Advection Model Research Articles

Observation-driven model for calculating water-harvesting potential from advective fog in (semi-)arid coastal regions

Abstract. Motivated by the need to find complementary water sources in (semi-)arid regions, we develop and assess an observation-driven model to calculate fog-harvesting water potential. We aim to integrate this model with routine meteorological data collected under complex meteorological and topographic conditions to characterize the advective fog phenomenon. Based on the mass balance principle, the Advective fog Model for (semi-)Arid Regions Under climate change (AMARU) offers insights into fog-water-harvesting volumes across temporal and spatial domains. The model is based on a simple thermodynamic approach to calculate the dependence of the liquid water content (rl) on height. Based on climatological fog collection records, we introduce an empirical efficiency coefficient. When combined with rl, this coefficient facilitates the estimation of fog-harvesting volumes (L m−2). AMARU's outputs are validated against in situ observations collected over Chile's coastal (semi-)arid regions at various elevations and during various years (2018–2023). The model's representations of the seasonal cycle of fog harvesting follow observations, with errors of ∼ 10 %. The model satisfactorily estimates the maximum rl (∼ 0.8 g kg−1) available for fog harvesting in the vertical column. To assess spatial variability, we combine the model with satellite-retrieved data, enabling the mapping of fog-harvesting potential along the Atacama coast. Our approach enables the application of the combined observation–AMARU model to other (semi-)arid regions worldwide that share similar conditions. Through the quantification of fog harvesting, our model contributes to water planning, ecosystem delimitation efforts, and the study of the climatological evolution of cloud water, among others.

Opposite effects of a reaction-driven viscosity decrease on miscible viscous fingering depending on the injection flow rate

When a less-viscous solution of a reactant $A$ displaces a more-viscous solution of another reactant $B$ , a fast bimolecular $A + B \rightarrow C$ reaction decreasing locally the viscosity can influence the viscous fingering (VF) instability taking place between the two miscible solutions. We show both experimentally and numerically that, for monotonic viscosity profiles, this decrease in viscosity has opposite effects on the fingering pattern depending on the injection flow rate. For high flow rates, the reaction enhances the shielding effect, creating VF patterns with a lower surface density, i.e. thinner fingers covering a smaller area. In contrast, for lower flow rates, the reaction stabilises the VF dynamics, i.e. delays the instability and gives a less-deformed displacement, reaching in some cases an almost-stable displacement. Nonlinear simulations of reactive VF show that these opposite effects at low or high flow rates can only be reproduced if the diffusivity of $A$ is larger than that of $B$ , which favours a larger production of the product $C$ and, hence, a larger viscosity decrease. The analysis of one-dimensional viscosity profiles reconstructed on the basis of a one-dimensional reaction–diffusion–advection model confirms that the VF stabilisation at low Péclet number and in the presence of differential diffusion of reactants originates from an optimum reaction-driven decrease in the gradient of the monotonic viscosity profile.

CHANG-ES

Context. Cosmic rays may be dynamically very important in driving large-scale galactic winds. Edge-on galaxies give us an outsider’s view of radio haloes, and of their extra-planar cosmic-ray electrons and magnetic fields. Aims. We present a new radio continuum imaging study of the nearby edge-on galaxy NGC 4217. We examine the distribution of extra-planar cosmic rays and magnetic fields. We observed it with both the Jansky Very Large Array (JVLA) in the S band (2–4 GHz) and the LOw Frequency ARray (LOFAR) at 144 MHz. Methods. We measured vertical intensity profiles and exponential scale heights. We re-imaged both the JVLA and LOFAR data at matched angular resolution in order to measure radio spectral indices between 144 MHz and 3 GHz. Confusing point-like sources were subtracted prior to imaging. We then fitted intensity profiles with cosmic-ray electron advection models, using an isothermal wind model that is driven by a combination of pressure from the hot gas and cosmic rays. Results. We discover a large-scale radio halo on the north-western side of the galactic disc. The morphology is reminiscent of a bubble extending up to 20 kpc from the disc. We find spectral ageing in the bubble, which allowed us to measure the advection speeds of the cosmic-ray electrons, which accelerate from 300 to 600 km s−1. Assuming energy equipartition between the cosmic rays and the magnetic field, we estimate the bubble may have been inflated by a modest 10% of the kinetic energy injected by supernovae over its dynamical timescale of 35 Myr. While no active galactic nucleus (AGN) has been detected, such activity in the recent past cannot be ruled out. Conclusions. Non-thermal bubbles with sizes of tens of kiloparsecs may be a ubiquitous feature of star-forming galaxies, and if so this would demonstrate the influence of feedback. Determining possible contributions by AGN feedback will require deeper observations.

Analysis of a vector-borne disease model with vector-bias mechanism in advective heterogeneous environment

Abstract This study proposed and analyzed a vector-borne reaction–diffusion–advection model with vector-bias mechanism and heterogeneous parameters in one-dimensional habitat. The basic reproduction number R 0 {{\mathfrak{R}}}_{0} in connection with principal eigenvalue of elliptic eigenvalue problem is characterized as the role of determining the threshold dynamics of the system. The main objective of this study is to investigate the asymptotic profiles and monotonicity of R 0 {{\mathfrak{R}}}_{0} with respect to diffusion rates and advection rates under certain conditions. Through exploring the level set of R 0 {{\mathfrak{R}}}_{0} , we also find that there exists a unique surface separating the dynamics. Our results also reveal that the infected hosts and vectors will aggregate at the downstream end if the ratio of advection rates and diffusion rates is sufficiently large.

Solar Wind With Field Lines and Energetic Particles (SOFIE) Model: Application to Historical Solar Energetic Particle Events

AbstractIn this paper, we demonstrate the applicability of the data‐driven solar energetic particle (SEP) model, SOlar‐wind with FIeld‐lines and Energetic‐particles (SOFIE), to simulate the acceleration and transport processes of SEPs and make forecast of the energetic proton flux at energies ≥10 MeV that will be observed near 1 AU. The SOFIE model is built upon the Space Weather Modeling Framework developed at the University of Michigan. In SOFIE, the background solar wind plasma in the solar corona and interplanetary space is calculated by the Stream‐Aligned Aflvén Wave Solar‐atmosphere Model(‐Realtime) driven by the near‐real‐time hourly updated Global Oscillation Network Group solar magnetograms. In the background solar wind, coronal mass ejections (CMEs) are launched by placing an force‐imbalanced magnetic flux rope on top of the parent active region, using the Eruptive Event Generator using Gibson‐Low model. The acceleration and transport processes are modeled by the Multiple‐Field‐Line Advection Model for Particle Acceleration. In this work, nine SEP events (Solar Heliospheric and INterplanetary Environment challenge/campaign events) are modeled. The three modules in SOFIE are validated and evaluated by comparing with observations, including the steady‐state background solar wind properties, the white‐light image of the CMEs, and the flux of solar energetic protons, at energies of ≥10 MeV.

Connecting the dots: Applying multispecies connectivity in marine park network planning

Marine ecosystems are highly dynamic, and their connectivity is affected by a complex range of biological, spatial, and oceanographic factors. Incorporating connectivity as a factor in the planning and management of marine protected areas (MPAs) is important yet challenging. Here, we implemented a novel integrative framework that uses intraspecific genetic and genomic data for multiple marine species to characterise connectivity across a recently established South Australian MPA network. We generated connectivity networks, estimated cross-species concordance of connectivity patterns, and tested the impact of key spatial and oceanographic factors on each species. Connectivity patterns varied markedly among species, but were most correlated among those with similar dispersal strategies. Ordination analyses revealed significant associations with both waterway distances and oceanographic advection models. Notably, waterway distances provided better predictive power in all-species combined analyses. We extended the practical relevance of our findings by employing spatial prioritisation with Marxan, using node values derived from both genetic and geographic connectivity networks. This allowed the identification of several priority areas for conservation, and substantiated the initial decision to employ spatial distance as a proxy for biological connectivity for the design of the South Australian marine park network. Our study establishes a baseline for connectivity monitoring in South Australian MPAs, and provides guidelines for adapting this framework to protected networks elsewhere in the world.

Advection-based multiframe iterative correction on PIV fields for improved pressure estimation

A novel method to improve the accuracy of pressure field estimation for advection-dominated flows from time-resolved Particle Image Velocimetry (PIV) data is proposed. Leveraging an advection model we can propagate in time velocity fields from each snapshot. The multiple time-series obtained from time propagation are used to smooth the nonphysical features in the original time-series. This correction is done iteratively. The technique reduces spatial noise by leveraging temporal information while simultaneously correcting temporal jitters using spatial data. Two validation methods are proposed to evaluate the method without knowing the true value of the pressure field. In this paper we provide a proof of the concept using a 3D synthetic dataset based on channel flow and a 2D PIV data set on the wake of a wing foil. Various noise models are tested by superimposing them onto the synthetic dataset, including Gaussian white noise and errors with spatial coherence. The results demonstrate that the proposed method outperforms conventional filters in improving the velocity and pressure fields from noisy velocity data, and in suppressing time jittering of the estimated pressure fields.

Dynamics of reaction–diffusion–advection system and its impact on river ecology in the presence of spatial heterogeneity

This study considers a two-species reaction–diffusion–advection (RDA) model in a heterogeneous advective environment with zero Neumann boundary conditions. We suppose that two species compete for the same food resource but have different diffusion and advection rates. The primary objective of this study is to investigate the global asymptotic stability and coexistence of steady state based on different and unequal diffusion and advection rates through theoretical and numerical analysis. We establish the local stability of two semi-trivial steady states of the competing species. Also, the non-existence of coexistence steady state is proved with the help of some non-trivial assumptions. Finally, we show the global stability with the help of monotone dynamical systems and combine the local stability and non-existence of coexistence steady state. If one species adopts a smaller diffusion and advection rate, the competition’s result depends on the advection and diffusion rate ratio. If the ratio is smaller, then the species will prevail. Also, the species with higher diffusion and smaller advection will win. Lastly, the effectiveness of the model in one and two-dimensional situations is shown by a series of numerical calculations, which is particularly important for environmental consideration.

Geochemical Signature of Deep Fluids Triggering Earthquake Swarm in the Noto Peninsula, Central Japan

AbstractOn New Year's Day 2024, a magnitude 7.6 event struck the Noto Peninsula in central Japan. Prior to this event, an intense earthquake swarm had persisted beneath the northeastern peninsula for more than five years. Geophysical evidence provides insight into the upwelling of deep fluids from the uppermost mantle that triggers the seismic swarm activity. The noble gases and their isotopes have been used as geochemical indicators to determine the origin of the fluids associated with the swarms and their upwelling. Gas samples collected from boreholes around the seismic source region are characterized by anomalously high 3He/4He ratios (∼3.9 RAcor), indicating infiltration of mantle fluids from the subcrustal lithosphere. Using a steady‐state advection model, we calculated mantle helium fluxes of 1.1–2.4 × 10−15 mol cm−2 a−1, similar to those estimated for other representative fault zones, such as the San Andreas and North Anatolian faults.

A nonlocal reaction–diffusion–advection model with free boundaries

A nonlocal reaction–diffusion–advection model with free boundaries

Phase-space entropy cascade and irreversibility of stochastic heating in nearly collisionless plasma turbulence.

We consider a nearly collisionless plasma consisting of a species of "test particles" in one spatial and one velocity dimension, stirred by an externally imposed stochastic electric field-a kinetic analog of the Kraichnan model of passive advection. The mean effect on the particle distribution function is turbulent diffusion in velocity space-known as stochastic heating. Accompanying this heating is the generation of fine-scale structure in the distribution function, which we characterize with the collisionless (Casimir) invariant C_{2}∝∫∫dxdv〈f^{2}〉-a quantity that here plays the role of (negative) entropy of the distribution function. We find that C_{2} is transferred from large scales to small scales in both position and velocity space via a phase-space cascade enabled by both particle streaming and nonlinear interactions between particles and the stochastic electric field. We compute the steady-state fluxes and spectrum of C_{2} in Fourier space, with k and s denoting spatial and velocity wave numbers, respectively. In our model, the nonlinearity in the evolution equationfor the spectrum turns into a fractional Laplacian operator in k space, leading to anomalous diffusion. Whereas even the linear phase mixing alone would lead to a constant flux of C_{2} to high s (towards the collisional dissipation range) at every k, the nonlinearity accelerates this cascade by intertwining velocity and position space so that the flux of C_{2} is to both high k and high s simultaneously. Integrating over velocity (spatial) wave numbers, the k-space (s-space) flux of C_{2} is constant down to a dissipation length (velocity) scale that tends to zero as the collision frequency does, even though the rate of collisional dissipation remains finite. The resulting spectrum in the inertial range is a self-similar function in the (k,s) plane, with power-law asymptotics at large k and s. Our model is fully analytically solvable, but the asymptotic scalings of the spectrum can also be found via a simple phenomenological theory whose key assumption is that the cascade is governed by a "critical balance" in phase space between the linear and nonlinear timescales. We argue that stochastic heating is made irreversible by this entropy cascade and that, while collisional dissipation accessed via phase mixing occurs only at small spatial scales rather than at every scale as it would in a linear system, the cascade makes phase mixing even more effective overall in the nonlinear regime than in the linear one.

A Quantile-Conserving Ensemble Filter Framework. Part III: Data Assimilation for Mixed Distributions with Application to a Low-Order Tracer Advection Model

Abstract The uncertainty associated with many observed and modeled quantities of interest in Earth system prediction can be represented by mixed probability distributions that are neither discrete nor continuous. For instance, a forecast probability of precipitation can have a finite probability of zero precipitation, consistent with a discrete distribution. However, nonzero values are not discrete and are represented by a continuous distribution; the same is true for rainfall rate. Other examples include snow depth, sea ice concentration, amount of a tracer or the source rate of a tracer. Some Earth system model parameters may also have discrete or mixed distributions. Most ensemble data assimilation methods do not explicitly consider the possibility of mixed distributions. The Quantile Conserving Ensemble Filtering Framework (Anderson 2022, 2023) is extended to explicitly deal with discrete or mixed distributions. An example is given using bounded normal rank histogram probability distributions applied to observing system simulation experiments in a low-order tracer advection model. Analyses of tracer concentration and tracer source are shown to be improved when using the extended methods. A key feature of the resulting ensembles is that there can be ensemble members with duplicate values. An extension of the rank histogram diagnostic method to deal with potential duplicates shows that the ensemble distributions from the extended assimilation methods are more consistent with the truth.

The convergence of high-accuracy three-point compact computational method for structural derivative anomalous diffusion–advection model

The convergence of high-accuracy three-point compact computational method for structural derivative anomalous diffusion–advection model

Feature Transportation Improves Graph Neural Networks

Graph neural networks (GNNs) have shown remarkable success in learning representations for graph-structured data. However, GNNs still face challenges in modeling complex phenomena that involve feature transportation. In this paper, we propose a novel GNN architecture inspired by Advection-Diffusion-Reaction systems, called ADR-GNN. Advection models feature transportation, while diffusion captures the local smoothing of features, and reaction represents the non-linear transformation between feature channels. We provide an analysis of the qualitative behavior of ADR-GNN, that shows the benefit of combining advection, diffusion, and reaction. To demonstrate its efficacy, we evaluate ADR-GNN on real-world node classification and spatio-temporal datasets, and show that it improves or offers competitive performance compared to state-of-the-art networks.

Modelling diagenetic reactions and secondary porosity generation in sandstones controlled by the advection of low‐molecular‐weight organic acids

AbstractHigher secondary porosity was observed in the centre of a sandstone unit in the Eocene Shahejie Formation fan delta front sandstones from the Bozhong Depression, Bohai Bay Basin. This differs from past studies showing secondary porosity mainly in the marginal parts of sandstones adjacent to shales. This study utilized reactive transport models involving low‐molecular‐weight organic acids (LMWOA) to discuss potential processes resulting in the contrary distribution of secondary porosity. An interface model simulating LMWOA diffusion from adjacent shales to the sandstone resulted in secondary porosity in sandstones adjacent to shales. In contrast, an advection model simulating advective transport of LMWOA parallel to the sandstone bedding successfully generated higher secondary porosity in the central part. The central part of the sandstone exhibited better grain sorting (greater depositional porosity) and significantly less early carbonate cements compared to the marginal sandstone parts. Consequently, the central part had greater porosity prior to the dissolution through LMWOA. The initially higher porosity in the central part allowed for a higher advective flux of LMWOA‐rich water and associated lower pH, resulting in decreased oligoclase saturation, higher oligoclase dissolution rates and ultimately higher secondary porosity. This study indicates that grain sorting during sediment deposition, early carbonate cementation, LMWOA production in adjacent shales, and advection processes collectively control the diagenetic reactions and the distribution of secondary porosity in sandstones.

Dynamical behavior of solutions of a reaction–diffusion–advection model with a free boundary

Dynamical behavior of solutions of a reaction–diffusion–advection model with a free boundary

Stress field disruption allows gas-driven microdeformation in bentonite to be quantified

Geological disposal of radioactive waste is being planned by many countries. Bentonite clay is often included in facility design, providing a barrier to radionuclide migration. Gas, generated by the waste or corrosion of waste canisters, may disrupt the properties of the bentonite. Robust prediction of this interaction is, therefore, necessary to demonstrate safe facility evolution. In some cases, gas may deform the clay, resulting in localised flow; however, the nature of this deformation has been widely debated. Accurate numerical representation of this behaviour has been limited by a shortage of information on the degree/distribution of deformation. Using experimental data from gas injection tests in bentonite, we show that first order fluctuations in the stress field can provide this information. We show that hundreds of microdeformation events can be detected, with similar characteristics to established fracturing phenomena, including earthquakes and acoustic emissions. We also demonstrate that stress field disruption (i) is spatially localised and (ii) has characteristics consistent with gas pathway ‘opening’ and ‘closure’ as gas enters and exits the clay, respectively. This new methodology offers fundamental insight and a new opportunity to parameterise and constrain gas advection models in clays and shales, substantially improving our capacity for safe facility design.

A Deep Learning Model for Precipitation Nowcasting Using Multiple Optical Flow Algorithms

Abstract The optical flow technique has advantages in motion tracking and has long been employed in precipitation nowcasting to track the motion of precipitation fields using ground radar datasets. However, the performance and forecast time scale of models based on optical flow are limited. Here, we present the results of the application of the deep learning method to optical flow estimation to extend its forecast time scale and enhance the performance of nowcasting. It is shown that a deep learning model can better capture both multispatial and multitemporal motions of precipitation events compared with traditional optical flow estimation methods. The model comprises two components: 1) a regression process based on multiple optical flow algorithms, which more accurately captures multispatial features compared with a single optical flow algorithm; and 2) a U-Net-based network that trains multitemporal features of precipitation movement. We evaluated the model performance with cases of precipitation in South Korea. In particular, the regression process minimizes errors by combining multiple optical flow algorithms with a gradient descent method and outperforms other models using only a single optical flow algorithm up to a 3-h lead time. Additionally, the U-Net plays a crucial role in capturing nonlinear motion that cannot be captured by a simple advection model through traditional optical flow estimation. Consequently, we suggest that the proposed optical flow estimation method with deep learning could play a significant role in improving the performance of current operational nowcasting models, which are based on traditional optical flow methods. Significance Statement The purpose of this study is to improve the accuracy of short-term rainfall prediction based on optical flow methods that have been employed for operational precipitation nowcasting. By utilizing open-source libraries, such as OpenCV, and commonly applied machine learning techniques, such as multiple linear regression and U-Net networks, we propose an accessible model for enhancing prediction accuracy. We expect that the improvement in prediction accuracy will significantly improve the practical application of operational precipitation nowcasting.

An interior penalty discontinuous Galerkin reduced order model for the variable coefficient advection–diffusion-reaction equation

An interior penalty discontinuous Galerkin reduced order model for the variable coefficient advection–diffusion-reaction equation

A second order directional split exponential integrator for systems of advection–diffusion–reaction equations

We propose a second order exponential scheme suitable for two-component coupled systems of stiff evolutionary advection–diffusion–reaction equations in two and three space dimensions. It is based on a directional splitting of the involved matrix functions, which allows for a simple yet efficient implementation through the computation of small sized exponential-like functions and tensor-matrix products. The procedure straightforwardly extends to the case of an arbitrary number of components and to any space dimension. Several numerical examples in 2D and 3D with physically relevant (advective) Schnakenberg, FitzHugh–Nagumo, DIB, and advective Brusselator models clearly show the advantage of the approach against state-of-the-art techniques.