…

The choice of a Lagrangian framework for this kind of investigation reflects a broader methodological trend in coastal transport studies. Unlike Eulerian approaches, which describe how a tracer concentration field evolves at fixed points in space, Lagrangian particle tracking follows individual water parcels along their trajectories, making it particularly well suited to problems in which the history of motion matters as much as the instantaneous flow field. For a shallow, semi-enclosed basin such as the Narta Lagoon, where currents are weak and highly variable in direction, the trajectory-based view exposes features that a snapshot of concentrations could easily obscure: narrow preferential pathways, stagnation regions, and the gradual separation of particles that started from the same point but experienced slightly different flow histories. The statistical descriptors applied to the simulated trajectories, drawn from the established literature on dispersion in geophysical flows, allow the authors to condense thousands of individual paths into a small number of interpretable quantities, such as mean squared displacement and related measures of spreading, which can then be compared across the six weekly scenarios.

The treatment of horizontal diffusion in the particle model deserves particular attention, because it illustrates a subtlety that is often overlooked in applied transport modelling. In a random-walk formulation, particles are displaced by both the resolved advective velocity and a stochastic term representing unresolved turbulent mixing. When the diffusion coefficient varies in space, as it does here, a naive implementation in which the stochastic displacement is drawn independently at each step systematically violates the well-mixed condition, the requirement that a uniformly distributed set of particles remains uniformly distributed over time. The consequence is a spurious drift of particles toward regions of low diffusivity, an artifact that could be mistaken for a physical accumulation zone. The correction introduced by Visser, which the authors adopt, adds an explicit gradient term to the particle displacement equation and evaluates the diffusivity at an intermediate position reached after applying half of the gradient drift. This two-stage procedure substantially reduces the bias, and its inclusion in the model design signals a careful attention to numerical fidelity that strengthens confidence in the resulting exposure maps and dispersion statistics.

The decision to represent the lagoon as a closed basin is a deliberate simplification with a clear evidential basis. Previous modelling work on the same system had shown that, even under idealized conditions with both inlets fully open, the exchange of water between the lagoon and the Adriatic Sea is remarkably weak, with the external sea level exerting a negligible influence on the internal circulation except in the immediate vicinity of the inlets themselves. By removing the open boundary altogether, the authors isolate the internal transport mechanisms, wind-driven circulation above all, and can attribute differences in plume behavior between scenarios directly to variations in the wind forcing rather than to changes in boundary exchange. This framing also carries a practical implication: if the lagoon behaves hydrodynamically like a nearly closed basin, then pollutants introduced into it are, to first order, retained within it, and the timescales over which they are redistributed internally become the relevant timescales for ecological exposure. The two inlets, whose operation is informal and unscheduled, therefore emerge not as reliable flushing conduits but as marginal contributors whose management status nonetheless shapes local conditions near the connections.

The six weekly wind scenarios were extracted from a forty-year historical record, which gives the scenario ensemble a degree of representativeness that single-case studies often lack. Rather than simulating one arbitrary week, the authors sampled the range of metocean conditions that the lagoon actually experiences, so that the contrast between scenarios reflects genuine climatological variability rather than an artifact of scenario selection. This approach sits between the two extremes commonly found in the literature: idealized forcing experiments, which are clean but may not correspond to real conditions, and long-term coupled simulations, which are realistic but computationally expensive and harder to interpret scenario by scenario. The weekly window itself is a meaningful choice for a shallow lagoon, since it is long enough for the wind-driven circulation to establish a coherent pattern and for particles to travel appreciable distances, yet short enough that the forcing can be treated as approximately stationary within each scenario.

The distinction between the two release configurations, instantaneous and continuous, addresses a question that is central to pollutant risk assessment but frequently glossed over in modelling studies. A single pulse release, such as an accidental discharge or an overflow event, produces a compact cloud of particles whose fate depends on the flow field encountered at the moment of release. A continuous release, such as the steady discharge from a sewage outfall, produces instead a stream of particles that sample the flow at many different phases of the circulation, and the resulting plume integrates over that variability. The finding that dispersion in some scenarios is sensitive to release timing, with particles either remaining close to the source or spreading more uniformly across the lagoon, indicates that the advective pathways within the lagoon are strongly organized by the wind regime. When the circulation is dominated by coherent, persistent flow structures, the moment of release largely determines which pathway a particle follows, and two releases separated by only hours or days can end up in entirely different regions of the basin. When the circulation is more dispersive, this sensitivity fades and the plume behaves more predictably. The authors attribute this sensitivity specifically to advection, which is a useful diagnostic: it means that the variability arises from the deterministic structure of the flow rather than from the stochastic diffusion term, and it suggests that even modest improvements in the timing of discharges, where such control is possible, could meaningfully reduce exposure in the most retention-prone conditions.

The exposure maps highlighting accumulation zones along the lagoon boundary carry direct management relevance. In a closed or nearly closed basin, material that is not flushed out must eventually be redistributed by the internal circulation, and the boundaries, where currents weaken and particles can strand in shallow areas or along the shoreline, act as natural sinks for floating matter. For floating pollutants, including oils, plastics, and buoyant sewage-associated debris, these boundary accumulation zones represent the locations where ecological contact and cleanup costs are likely to be concentrated. Identifying them in advance, and understanding how their location shifts between wind regimes, allows managers to prioritize monitoring stations, anticipate where visual or chemical impacts will appear after an event, and design interventions such as containment booms or targeted collection with some foreknowledge of where material will converge. The fact that the release point was chosen on the basis of previous field sampling that identified it as the most contaminated area of the lagoon further anchors the simulations in observed reality, ensuring that the modelled plumes originate from a location where pollutant inputs are known to occur rather than from a purely hypothetical source.

The ecological and economic context of the Narta Lagoon amplifies the significance of these results. The lagoon supports migratory birds, European eels, and local aquaculture activities that employ a substantial share of the nearby workforce, so water quality is not merely an environmental concern but a livelihood issue. The documented pressures on the system, including waste disposal serving Vlorë and surrounding towns, salt production, leather tanning, and incomplete wastewater treatment, mean that the pollutant loading simulated in this study is not an abstract scenario but a plausible representation of ongoing inputs. Shallow lagoons are especially sensitive in this respect because their limited depth means that floating material remains in close contact with the biologically productive surface layer, and their restricted exchange means that dilution rates are low. A pollutant that would be rapidly dispersed in an open coastal setting can persist in a lagoon of this type for weeks, repeatedly exposing the same benthic and pelagic communities.

The finding that advective flow plays the dominant role in determining plume behavior also has implications for how monitoring and modelling of such systems should be designed. If mixing were controlled primarily by diffusion, then coarse descriptions of the flow field would suffice, and dispersion could be parameterized with simple bulk coefficients. The dominance of advection implies instead that the spatial structure of the wind-driven circulation, including its gyres, shear zones, and stagnation points, is what controls where pollutants go. This raises the bar for the hydrodynamic model: the velocity fields must resolve the relevant circulation features accurately, because errors in the flow structure translate directly into errors in predicted exposure. It also suggests that wind forecasting, rather than tidal prediction, is the more valuable operational input for anticipating pollutant behavior in this lagoon, a somewhat counterintuitive conclusion for a coastal water body connected to the sea.

The observation that the northern inlet is prone to seasonal closure through sedimentation driven by littoral transport, and is manually reopened by fishermen roughly twice per year, adds a human dimension to the physical problem. The intermittency of this connection means that the lagoon’s effective degree of isolation varies through the year in an unmanaged way, and the southern inlet’s manually operated sluice gates introduce a further element of discretionary control. The authors’ emphasis on the importance of properly managing the two inlets follows logically from their results: if internal retention is already high when the lagoon is treated as closed, then informal or infrequent inlet operation can only prolong stagnation, and a more deliberate management regime, with scheduled openings timed to coincide with conditions favorable to exchange, could reduce the residence time of both water and pollutants. The study’s framing of the lagoon as a closed basin thus serves a dual purpose: it is a defensible modelling simplification supported by prior evidence, and it is also a conservative bounding case whose results quantify the worst-case retention that inlet management would seek to alleviate.

More broadly, the study contributes to a growing body of work demonstrating that semi-enclosed coastal systems cannot be managed by analogy with open coastlines. The combination of high-resolution hydrodynamic modelling, Lagrangian particle tracking, and statistically grounded dispersion descriptors offers a transferable template that can be applied to other shallow lagoons facing similar pressures, many of which are distributed along the Mediterranean and Adriatic coasts where urbanization, tourism, and aquaculture converge on ecologically fragile water bodies. The scenario-based design, in which a small number of representative forcing conditions is analyzed in depth, strikes a practical balance between computational cost and physical realism, and the explicit comparison of release configurations provides a dimension of insight that single-release studies cannot offer. As climate variability alters wind regimes and sea level modifies inlet dynamics in the coming decades, the kind of scenario library constructed here could be extended and reweighted to reflect future conditions, extending the usefulness of the modelling framework well beyond the present analysis of a single Albanian lagoon.

Subject of Research: Lagrangian particle-tracking simulation of pollutant plume dispersion in the Narta Lagoon under variable metocean conditions

Article Title: Assessing lagoon plume dispersion under variable metocean conditions

Article References: Assessing lagoon plume dispersion under variable metocean conditions. (n.d.). https://doi.org/10.3389/fenve.2026.1882143

Image Credits: AI Generated

DOI: 10.3389/fenve.2026.1882143

Keywords: coastal lagoon, Lagrangian particle tracking, plume dispersion, metocean conditions, Narta Lagoon, water quality, hydrodynamic modelling, advection, pollutant transport, Delft3D, exposure maps, Albania

The bottleneck the team attacked is one that anyone who has pushed a weather or air quality model to higher resolution knows well. Doubling the horizontal resolution of an air quality model quadruples the number of grid cells, and numerical stability then forces the model to take proportionally shorter time steps. The combined effect is punishing: previous research cited in the study estimates that increasing horizontal resolution eighteenfold inflates the computational load three hundred times. Operational forecasting systems today mostly run at horizontal resolutions of several to tens of kilometers, which is too coarse for the urban-scale, street-by-street predictions that city managers increasingly demand. Faster hardware and smarter code are therefore not luxuries but prerequisites for the next generation of forecasts.

Graphics processing units offer a way out, because their thousands of parallel processors excel at exactly the kind of repetitive grid arithmetic that atmospheric models perform. The scale of modern GPU power is striking: the El Capitan supercomputer, which topped the TOP500 list in late 2024, delivers 1.742 exaflops of double-precision performance largely through AMD Instinct MI300A accelerators, each of which alone outperforms the entire Earth-Simulator, the world’s fastest machine in 2003. Yet most atmospheric models, including EPICC-Model, were written in Fortran for CPUs, with loop structures and data flows that translate poorly to GPUs. Simply copying code across rarely works; the algorithms must be rethought for the hardware.

The EPICC-Model team had already seen this dynamic play out within their own code. In earlier work, Cao and colleagues ported the model’s gas-phase chemistry module, historically the dominant cost at more than 40 percent of simulation time, onto China’s domestically developed GPU-like accelerators using the Heterogeneous-compute Interface for Portability, or HIP, a programming framework analogous to NVIDIA’s CUDA. That port cut the chemistry module’s share of runtime from 45.7 percent to 29.9 percent, but it exposed a new culprit: the horizontal advection module, which moves pollutants across the model grid with the wind, jumped from 13.3 percent to 25.0 percent of total runtime and became the model’s leading bottleneck. The new study targets exactly that module.

The heart of the advection scheme is the piecewise parabolic method, or PPM, a high-order Godunov-type algorithm from 1984 that approximates transported quantities with parabolic functions and is prized for its precision and robustness. It is the same scheme used in the latest versions of the widely used CMAQ and CAMx models. The researchers first rewrote the Fortran HADVPPM subroutine in standard C, then extended it with HIP calls so it could run on the GPU-like accelerator, which has 3840 computing units and 16 gigabytes of device memory, at the Earth System Numerical Simulation Facility (EarthLab) in Beijing. The resulting package, GPU-HADVPPM4HIP V1.0, follows the familiar heterogeneous computing sequence: allocate device memory, copy data from CPU to accelerator, launch parallel kernels, and copy results back.

Precision was checked at every step. Comparing the original Fortran, the rewritten C, and the HIP versions on identical inputs, the team found mean relative errors on the order of 10 to the minus 7 percent under default compilation, rising only slightly to around 10 to the minus 6 percent with aggressive O3 optimization. Interestingly, most of the small error crept in during the Fortran-to-C rewrite rather than the C-to-HIP step, which makes sense because HIP is essentially an extension of standard C. In a full 28-hour coupled simulation, the GPU version reproduced the Fortran model’s fields almost exactly, with differences in ozone of about 10 to the minus 2 ppbV and in PM2.5 of about 10 to the minus 3 micrograms per cubic meter, and normalized mean biases near zero.

The performance story unfolded in stages. A naive coupling, dubbed HIP-Ori, was actually a disaster: because the model called the advection solver roughly 9.8 million times per time step, each call triggering its own CPU-to-GPU data transfers, a one-hour integration ballooned from 1015 seconds in the original Fortran code to 20,400 seconds. The first fix, HIP-Opt1, restructured the loop hierarchy and expanded one-dimensional arrays into four- and five-dimensional blocks so that entire pollutant categories could be processed in single GPU calls, cutting transfers from about 9.8 million to just 10 per time step. That single change yielded a 17-fold improvement in model-level efficiency. A second optimization, HIP-Opt2, assigned each horizontal grid cell to its own GPU thread through coordinated thread-block indexing, after decoupling iterative calculations so that no step depended on the previous one, adding another 1.5-fold gain.

The team also implemented a hybrid MPI-plus-HIP scheme across EarthLab’s heterogeneous cluster, mapping each CPU process to a dedicated GPU accelerator so that the model scales across many nodes. In the final configuration, a 28-hour simulation that took the unoptimized GPU version 149.7 hours of wall-clock time finished in just 6.0 hours, roughly a 25-fold cumulative improvement over the naive port. At the module level, the GPU advection solver including data transfer overhead ran 39.3 percent faster than the Fortran original; with transfers excluded, the kernel itself was 20.5 times faster. Offline, on an array of 100 million double-precision values, the HIP solver compiled with O3 optimization reached that headline 556.5-fold speedup over the unoptimized Fortran baseline, and still managed 128-fold when both were compiled with the same aggressive flags.

Perhaps the most instructive finding is where the remaining time goes. Profiling showed that for large inputs, memory copying between CPU and GPU consumes roughly half of total execution time, a share that keeps growing with data size. This confirms that data movement, not arithmetic, is the defining constraint of heterogeneous computing, and it explains why the coupled model gains far less than the raw kernel speedup. The authors point to remedies including pinned-memory chunked transfers, asynchronous communication, unified memory architectures, and mixed-precision computation, as well as newer PCIe interconnects whose per-lane data rates have climbed from 16 gigatransfers per second in PCIe 4.0, used at EarthLab, to a projected 128 in PCIe 7.0.

The work also carries a broader message about scientific software in the GPU era. The EPICC-Model with its new advection solver reproduced observed PM2.5 and ozone variations reasonably well across eight Chinese cities during July 2021, with mean correlation coefficients of 0.70 for PM2.5 and 0.76 for ozone, demonstrating that the accelerated code remains scientifically trustworthy on domestic hardware. As the authors note, achieving kilometer-scale pollution simulations, of the kind that recently won a Gordon Bell Prize for climate modeling using NVIDIA GH200 GPUs, will require adapting entire air quality models to heterogeneous supercomputers, where nine of the world’s ten fastest machines now reside. Porting a single module is only the beginning; the real challenge, and opportunity, lies in redesigning the whole computational workflow around the GPU’s massively parallel architecture.

Subject of Research: GPU acceleration of the advection module in the EPICC-Model air quality modeling system

Article Title: Enhancing the advection module performance in the EPICC-Model V1.6.0 via GPU-HADVPPM4HIP V1.0 coupling and GPU-optimized strategies

Article References: Cao, K., Wu, Q., Tang, X., Li, J., Chen, X., Chen, H., Wang, W., Wu, H., Kong, L., Li, J., Zhu, J., & Wang, Z. (2026). Enhancing the advection module performance in the EPICC-Model V1.6.0 via GPU-HADVPPM4HIP V1.0 coupling and GPU-optimized strategies. Geoscientific Model Development, 19(19), 9807-9829. https://doi.org/10.5194/gmd-19-9807-2026

Image Credits: AI Generated

DOI: 10.5194/gmd-19-9807-2026

Keywords: GPU computing, air quality modeling, EPICC-Model, advection, piecewise parabolic method, HIP, high-performance computing, heterogeneous computing, EPICC-Model V1.6.0, GPU-HADVPPM4HIP, EarthLab, numerical weather prediction

A team led by Casey E. Stowers and Thomas E. Yankeelov at the University of Texas at Austin and MD Anderson Cancer Center has now systematically tested how best to represent tumor cell movement in these predictive models. Their work, published in the Annals of Biomedical Engineering, draws on data from 141 patients with locally advanced triple-negative breast cancer enrolled in the ARTEMIS clinical trial at MD Anderson. Each patient received four cycles of Adriamycin and Cytoxan, with magnetic resonance imaging scans taken before treatment, after two cycles, and after four cycles. Patients whose tumors shrank by at least 70 percent on ultrasound went on to receive twelve cycles of Taxol, while others received experimental therapies according to trial guidelines. After the second course of therapy, all patients underwent surgery, at which point their pathological complete response status was determined.

The modeling framework rests on partial differential equations that track the number of tumor cells in every three-dimensional voxel of the breast over time. The number of cells in each voxel is estimated from diffusion-weighted MRI using an inverse relationship between the apparent diffusion coefficient of water in tissue and tumor cell density. The team compared four increasingly sophisticated models. The simplest, a reaction-only model, describes logistic proliferation of cells up to a carrying capacity and drug-induced cell death driven by a concentration map derived from dynamic contrast-enhanced MRI. The second adds a diffusion term, capturing cells migrating from regions of high density to low density. The third mechanically couples that diffusion term, damping the diffusion coefficient exponentially via the von Mises stress computed from a linear elastic mechanical model of the breast, reflecting the experimental observation that solid stress inhibits tumor cell invasion. The fourth and most complex model adds an advection term, in which cells are transported by a velocity field calculated as the time derivative of the mechanical displacement field—an approach originally developed for modeling glioma growth in the brain.

The rationale for exploring advection is subtle but important. In triple-negative breast cancer, tumors typically shrink during therapy rather than expand, and a diffusion term alone cannot physically represent the inward movement of cells that accompanies shrinkage. Advection, by contrast, can carry cells toward the tumor center as the mass effect diminishes with treatment-induced cell death. In the two example patients highlighted in the study—one who achieved a complete response and one who did not—the velocity maps revealed striking behavior. On days when the total tumor cell count was rising, the modeled velocities pointed outward, in the direction of growth. On days shortly after drug delivery, when cell counts were falling, the velocities reversed and pointed toward the tumor center, pulling cells inward and producing smaller, denser tumor maps that more closely matched the imaging data.

That mechanistic insight translated into measurable differences in model performance. For the patient who achieved a complete response, the advection model produced a concordance correlation coefficient of 0.44 at the calibration timepoint compared with 0.31 for the three simpler models, and a Dice score of 0.65 versus 0.58, indicating substantially better spatial overlap with the measured tumor. The advection model also predicted far fewer disconnected islands of tumor cells—two subvolumes instead of seven at the second imaging visit—producing tumor geometries that looked more biologically realistic. Similar patterns held for the non-responding patient, whose residual tumor was better captured by the advection model than by any of the alternatives.

Across the full cohort of 141 patients, however, the picture became more nuanced. At the calibration timepoint, the reaction–mechanically coupled diffusion–advection model was significantly more accurate than all three simpler models on every global and local metric examined, including the absolute difference in percent change of total tumor cell count and volume, voxel-wise mean square error, and concordance correlation coefficient. But at the prediction timepoint—the third MRI scan, which the models had never seen—no significant differences emerged among the four models. The median absolute difference between predicted and measured percent change in tumor volume across the cohort was 9.1 percent for both the reaction-only and reaction–diffusion models, and the advection model offered only a small, statistically insignificant improvement of roughly 4 to 5 percent in tumor volume error for the non-responding patients, who are precisely the group clinicians most need to forecast accurately.

The receiver operating characteristic analysis reinforced this equivalence. When the researchers used predicted total tumor cell count or tumor volume at the third scan to classify patients by their eventual pathological complete response status among the 102 patients who received Taxol as their second therapy, no significant differences appeared between the areas under the ROC curves for any of the four models—or, notably, between the model predictions and the measured imaging data themselves. In other words, even the simplest model predicted complete response status as well as the actual measurements did, and all four models achieved comparable accuracy in this clinically critical task.

Computational cost, however, separated the models dramatically. The reaction-only model calibrated in a median of about 0.31 minutes per patient, while the reaction–diffusion model took roughly 118 minutes, and the mechanically coupled diffusion and advection models required around 222 to 252 minutes each, because both demand a full mechanical equilibrium solve at every optimization iteration. Each calibration ran on a 24-core server, and the two calibrated parameters—global tumor cell proliferation rate and global drug efficacy—were identical across all four models, fitted using the Levenberg–Marquardt algorithm against the first two imaging visits. The authors suggest that reduced-order modeling techniques and higher-order numerical schemes could eventually narrow this efficiency gap for the most accurate model.

One of the study’s most consequential findings concerns the diffusion term itself. Adding diffusion, whether mechanically coupled or not, provided no measurable improvement in calibration or prediction accuracy compared with the reaction-only model. The researchers attribute this to the insensitivity of the diffusion coefficient in this disease setting, where tumors mostly shrink rather than expand; prior sensitivity analyses found the parameter’s influence fell below the threshold for importance even when varied over five orders of magnitude. Yet the authors caution against simply deleting the term: a reaction-only model cannot represent tumor invasion or any expansion in tumor volume, which would produce dangerously poor predictions for a patient whose disease progresses during therapy. Their recommendation is that, among models without advection, the reaction–diffusion model offers the best balance, capturing invasion while calibrating far faster than the mechanically coupled variant.

The implications extend well beyond breast cancer. Because the advection term was adapted from brain tumor modeling, and because the conclusions here apply to tumors that largely shrink under treatment, the framework could inform computational oncology across many solid tumor types. The authors outline several avenues for improvement: incorporating the Allee effect into the proliferation term to better capture the death of small tumors, subdividing tumor cells into sensitive and resistant populations, coupling hydrostatic stress to proliferation or drug resistance, and replacing the linear elastic tissue assumption with nonlinear hyperelastic or anisotropic material models. They also note that future validation should draw on multi-site datasets such as the I-SPY 2 trial, which spans multiple breast cancer subtypes. For now, the study delivers a clear practical message: the reaction term carries most of the predictive power for shrinking tumors, advection is the only term that can physically capture inward cell movement during treatment-induced shrinkage, and choosing among these formulations requires weighing calibration speed against the risk of missing a growing tumor.

Subject of Research: Partial differential equation modeling of tumor cell movement in triple-negative breast cancer receiving neoadjuvant therapy

Article Title: Characterizing Tumor Cell Movement in Partial Differential Equation Models of Triple-Negative Breast Cancer Receiving Neoadjuvant Therapy

Article References: Stowers, C. E., Wu, C., Lorenzo, G., Hormuth, D. A., II, Yam, C., Ma, J., Rauch, G. M., & Yankeelov, T. E. (2026). Characterizing Tumor Cell Movement in Partial Differential Equation Models of Triple-Negative Breast Cancer Receiving Neoadjuvant Therapy. Annals of Biomedical Engineering. https://doi.org/10.1007/s10439-026-04348-7

Image Credits: AI Generated

DOI: 10.1007/s10439-026-04348-7

Keywords: triple-negative breast cancer, neoadjuvant therapy, reaction-diffusion-advection, mathematical oncology, MRI, tumor forecasting, model calibration, advection, mechanical coupling, pathological complete response, partial differential equations, computational biology

The confusion stems from the fact that ‘groundwater age’ is not one quantity but three. The first is the Peak Age, sometimes called the piston-flow or advective age, which describes how long it takes the centre of a concentration front — the peak of a tracer pulse — to travel a given distance. The second is the Mean Residence Time, the average age of all the water molecules in a sample, equivalent to the centre of mass of the age distribution. The third is the Tracer Age, the number actually calculated from a measured tracer concentration using standard formulas such as the conventional radiocarbon age or the tritium–helium age. In a perfectly ordered, dispersion-free aquifer these three values coincide. In the real world, where groundwater always undergoes at least some dispersive mixing, they diverge — sometimes dramatically.

Suckow’s analysis rests on the one-dimensional advection–dispersion equation, the workhorse model of solute transport, in which the balance between advective flow and dispersive spreading is captured by a single dimensionless quantity: the Peclet number. A high Peclet number means advection dominates and the water moves like a piston; a low Peclet number means dispersion smears everything extensively. Drawing on the classic field-data review by Gelhar and colleagues, the study notes that Peclet numbers observed in aquifers span an enormous range, from about 0.1 to 1000, with a best estimate near 10. When Suckow computed tracer output concentrations across that range, the consequences were sobering. For a Peclet number of 0.1, the Mean Residence Time exceeds the Peak Age by a factor of sixty; even at a Peclet number of 1, the gap is still a factor of six.

The behaviour of individual tracers adds further layers of complexity. For radioactive tracers with a constant atmospheric input — a reasonable approximation for argon-39, carbon-14 and krypton-81 — the calculated Tracer Age starts out equal to the Mean Residence Time and only gradually approaches the Peak Age as the water ages toward the tracer’s detection limit. For helium-4, a stable isotope produced underground at a roughly constant rate by the decay of uranium and thorium, the situation is different again: because helium mixes linearly rather than exponentially, its Tracer Age always reflects the Mean Residence Time and never the advective velocity. The practical result is that a single water sample, measured with a suite of modern tracers, will yield systematically different ages that increase in the order of tracer half-life: tritium, then argon-39, then carbon-14, then krypton-81, then helium-4.

Some of these discrepancies are large enough to rewrite interpretations of published datasets. The study highlights that reported contradictions between carbon-14 ages and helium-4 ages in major aquifers — differences previously explained by invoking a mysterious ‘crustal flux’ of helium rising from deep strata — may simply reflect low Peclet numbers. In the Great Artesian Basin of Australia, Torgersen and Clarke reported in 1985 that helium-based ages exceeded hydrologic age estimates by a factor of seventy-four, remarkably close to the factor of sixty that pure dispersion produces at a Peclet number of 0.1. Suckow is careful not to dismiss crustal degassing as a real phenomenon, but points out that such an external flux could only be quantified once the Peclet number is known — and under low-Peclet conditions the inferred flux would be substantially smaller than previously claimed.

The timing of this theoretical advance is no accident. For decades, the tracers needed to test these ideas simultaneously simply could not be measured on the same sample. That changed with the advent of Atom Trap Trace Analysis, or ATTA, a laser-based technique developed for krypton-81 and argon-39 that has turned isotopes once considered unmeasurable into routine tools. Before ATTA, only around 300 argon-39 groundwater measurements existed worldwide; today the two ATTA laboratories, in Hefei, China and Heidelberg, Germany, each process on the order of a hundred samples per year. Combined with the established workhorses tritium–helium, radiocarbon and chlorine-36, and supplemented by new stable noble-gas methods, researchers can now assemble continuous groundwater dating records spanning from a few decades to more than a million years — precisely the range needed to exploit Suckow’s framework.

The practical payoff is a new method for determining Peclet numbers on time scales of centuries to many millennia, something field tracer tests and contaminant plume studies — typically confined to transport distances of tens to hundreds of metres — have never been able to deliver. The logic is elegant: because each tracer’s age responds differently to dispersion depending on its half-life, the spread of Tracer Ages measured along a flow path encodes the Peclet number itself. For Peclet numbers below about 2, the differences between tracers become large and systematic; above 2, all tracers converge on the same age. By fitting the advection–dispersion equation directly to multi-tracer data from a series of wells, both the advective velocity and the Peclet number can be recovered simultaneously. Suckow demonstrates the approach on two published datasets — the Guarani aquifer in South America and the western Great Artesian Basin in Australia — deriving Peclet numbers of roughly 0.2 and 0.1, and correspondingly higher flow velocities than the original studies had estimated, a result with direct consequences for groundwater resource management in arid regions.

The findings also cast new light on palaeoclimate records preserved in groundwater. Noble-gas palaeotemperatures dissolved in recharging water have long been used to reconstruct past climates, and multiple studies report that land temperatures during the Last Glacial Maximum were about six degrees Celsius cooler than today. But dispersion acts as a low-pass filter on any signal carried by groundwater. Suckow’s calculations show that at Peclet numbers of 10 or less, temporal variations in the palaeotemperature record are progressively ironed out, and the reconstructed glacial cooling becomes biased warm — by nearly a degree at a Peclet number of 10, and potentially by several degrees at lower values. The widespread six-degree figure, in other words, may partly be an artefact of dispersive smoothing, and the true Last Glacial Maximum cooling on land could have been colder than commonly stated. The study also suggests that groundwater realistically preserves climate signals only up to about 100,000 years, even under favourable transport conditions.

For practitioners, the message is a call to methodological reform. Tracer Ages, the study concludes, should only be interpreted as advective or piston-flow ages when the Peclet number is known to exceed 2 — a condition rarely demonstrated in historical studies. Tritium–helium ages deserve particular caution: for all realistic dispersive conditions with Peclet numbers below 10, they do not represent the movement of a concentration front, as generally assumed, but instead follow or exceed the Mean Residence Time before levelling off with distance. The strongest recommendation is to measure as many tracers with different time scales as possible on every sample along a flow path, since no single tracer can disentangle velocity from dispersion. In an era when aquifers supply drinking water to billions and host critical infrastructure from nuclear waste repositories to carbon storage sites, knowing how water — and whatever it carries — actually moves underground has never mattered more. What was once dismissed as pedantic quibbling over definitions now looks like the key to one of hydrogeology’s oldest unsolved problems.

Subject of Research: The effect of dispersion on tracer-derived groundwater ages and its use for deriving Peclet numbers in large-scale groundwater transport

Article Title: The effect of dispersion on the “age” of groundwater calculated from environmental tracers allows a novel way to derive Peclet numbers for large-scale groundwater transport

Article References: Suckow, A. (2026). The effect of dispersion on the “age” of groundwater calculated from environmental tracers allows a novel way to derive Peclet numbers for large-scale groundwater transport. Hydrogeology Journal. https://doi.org/10.1007/s10040-026-03156-6

Image Credits: AI Generated

DOI: 10.1007/s10040-026-03156-6

Keywords: groundwater, environmental tracers, dispersion, Peclet number, hydrogeology, radiocarbon dating, krypton-81, argon-39, helium-4, advection, Mean Residence Time, paleoclimate