite><a id='bib-key_detectability_1993'></a><a href="#cite-key_detectability_1993">Key, J., R. Stone, J. Maslanik, et al.</a>
(1993).
&ldquo;The detectability of sea-ice leads in satellite data as a function of atmospheric conditions and measurement scale&rdquo;.
In: <em>Annals of Glaciology</em> 17, pp. 227&ndash;232.
DOI: <a href="https://doi.org/10.3189/S026030550001288X">10.3189/S026030550001288X</a>.</cite></p>

<p><cite><a id='bib-peterson_evaluating_2011'></a><a href="#cite-peterson_evaluating_2011">Peterson, K. and D. Sulsky</a>
(2011).
&ldquo;Evaluating Sea Ice Deformation in the Beaufort Sea Using a Kinematic Crack Algorithm with RGPS Data&rdquo;.
In: 
<em>Remote Sensing of the Changing Oceans</em>.
Berlin, Heidelberg: Springer.
ISBN: 978-3-642-16541-2.</cite></p>

<p><cite><a id='bib-schreyer_elastic_2006'></a><a href="#cite-schreyer_elastic_2006">Schreyer, H. L., D. L. Sulsky, L. B. Munday, et al.</a>
(2006).
&ldquo;Elastic-decohesive constitutive model for sea ice&rdquo;.
In: <em>Journal of Geophysical Research: Oceans</em> 111.C11.
DOI: <a href="https://doi.org/10.1029/2005JC003334">10.1029/2005JC003334</a>.</cite></p>

<p><cite><a id='bib-willmes_pan-arctic_2015'></a><a href="#cite-willmes_pan-arctic_2015">Willmes, S. and G. Heinemann</a>
(2015).
&ldquo;Pan-Arctic lead detection from MODIS thermal infrared imagery&rdquo;.
In: <em>Annals of Glaciology</em> 56, pp. 29&ndash;37.
DOI: <a href="https://doi.org/10.3189/2015AoG69A615">10.3189/2015AoG69A615</a>.</cite></p>
</font>

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# Questions?
<br>
<br>
<svg aria-hidden="true" role="img" viewBox="0 0 512 512" style="height:1em;width:1em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:white;overflow:visible;position:relative;"><path d="M502.3 190.8c3.9-3.1 9.7-.2 9.7 4.7V400c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V195.6c0-5 5.7-7.8 9.7-4.7 22.4 17.4 52.1 39.5 154.1 113.6 21.1 15.4 56.7 47.8 92.2 47.6 35.7.3 72-32.8 92.3-47.6 102-74.1 131.6-96.3 154-113.7zM256 320c23.2.4 56.6-29.2 73.4-41.4 132.7-96.3 142.8-104.7 173.4-128.7 5.8-4.5 9.2-11.5 9.2-18.9v-19c0-26.5-21.5-48-48-48H48C21.5 64 0 85.5 0 112v19c0 7.4 3.4 14.3 9.2 18.9 30.6 23.9 40.7 32.4 173.4 128.7 16.8 12.2 50.2 41.8 73.4 41.4z"/></svg> **akleffner@huskers.unl.edu**
<svg aria-hidden="true" role="img" viewBox="0 0 496 512" style="height:1em;width:0.97em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:white;overflow:visible;position:relative;"><path d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z"/></svg> **alisonkleffner**

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