This document is intended as a technical note for pyompa (https://github.com/nitrogenlab/pyompa), a python package for conducting water mass mixing analysis (also known as “Optimum Multiparameter Analysis”, “OMP analysis” or “OMPA” in the literature). It is being made available in advance of a formal publication as an accompaniment to an upcoming paper by Lawrence et al. on the water mass analysis of the GP15 transect, and also so that it may be used as a reference for individuals who wish to use PYOMPA in their research today. PYOMPA contains several significant improvements over previously-published methods for conducting OMP analysis. These include a hard constraint on mass conservation, flexible definitions for both end-member composition and nutrient exchange ratios, a smooth penalty-based approach to encode prior knowledge of end-member distributions, support for reporting ambiguity when the solution is underdetermined, and a way to leverage knowledge from another model (such as an Ocean Circulation Inverse Model or OCIM) to select the best PYOMPA solution. This document also contains a description of additional analyses, such as archetype analysis for selecting end-member subtypes and an automated way to define the thermocline boundary, as they are often useful in conjunction with water mass mixing analysis. The focus of this document is on the mathematical formulations. Please refer to the github README or contact the authors for more information.