In large shallow lakes

where hydrodynamic conditions are relatively weak

biochemical processes play a dominant role in water quality evolution. This makes key parameters－such as the degradation coefficient and internal source strength－significantly impact water quality simulation. However

these parameters are often difficult to estimate directly due to the high complexity of biochemical processes in a natural water body

thereby posing a key challenge to the improvement of simulation accuracy. This paper formulates a gradient analytical expression of objective function with respect to parameters

focusing on degradation coefficient and internal source strength

through deriving an adjoint system of the depth-averaged convection-diffusion equation based on the adjoint equation method. Then

by applying the Broyden-Fletcher-Goldfarb-Shanno (BFGS) optimization algorithm

we construct a collaborative inversion framework for water quality parameters

and implement it on the OpenFOAM numerical platform. This joint inversion method is applied in a case study of CODMn analysis for the Naisi Lake of the East Route of the South-to-North Water Diversion Project. It shows conceptually reasonable ranges of the optimized degradation coefficient k = 0.0185 d-1 and internal source strength S = 0.179 g·m-2·d-1

and achieves the model simulations with relative RMSE values less than 16.6%

a significant reduction compared to the initial parameter scheme. The application also demonstrates its stable high-efficiency convergence in optimization calculations. Thus

this method can effectively improve the identification accuracy of parameters in the shallow lake water quality models

a useful approach to parameter inversion under complicated water environmental conditions.