Designing Robust Measurement Networks Using Universal Multiple Linear Regression

Abstract

Collecting hydrological data is essential for understanding system behavior and processes; without it, there is no basis for predictive modeling or risk assessment. Unfortunately, limited monitoring budgets often restrict measurement designs for field-based studies. Therefore, most field studies require some sort of data worth analysis to identify the most important data to collect with respect to the prediction(s) of interest. Data worth analyses can be either informal using methods such as trial-and-error, intuition, or rules of thumb, or formal using a quantitative metric to identify the most valuable data. My research focuses on a simple, computationally inexpensive formal data worth analysis which can be used in conjunction with more complex optimization approaches or when they are not warranted. A key to network design is that the selection of sensor type, timing, and placement should be both informative and efficient. There are many possible individual sensor types and installation depths, and the key is to determine which sets of observations would be most effective prior to data collection. My research explores a combination of a method called universal Multiple Linear Regression (uMLR) and Robust Decision Making (RDM) to identify these best observation sets. The uMLR method quantifies the explanatory power of all possible combinations of observations to the prediction(s) of interest and the RDM strategy further explores the impacts of user-defined uncertainties, including measurement error and parameter uncertainty, on these observation-set selections. Robust Decision Making is a concept developed by the Research and Development (RAND) Corporation and is designed to select a robust outcome under a range of uncertainty, at the risk of the selection being sub-optimal for any one specific uncertain outcome. Norgaard et al., (2014) previously used the uMLR approach to downsampling pre-existing data to identify a reduced set of parameters to describe the dispersibility of colloids. I offer an extension of the uMLR downsampling approach, based on model-simulated data, to consider optimizing data that have not yet been collected.