The St. Marys River is a key waterway that supports the navigation activities in the Laurentian Great Lakes. However, high year-to-year fluctuations in ice conditions pose a challenge to decision making with respect to safe and effective navigation, lock operations, and ice breaking operations. The capability to forecast the ice conditions for the river system can greatly aid such decision making. Small-scale features and complex physics in the river system are difficult to capture by process-based numerical models that are often used for lake-wide applications. In this study, two supervised machine learning methods, the Long Short-Term Memory (LSTM) model and the Extreme Gradient Boost (XGBoost) algorithm are applied to predict the ice coverage on the St. Marys River for short-term (7-day) and sub-seasonal (30-day) time scales. Both models are trained using 25 years of meteorological data and select climate indices. Both models outperform the baseline forecast in the short-term applications, but the models underperform the baseline forecast in the sub-seasonal applications. The model accuracies are high in the stable season, while they are lower in the freezing and melting periods when ice conditions can change rapidly. The errors of the predicted ice-on/ice-off date lie within 2–5 days.
Abstract The Laurentian Great Lakes are one of the most prominent hotspots for the study of climate change induced lake warming. Warming trends in large, deep lakes, which are often inferred by the observations of lake surface temperature (LST) in most studies, are strongly linked to the total lake heat content. In this study, we use a 3D hydrodynamic model to examine the nonlinear processes of water mixing and ice formation that cause changes in lake heat content and further variation of LST. With a focus on mechanism study, a series of process‐oriented experiments is carried out to understand the interactions among these processes and their relative importance to the lake heat budget. Using this hydrodynamic model, we estimate the lake heat content by integrating over the entire 3D volume. Our analysis reveals that (1) Heat content trends do not necessarily follow (can even be opposed to) trends in LST. Hence, using LST as a warming indicator can be problematic; (2) vertical mixing in water column may play a more important role in regulating lake warming than traditionally expected. Changes in the water mixing pattern can have a prolonged effect on the thermal structure; (3) Ice albedo feedback, even in cold winters, has little impact on lake thermal structure, and its influence on lake warming may have been overestimated. Our results indicate that climate change will not only affect the air‐lake energy exchange but can also alter lake internal dynamics, therefore, the lake's response to a changing climate may vary with time.
Abstract. Application of lake models coupled within earth-system prediction models, especially for short-term predictions from days to weeks, requires accurate initialization of lake temperatures. Here, we describe a lake initialization method by cycling within an hourly updated weather prediction model to constrain lake temperature evolution. We compare these simulated lake temperature values with other estimates from satellite and in situ and interpolated-SST data sets for a multi-month period in 2021. The lake cycling initialization, now applied to two operational US NOAA weather models, was found to decrease errors in lake temperature from as much as 5–10 K (using interpolated-SST data) to about 1–2 K (comparing with available in situ and satellite observations.
Abstract. The understanding of physical dynamics is crucial to provide scientifically credible information on lake ecosystem management. We show how the combination of in situ observations, remote sensing data, and three-dimensional hydrodynamic (3D) numerical simulations is capable of resolving various spatiotemporal scales involved in lake dynamics. This combination is achieved through data assimilation (DA) and uncertainty quantification. In this study, we develop a flexible framework by incorporating DA into 3D hydrodynamic lake models. Using an ensemble Kalman filter, our approach accounts for model and observational uncertainties. We demonstrate the framework by assimilating in situ and satellite remote sensing temperature data into a 3D hydrodynamic model of Lake Geneva. Results show that DA effectively improves model performance over a broad range of spatiotemporal scales and physical processes. Overall, temperature errors have been reduced by 54 %. With a localization scheme, an ensemble size of 20 members is found to be sufficient to derive covariance matrices leading to satisfactory results. The entire framework has been developed with the goal of near-real-time operational systems (e.g., integration into meteolakes.ch).
Abstract. Warming trends in the Laurentian Great Lakes and surrounding areas have been observed in recent decades, and concerns continue to rise about the pace and pattern of future climate change over the world's largest freshwater system. To date, most regional climate models used for Great Lakes projections either neglected the lake-atmosphere interactions or are only coupled with a 1-D column lake model to represent the lake hydrodynamics. This study presents a Great Lakes climate change projection that has employed the two-way coupling of a regional climate model with a 3-D lake model (GLARM) to resolve 3-D hydrodynamics essential for large lakes. Using the three carefully selected Coupled Model Intercomparison Project Phase 5 (CMIP5) general circulation models (GCMs), we show that the GLARM ensemble average substantially reduces surface air temperature and precipitation biases of the driving GCM ensemble average in present-day climate simulations. The improvements are not only displayed from an atmospheric perspective but are also evident in the accurate simulations of lake temperature and ice coverage. We further present the GLARM projected climate change for the mid-21st century (2030–2049) and the late 21st century (2080–2099) in the Representative Concentration Pathway (RCP) 4.5 and RCP 8.5 scenarios. Under RCP 8.5, the Great Lakes basin is projected to warm by 1.3–2.1 ∘C by the mid-21st century and 4.1–5.0 ∘C by the end of the century relative to the early century (2000–2019). Moderate mitigation (RCP 4.5) reduces the mid-century warming to 0.8–1.8 ∘C and late-century warming to 1.8–2.7 ∘C. Annual precipitation in GLARM is projected to increase for the entire basin, varying from 0 % to 13 % during the mid-century and from 9 % to 32 % during the late century in different scenarios and simulations. The most significant increases are projected in spring and fall when current precipitation is highest and a minimal increase in winter when it is lowest. Lake surface temperatures (LSTs) are also projected to increase across the five lakes in all of the simulations, but with strong seasonal and spatial variability. The most significant LST increases occur in Lakes Superior and Ontario. The strongest warming is projected in spring that persists into the summer, resulting from earlier and more intense stratification in the future. In addition, diminishing winter stratification in the future suggests the transition from dimictic lakes to monomictic lakes by the end of the century. In contrast, a relatively smaller increase in LSTs during fall and winter is projected with heat transfer to the deep water due to the strong mixing and energy required for ice melting. Correspondingly, the highest monthly mean ice cover is projected to reduce to 3 %–15 % and 10 %–40 % across the lakes by the end of the century in RCP 8.5 and RCP 4.5, respectively. In the coastal regions, ice duration is projected to decrease by up to 60 d.
Abstract This study investigates the inertial stability properties and phase error of numerical time integration schemes in several widely-used ocean and atmospheric models. These schemes include the most widely used centered differencing (i.e., leapfrog scheme or the 3-time step scheme at n-1, n, n+1 ) and 2-time step ( n, n+1 ) 1 st -order Euler forward schemes, as well as 2 nd -stage and 3 rd - and 4 th -stage Euler predictor-corrector (PC) schemes. Previous work has proved that the leapfrog scheme is neutrally stable with respect to the Coriolis force, with perfect inertial motion preservation, an amplification factor (AF) equal to unity, and a minor overestimation of the phase speed. The 1 st -order Euler forward scheme, on the other hand, is known to be unconditionally inertially unstable since its AF is always greater than unity. In this study, it is shown that 3 rd - and 4 th -order predictor-corrector schemes 1) are inertially stable with weak damping if the Coriolis terms are equally split to n +1 (new value) and n (old value); and 2) introduce an artificial computational mode. The inevitable phase error associated with the Coriolis parameter is analyzed in depth for all numerical schemes. Some schemes (leapfrog and 2 nd -stage PC schemes) overestimate the phase speed, while the others (1 st -order Euler forward, 3 rd - and 4 th -stage PC schemes) underestimate it. To preserve phase speed as best as possible in a numerical model, alternating a scheme that overestimates the phase speed with a scheme that underestimates the phase speed is recommended. Considering all properties investigated, the leapfrog scheme is still highly recommended for a time integration scheme. As an example, a comparison between a leapfrog scheme and a 1 st -order Euler forward scheme is presented to show that the leapfrog scheme reproduces much better vertical thermal stratification and circulation in the weakly-stratified Great Lakes.
In this paper, we discuss the validation of water level and current predictions from three coastal hydrodynamic models and document the resource and operational requirements for each modeling system. The ADvanced CIRCulation Model (ADCIRC), the Navy Coastal Ocean Model (NCOM), and Delft3D have been configured and validated for the Chesapeake Bay region during a Navy exercise. Water level predictions are compared with a NOAA/NOS water level gauge at the Chesapeake Bay Bridge Tunnel location while current predictions are validated with Acoustic Doppler Profiler (ADP) measurement records at three locations in the lower Chesapeake Bay. Statistical metrics such as correlation coefficient and root mean square error (RMSE) are computed. Both the vertically-integrated currents and currents at varying water depths are compared as well. The model-data comparisons for surface elevation indicate all three models agreed well with water level gauge data. The two-dimensional version of ADCIRC, ADCIRC2D, and NCOM yield better statistics, in terms of correlation and RMSE, than Delft3D. For vertically-integrated currents, ADCIRC2D has the smallest RMSE at Thimble Shoal and Naval Station locations while NCOM has the smallest RMSE at Cape Henry. For the horizontal currents over the water column, the fully three-dimensional, baroclinic ADCIRC model, ADCIRC3D, and NCOM both showed better agreement with the ADP measurements.
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