I have a planet orbiting a roughly Sun-like star, accompanied by a moon that's a bit more massive than our own Moon. The surface is about two-thirds water and one-third land, with most of the land in a large supercontinent. I'm looking to model the tides the coastal areas will experience, in particularly on one equatorial archipelago far out in the ocean.

I'm currently considering modeling the tidal elevation in the archipelago using Laplace's tidal equations. I want to try out a grid of different parameters, varying the orbits (primarily orbital radii) of the planet and moon. Doing this by hand would be extremely costly and time-consuming. Therefore, I'm hoping for some software that will solve the equations for me; I can iterate across the grid and compare the results, choosing the parameters that suit me best.

What software can help me with my tidal modeling? I have several criteria that would influence my choice:

  • Speed and efficiency. Since I'm going to be looking at a large number of sets of parameters, a fast tool is a must.
  • Precision. I would ideally like to calculate tidal elevations to within about one centimeter.
  • Tidal constituents. Ideally, the package would calculate as many tidal constituents as possible, for further analysis and edification.
  • Cost and accessibility. Free and open-source software would be nice.
  • Flexibility to different inputs. I obviously want to be able to input the various parameters - both for the planet (surface gravity and rotation) and the orbits.
  • Interface. Some sort of a graphic user interface would be nice, rather than just code run on the command line (although I would be okay with the latter).
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    $\begingroup$ We in the same boat. Am considering creating a program to do just that...although have limited coding experience :) I think it will be massive undertaking to model worlds, even roughly. $\endgroup$ Commented Sep 25, 2018 at 14:14
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    $\begingroup$ Curious if/how you have created a bathymetry to provide depth data to input into the Laplace equations? Especially if you wanting that 1cm degree of accuracy. $\endgroup$ Commented Sep 25, 2018 at 14:20
  • $\begingroup$ @EveryBitHelps I've been constructing a bathymetric map for the area immediately surrounding the archipelago, although not for the rest of the planet. $\endgroup$
    – HDE 226868
    Commented Sep 25, 2018 at 14:27
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    $\begingroup$ A search for "numerical tide modelling" gives about 3.4 million hits. Most of the first page seems to be links to scientific papers and/or pdfs, but reading through them might give you links to actual software. (Since many researchers do post code.) It's not likely to be easy to use, though. $\endgroup$
    – jamesqf
    Commented Sep 25, 2018 at 17:39
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    $\begingroup$ You could try Software Recommendations.SE or Earth Science.SE. Is there any reason you haven't tried there? $\endgroup$
    – John Locke
    Commented Sep 26, 2018 at 11:19

3 Answers 3


Unfortunately the answer is no. Serious props to you if you want to have a go at coding this. There is probably a PhD in it.

One of the primary resources on the topic is the Admiralty Manual of Tides (NP 120).

It has been a few years since I worked in the discipline and theory may have progressed but tidal prediction is primarily done by analysing harmonic constituents with a Fourier transform & then solving for succesive times (t). The problem is that not all constituents arise from gravitational potentials. The latitude, resonant frequencies of ocean and esturine basins also play a role as does local bathyimetry, orbital inclination and the inclination of the plane of an orbiting body (moon(s)). In long narrow bays there is also the seiche effect (Bay of Fundy). Also not to forget impacts like prevailing winds, storm surge and inertia (sea level on the Pacific coast of the Isthmus of Panama is 20m higher than the Atlantic coast).

Unless you are proposing a very unusual set of gravitational potentials this is one you can handwave. I'd look for a place on earth with a similar geography to your place of interest (Hawaii?) and use those tides. NP 120 describes how the tidal wave travels along N/S and E/W oriented coastlines if you want to realistically extrapolate.

My background is as Master Mariner / Harbour Master & Maritime academic & one piece of advice I would offer is, unless you have a plot need for cm accuracy don't sweat it. While calculations and predictions are done at that level of accuracy when it comes to afloat / not afloat no prudent mariner would depend on it. A healthy margin of error dependent on vessel size is always allowed.


First off, I am no expert in this field, simply a person who loves to study flow of fluid stuff so has gone about exploring fluid flow simulation tools and methods as a part of their weird list of hobbies

I am assuming here that (a) you would prefer a open source tool (since you have mentioned that you prefer this but not specified it) in which case I suggest you give Delft3D a try.link to open source version of this tool and specifications (I suggest you explore their website a bit. Nice demos and alternative tools and stuff)

(b) that the tidal wave simulation is based on the impact on the shore i.e. you are studying small surface area of impact with different parameters (which you think would be the result of having this earth like planet) and in turn try to deduce what could be the the result at a much larger scale and and a basic demo of how this would look like and what could be the parameters here and then gone back to area of interest to see what could be that impact of these deduced parameters in the area of interest in detail.

You could also check out these links for alternative tools this and this, I got by a basic online search. Hope this helps you out


After some searching, I found this site:


The application is called TSoft, and it is for modeling tides. I have never used this software, but looking at the screenshots and reading the descriptions, it seems to be a very advanced editor. It also appears to have a basic GUI as well.

In addition, TSoft offers the possibility to write scripts, which allow one to simplify and speed up routine tasks considerably.

If you can't find anything letting you change the parameters of the moon, sun, and other objects, which I doubt seeing as how it is made for editing tides, you can try writing a script for that.

Again, I can't vouch for what this application can or can't do because I do not know enough about it, but hopefully it will be what you're looking for.


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