Super Speedy Reef Modelling

Coral reefs and the islands that they protect from flooding are in big trouble. This is a recurring theme on this blog, and now it’s time for the latest update. We are currently building towards the development of an early flood warning system for low-lying tropical islands fronted by coral reefs. Our previous work on this topic has focused on finding ways to do this accurately for a wide variety of coral reef shapes and sizes, as well as different wave and sea level conditions. However, it’s not enough to be accurate- to deliver timely early warnings, you also need to be fast.

That’s where the latest research of Vesna Bertoncelj comes in.

I am extremely proud to announce that Vesna Bertoncelj has successfully defended her MSc thesis, “Efficient and accurate modeling of wave-driven flooding on coral reef-lined coasts: On the interpolation of parameterized boundary conditions“. I had the great privilege of sitting on her graduation committee and working with her over the past year or so.

Vesna’s research provides us with new approaches for making highly accurate predictions of coastal flooding, at limited computational expense. The numerical models that we use to estimate flooding often take a long time to simulate, since they resolve many complex physical processes at high resolution in space and time. However, by paring down these models to only the most essential components for the task at hand, we can do this much faster. My colleagues at Deltares recently developed the SFINCS model, which has been successfully used to predict flooding in a fraction of the time that our standard models take. But how do we put all these different pieces together?


A schematic overview of Vesna’s research methodology. [Source].

First, Vesna established a baseline for model performance by running a computationally intensive XBeach Non-Hydrostatic model (XB-NH+), and a much faster SFINCS model. These models provide an estimate for runup (R2%), which can be taken as a proxy for coastal flooding. In the second step, she used a lookup table (LUT) of pre-computed XBeach model output and to derive the input for the SFINCS model. The crucial task is doing this quickly and accurately, so she experimented with different interpolation techniques for deriving that input. She then compared her new approach with the standard models to find the fastest and most accurate combination.

Her research gives us a useful methodology that we can implement to speed up our early flood warning system, saving time and hopefully someday saving lives.

Vesna’s quality of work is excellent and she has a fantastic attitude towards research and collaboration. Her curiosity, professionalism, and diligence will undoubtedly serve her well in the years to come. I hope that we will have other opportunities to collaborate in the future. If anybody out there needs a bright young coastal researcher and/or modeller, hire her!

Restoring Coral Reefs for Flood Protection

We frequently hear in the news about dying coral reefs, and also about the threats of sea level rise and climate change. But there is a key gap: what if we can hit two birds with one stone, and restore damaged ecosystems while providing vital protection against flooding? Our latest research demonstrates how coastal managers and ecologists can join forces to achieve both goals, which may help stretch limited funding further.

I am extremely proud to share Floortje Roelvink’s first scientific paper, “Coral reef restorations can be optimized to reduce coastal flooding hazards“, published in Frontiers of Marine Science. I had the great privilege of sitting on her MSc thesis committee two years ago, and she has been our colleague at Deltares ever since.

Continue reading Restoring Coral Reefs for Flood Protection

Ebb-tidal deltas: Badass Morphological Features (BAMFs)

At TU Delft, a requirement for our PhD defense is to make ten propositions based on what we have learned during the previous years. Claims posed by my friends and colleagues deal with the nitty gritty details (“All diffusive processes can be derived from an advective one, and failing to do so yields incorrect modelling[1]) but also the bigger picture of how we do what we do (“The way morphological models are presented and interpreted has a lot in common with predictions of snow depth in five years on December 26th at 4pm. The knowledge in these models deserves a better presentation[2]).

The propositions must be both defendable and opposable, so as to stimulate an interesting debate during the defense. Some of the propositions should reflect the findings of our research, but it is also traditional to include statements that have nothing to do with it. One colleague[3] even suggested (tongue in cheek) that the increase in the height of Dutch men over time could be explained by sea level rise. I couldn’t resist analyzing the data myself, and the results were surprisingly good:

Spurious correlation of the week! As John von Neumann said, “With four parameters I can fit an elephant, and with five I can make him wiggle his trunk.”

These propositions are a chance to inject a bit of last-minute philosophizing into our Doctorates of Philosophy, and range from the wise (“No wind is favourable if a person does not know to what port (s)he is steering – Seneca[4]) to the downright cheeky (“This proposition is not opposable[1]).

What I Learned by Counting Sand for 5 Years

As the clock is ticking on my own PhD (259 days, 13 hours, 39 minutes, and 51 seconds, but who’s counting? *eye twitches*), I started preparing some propositions of my own (obviously in a fit of procrastination on my dissertation). After nearly five years of scrutinizing sand and contemplating connectivity, my research has led me to an inescapable conclusion:

Ebb-tidal deltas are badass morphological features (BAMFs),
(c.f. Phillips [2015]).


What, pray tell, is an ebb-tidal delta, and why is it so badass? Ebb-tidal deltas are large underwater piles of sand at the mouth of estuaries and tidal inlets, deposited by outflowing tides and reshaped by waves. I spend my days studying how waves and tides move sand around on the Ameland ebb-tidal delta in the northern part of the Netherlands (see below). We need to know this in order to plan ecologically-sustainable flood protection measures for the Dutch coast. A morphological feature is just a fancy name for some part of a landscape, like a hill or a valley or a beach.

An ebb-tidal delta is the giant pile of sand located at the mouth of a tidal inlet like this one. This may not sound glamorous, but understanding the way it moves around is extremely important for ensuring safe navigation and for predicting erosion and flooding of adjacent coasts.

What makes a badass “badass”?

Phillips[5] defines the archetypal badass as “individualistic, non-conformist, and able to produce disproportionate results”, and applies this concept to geomorphology (the study of how landscapes evolve, at the crossroads of geology and physical geography). Ebb-tidal deltas meet these three criteria, which makes them badass morphological features (BAMFs):

  1. Ebb-tidal deltas are each unique (in shape, location, composition, and in terms of the environmental forces shaping them (like waves and tides)), and hence individualistic.
  2. Ebb-tidal deltas are chaotic systems which defy accurate prediction using physics-based numerical models[6], and hence are non-conformist or “naughty”[7]. This numerical naughtiness is a serious problem for coastal engineers and scientists, since a failure to accurately predict ebb-tidal delta evolution can threaten public safety and lead to costly property or infrastructure damage. They do not “play by the rules” of our existing physics-based deterministic models. 
  3. Ebb-tidal deltas are highly nonlinear systems which can greatly amplify small instabilities[8], and hence produce disproportionate results.

In addition to the strict definitions of Phillips[5], ebb-tidal deltas are also “belligerent or intimidating, ruthless, and tough”, other traits reflective of badassery [Oxford Engish Dictionary]. The Columbia River ebb-tidal delta alone is responsible for dozens shipwrecks in the past century, and Ameland ebb-tidal delta has also featured numerous wrecks throughout its history.

Quoting Thomas Pynchon[9], Phillips also notes that badasses are “able to work mischief on a large scale”. Ameland ebb-tidal delta covers an area of approximately 100 square kilometers, roughly the size of The Hague. Many ebb-tidal deltas around the world are even larger!

Seriously?

Now admittedly, ebb-tidal deltas are just big piles of sand. A big pile of sand is probably not the first thing that comes to mind when you hear the word “badass”, unless you are Ralph Bagnold or a Sarlacc. This could probably also be considered gratuitous personification or anthropomorphization.

I’m sure that many of my friends and family have been scratching their heads as to why I would sacrifice the latter half of my 20s to understand them better. A critical reader might ask, “is it possible that you have only convinced yourself that ebb-tidal deltas are cool out of self-preservation?” And the answer is yes. Yes, I have. Nonetheless, I remain steadfast in my assertion that ebb-tidal deltas exhibit major symptoms of geomorphological badassery.

Although the concept of geomorphological badassery may seem silly at first, it illuminates several important truths of our (mis)understanding of these complex bathymetric features. Ebb-tidal deltas are important to study for reasons of coastal flood protection, navigational safety, and ecological value, but we are bad at predicting how they will evolve. This is because each ebb-tidal delta is unique, making it challenging to generalize their behavior.  Furthermore, their chaotic, non-conformist behavior renders many of our usual deterministic prediction techniques ineffective.  Lastly, the amplifying effect of highly nonlinear physical processes means that small physical changes (e.g., the development of a tiny shoal) could have disproportionately large consequences (e.g., relocation of a channel several kilometers wide).  As such, badassery provides a useful conceptual framework for describing the challenges presented by ebb-tidal deltas to coastal engineers and scientists. 

Badass.

References

[1] Chavarrias Borras, V. [2019]. Obtaining well-posedness in mathematical modelling of fluvial morphodynamics. PhD Thesis, Delft University of Technology.
[2] de Schipper, M.A. [2014]. Alongshore variability of nourished and natural beaches. PhD Dissertation, Delft University of Technology.
[3] Meirelles Nunes da Rocha, S. Effects of a stratified tidal flow on the morphodynamics. PhD Dissertation, Delft University of Technology.
[4] de Vet, P.L.M. [2020]. Intertidal Flats in Engineered Estuaries: On the Hydrodynamics, Morphodynamics, and Implications for Ecology and System Management. PhD Dissertation, Delft University of Technology.
[5] Phillips, J. D. (2015). Badass geomorphologyEarth Surface Processes and Landforms40(1), 22-33. (Yes, this is a legitimate scientific publication!)
[6] Elias, E., Teske, R., van der Spek, A., & Lazar, M. [2015]. Modelling tidal-inlet morphodynamics on medium time scales. In The Proceedings of the Coastal Sediments 2015.
[7] Kennedy, B. A. [1979]. A naughty world. Transactions of the Institute of British Geographers, 550-558.
[8] Elias, E. P., Van der Spek, A. J., Pearson, S. G., & Cleveringa, J. [2019]. Understanding sediment bypassing processes through analysis of high-frequency observations of Ameland Inlet, the Netherlands. Marine Geology, 415, 105956.
[9] Pynchon T. [1984]. Is it O.K. to be a Luddite? The New York Times Book Review (October 28): 40–41.

The Side Effects of Trying to Keep Our Feet Dry

In an era of rising sea levels, ambitious plans for coastal protection works are emerging around the world. One such plan is the Delta21 project, proposed by group of Dutch coastal engineers and entrepreneurs. Their goal is to improve flood protection at the mouth of the Haringvliet estuary and develop a tidal power facility, all in one integrated project.

However, the law of unintended consequences often looms large in these sorts of massive infrastructure projects, particularly for environments as complex as estuaries. After a massive flood in 1953, the Dutch constructed the Delta Works, damming most of the estuaries in the southern half of the Netherlands. Prior to that, the Afsluitdijk was constructed across the Zuiderzee in the northern part of the country. These protection works have had dramatic consequences on the physical and ecological development of the Dutch coast, and many of my colleagues here have devoted their careers to analyzing the impact of these interventions.

But instead of just looking back and dissecting the successes and failures of 50 or 100 years past, what if we could also use our latest diagnostic tools for predicting the potential impact of bold future interventions? If the Delta21 plan goes ahead, how will the mouth and ebb-tidal delta of the Haringvliet estuary and surrounding coastline evolve? Will existing habitats (particularly in vital intertidal areas) be preserved, disappear, or even expand?

Today, Mayra Zaldivar Piña tackled these questions head on, and successfully defended her master’s thesis, “Stability of intertidal and subtidal areas after Delta21 plan“. I had the pleasure of co-supervising Mayra’s work throughout the last eight or so months, and am very proud of her. She embarked on a challenging modelling project and showed an exemplary critical scientific attitude. I was also so impressed with the persistence and tenacity she showed in doing nearly her entire project during the pandemic. Writing your thesis is a difficult and isolating experience at the best of times, and these are not the best of times. Nonetheless, she kept at it and delivered an impressive thesis in the end!

Congratulations Mayra, and best of luck in the next steps of your career!

Ameland Datapalooza!

Check out our new paper here!

Three years ago, I experienced one of the highlights of my professional career so far. Alongside researchers from 3 universities, the Dutch government, and several other institutions, we carried out a 40-day field measurement campaign at Ameland Inlet in the north of the Netherlands. We deployed several frames loaded up like Christmas trees with every instrument imaginable: ADVs and ADCPs to measure waves and currents, LISSTs and OBSs to measure suspended sediment, a YSI multiprobe to measure salinity and other water quality indicators, and even a 3D sonar to track the migration of ripples along the seabed.

One of the five measurement frames that we deployed in Ameland back in Fall 2017. It was stacked full of instruments to measure the waves, currents, suspended sand and mud, salinity, ripples, and more.

Four of our five frames survived the relentless ebb and flow of the tide, and even two major storms (one of which left me stranded in Germany after the wind blew down all the overhead train power lines between Berlin and Amsterdam!). In the end, we obtained enough data to keep me busy for probably 3 PhDs, if not the rest of my career. This is just as well, since that last frame was buried in the storm, and based on our understanding of the local dynamics, it will likely re-emerge in another few decades, just in time for my retirement! I look forward to sharing my other findings with you here in the next few months!

Although it used to be the norm for scientists to squirrel away their data, there is an increasing movement towards open accessibility of research data. This improves transparency and accountability in the scientific process, and opens up new opportunities for collaboration. The data we collected is now available in its entirety here on the 4TU web portal or on Rijkswaterstaat’s interactive web viewer.

However, there is a lot of data – I mean A LOT! To help researchers interpret the contents of this database, we prepared an overview paper, which was finally published in the journal of Earth System Science Data! It is also accompanied by a more detailed report, which gets into the nitty-gritty details we didn’t have room to describe in the paper. Nobody likes to read a phonebook-sized report, but it’s nice to have the information there for the few brave souls who do want to comb through our dataset.

Sailing across the Vlie ebb-tidal delta on our way to retrieve the measurement frames at the end of the field campaign.

It was all a huge team effort, as evidenced by the 20+ co-authors. My contribution to this paper focused on the processing of the LISST and YSI multiprobe data, which tell us about the size of particles floating through the water, and how salty that water is. I also designed the maps. As a kid, I loved to read and draw maps, and I think that 7-year-old Stuart would have been tickled to know that he would still be dabbling in cartography all these years later.

As the research in the rest of my PhD (and beyond!) will continue to focus on the fruits of this measurement campaign, I am very keen to work together and collaborate with other researchers who have an interest in this dataset. Please get in touch if you are interested!

Rolling the Dice: Dealing with Uncertainty in Coastal Flood Predictions for Small Island Developing States

Small island developing states around the world are especially vulnerable to the hazards posed by sea level rise and climate change. As engineers, we have a number of tools in our toolbox for reducing the risk posed by coastal flooding and for planning adaptation measures. We often rely on predictive models which combine information about expected wave and sea level conditions, the topography of the coast, and vulnerable buildings and population to estimate potential flooding and expected damage.

However, to use these types of models, we first need to answer a lot of questions: what exactly are the expected wave and sea level conditions? What if detailed topographic measurements are unavailable? What if the population of a given coastal area increases? How are the local buildings constructed, and what are the consequences of that for estimating damage from flooding?

If our information is imperfect (which it almost always is), all is not lost: we can still make educated guesses or test the sensitivity of our models to a range of values. However, these uncertainties can multiply out of control rather quickly, so we need to be able to quantify them. There is no sense in spending the time to develop a detailed hydrodynamic model if your bathymetry data is crap. Can we get a better handle on which variables are the most important to quantify properly? Can we prioritize which data is the most important to collect? This would help us make better predictions, and to make better use of scarce resources (data collection is expensive, especially on remote islands!).

Matteo Parodi investigated these questions in his master’s thesis, and just published his first paper, “Uncertainties in coastal flood risk assessments in small island developing states“. I had the great privilege and joy of co-supervising Matteo during his thesis, and I am immensely proud of him and his work!

Based on a study of the islands of São Tomé and Príncipe, off the coast of Africa, Matteo found that topographic measurements and the relationship between flood depth and damage to buildings were the biggest uncertainties for predicting present-day flood damage. This means that measuring topography of vulnerable coastal areas in high resolution, and performing better post-disaster damage surveys will provide the best “bang for your buck” right now. However, for longer time horizons (i.e. the year 2100), uncertainty in sea level rise estimates become most important.

Matteo’s work will help coastal managers on vulnerable islands to better prioritize limited financial resources, and will improve the trustworthiness of our predictive models. Great job, Matteo!

Can 3D-Printed Corals Help Us Prevent Flooding?

Coral reefs around the world are dying; that much is clear from the headlines we see in the news that grow increasingly distressed with each passing year. This is an ecological catastrophe, but are we also losing another key benefit of reefs? Coral reefs provide a form of natural protection against wave-driven flooding on tropical coastlines. This is partly because the physical form of the reef (often a big rocky shelf) serves as a sort of natural breakwater, but is also due to the frictional effects of the corals themselves.

Many species of coral have complex shapes that disrupt the flow of water across reefs, generating turbulence and dissipating energy. This has the effect of reducing the height of waves as they travel across the reef towards the shore. However, these effects are incredibly complex and poorly understood, so we usually just simplify them in our predictive models by considering a reef to be more “hydraulically rough” than a sandy beach, for example. But we need to do better: these models are used to forecast flooding and estimate the impact of future climate change on vulnerable coasts.

How can we improve this? In coastal engineering, we often conduct experiments in the laboratory to test our theories and understand the chaos of natural systems in more controlled settings. What if we could make a scale model of a coral reef and measure exactly how waves are dissipated?

I am extremely proud to announce the graduation of Paul van Wiechen, one of the Master’s students whom I have had the pleasure of supervising. Yesterday, he defended his thesis, “Wave dissipation on a complex coral reef: An experimental study“, where he built a tiny coral reef in the TU Delft wave flume (a 30-m long bathtub with a wave-making paddle at one end) using hundreds of 3D-printed coral models.

Paul’s thesis, “Wave dissipation on a complex coral reef: An experimental study“.

It was one of the coolest projects I have ever seen, and his research provides us with valuable measurements that give us a deeper understanding of the vital role that corals play in protecting our coasts.

He also did all of this in the middle of a global pandemic, and somehow managed to stay completely on schedule. We are very lucky, because Paul will be joining the Coastal Engineering department here at TU Delft to start a PhD on dune erosion this fall. We are all glad to have him on the team and eager to see what his research unveils next!

Clustering Coral Reefs for Coastal Flood Forecasting

Many of the world’s idyllic tropical coasts are facing threats on multiple fronts.  Rising seas threaten the very habitability of many low-lying islands, and the coral reefs that often defend these coasts from wave attack are dying, too.  Compounding this problem is the sheer number and variety of these islands: there are thousands of islands, and the coral reefs surrounding them come in all shapes and sizes.  Located around the globe, these islands are each exposed to a unique wave climate and range of sea level conditions. This variability in reef characteristics and hydrodynamic forcing makes it a big challenge to forecast how waves will respond when they approach the shore, something that is quite tricky even at the best of times.  Under these circumstances, how can we protect vulnerable coastal communities on coral reef coasts from wave-driven flooding?

This is the problem that my fantastic former student, Fred Scott (now at Baird & Associates in Canada), tackled in his paper, Hydro-Morphological Characterization of Coral Reefs for Wave Runup Prediction, recently published in Frontiers in Marine Science.  Working in partnership with Deltares and the US Geological Survey for his master’s thesis, Fred came up with a new methodology for forecasting how waves transform in response to variations in the shape and size of coral reefs.

fredFigure1
(A) This is a typical fringing coral reef cross-section, showing waves approaching from the right, with the shore on the left. (B) Fred came up with a number of algorithms for classifying and organizing the massive dataset of coral reef cross-sections. (C) The measurements used in our study are from sites around the globe. (D) This is what 30,000 reef cross-sections look like when you try to plot them all on top of one another- clearly we need to whittle those down a bit… [Source: Scott et al, 2020]
In our previous research on this topic, we tried to predict flooding on coral reef-lined coasts using a very simplified coral reef shape.  This was fine as a first guess, but most reefs are bumpy and jagged and bear little resemblance to the unnaturally straight lines in my model. We couldn’t help it though: there just wasn’t enough data available when I started my thesis four years ago, so we did the best we could with the information we had at the time. On the bright side, using a single simple reef shape meant that we could easily run our computer simulations hundreds of thousands of times to represent a wide range of wave and relative sea level conditions.

Fast forward three years to when Fred began his own thesis. We now had access to a mind-boggling dataset of over 30,000 measured coral reef cross-sections from locations around the world!  However, instead of too little data, we now had too much!  If we wanted to simulate a whole range of wave and sea level conditions on each of the reefs in our dataset, it might take months or even years to run our models! Fred had the daunting task of distilling that gargantuan database down to a more manageable number of reef cross-sections.

But how do we choose which cross-sections are the most useful or important to look at?  Even though every coral reef is, like a beautiful snowflake, utterly unique, surely there must be some general trends or similarities that we can identify, right?  This question lies at the heart of Fred’s research, and to answer it, he turned to many of the same powerful statistical and machine-learning techniques used by the likes of Google and Facebook to harvest your life’s secrets from the internet or power self-driving cars.  Maybe we can use some of this technology for good, after all!

The main approach that Fred used in this study was cluster analysis, a family of techniques that look for similarities or differences between entries in a dataset, and then group the entries accordingly into clusters.  The entries within one cluster should be more similar to each other than to the entries in other clusters.  In our case, this meant grouping the reefs into clusters by similar shape and size. This allowed us to increase efficiency and reduce redundancy by proceeding with 500 representative cross sections, instead of the entire database of 30,000.

zoom
These days when I’m lonely, I Zoom with 500 of my favourite coral reef profiles…

Other studies in our field have tried similar approaches (such as this Brazilian study of coral reef shape), but the innovative part of Fred’s technique was to also account for similarities in the hydrodynamic response of the waves to each reef via a second round of clustering. Wave transformation on coral reefs can be immensely complicated, so it is entirely possible that two reef profiles could look very different, but lead to the same amount of flooding in the end.  Since we are mainly concerned about the flooding (rather than a classification for ecological or geological purposes about coral reef formation and evolution), this suits us just fine!

In the end, Fred was able to distill this colossal dataset into between 50-312 representative cross sections that can forecast wave runup with a mean error of only about 10%, compared to predictions made using the actual cross sections.  This opens the door wide for a range of future applications, such as climate change impact assessments or coral reef restoration projects.  Right now, we are working on a new project that will apply Fred’s approach to the development of a simplified global early-warning system for wave-induced flooding on coral reef-fronted coasts.

Great work, Fred, and congratulations on your first publication! I am excited to see where this road takes us!

Sources:

  1. Scott, F., Antolinez, J.A.A., McCall, R.C., Storlazzi, C.D., Reniers, A.J.H.M., & Pearson, S.G. (2020). Hydro-morphological characterization of coral reefs for wave-runup prediction. Frontiers in Marine Science. [Link]
  2. Scott, F. (2019). Data reduction techniques of coral reef morphology and hydrodynamics for use in wave runup prediction. [Link]. TU Delft MSc thesis in cooperation with Deltares and the US Geological Survey.
  3. Scott, F., Antolinez, J.A., McCall, R.T., Storlazzi, C.D., Reniers, A., and Pearson, S., 2020, Coral reef profiles for wave-runup prediction: U.S. Geological Survey data release [Link].

Do You Know the Way to San Jose? This Sediment Does…

What pathways does sediment take as it travels through an estuary?  Yesterday, Laurie van Gijzen defended her thesis, entitled “Sediment Pathways and Connectivity in San Francisco South Bay“. Laurie is one of the master’s students that I supervise, and she has done a great job on this project.

San Francisco Bay is a massive estuary, with over six million people living nearby.  In addition to San Francisco, Silicon Valley sits on its shores.  Some of the biggest tech companies in the world like Google and Facebook have their head offices right next to the Bay.  For over 150 years, the ecological health of the bay has deteriorated, in part due to land reclamations and contaminated sediment from gold mining. The dynamics of San Francisco thus have a huge economic, social, and environmental impact.

Laurie’s work focused on calibrating and improving a sediment transport model of the bay, in order to track the pathways of fine sediment (i.e., mud).  She worked with a notoriously fickle model (DELWAQ) and succeeded in greatly improving its calibration.

laurieSummary
Laurie’s thesis summarized into a single diagram (Figure 6.1 from her report).  She shows the dominant sediment pathways as dark arrows, and the net accumulation (import, in orange) or depletion (export, in blue).  Also indicated are the dominant physical processes responsible for sediment transport in the different parts of the bay.  The baroclinic processes mentioned here are currents resulting from density differences in seawater due to changes in salinity and temperature.

Another cool thing about her work is that Laurie was the first person to apply the coastal sediment connectivity framework that I have been developing!  She was able to use this to identify key transport pathways and critical locations in the bay. It was extremely helpful for my research, as it gives us a proof of concept that our framework is applicable to multiple sites and can tell us something useful.

Her work was also accepted for a presentation at the NCK Days conference, which was meant to be held this week in Den Helder, but was cancelled due to ongoing societal chaos. Great job, Laurie!

The Magical Figure that Changed My Entire PhD

It was Christmas 2016, and I felt like I had bitten off more than I could chew.  I’m not talking about turkey, though.  Four months into my PhD, I was feeling completely overwhelmed and starting to wonder what I had gotten myself into.

The goal of my project is to identify the pathways that sand takes as it moves in and around the Wadden Islands in the northern part of the Netherlands.  Since the Dutch coast has a chronic erosion problem, accurately accounting for the whereabouts of their sand is a matter of national security.  Right now, the Dutch deal with a deficit in their coastal sediment budget by adding more sand or “nourishing” wherever there is a shortfall.

Knowing when, where, and how much sand to add is especially challenging around these islands.  Here, the persistent push and pull of the tide competes with the chaotic brutality of the waves to move sediment in complex patterns.  These patterns are hard to predict with our usual box of tools, so we planned to throw everything we had at the problem: state-of-the-art field measurements, sophisticated computer models, reams of historical data, and a support team of experts from across the Netherlands.  As PhD students go, I felt [and still feel!] pretty darn lucky to be a part of such a large and well-conceived project.

The Spaghetti Problem

However, as I started reading more and more about my topic, my initial enthusiasm began to wane.  I was floored by just how much research had already been done on what I had thought was a fairly specific niche.  The Dutch have been scrutinizing their coast for centuries, and to my inexperienced eyes, it seemed like they had already thought of everything.

There was another problem: at the end of almost every study about sediment pathways, there seems to be a diagram summarizing all the paths with lots of curvy arrows flying all over the place. This veritable plate of spaghetti makes for a nice conceptual drawing, but how can you statistically compare two plates of spaghetti with one another? A “past spaghetti” and a “future spaghetti”, to help understand potential responses to climate change? A “Dutch spaghetti” and an “American spaghetti”, to make my findings more general and useful for other places? If I was going to get anywhere with my PhD, I needed a spaghetti system.

Spaghetti wound on a fork close-up
Mmm, sediment pathways… Also, to be clear, this is not The Magical Figure That Single-handedly Changed My PhD. [Source: Flickr]
By Christmas, I felt like I was in a weird purgatory between “it’s all been done before! I’ll never come up with anything original!” and “this is insurmountably complex and you’re foolish to think you’ll ever figure this out”. And just a dash of “how-did-I-get-here?” imposter syndrome, for good measure. I spent much of my holiday feeling overwhelmed and inadequate, like I couldn’t possibly live up to my own expectations, or (what I thought to be) the expectations of those around me.

But: new year, new start. On January 11th, 2017, my first day back in the Netherlands from holidays, a paper about coral reef hydrodynamics popped up in my Google Scholar alerts.  At that time, I was also finishing up a paper about predicting floods on tropical islands, and I liked to keep an eye on the latest developments in that topic.

A coupled wave-hydrodynamic model of an atoll with high friction: Mechanisms for flow, connectivity, and ecological implications“. Sounds promising, I like wave models.

In this paper, they wanted to understand how waves and ocean currents move water around Palmyra Atoll, a coral island in the middle of the Pacific. Coral reefs all around the world are in big trouble, and to help them we must first understand the physical processes governing the life and death of corals.

Palmyra Atoll, a coral island in the middle of the Pacific. Unfortunately not my PhD study site… [Source: Wikipedia]
This was all very interesting stuff, though not particularly relevant to my research about flood prediction, since they seemed more focused on the ecological impact of their results. It was seemingly even less relevant to my PhD topic on Dutch sand- stay focused and stop wasting your time, Stuart! But then I turned the page and there it was:

The Magical Figure That Singlehandedly Changed My PhD

Rogersetal2015_Figure13
The Magical Figure That Singlehandedly Changed My PhD, Figure 13 from Rogers et al (2017). “Connectivity between hydrodynamic zones. (a) connectivity matrix showing the probability a water parcel passing through a destination zone came from a given source zone, and (b) geographic connectivity of top 10% of pathways, where shading is relative importance as an overall source, width of line is relative strength of connection.”

Essentially, the authors had summarized the pathways that coral larvae can take around an island in a mathematically elegant way. This was pretty much identical to the goal of my PhD, if you substitute coral larvae for sand, and an idyllic Pacific island for a stormy estuary in Holland. They did it with a concept called “connectivity”, and it became immediately apparent that I had some homework to do.

So what the heck is connectivity?

So what exactly do they mean by connectivity, and how are we meant to interpret that magical diagram?  Let’s start at the top.  The upper panel is what we call an “adjacency matrix”, but you can think of it just like one of those mileage charts that you sometimes see in the corner of highway maps.

Image result for mileage chart
A mileage chart, which you can read in the same way as the adjacency matrix above. If you want to get between two points, just find the intersection between your row and column of choice. 290 miles from Birmingham to Edinburgh doesn’t sound too bad, until you encounter the menace that is Birmingham traffic… [Source: The Open University]
Instead of looking at the distance between two points like in a mileage chart, the authors of the reef paper consider the likelihood of water travelling from one point to another. Darker squares show a higher chance of connection, and lighter squares, a lower chance. For instance, if we look at the first column, water is more likely to flow from the point they call “WT FR NW” to point “WT W” than it is to flow to “WT FR SW”.

The second panel shows the same information as the matrix, but this time actually showing the connections on a map – a “network diagram”. The thickness of the blue lines on the network diagram indicate how strong a connection between two points is. If all this seems rather familiar, then that’s probably because you’ve already met our network diagram’s more famous cousin, the transit map:

londonTubeMap
Harry Beck’s famous map of the London Underground. This map is a network diagram, much like the coral atoll connectivity map shown earlier. It represents the stations as nodes, and the train lines between them as links. It shows the connections symbolically, rather than at their true geographical locations, but this makes it easier for use to focus on the important things, like knowing where we need to switch train lines to get back to our hotel. [Source: Transport for London]

Cool maps. So what?

After seeing the coral reef connectivity diagram, I started googling and soon realized that I had been woefully ignorant of an entire mathematical discipline. Network theory represents complex systems as a series of points and the links between them. Once you’ve done that, interesting patterns start to emerge, such as the “six degrees of separation” or “small-world” phenomenon. It has been used in neurology, sociology, ecology, epidemiology, geomorphology, and basically every kind of “-ology”, except for coastal science and engineering. As far as I can tell, we seem to be the last ones to the party.

The more I read, the more excited I became, and the more vital it seemed for our field to catch up. Connectivity could help us quantify and bring order to the chaotic spaghetti churned out by our models and measurements – if we could figure out how to adapt it.

The course of my PhD was changed instantly with the discovery of that figure. Not only did connectivity provide a potentially useful tool, but it jolted me out of my funk and got me excited about my PhD again.  It was an important finding for my research but not a “eureka moment” where everything was suddenly solved- far from it.  It has been a long uphill slog since then, but with the help of some very clever people, I think we have almost reached our first milestone. We presented our early findings at a conference in 2017, and right now we’re in the final stages of preparing a scientific article about our ideas.  That paper will then have to survive the woodchipper of peer-review, so it may still be many months before my work sees the light of day.  But I remain hopeful.

Would I have stumbled upon connectivity eventually, had I not seen The Magic Figure? Probably not if I had only stuck to reading papers about coastal sediment transport. This finding has shaped my attitude towards coastal engineering research- I believe that the next advances in our field will not come from developing a new bedload equation, but from adopting new tools and techniques from other disciplines. Not that we don’t need better bedload equations – I just don’t think I’m the guy to do it, and I think that we could all benefit from looking over the fence at our neighbours in other fields from time to time. As William Zinsser nicely put it:

“Think flexibly about the field you’re writing about. Its frontiers may no longer be where they were the last time you looked.”


Sources:

Rogers, J. S., Monismith, S. G., Fringer, O. B., Koweek, D. A., & Dunbar, R. B. (2017). A coupled wave-hydrodynamic model of an atoll with high friction: Mechanisms for flow, connectivity, and ecological implications. Ocean Modelling, 110, 66-82.

Zinsser, W. K. (1989). Writing to learn (pp. 224). New York: Harper & Row.