Modeling time series radon inventory and constraints on the submarine groundwater discharge mass balance of a well-mixed, highly dynamic estuary

Abstract

Although often diffuse and over-shadowed by surface-water inputs, submarine groundwater discharge (SGD) represents a significant source of freshwater and solutes to many sensitive marine environments. Radon (222Rn) is an effective naturally occurring tracer of SGD due to its non-reactive nature and dominant terrestrial source. However, limited continuous measurements and poor constraints on temporal 222Rn variability in shallow-turbulent estuaries introduce large uncertainties to SGD rate estimation. We hypothesize that nonlinear regression analysis (e.g., generalized additive model [GAM]) and machine learning (ML) algorithms could explain radon trends and resolve limitations of the traditionally used mass balance for estimating SGD in shallow and vertically mixed estuaries, thus enabling preliminary insights related to wind-driven mixing losses using sporadic groundwater tracer measurements and publicly available hydroclimatic parameters. Cross-correlation functions and a generalized additive model [GAM] were employed to quantify atmospheric and hydrologic controls and predict, respectively, 222Rn inventory variability modulated by windspeed and direction. Two ML models, neural network (deep-learning neural network [DNN]) and decision tree (random forest [RF]) based models, were trained on an intermittent 24-month 222Rn (n = 10,660, 30 min interval) dataset (2019–2021) collected from a well-mixed northwestern Gulf of Mexico estuary (Corpus Christi Bay, Texas) with publicly available inputs (e.g., windspeed/direction, tide levels, water temperature, creek discharge and barometric pressure, n = 35,088). Both ML models can predict observed radon concentrations with r2 > 0.90, however, only the RF model is able to predict within the observed range of the 222Rn magnitude dataset and finds the relevant hydroclimatic parameters (e.g., streamflow and wind direction) highly responsible for the seasonal and daily variability in the inventory, respectively. The DNN model can more closely predict extremely high inventories, but it overpredicts lows, resulting in numerous negative values, which suggests that large data gaps in the groundwater tracer cause overfitting and underperformance of this model in a wind-mixed estuary. Using the GAM predicted 222Rn dependency on wind direction and speed, the adjusted mass balance reduces overestimation of wind-mixing losses and results in overall lower fluxes. This research provides new opportunities to: 1) predict radon inventories in regions with large temporal data gaps using only publicly available hydroclimatic parameters and 2) better constrain SGD estimates in windy coastal areas, allowing for insights that can be used to plan field excursions and management strategies for coastal water and solute budgets.