The GRACE Plotter, soon to be released on the classic Nintendo Entertainment System (NES)
Welcome to another episode of the GRACE Plotter series. If you haven’t read those articles, you should start with them first: Da Vinci, St-Exupéry and the old Irish distillery, and Engineering a fluid solution to a water problem. We also wrote two related pieces that are more business oriented, and by “business” we simply refer to the ideas and philosophy with which we run our company. They are: Fish, tools and investment, and Pleasure at work. There will be more of those over time, both for your entertainment and to serve us as an illustrated business card. Now, with this introduction out of the way, let’s jump right into it.
Don’t stop playing (says a famous writer)
So the initial goal of the GRACE Plotter was to simplify and accelerate our scientific work on gravity field. But, in addition to the scientific value, we couldn’t resist to make it fun to use. Or should we say play with? George Bernard Shaw once said: “You don’t stop playing before you grow old, you grow old because you stop playing”. Pay attention to the advice — especially if you’re starting to feel a little depressed when you look at your grey hair — it is of great value! By the way, the gentleman lived until 94, so he knew what he was talking about. We haven’t lost our children soul yet, and we beg you not to lose yours. Besides, everyone can take ageing as an opportunity to become a wiser, more experienced player. Be like a good wine, better with time. Back to the GRACE Plotter, the word “play” is not even ours. It’s our users’ word. A regular user once called it “downright addictive”. We took it as a compliment. Of course, we gladly admit that you have to be a little bit of a geek to be addicted to time series of gravity field. But that’s OK, we love geeks. Maybe we are a little bit geek ourselves. It takes all sorts to make a world.
What news since the Nintendo?
So when we designed this interactive tool, we took astute pleasure in drawing the thinnest possible line between the scientific program and the video game. For those who are born in the eighties, we have a reference that’s stuck in our mind forever. The pinnacle of video games, the mother of interactive softwares, the king of all… You guessed it. Super Mario Bros. Of course, we’re not certain that the GRACE Plotter is as entertaining as the illustrious video game, nor that it will gather as many fans around the world, but we tried as much as we could! And, just as in the Nintendo game, we dropped a few hidden secrets inside the game for dedicated players to discover. So let’ s unveil a few form tips, map tricks, graph clues and data hints!
Without further ado, let’s introduce you to several tips within the form.
Time series form
Title, gravity functional, and data center
You already know the basics. You can fill in a custom title, choose the gravity functional (geoid heights, gravity anomalies, equivalent water heights and spherical harmonics), the data center and the release of the product.
Then you can choose the area type for the time series extraction. This field offers multiple possibilities: point, rectangle, triangle, polygon, as well as a long list of over a hundred predefined hydrological basins.
Latitude and longitude
You can set up the position of the marker interactively with the mouse over the map section. However, if you are the kind of person who wants exact control over what they are doing, you can fill in the latitude and the longitude here with 6 digits.
Example with a custom pentagon to model Iceland
Example of predefined hydrological basins
Address (reverse geocoding)
The next field is the address. Try to enter your own city, the Eiffel Tower, the Statue of Liberty, or a historic monument, and the website will automatically do the reverse geocoding for you. That’s useful if you have a name in mind but forgot the directions.
The next field, “regression”, allows you to fit an analytical model over the series.
Choices of adjusted analytical models
Let’s show you a simple example of a linear fit over Iceland, to see how fast the ice is melting. The numerical value appears directly in the legend.
Adjusted linear trend over Iceland
You have plenty of other choices (including exotic ones), and we have a dedicated paragraph below to explore them.
Bias and scale
The two last fields allow you to add a biais to the time series or to multiply it by a scale factor. The bias can be useful for series that have a different reference, and the scale factor for series of different nature (for example geoid heights and equivalent water heights).
Let’s now introduce you to the map controls:
The “Go to” button recenters the Google Map over the chosen marker. This is especially useful if one of your marker is in Djibouti, the other one in Vladivostok and the last one in San Francisco. You could drag the map every time along the whole stretch of longitudes, but with the click, you can directly teleport.
Apply to all series
The “Apply area” button automatically sets the area of all series to the selected one. Suppose you are currently studying five different data centers. Change the area of the first series, click on the button and the areas of the four other series will synchronize in harmony.
Plot, add, and remove series
Those commands are self-explanatory.Plot the graph, add or remove series.
The share button gives you a link that memorizes your whole configuration. You can then share your current work with your colleagues simply by sharing that link. Or you can save it to your computer, and keep track of all your discoveries.
Google Maps backgrounds
These are the standard Google choices for the background (map, satellite, etc.).
Zoom in/out and full screen
Standard controls from Google.
This one is cool: you can set a custom gravity background. These are maps of trends, annual signal and semi-annual signal from different groups. Those backgrounds are extremely useful because they will immediately guide you to areas of interest. Icing on the cake, you can also control the level of transparency with the sunshine icon.
Choice of custom gravity background
Below are two examples of using the background maps to pilot the analysis, one with the trend, and the other with the annual amplitude.
Trend map (mass losses and mass gains)
Graph for the two selected points (with the linear regressions)
Annual amplitude map
Graph for the two selected points (the map was right)
Let’s continue the journey with the graph section. There you will find what you expect (the graph!) and a few options. Notice the tooltip that appears with numerical values when you hover your cursor over the curve. You can also zoom in and out directly by selecting a zone in the graph with your mouse.
In the menu, you can find usual commands, such as “Replot”, “Share”, and “Back to form”, as well as three options: lines or splines for the curve, an option to edit the titles (general graph title and axes), and the most useful one: export the graph to PNG format.
Commands and options
(You might smile at the fl. oz. units, but you can actually do it for real with the scale factor in the form)
After you’ve played around with the graphical user interface (GUI), now comes the hard work of meddling with the numbers. This is the data section. You can download each numerical series with a single click. The information inside is very rich. You will find:
- The identification of the data you plotted (data center, release, gravity functional).
- The area type, and the complete list of grid points included in the selection, with the weighting of each point.
- Some statistics about the area (the surface area in kilometers square and degrees square).
- Some statistics about the time series (min, max, mean, rms, etc.).
- Some statistics about the linear and periodic regressions (even if you don’t ask them on the graph), i.e. the trend and the amplitude of the annual and semi-annual signals, as well as the dates of minimum and maximum within the year, and the sum of the squares of the residuals between the model and the real series.
- Finally, the time series itself, with several possibilities for the time unit.
We included a screen capture below to illustrate the listed points.
Help and information
You can find help and information in the header section (click on the blue bar to make it appear), and in the footer section.
Focus on special features
And to finish the article, let’s focus on two special features, the “Share” button, and the regression options.
When you click on the Share button, a modal window will open, like this:
Share modal window
The link in blue contains your full configuration (time series, background map, etc.). You can copy the link, and save it on your computer, or send it via email to your colleagues to share your discoveries. Your whole configuration will reappear again, all by magic! No need to create an account, no need to fill paperwork nor to submit your ID or your fingerprints. Just simple useful service, to make your scientific research easier.
Just before leaving, let’s add a few words about the regression feature. This feature took a long time to develop. This is done by least squares in several consecutive steps, with constraints at the limits for the more sophisticated options. It is a little bit artistic in some regards, but it was necessary and it works very well.
Here are your choices:
The linear one is simple. The parabolic also. The polynomial goes up to degree 12. The periodic has a trend, an annual signal and semiannual signal. The periodic+ is the same, but it also displays the individual components. That is very useful if you want to observe things in detail. The only limitation of the periodic model is that the annual or semiannual amplitudes are the same over the whole period (20 years). But in reality, the water cycle has not the same amplitude every year. So how do we do? This is why we imagined the “advanced” model. The trend is replaced by a polynomial, and the periodic sinus and cosinus are also modulated by polynomials! (of degree 12 too). This gives us almost perfect analytical modelling of the series. Of course, the number of parameters starts to almost be as big as the number of points, but still, it is theoretically interesting. Here are a few examples for a given point in Brazil:
Periodic model (notice the useful information in the legend)
Periodic+ model: a closer look at the individual components
Advanced model: the fit is almost perfect
Advanced+ model: a closer look at the individual components
Advanced+ model: a zoom on the annual modulation
That’s it for the demo! We tried to be mathematically creative and to stay simple and minimalist. We hope you will enjoy the results. But for this, there is only one possibility: practice it yourself!Legacy version Modern version
A far away ancester