Ebb-tidal deltas are gigantic piles of sand that form at the seaward mouth of tidal inlets. They are constantly on the move, shifting shape and size in response to the waves and tides. Where exactly is that sand going? This is a question I have been struggling with for the past 5 years during my PhD, and we have recently made great strides in part due to the efforts of Paula Lambregts.
Yesterday, Paula Lambregts successfully defended her master’s thesis, “Sediment bypassing at Ameland inlet“. I had the great honour of co-supervising Paula’s researcher throughout the last ten or so months, and I am enormously proud of her. Her project encompassed a range of approaches, including bathymetric analysis and numerical modelling, to solve the mystery of the sediment pathways.
First, Paula’s detective work led her to examine detailed measurements of the seabed bathymetry at Ameland Inlet in the Netherlands, taken over the past fifteen years. These measurements give snapshots of the underwater delta landscape. By comparing the bathymetry from different months or years, we can track the delta’s evolution. In the image below, we see four snapshots of the ebb-tidal delta before and after the construction of a sand nourishment (i.e., the large pile of sand that appears in panel B). This nourishment was a large-scale pilot test to determine if creating sand deposits like this is a viable strategy for strengthening the coast of nearby islands.
After describing how the delta has evolved in the past, Paula developed hypotheses about the physics underlying this behaviour- how do waves and tides move the sand around to create the patterns we observe? To answer this question, she used a combination of computer models to estimate sand transport pathways. This allows us to “connect the dots” and explain how the sand moved from one place to another. The first component was a D-Flow FM model, which is used to simulate the hydrodynamics (waves and tides) and sediment transport (where and how much sand moves). The second component of her modelling approach was to apply SedTRAILS, a brand-new tool developed by my colleagues and I at Deltares for visualizing predicting sediment transport pathways. Using SedTRAILS, she was able to create some really cool maps that indicate where the sand goes.
Drawing on her prior expertise in geology, Paula combined those two lines of evidence (the measurements of the seabed and the modelled sediment pathways), to come up with a series of fantastic conceptual diagrams. These diagrams distill the mysterious piles of sand and complex spaghetti of the images above into a more easily understandable picture:
The work that she did is extremely valuable for coastal management, since it gives more insight into where (and where not!) to construct sand nourishments. It also brings new insights to science about how these complex systems work. Last of all, it is enormously helpful for the research that we are continuing to do at TU Delft and Deltares. In September I will continue on with the work on sediment transport pathways at tidal inlets begun during my PhD, and build on the work that Paula has carried out in her thesis project. I am extremely proud of her and hope that we can continue to collaborate in the future!
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.
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“) 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“).
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 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:
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“) to the downright cheeky (“This proposition is not opposable“).
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 ).
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.
What makes a badass “badass”?
Phillips 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):
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.
Ebb-tidal deltas are chaotic systems which defy accurate prediction using physics-based numerical models, and hence are non-conformist or “naughty”. 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.
Ebb-tidal deltas are highly nonlinear systems which can greatly amplify small instabilities, and hence produce disproportionate results.
In addition to the strict definitions of Phillips, 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, 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!
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.
It has been a crazy year, but work-wise I am on the final stretch, at least. Tonight at the ungodly hour of 12am CET, I will present my poster at the American Geophysical Union conference. It is at a much more reasonable 3pm PST in California where the conference organizers are located. If you have registered for the conference, you can see the poster via this link. Otherwise, I will try to put you in the loop here.
Estuaries are complex environments shaped by the interaction of waves, tides, rivers, and humans. Understanding how sand and mud move through estuaries is essential for their effective management. In an approach known as connectivity, the pathways taken by sand and mud through estuaries can be represented as a connected network of nodes and links, similarly to a subway map. Connectivity provides numerous mathematical techniques and metrics that are well-suited to describing and comparing these pathways in estuaries.
We use connectivity to map out and analyze sand and mud pathways in four estuaries around the world: the Wadden Sea (the Netherlands), Western Scheldt (NL), San Francisco Bay (US), and Columbia River (US). Our analysis is based on the outcome of numerical simulations, and we explore the benefits of different simulation techniques. We conclude that connectivity is a useful approach for visualizing and comparing the pathways that sand and mud takes through different estuaries. We can use this method to plan and predict the impact of human interventions in these environments, such as dredging.
However, a comparison of connectivity metrics suggests a dependency not just on sediment transport processes, but also on the choices made in schematizing networks from underlying models. Essentially, we’re not comparing apples to apples yet, so if we are going to make comparisons between different estuaries, we need to make sure that we set up our models in an equivalent way. Our ongoing research will focus on optimizing these numerical models to make more meaningful quantitative comparisons of different estuaries.
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.
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.
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!
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]
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.
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].
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 almosteverystudyaboutsedimentpathways, 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.
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.
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…
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.
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:
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 techniquesfrom 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.”