Using Logistic Regression to Identify the Key Hydrologic Controls of Ice-Jam Flooding near the Peace–Athabasca Delta: Assessment of Uncertainty and Linkage with Physical Process Understanding

Abstract

The Peace–Athabasca Delta (PAD) in northern Alberta is one of the world’s largest inland freshwater deltas and is home to many species of fish, mammals, and birds. Over the past five decades, the PAD has experienced prolonged dry periods in between rare floods, accompanied by a reduction in the area comprised of lakes and ponds that provide a habitat for aquatic life. In the Peace sector of the PAD, this likely resulted from a reduced frequency of spring flooding caused by major ice jams that form in the lower Peace River. There is debate in the literature regarding the factors that promote or inhibit the formation of such ice jams, deriving from physical process studies, paleolimnological studies, and—recently—statistical analysis founded in logistic regression. Logistic regression attempts to quantify ice-jam flood (IJF) probability, given the values of assumed explanatory variables, involve considerable uncertainty. Herein, different sources of uncertainty are examined and their effects on statistical inferences are evaluated. It is shown that epistemic uncertainty can be addressed by selecting direct explanatory variables, such as breakup flow and ice cover thickness, rather than through more convenient, albeit weak, proxies that rely on winter precipitation and degree-days of frost. Structural uncertainty, which derives from the unknown mathematical relationship between IJF probability and the selected explanatory variables, leads to different probability predictions for different assumed relationships but does not modify assessments of statistical significance. The uncertainty associated with the relatively small sample size (number of years of record) may be complicated by known physical constraints on IJF occurrence. Overall, logistic regression corroborates physical understanding that points to breakup flow and freezeup level as primary controls of IJF occurrence. Additional influences, related to the thermal decay of the ice cover and the flow gradient during the advance of the breakup front towards the PAD, are difficult to quantify at present. Progress requires increased monitoring of processes and an enhanced numerical modelling capability.