The campaign involved citizen contributions both for the funding and the observation and recovery of the drifters. Before the campaign, the University Fund of Utrecht University organized a crowdfunding campaign for the project. During the campaign, citizens were involved because the drifters are spotted once washed ashore. Anticipating this, we designed the sticker shown in Appendix  to convey a brief message to finders. The intention was that finders send an email with a picture of the drifter for documentation, without moving the drifter to another location. In this manner, grounding and resuspension processes of the drifters should remain part of the observations. In addition, once a reported drifter had reached the end of its measurement period, we asked the finders to return the drifter via post. We received 35 sightings, and recovered 12 of the 24 released drifters.

We collected the transmitted measurements and manually removed any sections at the end of the recordings that originated from the transport of the drifters by people on land. Some drifters have also been redeployed after a first collection, which we record as independent deployments. The analysis that follows is based on the drifter trajectories of this dataset ().

The raw trajectories are processed to derive a set of homogeneous time-series. In a first step, we remove outliers that appear as abrupt changes of location. It was found that filtering out displacements between consecutive measurements of more than 50 km in either the longitudinal or latitudinal direction provides satisfactory results. In the second step, we regularized the time-steps of the trajectories by splitting up the trajectories at time-steps larger than a chosen threshold tmax, and by averaging the timestamps and positions of consecutive measurements with time-steps smaller than a chosen threshold tmin. This step resulted in a few trajectories with only a small number of positions. We removed these in a third step by requiring a minimum total duration Tmin and a minimum number of samples Nmin of a time-series. The parameter choice for the analysis here are 20 min for tmax, 2.5 min for tmin, 1.5 h for Tmin, and 12 for Nmin.

We recreate the water levels, the topological surroundings, and the wind conditions encountered by the drifters from a MATROOS dataset (), a high-resolution regional bathymetry map (), OpenStreetMap (), and the ERA5 reanalysis ().

We visually inspected and annotated the trajectories with labels for grounding and resuspension events, based on the guideline described in Appendix . Each trajectory time-step is then annotated as (manual) grounded or (manual) floating. For validation, ten trajectories were annotated by two coders. Comparing the two outcomes per time-step gives an agreement of 94 % for one trajectory, and above 97 % for the other nine ones. A comparison per event shows that roughly 75 % of the labels have a correspondence within five time-steps (30 min), 10 % agree within up to 19 time-steps (2 h), and 15 % of the annotations do not have a correspondence. The mismatches from the last category are annotations of four shorter grounded sections, where the grounding and resuspension events are 30–60 min apart.

The plots in Fig.  show that quantities derived from the trajectories display characteristic behaviors in correlation with grounded sections. We subsequently formalize this observation to design a statistic that indicates a grounded drifter, which should be applicable for different GNSS systems and sampling strategies. The GNSS trajectories can be written as time series of positions p(t)=(lon(t),lat(t)) at sampling times t=t1,t2,…,tN. We measure distances between recorded positions with the geodetic distance dg(p1,p2):=|p2-p1| and locally define angles between displacements ∡(p2-p1,p3-p1)∈[-180°,180°] from a projection of the positions to rectangular coordinates.

The speed v(t) as a discrete time derivative of the position v(ti):=|p(ti+1)-p(ti)|ti+1-ti is low when the drifter is immobile. This occurs when a drifter is suspended on land, but it can also be the result of specific states of the water surface, for example at the turning points of tidal cycles. A related quantity is the displacement D(t,ΔT) during a chosen time interval ΔT D(t,ΔT):=|p(t+ΔT/2)-p(t-ΔT/2)| where the continuous time t±ΔT/2 can be matched to the discrete recorded times ti by an interpolation scheme. We choose to use nearest neighbor interpolation p(t)→p(ti), i=argmin{|ti-t|}. The distance D(t,ΔT) remains small when the drifter is immobile. Since the trajectories of drifters on the water surface with slow currents usually follow a smooth path at low speeds, this metric is expected to be more suitable than speed for separating situations like the turning points of tides from grounded sections.

The change in direction α(t) over consecutive measurements α(ti):=∡(p(ti+1)-p(ti),p(ti)-p(ti-1)) is small for smooth parts of the GNSS trajectories. We make use of a preprocessing step to standardize the computation of α(ti), as described in Appendix . When a drifter is following surface currents, the distances between subsequent measurements are larger than the inaccuracy of the positioning system. This, combined with the continuity of the currents at the sensitivity scale of the drifter, creates a correlation between small values of α(t) and the drifter being afloat. This is in contrast to situations when the drifter is immobile, where the jitter is the dominant contribution to differences between consecutive measurements. This quasi-random displacement generates star-shaped patterns that coincide with abrupt directional changes and thus large values of α(t) that fluctuate over time. In order to quantify this characteristic behavior, the average A(t,ΔT) of the absolute directional changes |α(ti)|∈[0°,180°] during a time interval ΔT can be computed as A(t,ΔT):=1|W|∑ti∈W|α(ti)|with W:=W(t,Δt)={ti|ti-ΔT/2≤t≤ti+ΔT/2}

Similar to the discussion above about velocity and displacement, the extension of an instantaneous metric to a time-window makes it possible to better separate the smoother turns in the trajectory of a floating drifter, where large changes in direction can occur over only a few measurements, from the more constant appearance of large directional changes when the physical position of the drifter does not change.

Both D and A are independent of the time intervals ti+1-ti between measurements i∈I. This choice was motivated by considering trade-offs between accuracy and simplicity of the detection method, and the robustness to sparse and irregular sampling. In principle, one can choose two different time-windows ΔTD and ΔTA. The prediction of grounded sections in the time series follows by introducing thresholds Dth and Ath. For a time ti, the time-window defines the set of associated entries that are used to test if a threshold is crossed. If this is the case, all entries of this set are considered grounding candidates: if D(ti,ΔTD)<Dththen  groundedD(ti)=True, for all tk∈W(ti,ΔTD),if A(ti,ΔTA)>Aththen  groundedA(ti)=True, for all tk∈W(ti,ΔTA).

From this, grounding is predicted for an entry where both quantities indicate grounding: grounded(ti):=groundedD(ti)∧groundedA(ti).

The statistical method has four parameters summarized in Table , which we reduce to three parameters by using one time-window ΔT for both ΔTD and ΔTA. Since we rely on a sparse dataset with a limited number of grounded and floating sections, we choose the values of these parameters guided by considerations of characteristics of the measurements and of the physical processes, rather than by using statistical tools.

The time-window ΔT sets a lower bound for the temporal detection of grounded sections, the duration of which can vary between a few minutes and days. The position sampling frequency implies an average number of entries that fall within each time-window, which sets a lower bound for ΔT. Its value should be chosen close to this lower bound, in order to increase the temporal resolution of the grounding detection, and to avoid interference from physical transport processes at higher timescales. In the case of the Wadden Sea, the semidiurnal tidal cycles have a major impact on current patterns. Splitting cycles up into rising-, high-, falling-, and flat-tide phases gives a temporal scale of 3 h, thus ΔT≤ 3 h.

The apparent displacement of a drifter at rest is caused by the uncertainty of the GNSS system, which sets a lower bound for the choice of Dth. This has to be balanced against the slowest observed displacements of a floating drifter during the characteristic time ΔT. This can for example be inferred from the lowest characteristic surface current that the drifter is sensitive to. For the Wadden Sea, slow surface currents may be on the order of 1 cms-1 and assuming this speed constant during high- or flat-tide leads to a characteristic minimal displacement of 1 cms-1 × 3 h ∼ 100 m ≥ Dth. Comparing different choices for Dth showed that the standard deviation of the recorded position of a drifter at rest works well for grounding detection. Since the accuracy of a GNSS system can be different in the north and east direction, we compute the standard deviations σN,σE in either direction for the trajectory of a drifter at rest, and set Dth=max⁡{σN,σE}.

Similar arguments can be made for the choice of Ath, but the dependencies of sampling accuracy, frequency, regularity, and the movements of the drifter are more complex. An order estimation for a characteristic reorientation of floating drifters comes from assuming that the travel direction is reversed during falling- and rising-tide phases, such that 180°/n(3h)≤Ath, with the average number of samples n(3 h) during 3 h. A useful reference to set this threshold can be derived from the assumption that the changes in direction of a GNSS receiver at rest follow a uniform random distribution: For a set of random variables {ai}i=0,1,…∼Unif[-180,180] and with the probability p=P[θp=(1-p)⋅180°≤|a0|] it follows that p=P[θp≤A|{a0}] for one angle. In accordance with the choice of the previous paragraph of one standard deviation for the threshold of the displacement Dth, a lower bound for this threshold is thus p=0.68→θ0.68=57.6°≤Ath. On the other hand, the expected value of the metric E[A|{a0,a1,…}] = 90° is independent of the number of samples in each time-window, providing an upper bound. It was found that setting Ath = 58° resulted in satisfactory results.

Two metrics are used to quantify the agreement of the manually observed groundings with the predictions from the grounded statistic. The first metric makes a comparison for each entry in each time-series. While this approach shows the fraction of correct and incorrect predictions on a time-step basis, it does not indicate the effectiveness of the statistic to identify individual floating and grounded sections. These vary greatly in duration, such that misidentified shorter sections are less apparent. Furthermore, some sections have durations smaller than the chosen time-window and therefore lie outside the scope of the statistic. For these reasons, a second metric is used that compares observations and predictions on a section basis. When examining a recorded trajectory for groundings, sections where the drifter is afloat should have no indication of grounding for the entire duration, and sections where the drifter is on land should have at least one indication of grounding. For this reason, the second metric counts floating sections with the absence of any grounding prediction as one correct floating prediction, and otherwise counts the number of separate subsections of false grounding indications as wrong floating predictions. A grounded section counts as one correct grounding prediction if the grounding is indicated at least once, and as one incorrect grounding prediction otherwise. Sections with durations smaller than ΔT are not taken into account.

The reliability and adaptability of the grounded statistic is evaluated for different re-samplings of the trajectories. The entries were either selected with a uniform stride, or by dropping a fraction of the entries at random. For either method, the number of entries was repeatedly divided by two, in parallel to the reduction of the time-window for the grounding detection. This results in the average number of entries in the time-windows used for the evaluation being similar for different reductions of the trajectory and/or time-window.

We want to identify environmental conditions and other factors that explain the manually observed groundings and resuspensions, where we focus on the situation that a drifter is already in a region where groundings can occur. Since the events happen at the intersection between the water surface and coast, we consider the changes in water level over time in combination with the bathymetry as a proxy for water depth, which in turn informs near coast surface currents, and whether an intertidal zone is flooded or not. Local wind also impacts both the water surface and drifter movements ().

Since tides are the main drivers of dynamic changes in the Wadden Sea, we extract the tidal phase from the M2 constituent of the 48 h water level time series at an event location. This is to determine whether an event happens during high, falling, low or rising tides. Wind is characterized by its speed and its direction with respect to the local shoreline orientation of the coast or mudflat. Since determining this orientation appropriately is challenging, we describe our approach and a sensitivity analysis in Appendix . We separate the local wind direction into four sectors of directly towards shore, diagonally towards shore, diagonally from shore and directly from shore. The observed groundings occurred on slopes with a large variation of directions, which is why we do not differentiate between the two mirrored wind directions with the same angle to the shore. Furthermore, we determine the duration of the sections that follow each transition. Lastly, since the Wadden Sea area and its coast comprise of different landscapes and human-made structures, we also derive a topographical categorization of the areas where the transitions occurred. We first determine whether an event is or is not located within 50 m of a human-made structure. We then further separate the event surroundings by determining one predominant topographical feature per event. Table  summarizes the factors we choose for the analysis.

Since we use the manual coding of the transition events for the characterization, this analysis is independent from the grounded statistic. While transition events can be extracted from a time-series where the statistic is evaluated for each time-step of the trajectories, the statistic is designed to indicate the occurrence of grounded sections rather than to identify transitions.