TMDL: Sensitivity of CBOD Point and Non-Point Sources on DO Using the Adjoint Method

Total Maximum Daily Load (TMDL) developments for the nations impaired streams have become a major focus of activity over the past few years. This concept encompasses the determination of the Load Capacity (LC) of a stream and the associated Waste Load Allocation (WLA) for point and Load Allocation (LA) for non-point source pollutants. Even though guidelines exist and continue to be expanded and changed EPA is not very specific of how the components of the TMDL need to be determined, which has left much of the development at the discretion of the responsible agencies. As a result many different approaches exist to comply with the objectives of an acceptable TMDL. One of these objectives is to ensure the use of state of the art science, while another demands equity among the discharges. It is therefore imperative to include a framework that allows optimization as the omission of the latter causes excess costs that otherwise could potentially be reduced. This paper presents a methodology to effectively compute sensitivities that can be used at a later state to develop an efficient WLA procedure in for the case of CBOD/DO load scenarios. Sensitivities for steady state and unsteady flow scenarios are presented. It is shown that using a 2-dimensional dynamic modeling approach permits identification of a large number of temporally distributed sensitivities for sources along a highly dynamic estuary.