Imperfect slope measurements drive overestimation in a geometric cone model of lake and reservoir depth

Lake and reservoir (waterbody) depth is a critical characteristic that influences many important ecological processes. Unfortunately, depth measurements are labor-intensive to gather and are only available for a small fraction of waterbodies globally. Therefore, scientists have tried to predict depth from characteristics easily obtained for all waterbodies, such as surface area or the slope of the surrounding land. One approach for predicting waterbody depth simulates basins using a geometric cone model where the nearshore land slope and distance to the center of the waterbody are assumed to be representative proxies for in-lake slope and distance to the deepest point respectively. We tested these assumptions using bathymetry data from similar to 5000 lakes and reservoirs to examine whether differences in waterbody type or shape influenced depth prediction error. We found that nearshore land slope was not representative of in-lake slope, and using it for prediction increases error substantially relative to models using true in-lake slope for all waterbody types and shapes. Predictions were biased toward overprediction in concave waterbodies (i.e., bowl-shaped; up to 18% of the study population) and reservoir waterbodies (up to 30% of the study population). Despite this systematic overprediction, model errors were fewer (in absolute and relative terms, irrespective of any specific slope covariate) for concave than convex waterbodies, suggesting the geometric cone model is an adequate representation of depth for these waterbodies. But because convex waterbodies are far more common (>72% of our study population), minimizing overall depth prediction error remains a challenge.

Automated summary

The depth of lakes and reservoirs is an important characteristic that affects ecological processes. However, measuring depth is a time-consuming task and data is only available for a small percentage of waterbodies worldwide. Scientists have tried to predict depth using easily obtainable characteristics such as surface area or land slope. This study found that using nearshore land slope as a proxy for in-lake slope increased prediction errors. Predictions were biased towards overestimation in concave waterbodies and reservoirs. The geometric cone model was found to be a satisfactory representation of depth for concave waterbodies, but minimizing overall depth prediction error remains a challenge due to the prevalence of convex waterbodies.