This project will develop a comprehensive framework to enable the long-term, measurement and analysis of multiple water quality and water quantity stressors across massive regions. The Great Lakes watershed will be studied as a motivating example, where, by most metrics, water quality is in dire need of restoration. While a large number of monitoring and restoration initiatives are presently being conducted by state and federal agencies, a quantitative framework for assessing the large-scale, long-term impacts of these initiatives is still lacking. More measurements of water quality and water quantity are needed, but appropriate sampling methods and sensor technologies have yet to be developed.
Given resource constraints of large instrumentation campaigns, future measurements must minimize the number of required sensors while maximizing the amount of acquired information. Such optimizations can often be carried out with knowledge of the covariance structure of the underlying process. The estimation of this covariance structure hinges directly upon an analysis of historical data. For large geographic regions such historical data sets can be overwhelming in size and dimension. This is particular true of the Great Lakes, where “big” amounts of water data have been collected across many decades. New methods are required to study this vast data set in its entirety. It is well known, however, that covariance matrix estimation is a very difficult in high-dimensional within math, statistics, optimization, and machine learning. One issue for covariance estimation which has not yet been studied in this context is when there are missing data points in the vector variables. This is particularly true of the water quality and water quantity data of the Great Lakes.
A team will be assembled to address a core suite of goals: 1) Formulation of tools to address covariance matrix estimation for high-dimensional problems with few, or missing, data points, 2) development of a sampling framework to reduce laborious data collection while maximizing acquired information, 3) formal recommendations detailing the system-level components (software, hardware, sensors, and theoretical methods) that will be necessary for the long-term, persistent measurement and analysis of the water balance and water quality across massive regions, 4) study of the socioeconomic benefits resulting form improved, real-time assessments of water quality and water quantity.
Published in IEEE Transactions on Signal Processing, 2017
Published by 53rd Allerton Conference on Communication, Control, and Computing, 2015
Presented at the Hydroinformatics International Conference, Seoul, Korea, 2016