Three‐dimensional simulation of lake and ice dynamics during winter

Abstract

An ice-formation algorithm is implemented in the three-dimensional Estuary and Lake Computer Model, to allow simulation of hydrodynamics and the thermal structure beneath the ice during winter. The one-dimensional governing equation of heat conduction among the three layers of white ice, blue ice, and snow is solved for the formation of ice cover considering the heat flux through air and water. This algorithm is applied independently in each grid cell within the simulation domain, allowing for spatially variable ice formation. The model was validated against observed data from both a large and a small Canadian mid-latitude lake (Lake Ontario and Harmon Lake, respectively). The lake surface temperature and the distribution and thickness of ice cover on Lake Ontario were predicted successfully during the 2006-2007 winter period. The model also accurately simulated spring 2007 temperature profiles, as typically used for the initial conditions for a summer simulation. The variation of ice and snow thickness, and vertical temperature profiles, were well-simulated for Harmon Lake during winter 1990-1991. These comparisons demonstrate the applicability of the model for year-round simulation of mid-latitude lakes of varying size.Coupled hydrodynamic and biogeochemical computational lake models have been developed for simulation of lake circulation and management of water quality (Chapra 1997; Hodges 2009). However, attempts at simulation of water quality during winter have had mixed results and remain unpublished (see discussion in Gosink 1987). More recently, Hamilton et al. (2002) applied the one-dimensional (vertical) hydrodynamic and water quality model Dynamic Reservoir Simulation Model-Water Quality (DYRESM-WQ), coupled with an ice model to simulate the changes in tropic status in a small lake, resulting from atmospheric nutrient deposition and climate change. To our knowledge, simulation of lake biogeochemistry beneath ice cover in three dimensions has not been attempted. Consequently, processes such as winter primary production, the winter mixing of phosphorus (for example, which released from sediments during late-autumn hypoxia or introduced during the spring freshet) remain comparatively unexamined. Ice cover significantly modifies lake hydrodynamics, inhibiting wind stress, so that vertical mixing is sustained only by natural convection (Farmer 1975). Therefore, correct modeling of lake dynamics during the ice-covered season requires accurate simulation of ice cover and its effects on heat and momentum transfer.Several thermodynamic models for ice formation have been developed over the past few decades. We find the existing models to be unsuitable for research on lake management, because they are either overly simplified three-dimensional (3D) ice-formation and transport models or more detailed one-dimensional (vertical) models that neglect water column dynamics and biogeochemistry. Most of these models are applying simplified assumptions for energy fluxes in the formation of ice (Maykut and Unterste...

One-dimensional simulation of lake and ice dynamics during winter

“…We have shown that for temperate mid-latitude lakes, capturing these interactions requires modeling the effects of transient mid-latitude meterological processes, such as snowmelt due to rain and variation of snow and ice albedo, because these lead to relatively rapid changes in the characteristics of the snow and ice layers. Changes in these layers ultimately influence the heat fluxes to the underlying water column and the resultant winter circulation dynamics (Wang et al, 2010;Oveisy et al, 2012;Yang et al, 2012;Kirillin et al, 2012); therefore, accurate estimation of these parameters is very important. The model accuracy in Harmon Lake (ice thickness, MBD=-1.1% and RMSD=0.01 m; snow thickness, MBD=-3.1 % and RMSD=0.02 m) is higher than in previous 1D simulations of lake ice (e.g., Rogers et al, 1995: ice thickness, MBD=-10.6% and RMSD=0.06 m; snow thickness, MBD=-9.6% and RMSD=0.03 m; Patterson and Hamblin, 1988: ice thickness, MBD=52.9% and RMSD=0.14 m; snow thickness, MBD=22.3% and RMSD=0.07 m).…”

“…Three-dimensional modeling of Harmon Lake using ELCOM (Oveisy et al, 2012) showed similar accuracy in predicting ice thickness (RMSD=0.01 m), snow thickness (RMSD=0.02 m), and temperature profiles (MBD=1.23% and RMSD=0.40°C) to the current 1D model using similar ice formation algorithms, confirming that in small lakes with simple geometries, a 1D vertical model can estimate ice and snow thickness and, therefore, inter-annual temperature dynamics, as accurately as a 3D model. This has implications for the inclusion of the many small mid-latitude lakes in climate models (Mackay, 2012).…”

“…Rainfall was measured at Merritt, 15 km northwest of Harmon Lake, and snowfall was measured at Menzies Lake using a snowboard with an accuracy of ±1 cm after each snow event; however, reported errors are much greater (Rogers et al, 1995) due to significant snow compaction. Because of potential inaccuracies in precipitation measurements related to local conditions (e.g., snow drift), and the strong influence of precipitation on ice formation, observed snow and rainfall values at Menzies Lake were compared with the observed snow thickness at Harmon Lake, and the adjusted values of Oveisy et al (2012) were used to compensate for snow drift and other inconsistencies. In small lakes, sediment heat flux is typically 1-5 Wm -2 ; here we follow the suggestion of Rogers et al (1995) and use a constant 2.8 Wm -2 during the simulation.…”

“…Three-dimensional (3D) Reynolds-averaged lake models have recently implemented ice-cover algorithms (Wang et al, 2010;Oveisy et al, 2012), that are suited for seasonal process-oriented simulations. However, for long-term studies (tens to hundreds of years) involving coupling between climate and lake biogeochemistry, 3D models are computationally prohibitive and one-dimensional (1D) vertical models with ice cover are required (see discussion in Sahoo and Schladow, 2008;Mackay et al, 2009;Yang et al, 2012).…”

Implementation of a 3D ocean model to understand upland lake wind-driven circulation

“…In small lakes, 3D hydrodynamic modelling has been performed to investigate the fate and transport of buoyant storm-river water and the implications of plume mixing dynamics on lake ecological functioning [56]. Other recent studies have investigated the effects of ice layers on small lake hydrodynamics and thermal structure [50], and the effect of wind-driven circulation on phytoplankton distribution [68]. However, the 3D modelling of small upland lakes remains uncommon, probably because 1D models are considered adequate to resolve the evolution of lake thermal structure at seasonal and longer timescales [19].…”