Horizontal Pressure Gradient Parameterization for One‐Dimensional Lake Models

摘要

This work presents a new method for closure of horizontally averaged 1‐D thermohydrodynamic equations in an enclosed reservoir by parameterizing the horizontal pressure gradient usually omitted in 1‐D lake models. Horizontal pressure gradient is computed using an auxiliary multilayer model where horizontal structure of speed and pressure is given by 1‐st Fourier mode. A major effect of new parameterization in 1‐D lake model is the emergence of explicitly reproduced H1 seiche modes. The parameterization is implemented in the LAKE model, with minor (2–4%) extra computational cost imposed. The model is applied to Lake Iseo (Italy), and calculated temperature series are compared to measured ones in upper, middle, and deep portions of metalimnion. The amplitude of seiche‐induced temperature oscillations well matched the observed amplitude by tuning the bottom friction coefficient only. The synoptic variability of thermocline vertical displacement caused by wind events is well reproduced by the model. The dominant peak of quasi‐diurnal period in temperature power spectrum was captured in simulations as well. Using the new parameterization of horizontal pressure gradient extends the applicability of a 1‐D lake model formulation to small lakes, which size is less than internal Rossby radius, and where pressure gradient dominates over Coriolis force. Plain Language Summary One‐dimensional lake models are computationally cheap and thus well suited for long‐term simulations and application in weather and climate models. However, until recently, only thermodynamic variables have been well reproduced, whereas main features of water motions in a lake have not been captured. This paper presents a new approach to include into a 1‐D model the explicit dynamics of basin‐scale intertia‐gravity motions, containing most of kinetic energy in most lakes. Essentially, this elaboration goes at a small computational cost for 1‐D model. Comparison of simulation results to measurements of seiche‐induced temperature oscillations in a large Lake Iseo (Italy) demonstrates a good skill of the model proposed.