
NSF Org: |
DMS Division Of Mathematical Sciences |
Recipient: |
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Initial Amendment Date: | July 24, 2015 |
Latest Amendment Date: | July 8, 2017 |
Award Number: | 1463642 |
Award Instrument: | Continuing Grant |
Program Manager: |
Gabor Szekely
DMS Division Of Mathematical Sciences MPS Directorate for Mathematical and Physical Sciences |
Start Date: | August 1, 2015 |
End Date: | July 31, 2019 (Estimated) |
Total Intended Award Amount: | $129,326.00 |
Total Awarded Amount to Date: | $129,326.00 |
Funds Obligated to Date: |
FY 2016 = $39,619.00 FY 2017 = $52,149.00 |
History of Investigator: |
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Recipient Sponsored Research Office: |
13001 E 17TH PL STE F428 AURORA CO US 80045-2571 (303)724-0090 |
Sponsor Congressional District: |
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Primary Place of Performance: |
1201 Larimer Street, Suite 4000 Denver CO US 80217-3364 |
Primary Place of
Performance Congressional District: |
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Unique Entity Identifier (UEI): |
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Parent UEI: |
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NSF Program(s): | STATISTICS |
Primary Program Source: |
01001617DB NSF RESEARCH & RELATED ACTIVIT 01001718DB NSF RESEARCH & RELATED ACTIVIT |
Program Reference Code(s): |
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Program Element Code(s): |
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Award Agency Code: | 4900 |
Fund Agency Code: | 4900 |
Assistance Listing Number(s): | 47.049 |
ABSTRACT
This project focuses on the development of statistical tools to model the spatial and temporal structure of environmental and climate extreme events. Most climate and environmental data sets can be viewed as collections of curves, one curve per year, available at several locations within a region. For example, temperature at a specific location has an annual pattern. The shapes of such annual curves change from year to year, and from location to location. Extreme departures from a typical pattern over a sizeable region can impact agricultural production and public health. The economic impacts are considerable, particularly, if they occur at unexpected times and locations. An unusual timing of a heat wave over a large area may cause significant economic damage due to crop failure and forest fires, and also affect the level of preparedness of public health services. Similarly, long spells of cold, storm-free winter time weather often lead to an increase in particulate pollution levels in densely populated mountain valleys. It is important that public officials are well-informed about the possible range and impact of such extreme events. This project will contribute toward a rigorous and objective understanding of the risks involved, and provide quantitative tools for researchers and decision makers in the fields of agriculture, public health, actuarial science, climatology and ecology.
The project seeks to develop a statistical framework for a quantitative assessment of possible extremal departures from the usual annual pattern over a region, i.e. departures of the form that have not been observed in historical records, but can occur with a positive probability. The primary focus of the project is the creation of a mathematical framework, and implementation through the development of statistical software. Building on recent advances in functional data analysis, extreme value theory and spatio-temporal statistics, methodology for modeling the extremal distributions of curves observed at spatial locations will be developed. Extreme curves will be determined by functionals defined on a function space in which the curves live. The work will be guided and validated by the analysis of several historical, derived, and computer data sets. Exploratory analysis will reveal the most prominent properties of extremal shapes. This will be followed by model building and the development of asymptotic theory needed to evaluate probabilities of events not previously observed. The models will reveal extremal features of the spatially indexed functional data that are not apparent from the exploratory analysis. Procedures for the construction of confidence regions, where extremal departures may occur with prescribed probability, will be obtained. Exploratory and inferential tools for the assessment of trends in the extremal shapes and regions over which they occur will also be derived.
PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH
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PROJECT OUTCOMES REPORT
Disclaimer
This Project Outcomes Report for the General Public is displayed verbatim as submitted by the Principal Investigator (PI) for this award. Any opinions, findings, and conclusions or recommendations expressed in this Report are those of the PI and do not necessarily reflect the views of the National Science Foundation; NSF has not approved or endorsed its content.
This project used advances in functional data analysis, extreme value theory and spatio-temporal statistics to develop methodology for modeling extreme behavior in spatio-temporal data. Advances were made in formally defining extreme features of spatio-temporal functional data with respect to amplitude, duration, and spatial extent and developing risk quantification measures for such characteristics using extreme value theory. Methodology was also developed for constructing confidence regions where departures from expected behavior may occur with prescribed probability. Procedures were developed for correctly identifying the starting and ending times of extreme events observed over time, as well as identifying their spatial extent. New methodology for was developed for describing massive spatio-temporal data sets as functions, which is critical for more detailed examination of their characteristics.
Extreme events related to climate and health can have considerable economic impacts. An unusual timing of a heat wave or cold spell over a large area can have significant impacts on crop production, risk of forest fire, public safety, and energy production. This in turn affects consumer food prices, insurance premia, health services availability, etc. This project applied developed methodology in quantifying extreme climate risk, assessing the similarity in future climate predictions, and identifying the duration and spatial extent of disease outbreak, all of which are useful in helping scientists, researchers, and public officials make well-informed decisions about the possible range and impact of extreme events affecting the public. Free, user-friendly software was created for this project to allow capable parties to apply and extend these methods for further examination of important topics. Several students were trained and supported under this research, increasing the availability of data scientists well-equipped to study and address important scientific and societal issues.
Last Modified: 11/22/2019
Modified by: Joshua French
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