Using heat as a tracer to map and quantify water infiltration and exfiltration along a complex high energy beach face

The flux of water, nutrients, carbon and salt through the subsurface at the land-sea interface is an important control on coastal nutrient processes, salinization of coastal aquifers and carbon balances of the coastal zone. However, these fluxes are often spatially and temporally complex and difficult to quantify, especially in high-energy mesotidal systems. Here we use vertical temperature profiles along a morphologically complex mesotidal high-energy beachface to map and quantify water infiltration and exfiltration on the island of Spiekeroog, Germany. Water fluxes were quantified using heat transport calculations from three solutions to the 1D heat transport equation, and include 1) a steady state analytical solution, 2) a non-steady state numerical model and 3) a non-steady state analytical solution. The temperature profiles could clearly map areas of upwelling warm (up to 10 °C) groundwater during the winters of 2018 and 2019. These upwelling zones were focused on an intertidal runnel system and at the low water line, consistent with the current understanding of the site based on visual observations and hydrogeological models. The steady state model provided good fits to the measured data in the winter when the seawater temperatures were not changing significantly, but was less able to reproduce the measured profiles in spring when seawater was warming. The steady state flux rates ranged from −110 to −43 mm d−1 in the runnel and low water line to +43 mm d−1 towards the high water line. The dynamic numerical model successfully captured the propagation of the seawater temperature signal into the subsurface and was able to reproduce the temperature profiles during both seasons. The flux estimates tended to be larger with the numerical model, with up to −150 mm d−1 in the runnel and +110 mm d−1 towards the high water line. The non-steady state analytical solution could only be applied to a limited time series due to the difficulty of logging temperatures in the subsurface at this highly dynamic site. Up to 1.5 days of data suggested fluxes that were considerably higher than the other two methods with best-estimates of −400 to −900 mm d−1. Thermal Peclet numbers ranged from 0.2 to 2 suggesting that both conduction and advection of heat is important. This study demonstrates that the morphology of the beach face is an important control on spatial distribution of down-welling and upwelling zones along the beach and that temperature measurement combined with heat modelling are potentially useful methods for understanding the interactions between groundwater and the sea.