Can we estimate the lake mean depth and volume from the deepest record and auxiliary geospatial parameters?

The accurate quantification of lake volume is essential for regional water resources management and ecosystem health. Because of the high cost of traditional full-lake depth measurements, the bathymetric and volume information for most lakes globally is inaccessible. Whether the limited field measurements over the lake can be used to estimate lake volume is worth investigating. This study aims to propose an effective method for estimating lake mean depth/volume based on the lake deepest record. We first constructed the empirical model that relies on the linear relationship between lake maximum depth and lake mean depth/volume. The different machine learning (ML) methods were then developed and tested based on the available lake deepest record and multi-type geospatial parameters. Although the linear model shows good performance for estimating lake mean depth (R2 = 0.83), it is difficult to predict lake volume (R2 = 0.23). Most ML models perform better (R2 ≥ 0.85) than linear models. However, the support vector machines (SVM) model (SVM-3: R2 = 0.54, MAPE = 134.93 %) and deep neural network (DNN) model (DNN-3: R2 = 0.83, MAPE = 82.56 %) constructed with low influential input parameters performed poorly. In contrast, extremely gradient boosting tree (XGBoost) and random forest (RF) methods have high stability and accuracy both in predicting lake mean depth (XGBoost-1: R2 = 0.87, MAPE = 23.35 %; RF-1: R2 = 0.90, MAPE = 22.75 %) and volume (XGBoost-3: R2 = 0.99, MAPE = 31.03 %; RF-3: R2 = 0.98, MAPE = 32.63 %). The RF and XGBoost models constructed with a small amount of measured lake depth data in a different region also had a good performance. Generally, the results suggest that the XGBoost and RF methods have great potential in lake volume estimation. This research is expected to provide a feasible approach to predict lake volume and benefit lake water resources management.