In recent years, considerable efforts have been made to restore turbid, phytoplankton‐dominated shallow lakes to a clear‐water state with high coverage of submerged macrophytes. Various dynamic lake models with simplified physical representations of vertical gradients, such as PCLake, have been used to predict external nutrient load thresholds for such nonlinear regime shifts. However, recent observational studies have questioned the concept of regime shifts by emphasizing that gradual changes are more common than sudden shifts. We investigated if regime shifts would be more gradual if the models account for depth‐dependent heterogeneity of the system by including the possibility of vertical gradients in the water column and sediment layers for the entire depth. Hence, bifurcation analysis was undertaken using the 1D hydrodynamic model GOTM, accounting for vertical gradients, coupled to the aquatic ecosystem model PCLake, which is implemented in the framework for aquatic biogeochemical modeling (FABM). First, the model was calibrated and validated against a comprehensive data set covering two consecutive 7‐yr periods from Lake Hinge, a shallow, eutrophic Danish lake. The autocalibration program Auto‐Calibration Python (ACPy) was applied to achieve a more comprehensive adjustment of model parameters. The model simulations showed excellent agreement with observed data for water temperature, total nitrogen, and nitrate and good agreement for ammonium, total phosphorus, phosphate, and chlorophyll a concentrations. Zooplankton and macrophyte coverage were adequately simulated for the purpose of this study, and in general the GOTM‐FABM‐PCLake model simulations performed well compared with other model studies. In contrast to previous model studies ignoring depth heterogeneity, our bifurcation analysis revealed that the spatial extent and depth limitation of macrophytes as well as phytoplankton chlorophyll‐a responded more gradually over time to a reduction in the external phosphorus load, albeit some hysteresis effects still appeared. In a management perspective, our study emphasizes the need to include depth heterogeneity in the model structure to more correctly determine at which external nutrient load a given lake changes ecosystem state to a clear‐water condition.

中文翻译：

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使用水生生态系统模型预测浅水湖泊中的生态系统状态变化：丹麦铰链湖为例。

近年来，已经做出了相当大的努力来将浑浊的、以浮游植物为主的浅水湖泊恢复到清澈的水体状态，并具有高覆盖率的沉水植物。具有垂直梯度的简化物理表示的各种动态湖泊模型，例如 PCLake，已被用于预测这种非线性状态转变的外部养分负荷阈值。然而，最近的观察性研究通过强调逐渐变化比突然变化更常见来质疑政权更迭的概念。我们研究了如果模型通过包括整个深度的水柱和沉积层中的垂直梯度的可能性来考虑系统的深度依赖性异质性，则政权转变是否会更加渐进。因此，使用一维流体动力学模型 GOTM 进行分叉分析，考虑垂直梯度，与水生生态系统模型 PCLake 耦合，该模型在水生生物地球化学模型 (FABM) 框架中实施。首先，该模型针对一个综合数据集进行了校准和验证，该数据集涵盖了来自丹麦的一个浅水、富营养化湖泊铰链湖的两个连续 7 年时期。应用自动校准程序Auto-Calibration Python（ACPy）实现模型参数的更全面调整。模型模拟显示水温、总氮和硝酸盐的观测数据与铵、总磷、磷酸盐和叶绿素的良好一致性 该模型是针对一个综合数据集进行校准和验证的，该数据集涵盖了来自丹麦的一个浅水、富营养化湖泊铰链湖（Lake Hinge）的两个连续 7 年时期。应用自动校准程序Auto-Calibration Python（ACPy）实现模型参数的更全面调整。模型模拟显示水温、总氮和硝酸盐的观测数据与铵、总磷、磷酸盐和叶绿素的良好一致性 该模型是针对一个综合数据集进行校准和验证的，该数据集涵盖了来自丹麦的一个浅水、富营养化湖泊铰链湖（Lake Hinge）的两个连续 7 年时期。应用自动校准程序Auto-Calibration Python（ACPy）实现模型参数的更全面调整。模型模拟显示水温、总氮和硝酸盐的观测数据与铵、总磷、磷酸盐和叶绿素的良好一致性a浓度。出于本研究的目的，对浮游动物和大型植物的覆盖进行了充分模拟，总体而言，与其他模型研究相比，GOTM-FABM-PCLake 模型模拟表现良好。与之前忽略深度异质性的模型研究相比，我们的分岔分析表明，随着时间的推移，大型植物以及浮游植物叶绿素a的空间范围和深度限制对外部磷负荷的减少的反应更加缓慢，尽管仍然出现了一些滞后效应. 从管理的角度来看，我们的研究强调需要在模型结构中包括深度异质性，以更准确地确定给定湖泊在何种外部养分负荷下将生态系统状态变为清水状态。