Estimating Lake Water Volume With Regression and Machine Learning Methods

Abstract

The volume of a lake is a crucial component in understanding environmental and hydrologic processes. The State of Minnesota (USA) has tens of thousands of lakes, but only a small fraction has readily available bathymetric information. In this paper we develop and test methods for predicting water volume in the lake-rich region of Central Minnesota. We used three different published regression models for predicting lake volume using available data. The first model utilized lake surface area as the sole independent variable. The second model utilized lake surface area but also included an additional independent variable, the average change in land surface area in a designated buffer area surrounding a lake. The third model also utilized lake surface area but assumed the land surface to be a self-affine surface, thus allowing the surface area-lake volume relationship to be governed by a scale defined by the Hurst coefficient. These models all utilized bathymetric data available for 816 lakes across the region of study. The models explained over 80% of the variation in lake volumes. The sum difference between the total predicted lake volume and known volumes were <2%. We applied these models to predicting lake volumes using available independent variables for over 40,000 lakes within the study region. The total lake volumes for the methods ranged from 1,180,000- and 1,200,000-hectare meters. We also investigated machine learning models for estimating the individual lake volumes and found they achieved comparable and slightly better predictive performance than from the three regression analysis methods. A 15-year time series of satellite data for the study region was used to develop a time series of lake surface areas and those were used, with the first regression model, to calculate individual lake volumes and temporal variation in the total lake volume of the study region. The time series of lake volumes quantified the effect on water volume of a dry period that occurred from 2011 to 2012. These models are important both for estimating lake volume, but also provide critical information for scaling up different ecosystem processes that are sensitive to lake bathymetry.