NSF CAREER: Developing Spatiotemporal Relational Models to Anticipate Tornado Formation

PI: Amy McGovern

July 1 2008 - June 2013 (no cost extension until June 2015)

Abstract and Project Goals

The goal of this research is to revolutionize the ability to anticipate tornadoes by developing advanced techniques for statistical pattern discovery in spatially and temporally varying relational data. These models are applied to complete fields of meteorological quantities obtained through data assimilation and simulation. Doppler radar data is limited and, while modern data assimilation techniques allow the unobserved quantities to be estimated, the resulting four-dimensional fields are too complicated for the extraction of meaningful, repeatable patterns by either humans or current data mining techniques. By studying a full field of variables, the models can identify critical interactions among high level features. The models are developed and verified in close collaboration with domain experts.

The interdisciplinary research is used to improve retention and recruitment in computer science (CS). This draws on recent evidence that underrepresented groups are not drawn to computing careers because they do not appreciate how computing can be used to solve real world problems. Introducing authentic projects into both early CS and meteorology classes will improve the number of technically trained students in both majors.

The primary broader impact of this research is to society, through the potential for reduction in loss of human life, property, and money. Models will be made available to operational meteorologists as they are verified. Another broader impact will come from increasing the number of computing oriented minors and majors through authentic projects. All data and results will be disseminated through peer reviewed publications and via open source online repositories.

Students who received funding by the grant (by working date)

• Graduate students
  • Brittany Dahl (MS student, OU's School of Meteorology)
  • Andrew Mackenzie (MS student, Interdisciplinary degree)
  • David John Gagne II (MS student, OU's School of Meteorology)
  • Zachery Tidwell (MS Student, School of Computer Science)
  • Nathaniel Troutman (MS student, School of Computer Science)
  • Matthew Collier (PhD student, Department of Geography)
  • Nathan Hiers (MS student, School of Computer Science)
• Research Experiences for Undergraduates
  • Zachary Roux (REU student, summer 2014-spring 2015)
  • David Harrison (REU student, summer 2013-spring 2015)
  • Branden Katona (REU student, summer 2012 - fall 2012, summer 2013, OU's School of Meteorology)
  • Marissa Beene (REU student, summer 2013-falll 2013)
  • Andrea Balfour (REU student, summer 2013-fall 2013)
  • Ross Kimes (REU student, summer 2010 - 2012, OU's School of Meteorology)
  • Bradley Pirtle (REU student, summer 2010 - 2012, OU's School of Electrical and Computer Engineering
  • Timothy Sliwinski (REU student, summer 2010)
  • Jonathan Trueblood (REU student, summer 2010)
  • David John Gagne II (REU student, OU's School of Meteorology, summer 2008-spring 2010 (except summer 2009))
  • Timothy Supinie (REU student, OU's School of Meteorology, summer 2008 - spring 2010)

Collaborators

• Kelvin Droegemeier (OU's School of Meteorology)
• Rodger A Brown (National Severe Storms Laboratory)
• John Williams (National Center for Atmospheric Research)
• Jennifer Abernethy (National Center for Atmospheric Research)
• Louis Wicker (National Severe Storms Laboratory)

Research Challenges

• The research challenges for this project span both computer science and meteorology.
  • One of the primary CS goals for this project is to automatically create human readable networks of dependencies in large dynamic relational data sets, specifically focusing on severe storms. Creating a machine learning technique to accomplish this in near real-time poses a number of challenges. The primary challenge comes from the exponential increase in model complexity introduced by temporal data and temporal dependencies. Search techniques must handle this efficiently or the models will not be able to be learned. To address this issue, we will draw on our success with Relational U-Tree (Dabney & McGovern, 2007) where we used stochastic sampling as introduced by Srinivasan (1999) in conjunction with temporal sampling to address temporal autocorrelation issues. A second challenge comes from the fact that, unless one could sense the state of every molecule in the atmosphere, weather data will be partially observable. Finally, learning a human readable model of dynamic data introduces a challenge in both representing the dynamic relational data and in representing the model itself. The representations need to be simple enough to be easily understood by scientists outside computer science (CS) yet rich enough to not overly bias the model.
  • In meteorology, the key challenges (and contributions) come from our novel use of a complete field of meteorological variables. As an integral part of applying the proposed model to tornado anticipation, we will be developing automated techniques to identify and extract high-level storm features such as regions of potentially dangerous winds, large hail, or torrential rain. Identifying and tracking such features in a near real-time scale is critical to successful model learning yet presents difficulties than include object permanence and data overload.

Peer reviewed publications (Journals, book chapters, conferences, workshops)

• McGovern, Amy and Potvin, Corey and Brown, Rodger A. (to appear) Using Large-scale Machine Learning to Improve our Understanding of the Formation of Tornadoes. Invited chapter in Large-Scale Machine Learning in the Earth Sciences.

• McGovern, Amy McGovern and Balfour, Andrea and Beene, Marissa and Harrison, David (2015) Storm Evader: Using an iPad To Teach Kids about Meteorology and Technology. Bulletin of the American Meteorological Society, Volume 96, Issue 3, pages 397-404. Final pdf

• McGovern, Amy and Rosendahl, Derek H. and Brown, Rodger A.(2014) Toward Understanding Tornado Formation Through Spatiotemporal Data Mining. Book chapter in Data Mining for Geoinformatics: Methods and Applications, edited by Cervone, Guid and Lin, Jessica and Waters, Nigel. 29 DOI 10.1007/978-1-4614-7669-6 2, Springer Science Business Media New York 2014. [link to a pre-print of the pdf. The officially formatted pdf is linked above.]

• McGovern, Amy and Gagne II, David J. and Williams, John K. and Brown, Rodger A. and Basara, Jeffrey B. (2014) Enhancing understanding and improving prediction of severe weather through spatiotemporal relational learning. Machine Learning. Vol 95, Issue 1, pages 27-50. [online version, open access]

• McGovern, Amy and Troutman, Nathaniel and Brown, Rodger A. and Williams, John K. and Abernethy, Jennifer. (2013) Enhanced Spatiotemporal Relational Probability Trees and Forests. Data Mining and Knowledge Discovery, Volume 26, Issue 2, pages 398-433. [online first version, open access]

• Pirtle, Bradley and Kimes, Ross and McGovern, Amy and Brown, Rodger A. (2012) Using the XSEDE Supercomputing and Visualization Resources to Improve Tornado Prediction Using Data Mining. Presented at the XSEDE 2012 Conference. [extended abstract pdf]

• Gagne II, David John and McGovern, Amy and and Basara, Jeffrey and Brown, Rodger A. (2012) Tornadic Supercell Environments Analyzed Using Surface and Reanalysis Data: A Spatiotemporal Relational Data Mining Approach. Journal of Applied Meteorology and Climatology. Vol. 51, No. 12, pages 2203-2217.

• McGovern, Amy and Troutman, Nathaniel and Brown, Rodger A. and Williams, John K. and Abernethy, Jennifer. (2012) Enhanced Spatiotemporal Relational Probability Trees and Forests. To appear in Data Mining and Knowledge Discovery. [online first version, open access]

• McGovern, Amy and Gagne II, David John and Troutman, Nathaniel and Brown, Rodger A. and Basara, Jeffrey and Williams, John. (2011) Using Spatiotemporal Relational Random Forests to Improve our Understanding of Severe Weather Processes. Statistical Analysis and Data Mining, special issue on the best of the 2010 NASA Conference on Intelligent Data Understanding. Vol 4, Issue 4, pages 407-429. [pdf preprint (1.4M), link to official online version]

• McGovern, Amy and Rosendahl, D and Brown, R and Droegemeier, K. (2011) Identifying Predictive Multi-Dimensional Time Series Motifs: An application to severe weather. Data Mining and Knowledge Discovery. Volume 22, Issue 1, pages 237-258. [pdf (2.0M). Link to official springer version.]

• McGovern, Amy; Supinie, Timothy; Gagne II, David John; Troutman, Nathaniel; Collier, Matthew; Brown, Rodger A.; Basara, Jeffrey; Williams, John. (2010) Understanding Severe Weather Processes through Spatiotemporal Relational Random Forests. Proceedings of the NASA Conference on Intelligent Data Understanding: CIDU 2010. pdf (500K)

• Supinie, Timothy and McGovern, Amy and Williams, John and Abernethy, Jennifer. (2009) Spatiotemporal Relational Random Forests. Proceedings of the 2009 IEEE International Conference on Data Mining (ICDM) workshop on Spatiotemporal Data Mining. [pdf (272 K)]

• Bodenhamer, Matthew; Bleckley, Samuel; Fennelly, Daniel; Fagg, Andrew H. and McGovern, Amy. (2009) Spatio-temporal Multi-Dimensional Relational Framework Trees. Proceedings of the 2009 IEEE International Conference on Data Mining (ICDM) workshop on Spatiotemporal Data Mining. [pdf (305 K)]

• Gagne II, David J.; McGovern, Amy; Brotzge, Jerry. (2009). Classification of Convective Areas Using Decision Trees. Journal of Atmospheric and Oceanic Technology. Vol 26, Issue 7, pages 1341-1353. [pdf (1.1 MB)]

• McGovern, Amy and Hiers, Nathan and Collier, Matthew and Gagne II, David J. and Brown, Rodger A. (2008). Spatiotemporal Relational Probability Trees. Proceedings of the 2008 IEEE International Conference on Data Mining, Pages 935-940. Pisa, Italy. 15-19 December 2008. [pdf (326K)]

• Collier, Matthew and McGovern, Amy. (2008). Kernels for the Investigation of Localized Spatiotemporal Transitions of Drought with Support Vector Machines. Proceedings of ICDM 2008, the 8th IEEE International Conference on Data Mining Workshops. Pisa, Italy. 15-19 December 2008, pages 359-368. [pdf (400K)]

Presentations

The presentations below include links to the actual talks themselves (for AMS talks) and videos and associated slides. The earlier presentations include some of the preliminary results that we used to demonstrate the feasibility of this study for the CAREER award.

• Harrison, David and Roux, Z. A. and McGovern, Amy and Blumberg, W. G. (2015) Promoting a Weather Ready Nation Through Serious Games. Presented at the 24th Symposium on Education at the annual American Meteorological Society meeting.
  • Abstract and recorded presentation

• Katona, Branden T. and McGovern, Amy and Lakshmanan, V. and Clark, Adam J. (2014) Automated Identification of Cold Pools in a Convection-permitting model. Presented at the 12th Conference on Artificial and Computational Intelligence and its Applications to the Environmental Sciences at the annual American Meteorological Society meeting.
  • Abstract and recorded presentation

• MacKenzie, Andrew J. and McGovern, Amy and Lakshmanan, V. and Clark, Adam J. and Brown, Rodger A. (2014) A 3-Dimensional Watershed Transform Technique for Storm Extraction on Gridded Data. Presented at the 12th Conference on Artificial and Computational Intelligence and its Applications to the Environmental Sciences at the annual American Meteorological Society meeting.
  • Abstract and recorded presentation

• MacKenzie, Andrew J. and Lakshmanan, V. and McGovern, Amy and Brown, Rodger A. and Clark, Adam J. (2014) An Automated, Multi-parameter Dry line Detection Algorithm. Presented at the 12th Conference on Artificial and Computational Intelligence and its Applications to the Environmental Sciences at the annual American Meteorological Society meeting.
  • Abstract and recorded presentation
• Dahl, Brittany and Potvin, Corey K. and Wicker, Louis J. and Brown, Rodger A. and McGovern, Amy (2014) Dependence of Vortex Characteristics on Grid Resolution in Simulated Supercells. Presented at the 12th Conference on Artificial and Computational Intelligence and its Applications to the Environmental Sciences at the annual American Meteorological Society meeting.
  • Abstract and recorded presentation
• Katona, Branden and Pirtle, Bradley and McGovern, Amy (2013) Using iPads to Teach Artificial Intelligence through Meteorology. Presented at the 22nd Symposium on Education at the annual American Meteorological Society meeting..
  • Abstract and recorded presentation
• Dahl, Brittany and Katona, Branden and Pirtle, Bradley and McGovern, Amy and Brown, Rodger A. and Wicker, Louis J. (2013) Applications of Data Mining to Supercell Tornadogenesis. Presented at the 11th Conference on Artificial and Computational Intelligence and its Applications to the Environmental Sciences at the annual American Meteorological Society meeting.
  • Abstract and recorded presentation
• McGovern, Amy; Kimes, Ross; Pirtle, Bradley; Brown, Rodger A. (2012). Spatiotemporal Data Mining of High Resolution Simulations of Tornadoes. Presented at the Tenth Conference on Artificial Intelligence and its Applications to the Environmental Sciences.
  • Abstract and recorded presentation
• Gagne II, David John; McGovern, Amy; Basara, Jeffrey B.; Brown, Rodger A. (2011). Tornadic supercell analysis from Oklahoma Mesonet and proximity sounding observations: a spatiotemporal relational data mining approach. Presented at the Ninth Conference on Artificial Intelligence and its Applications to the Environmental Sciences.
  • Abstract and recorded presentation
• Sliwinski, Timothy; Trueblood, Jonathan; Gagne II, David John; McGovern, Amy; Williams, John K.; Abernethy, Jennifer. (2011) Using spatiotemporal relational random forests (SRRFs) to predict convectively induced turbulence. Presented at the Ninth Conference on Artificial Intelligence and its Applications to the Environmental Sciences.
  • Abstract
  • Slides from the talk
• Trueblood, Jonathan; Sliwinski, Timothy; Gagne II, David John; McGovern, Amy; Williams, John K.; Abernethy, Jennifer. (2011) Spatiotemporal relational random forest (SRRF) prediction of convectively-induced turbulence: a severe encounter case study. Presented at the Ninth Conference on Artificial Intelligence and its Applications to the Environmental Sciences.
  • Abstract and recorded presentation
  • Slides from the talk
• Gagne II, David John; Supinie, Timothy A.; McGovern, Amy; Basara, Jeffrey B.; Brown, Rodger A. (2010). Analyzing the effects of low level boundaries on tornadogenesis through spatiotemporal relational data mining. Presented at the Eighth Conference on Artificial Intelligence and its Applications to the Environmental Sciences.
  • Recording of the presentation at AMS
  • Extended abstract
• Abernethy, Jennifer; Supinie, Timothy A.; A. McGovern, and Williams, J. K. (2010) Capturing relationships between coherent structures and convectively-induced turbulence using Spatiotemporal Relational Random Forests. Presented at the Eighth Conference on Artificial Intelligence and its Applications to the Environmental Sciences.
  • Recording of the presentation at AMS
• Gagne II, David John; McGovern, Amy; Hiers, Nathan C.; Collier, Matthew; Brown, Rodger A. (2009 ). Expanding the Spatial Awareness of Spatiotemporal Relational Probability Trees to Improve the Analysis of Severe Thunderstorm Models. Preprints of the Seventh Conference on Artificial Intelligence and its Applications to the Environmental Sciences.
  • Recording of the presentation at AMS
• Hiers, Nathan; McGovern, Amy; Rosendahl, Derek H.; Brown, Rodger A; Droegemeier, Kelvin K. (2008). Using Spatiotemporal Relational Data Mining to Identify the Key Parameters for Anticipating Rotation Initiation in Simulated Supercell Thunderstorms. Preprints of the Sixth Conference on Artificial Intelligence and its Applications to the Environmental Sciences, joint session with the 24th Conference on International Interactive Information and Processing Systems (IIPS) for Meteorology, Oceanography, and Hydrology.
  • Recording of AMS presentation
  • Extended abstract
  • Movies (linked below as well):
    • Three dimensional view of a storm taken every 30 seconds for the storm's lifetime. The red regions show strong updrafts, the blue shows strong downdrafts, and the green and yellow show strong vorticity. This storm was generated using ARPS.
    • Two dimensional movie of storm region and tracking algorithm. The left panel shows each storm region (highlighted using colored regions) and the right panel shows the reflectivity of the storm at 4km. These storms were generated using ARPS. This algorithm is used to create our relational data as well.

• McGovern, Amy, and Rosendahl, Derek H., and Kruger, Adrianna, and Beaton, Meredith G., and Brown, Rodger A., and Droegemeier, Kelvin K. (2007) Understanding the formation of tornadoes through data mining. Preprints of the Fifth Conference on Artificial Intelligence and its Applications to Environmental Sciences at the American Meteorological Society annual conference.
  • Recording of AMS presentation
  • Extended abstract
  • Movies (linked below as well):
    • Two dimensional movie of storm tracking and splitting. The left panel shows the reflectivity at 4km and the right panel shows the storm regions. Each distinct color is a distinct storm.

Multimedia: Images and Videos

• We have switched to CM1 for our simulation system. This system is efficient at designed for the high resolution simulations we are generating. We have explored friction and very high resolutions and some of the movies from these can be found below.
  • Reflectivity at 100m horizontal resolution with the updraft and downdrafts highlighted for tracking
  • Defining and tracking tornadoes in a 100m resolution simulation
• Generation of high resolution storm simulations for 75 m simulations:
  • We generated a number of 75 m simulations but only a few turned out to be both numerically stable and meteorologically plausible.
  • Our first simulation created a definite hook echo with a tornado around 9000 seconds into the simulation. The still images of the reflectivity and pressure/wind/vorticity can be found here. This contains images every 30 minutes for multiple altitudes.
  • Movies of the surface reflectivity for each storm can be found here. They are named by the storm parameters and then dBZ.
  • Movies of the wind directions (arrows), pressure (contour lines), and vorticity (color) at the surface for the same set of simulations can also be found here. These are also named by storm parameters and then Vorticity.
• Generation of high resolution storm simulations (movies and images from 2010):
  • As of April 2010, the high resolution storm simulations are still a work in progress. Although we have generated one successful simulation (movie below), there is considerable numerical instability in the model. Our analysis of the storm that did run successfully indicated that there was a tornado but the storm ran off the edge of the model very shortly after the tornado appeared. We have been investigating the storm tracking and also the edge effects in the model. We anticipate a full set of storms to be completed by July 2010.
  • Surface reflectivity at 4500 seconds, 7200 seconds, and 10800 seconds. These are taken from a 75 m horizontal resolution run.
  • Vertical vorticity and wind overlaid on a single plot. This is for 6600 seconds into the storm.
  • Vertical vorticity and pressure pertubation lines overlaid at 7200 seconds into the storm.
  • A snapshot of the surface reflectivity at 6600 seconds into the storm. This is right before the storm goes numerically unstable. While trying to figure out why it went unstable, we looked into the u and v components of the wind. This is a composite of u and a composite of v. This one is the overall wind speed at vertical level 41 of the simulation (this picture is rotated from where it should be but it was used for debugging). These pictures made it very clear that the problem is how the boundary of the domain is being handled numerically.
  • A snapshot of surface reflectivity from one of the simulations (still investigating the storm tracking) at 1800 seconds, 1830, and 1860 seconds.
• Generation of high resolution storm simulations (movies and images from 2009):
  • Movie of the clouds from one of our preliminary 100m simulations. The idea was to generate a movie that showed a tornado but the tornado seems to be rain-wrapped (which happens in real life too!). The associated analysis of this simulation demonstrated that there was a tornado in the storm. This can be seen from the movie of the pressue and vorticity at the surface.
    • The vorticity and pressure pertubations at 9990 seconds and 10200 seconds
  • The following movies are from our analysis of our first 75 m horizontal resolution simulation.
    • Vorticity and pressure pertubution at the surface
    • Reflectivity at 4km altitude
• Analysis of supercell storms and frontal passages in Oklahoma (2009 - 2010):
  • Spaghetti graph of the path of the tornadic supercells across Oklahoma (data from 1994-2003)
  • Frequency of the tornadic supercells across Oklahoma (similar to previous graph but this one is density based instead of spaghetti lines)
  • Density plot without the county names (and with the legend and colors cleaned up. Both this graph and the previous are given since one may glean different information from them)
  • Frequency of the non-tornadic supercells across Oklahoma (same period as the previous graph but this only looks at the supercells that did NOT generate a tornado)
  • Histogram of the frontal passages by month and by year through Oklahoma
  • As part of this project, Gagne developed an automated frontal passages identification system and applied it to over 10 years of Oklahoma mesonet data. The following three movies highlight this system across a variety of storm days.
    • Fronts on May 3, 1999 (a very chaotic day)
    • Fronts on Nov 29, 2006 (a more stable, single large front that moves through OK)
    • Fronts on May 7, 1994 (a day with multiple fronts but not as chaotic as May 3)
  • Two movies of the storms passing through Oklahoma on specific days. The movie shows theta-e, the wind, and the position of the storm.
    • April 2, 1994
    • May 3, 1999
  • Histogram of the Enhanced Fujita rating of the tornadoes through Oklahoma in 1994-2003
• From the 2008 AMS meeting: Three dimensional view of a storm taken every 30 seconds for the storm's lifetime. The red regions show strong updrafts, the blue shows strong downdrafts, and the green and yellow show strong vorticity. This storm was generated using ARPS.
• From the 2008 AMS meeting: Two dimensional movie of storm region and tracking algorithm. The left panel shows each storm region (highlighted using colored regions) and the right panel shows the reflectivity of the storm at 4km. These storms were generated using ARPS. This algorithm is used to create our relational data as well.
• From the 2007 AMS meeting: Two dimensional movie of storm tracking and splitting. The left panel shows the reflectivity at 4km and the right panel shows the storm regions. Each distinct color is a distinct storm.
  

Data

• The full set of simulated storms used in the 2007 and 2008 AMS presentations is available by request. Note that the total size is nearly 6TB.
• Any of our storm simulations are available by request. Note that they are over 1 TB each. The 100m resolution ones are multiple TB each.

Broader Impacts

• Public talks:
  • Dr McGovern gave a public talk at the local Norman Science Cafe on Dec 2, 2010. The slides for this presentation are available here. Note that it is a 80 MB powerpoint file due to the embedded movies.
• REU
  • Since the grant began in 2008, it has funded the following REU students:
    • David John Gagne II (BS student, OU's School of Meteorology)
    • Timothy Supinie (BS student, OU's School of Meteorology)
    • Ross Kimes (REU student, summer 2010-spring 2012, OU's School of Meteorology). He used the simulation data for his CAPSTONE project and his website for this project is here.
    • Timothy Sliwinski (REU student, summer 2010)
    • Jonathan Trueblood (REU student, summer 2010)
    • Bradley Pirtle (REU student, summer 2010-spring 2013)
    • Branden Katona (REU student, summer 2012-fall 2012, summer 2013-now)
    • Marissa Beene (REU student, summer 2013-fall 2013)
    • Andrea Balfour (REU student, summer 2013-fall 2013)
    • David Harrison (REU student, summer 2013-spring 2015)
    • Zachaery Roux (REU student, summer 2014 - spring 2015)
  • These students have participated in all of the publications (see above) and in addition have received numerous awards including:
    • David Shellberg Memorial Scholarship winner
    • NSF graduate fellowships
    • Honorable mention in the NSF graduate fellowship
    • Outstanding senior for the College of Atmospheric and Geographic Sciences
    • Letzeiser Honor List for Top Outstanding Senior Men
    • School of Meteorology Outstanding Service to the Department as an Undergraduate
    • Hollings Scholarship
    • McNair Fellowship
• Classroom work
  • An integral part of the CAREER work focuses on retention and recruitment for under-represented minorities in CS. This is happening through the development of authentic weather-based examples, problem sets, homeworks, and project sets for CS classes from freshman year through senior year. These authentic examples will demonstrate to the students that CS can be used for real-world applications. We proposed to begin the work at the senior level and move back towards freshman each year. This work is in progress.
    

Highlights, Press, Awards, Demos, ...

• The REU students from the summer of 2013 (David Harrison, Andrea Balfour, Marissa Beene) created a free education iPad app called Storm Evader that received a lot of press recently. The app is available on the iTunes store for any iPad!
  • Link to download the app
  • Press release from OU
  • Video on Science Now
  • Highlight to NSF
  • The Norman Transcript:
    • Article on their website
    • pdf archive
  • The Fox 25 article (with video embedded)
    • The Fox 25 video (in case it is gone from the above URL)
    • The Fox 25 article as a pdf
  • The OU daily (student newspaper for OU) also covered the story
    • OU Daily article
    • pdf archive
• We were featured in the XSEDE/NICS news for two articles:
  • "Professor Amy McGovern Advocates Encouragement and Practical Instruction to Bridge the Gender Gap in Computer Science" (this one went to NSF News from the Field also, at this URL)
  • "An Update on Research Directed at Revolutionizing Tornado Prediction"
• We appeared in the International Science Grid This Week in the article Five ways to anticipate natural disasters
• Our NSF Highlight featured on research.gov can be found here
• We were featured in NSF's Science Nation here.
• We were featured in an NSF discoveries item here.
• We were featured in the TeraGrid news here
• Our 2011 NSF Highlights can be found here
• Our 2010 NSF highlight can be found here
• Our annual NSF reports can be obtained by emailing Amy McGovern.
  

Acknowledgements

This material is based upon work supported by the National Science Foundation under Grant No. IIS .0746816. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

Point of contact: Amy McGovern. Last updated August 29, 2015 11:10 AM