Clearing up the confusion on copyright and ownership of models, equations, programs and publications.

The antecedent moisture model (AMM) has recently been placed in the public domain. What does that really mean? What rights do you have to use the AMM, and how does that relate to the copyrights that are referenced in the learning library, the AMM papers and the master companion spreadsheet? And how does all of that relate to the licensing and use of the AMM tools in the H2Ometrics platform? These and other items are covered in this article.


Starting with some basic definitions to get us all on the same page about the terms that are used in this article.

  • Copyright – According to Wikipedia, copyright is a type of intellectual property that gives its owner the exclusive right to make copies of a creative work, usually for a limited time.
  • Public Domain – according to Wikipedia, the public domain consists of all the creative work to which no exclusive intellectual property rights apply. Those rights may have expired, been forfeited, expressly waived, or may be inapplicable.
  • Open Source – According to Wikipedia, open source is source code that is made freely available for possible modification and redistribution. Open source refers to computer code that can be used by anyone.
  • Proprietary – Refers to the ownership rights of tangible or intellectual property. In the case of software, this refers to programs that are not in the public domain, and are commercially available via purchase or subscription, like Microsoft Windows, Zoom or H2Ometrics.
  • Trade Secret – According to Wikipedia, trade secrets are a type of intellectual property that comprise formulas, practices, processes, designs, instruments, patterns, or compilations of information that have inherent economic value because they are not generally known or readily ascertainable by others
  • Models – A model is an equation or a series of equations that can be used to compute a prediction of a system output from a system input. Models are mathematical algorithms. Legally, mathematical equations cannot be copyrighted.
  • Programs – A program is a collection of computer code that is designed to perform some useful function on a computer. This is also known as software. A program might be public domain software, like EPA-SWMW, or it might be proprietary like H2Ometrics.

Many people use the terms “program” and “model” interchangeably, like “the SWMM model”. However, this can be confusing when discussing copyright and ownership rights, as the underlying model (i.e. the equations) and the software program might have different copyright, ownership and use restrictions. Programs and models are different.

AMM in the Public Domain

In the publications of the AMM, it is stated that the AMM is in the public domain. So what does that mean? We have published papers that contain the model equations, model process and methodology (i.e. steps to go through to build a model). This information is in the public domain, meaning that neither H2Ometrics, nor the developers of the equations, nor anyone else has any intellectual property rights to these items. The reason for this is that ideas, methods, equations, and mathematical formulas cannot be protected by copyright according to U.S. law. Prior to the publications of these items in 2020, they were held as trade secrets by H2Ometrics. H2Ometrics had exclusive use of the equations, because they were a secret. Now that they have been published, and because the equations and model process cannot be copyrighted, anyone is free to use them. They are in the public domain. Just like the Pythagorean theorem is in the public domain. You can freely use it because no one holds any copyrights to it, because formulas and equations cannot be copyrighted.

Block diagram of the AMM

What is not in the Public Domain?

The publications themselves, i.e. the papers, publications, blog posts, images, companion spreadsheet, etc., are all protected by various copyrights. Some of these copyrights are held by H2Ometrics and some are held by the organizations who published the papers (like WEF or the Journal of Water Management Modeling). A lot of time and energy went into writing these papers and publications. Both the author of the publications and the publishers desire to retain copyrights so that they have exclusive rights to publish the work. There is great time and expense taken to develop a paper and publish it, and so the authors and publishers would prefer that others cannot copy this work and present it as their own. That is why these works are copyrighted.

How does this relate to the H2Ometrics Platform?

H2Ometrics is a proprietary software program that is a cloud-based water and sewer data analytics and modeling platform. We have spent years and extensive money and effort to build the platform, make it fast, design it to be easy to use, and incorporate the AMM equations and process. The tools inside of H2Ometrics make it perhaps 10x to 100x faster to develop AMMs compared to using spreadsheets, depending on how complex the model and source data are. We fund the development and maintenance of H2Ometrics (and the R&D that led to the development of the AMM), by selling subscriptions to the platform. H2Ometrics is not an open-source software package. It is a proprietary software program that has incorporated the public domain AMM equations and model process. This is no different than a proprietary program like PC-SWMM that makes use of the public domain Saint Venant equations for hydraulic computations.

We believe that H2Ometrics adds a tremendous amount of value to the AMM equations. Your time as a modeler is valuable. H2Ometrics makes it faster and easier to build models, and our tools will help you build better and more accurate models. This will save you and your organization time and money. That is what you are paying for when you use H2Ometrics. You are not paying for access to the AMM equations, because those are in the public domain and free to use.

Why is the Companion Spreadsheet Copyrighted?

A companion spreadsheet to the AMM was developed and published to help understanding how to use the AMM. The spreadsheet itself, including the design, graphics, text inserted into it, narrative about how to use, etc., are copyrighted and property of H2Ometrics. This was done so that someone could not take the spreadsheet and present it as their own work. But the equations contained inside the spreadsheet and the model process described are in the public domain.

This might be confusing at first, and maybe even seem like a hidden “gotcha” on using the AMM, but it really is not. With a little explanation, it becomes clear why this was done. The companion spreadsheet itself is like a very technical paper, organized very carefully and conveniently to make it easy to follow and digest with a lot of carefully written text and imagery. It is a lot of work to make something like this. It took me something like a few hundred hours just to make the companion spreadsheet. I’d prefer that someone else not take that work and represent it as their own. I’d like to get credit for my work and have exclusive rights to publish the companion spreadsheet. For these reasons, H2Ometrics is maintaining a copyright on the companion spreadsheet.

But the spreadsheet itself contains thousands of cells with things like this in them:

=B14*C$8 + C$9*C13

Formulas and equations cannot be copyrighted or patented. That’s long standing established copyright law. So anyone is welcome to take the cells and formulas themselves and copy them to make their own models. In fact, feel free to copy and paste the cells and formulas into your own modeling spreadsheet. What you cannot do is copy the contents of the spreadsheet like the images, explanatory text, and elegant design, and publish it or present it as your own work. I hope this makes sense. It was a lot of work to make this spreadsheet, and we would simply like to get credit for it and retain exclusive rights to publish it at the blog.


In short, the AMM equations, model process and methodology are in the public domain and free for you to use. H2Ometrics is a proprietary software program that is commercially available that makes use of the public domain AMM equations and makes is fast and easy to build models. The papers, publications, blog posts and companion spreadsheet are copyrighted with all rights reserved. Of course, these publications contain the equations themselves that you are free to replicate and use in your own work, because equations cannot be copyrighted. We copyrighted these various publications because they take a lot of time and energy to develop, and we would like to retain exclusive rights to publish these works as our own. That being said, if you have a great opportunity to showcase this work that will promote the model, the authors, or H2Ometrics, please get into contact with us, and we will work something out.

It might be confusing at first to understand what we are doing and why with the copyrights. But there is a perfectly legitimate and reasonable basis for everything. This solution should simultaneously satisfy both our need to protect the publications we put so much time into, and your ability to freely use the equations and model process that are described in these publications.