Lateral Flows Research Articles

Hydrological modelling on atmospheric grids: using graphs of sub-grid elements to transport energy and water

Abstract. Land surface models (LSMs) use the atmospheric grid as their basic spatial decomposition because their main objective is to provide the lower boundary conditions to the atmosphere. Lateral water flows at the surface on the other hand require a much higher spatial discretization as they are closely linked to topographic details. We propose here a methodology to automatically tile the atmospheric grid into hydrological coherent units which are connected through a graph. As water is transported on sub-grids of the LSM, land variables can easily be transferred to the routing network and advected if needed. This is demonstrated here for temperature. The quality of the river networks generated, as represented by the connected hydrological transfer units, are compared to the original data in order to quantify the degradation introduced by the discretization method. The conditions the sub-grid elements impose on the time step of the water transport scheme are evaluated, and a methodology is proposed to find an optimal value. Finally the scheme is applied in an off-line version of the ORCHIDEE (Organising Carbon and Hydrology In Dynamic Ecosystems) LSM over Europe to show that realistic river discharge and temperatures are predicted over the major catchments of the region. The simulated solutions are largely independent of the atmospheric grid used thanks to the proposed sub-grid approach.

Effects of Lateral Flows on the Supercavitation and Hydrodynamic Characteristics of Underwater Series and Parallel High-Speed Projectiles

In this paper, the supercavitation of the parallel and tandem projectiles moving underwater with high-speed under the condition with/without lateral flows is numerically simulated by the volume of fraction (VOF) model. The motion of the projectiles was handled by the overlapping grid and six degrees of freedom (DOF) techniques. The supercavitation evolution and the hydrodynamic characteristics of the projectiles were analyzed for the parallel and tandem projectiles under different conditions. The results show that the cavity shape is symmetrical under the condition without lateral flows, but is no longer symmetrical under the conditions with lateral flows. The asymmetry of the cavity contour increases with the velocity of the lateral flow. For the parallel projectiles, the change trends of the axial velocity of projectile 1 and projectile 2 are nearly the same. The offset velocity of projectile 1 and projectile 2 increases with the increase in the velocity of the lateral flow. The deflection angle of projectile 1 decreases with the increase in the lateral flow velocity but that of projectile 2 increases with the increase in the lateral flow velocity. At t = 3.0 ms, the deflection angle of projectile 2 is up to 20° under the condition of the lateral flow velocity of 11.25%, while the deflection angle of projectile 1 and 2 under other conditions is in the range of 5°. For the tandem projectiles, the axial velocity of projectile 1 gradually decreases. The change trend of the axial velocity of projectile 2 at first is the same as that of projectile 1, and then the change is dependent on the velocity of the lateral flow. Under the condition of the lateral flow velocity with 11.25%Vp, projectile 2 cannot enter the cavity of the front projectile. The change trend of the axial velocity of projectile 2 is similar as but somewhat slower than that of projectile 1. For the parallel projectiles, the ballistic stability of the projectile on the oncoming side is better than that of the projectile on the backflow side. Whether parallel or tandem projectiles, the ballistic stability of projectile 2 becomes worse with the increase in the lateral flow velocity.

Distribution and accumulation of heavy metals in the catchment catenary complex and bottom sediments of the water body in an urban environment

Problem Statement. The pollutant intake into water bodies is one of the issues of urban areas. The pollutant input from the residential area of the city with surface runoff can many times exceed the input of pollutants from industrial and recreational areas, as well as from point pollutant sources. The objective of the study is 1) assess the distribution of chemical elements in catchments of water bodies in an urbanised area, 2) accumulation of chemical elements in solid matter of bottom sediments of surface water bodies with catchments in the functional areas of the city, 3) identify the main mechanisms of transfer of elements in solid matter from catchments to water bodies. The study was conducted on the example of Ekaterinburg (Russia). The material for the study consisted of the results of a landscape environmental and geochemical survey carried out in the city area in 2019–2021. Results. The distributions of element concentrations between functional landscape zones in the catenaries of the Kharitonovsky Garden and Chemodanchik reservoir catchments in Ekaterinburg were obtained. The distributions of metal concentrations in the catchment components show a tendency for the transfer of substance of different origin from the landscape components by lateral migration flows to the local basis of denudation (a drainless surface water body). At the same time in the bottom sediments of the reservoir there is a multiple accumulation of both pollutants and elements of typomorphic association. Dust fractions are the main carrier of contaminants in catchments.

Carbon fluxes and soil carbon dynamics along a gradient of biogeomorphic succession in alpine wetlands of Tibetan Plateau.

Hydrological changes under climate warming drive the biogeomorphic succession of wetlands and may trigger substantial carbon loss from the carbon-rich ecosystems. Although many studies have explored the responses of wetland carbon emissions to short-term hydrological change, it remains poorly understood how the carbon cycle evolves with hydrology-driven wetland succession. Here, we used a space-for-time approach across hydrological gradients on the Tibetan Plateau to examine the dynamics of ecosystem carbon fluxes (carbon dioxide (CO2) and methane (CH4)) and soil organic carbon pools during alpine wetland succession. We found that the succession from mesic meadow to fen changed the seasonality of both CO2 and CH4 fluxes, which was related to the shift in plant community composition, enhanced regulation of soil hydrology and increasing contribution of spring-thaw emission. The paludification caused a switch from net uptake of gaseous carbon to net release on an annual timescale but produced a large accumulation of soil organic carbon. We attempted to attribute the paradox between evidence from the carbon fluxes and pools to the lateral carbon input and the systematic changes of historical climate, given that the wetlands are spatially low-lying with strong temporal climate-carbon cycle interactions. These findings demonstrate a systematic change in the carbon cycle with succession and suggest that biogeomorphic succession and lateral carbon flows are both important for understanding the long-term dynamics of wetland carbon footprints.

The effects of swirling purge leakage on aerothermal performance of flat and non-axisymmetric endwalls

The relative rotation of turbine rotor determines the velocity triangle of the purge flow, which significantly influences the aerothermal performance of turbine endwalls. In this paper, a turbine cascade model is constructed to simulate the relative motion effect between the rotor endwall and the purge leakage. The effects of the swirl ratio of the purge leakage on the aerothermal performance of two endwall schemes (flat endwall and non-axisymmetric endwall) are investigated and compared. The results show that due to the relative motion, the purge leakage's flow direction and migration trajectory shift towards the blade suction side. The cooling jets tend to push the boundary layer towards the suction side, thus enhancing the lateral secondary flows. At a low MFR, with the decrease of swirl ratio, both endwalls' film cooling effectiveness is gradually reduced, with the aerodynamic performance and heat transfer coefficient changing very little. At a high MFR, with the decrease of swirl ratio, the aerodynamic loss and heat transfer coefficient of both endwalls are gradually increased, while the endwall film cooling effectiveness is gradually decreased. Globally, compared to the flat endwall, the non-axisymmetric endwall can dramatically enhance the film cooling effectiveness while effectively reducing the aerodynamic loss and heat transfer levels for all swirl ratios and MFRs investigated.

3-D azimuthal anisotropy structure reveals different deformation modes of the crust and upper mantle in the southeastern Tibetan Plateau

The tectonic evolution and deformation process of the southeastern Tibetan Plateau has been one of the focuses of the geoscience community in recent decades. However, the crustal and mantle deformation mechanism in the southeastern Tibetan Plateau is still under debate. Seismic anisotropy inferred from surface wave tomography could provide critical insights into the deformation mechanism of the Earth’s tectonosphere. Here, we constructed a 3-D azimuthal anisotropy velocity model with Rayleigh wave phase velocity dispersion data from 132 permanent stations to analyze the deformation modes in the southeastern Tibetan Plateau. In the upper crust, the azimuthal anisotropy near the main strike-slip faults exhibits strong magnitude with fast axis subparallel to the fault strike, which is consistent with the rigid block extrusion pattern. In the mid-lower crust, two low-velocity anomalies appeared beneath the Sonpan-Ganzi Terrane and Xiaojiang Fault zone with strong azimuthal anisotropy, which may indicate ductile deformation of the weak mid-lower crust. However, the two low-velocity anomalies are separated by a high-velocity barrier with weak azimuthal anisotropy in the inner zone of the Emeishan large igneous province. In the upper mantle, the anisotropy pattern is relatively simple in the rigid Yangtze Craton and mainly represents fossil anisotropy. In the southern part, the lithosphere thinned beneath the Indochina and Cathaysia Blocks, and the anisotropy is plausibly caused by the upwelling and lateral flows of upwelling hot asthenospheric materials.

Flow around porous square cylinders with a periodic and scalable structure

This study experimentally explores the effect of permeability as an isolated control parameter on the downstream wake structure and the aerodynamic properties of the porous square cylinder. An addictive manufacturing technique was utilized to fabricate the porous cylinder, comprised of a simple cubic lattice structure. This unique manufacturing technique, coupled with a periodic and scalable lattice structure, allows us to decouple the permeability from the porosity. Based on permeability measurements in this study, Darcy number (Da) of the porous cylinder varies in a range of 2.44×10−5−4.07×10−4, while its porosity (Φ) is fixed at 0.7. Interesting features in the downstream wake are observed due to the mutual interaction between longitudinal and lateral bleeding flows. This mutual interplay prevents wake entrainment, relocating a recirculation bubble downstream and making its size smaller with increasing Da. When Da>2.0×10−4, in particular, a steady wake is observed in the near-wake despite the low degree of porosity. Finally, we proposed a new approach to defining the length scale of the flow adjustment that is suitable for the porous square cylinder and comparable to the porous cylinder with a circular cross-section.

Effects of inlet junctions on horizontally stratified flows

Horizontally stratified flows can be seen in a wide variety of micro-scale engineering problems. Recent studies have shown that diffusion at the interface between two liquids leads to a lateral flow, causing the fluid to rotate around the central axis of the channel. This lateral flow has the potential to disrupt the intended mechanism of the device or can be exploited for new device designs. The present investigation presents numerical and experimental results that provide important insights into the effects of the inlet junction on the flow field throughout the microfluidic device. The effects of four different archetypal inlet junctions—an idealized single inlet, counter-flow T junction, perpendicular flow T junction, and Y junction are considered. The results show that counter-flow T junction results in the least amount of lateral flow, while the straight channel results in the highest. The Y channel induces the second least rotation, and the perpendicular T junction creates slightly stronger lateral flows. Furthermore, based on lateral streamlines, it is suggested that the reason for the difference between these junctions can be explained by the interaction of the Dean vortices formed by the rotation of the fluid at the junction and the interaction of the Dean flow with the diffusion-induced vortices. To test this hypothesis, a less common junction (Y junction with angles higher than 180°) is modeled and has shown to reduce the lateral flow even further. Understanding the differences between the junctions would allow for more efficient microfluidic designs for various applications.

Automatic water level regulator with flexible working bodies in form of partition structure for trapezoidal channels

To improve the designs of hydraulic automatic water level regulators with flexible working bodies for channels, the object of research was developing and studying an innovative design of an autoregulator of the water level with flexible working bodies in the form of a partition structure for trapezoidal channels. The study℉s main purpose was to create a design for trapezoidal channels that do not allow channel narrowing and provides automatic level control, draining excess water, washing deposits in front of the partition, and determining its throughput. The developed design consists of a gate with flexible working bodies and a water level regulator combined with it. The article presents a theoretical formula for determining the flow rate of lateral water flows through the gate of the water level autoregulator. Experimental studies were carried out on an experimental installation by the method of physical modeling using the criterion of geometric similarity of the model and nature. As a result of these studies, simpler formulas were obtained for determining the flow rate of lateral water flows through the gate and a formula for determining the total flow rate of water passing through the gate of the water level autoregulator with flexible working bodies for trapezoidal channels for use during operation.

Autoregulatory of water level with flexible working bodies for partition structures on channels

To improve the existing designs of hydraulic automatic gates with flexible working bodies for partition structures on channels, the object of the study was the development and study of an innovative design of an autoregulator of the water level with flexible working bodies. The study's main objective was to create a structure that provides automatic level control, discharge of excess water, washing of deposits in front of the partition, and determining its throughput. The developed design consists of a gate with flexible working bodies and a water level regulator combined with it. The article provides a theoretical formula for determining the flow rate of lateral water flows through the gate of the water level autoregulator. Experimental studies were carried out on an experimental installation by the method of physical modeling using the criterion of geometric similarity of the model and nature. As a result of these studies, simpler formulas were obtained for determining the flow rate of lateral water flows through the gate and a formula for determining the total flow rate of water passing through the gate of the water level autoregulator with flexible working bodies for use during operation.

Tangential Navier–Stokes equations on evolving surfaces: Analysis and simulations

The paper considers a system of equations that models a lateral flow of a Boussinesq–Scriven fluid on a passively evolving surface embedded in [Formula: see text]. For the resulting Navier–Stokes type system, posed on a smooth closed time-dependent surface, we introduce a weak formulation in terms of functional spaces on a space-time manifold defined by the surface evolution. The weak formulation is shown to be well-posed for any finite final time and without smallness conditions on data. We further extend an unfitted finite element method, known as TraceFEM, to compute solutions to the fluid system. Convergence of the method is demonstrated numerically. In another series of experiments we visualize lateral flows induced by smooth deformations of a material surface.

Opportunities for variable rate application of nitrogen under spatial water variations in rainfed wheat systems—an economic analysis

In fields of undulating topography, where rainfed crops experience different degrees of water stress caused by spatial water variations, yields vary spatially within the same field, thus offering opportunities for variable rate application (VRA) of nitrogen fertilizer. This study assessed the spatial variations of yield gaps caused by lateral flows from high to low points, for rainfed wheat grown in Córdoba, Spain, over six consecutive seasons (2016–2021). The economic implications associated with multiple scenarios of VRA adoption were explored through a case study and recommendations were proposed. Both farm size (i.e., annual sown area) and topographic structure impacted the dynamics of investment returns. Under current policy-price conditions, VRA adoption would have an economic advantage in farms similar to that of the case study with an annual sown area greater than 567 ha year−1. Nevertheless, current trends in energy prices, transportation costs and impacts on both cereal prices and fertilizers costs enhance the viability of VRA adoption for a wider population of farm types. The profitability of adopting VRA improves under such scenarios and, in the absence of additional policy support, the minimum area for adoption of VRA decreases to a range of 68–177 ha year−1. The combination of price increases with the introduction of an additional subsidy on crop area could substantially lower the adoption threshold down to 46 ha year−1, making VRA technology economically viable for a much wider population of farmers.

A Regime Diagram for Internal Lee Waves in Coastal Plain Estuaries

Abstract Using an idealized channel representative of a coastal plain estuary, we conducted numerical simulations to investigate the generation of internal lee waves by lateral circulation. It is shown that the lee waves can be generated across all salinity regimes in an estuary. Since the lateral currents are usually subcritical with respect to the lowest mode, mode-2 lee waves are most prevalent but a hydraulic jump may develop during the transition to subcritical flows in the deep channel, producing high energy dissipation and strong mixing. Unlike flows over a sill, stratified water in the deep channel may become stagnant such that a mode-1 depression wave can form higher up in the water column. With the lee wave Froude number above 1 and the intrinsic wave frequency between the inertial and buoyancy frequency, the lee waves generated in coastal plain estuaries are nonlinear waves with the wave amplitude Δh scaling approximately with , where V is the maximum lateral flow velocity and is the buoyancy frequency. The model results are summarized using the estuarine classification diagram based on the freshwater Froude number Frf and the mixing parameter M. The Δh decreases with increasing Frf as stronger stratification suppresses waves, and no internal waves are generated at large Frf. The Δh initially increases with increasing M as the lateral flows become stronger with stronger tidal currents, but decreases or saturates to a certain amplitude as M further increases. This modeling study suggests that lee waves can be generated over a wide range of estuarine conditions.

Subsurface Lateral Flows Buffer Riparian Water Stress Against Snow Drought

AbstractIn the Sierra Nevada, CA, the Mediterranean climate exposes montane forests to water stress during the summer drought. Normally, spring snowmelt alleviates summer water stress, especially in riparian ecosystems that receive subsurface lateral inputs from groundwater. However, snow drought could potentially eliminate these beneficial effects. This research investigates how subsurface lateral redistribution mediates hillslope‐scale vegetation responses to snow drought. We apply a spatially‐distributed ecohydrologic model (Regional Hydro‐Ecologic Simulation System (RHESSys)) to a snow‐dominated watershed in the Sierra Nevada. We incorporate observed sap flow data along a hillslope to estimate relative differences in water stress for upslope and riparian sites, and constrain RHESSys drainage parameter uncertainty. Our model results show that subsurface lateral inputs buffer riparian water stress against snow drought. For all drought types, both upslope and riparian sites experience substantial losses of net primary productivity (NPP), and on average upslope sites are more adversely affected (upslope loss of NPP = 45% vs. riparian = 28%). Dry droughts from a lack of rain or snow induce substantial loss of biomass for upslope and riparian trees because of low annual precipitation, but a small snowpack retained during cold, dry years slightly alleviates these effects and delays water stress by 2 weeks in riparian areas and 3 weeks upslope. While riparian forests are often buffered against drought stress, our study also shows that riparian forests can suffer from water stress. We found 21% of drought scenarios where riparian trees experience greater water stress than upslope trees that were mostly associated with wet and warm snow droughts.

Exploring the feasibility of using the soil temperature to identify preferential and lateral subsurface flows

AbstractSoil temperature can be influenced by rapidly infiltrating water. Deviations from a uniform soil heat distribution could result from vertical preferential flow (VPF) and lateral subsurface flow (LSF) events. The objective was to identify the effect of infiltration on the soil temperature time series in a lysimeter with forced vertical movement and that in a sloping field to distinguish between VPF and LSF. Wavelet coherence analysis (WCA) was used to analyze soil temperature time series measured in a Colluvic Regosol close to the surface (15‐cm depth) and below (80‐cm depth) in a horizon with possible LSF occurrence. The soil temperatures in these depths were correlated at a daily scale reflecting diurnal fluctuations of air temperatures. A correlation at a monthly scale was similar to the periodicity in the wavelet spectrum of the precipitation from May through October 2015. In this period, soil temperatures at 80‐cm depth changed faster in the lysimeter than in the field, indicating a dominating infiltration‐induced vertical heat movement in the lysimeter. When assuming a temperature‐dampening effect in the sloping field soil by laterally moving temperature‐equilibrated soil water, observed deviations in soil temperature profiles between lysimeter and field could be indicative for LSF in the field. However, LSF occurrence could only be verified by soil water content measurements for single rainfall events in October and May. The analysis was useful to identify qualitatively relevant events in a time series. For quantitative analysis, soil moisture data need to be considered.

Automated Supramolecular Polymerization in a Microflow: A Versatile Platform for Multistep Supramolecular Reactions.

This work reports a basic microflow system capable of performing multistep supramolecular polymerization. In this system, injection of the monomer, directional supramolecular copolymerization, removal of the unreacted monomer, and purification of the product supramolecular diblock copolymers are realized along a three-stream flow. When injecting a supramolecular polymer into the central stream of the three-stream flow, the supramolecular polymerization always occurs in the central flow, with the two lateral flows serving as supply and removal lines for the monomer. Employing two kinds of perylene bisimide derivatives as monomers, we confirmed that the reaction occurred selectively at the forward-facing terminus of the supramolecular polymer, along with recovery of the unreacted monomer, ultimately leading to a high-purity supramolecular diblock copolymer. Diblock copolymers are basic units for preparing multicomponent supramolecular block copolymers. Thus, connecting the present system in series would, in principle, result in a "microplant" capable of producing supramolecular polymers having desired inner complexity.

Experimental analysis of combined side weir-gate located on a straight channel

Flow measurement and control in open channel system for lateral flow is important to support the system management. The flow characteristics of combined side weir-gate are complicated due to changes in flow conditions along the side weir-gate section. Experimental investigation of the flow characteristics of both weir and sluice gates is crucial for predicting the flow through a combined side weir-gate structure. Although weir-gate structures are widely used for frontal flow in hydraulic structures, the same is not true for lateral flows. In this study, 650 laboratory tests were conducted to determine the flow characteristics of combined side weir-gate for subcritical flow, and the experimental results were analyzed to determine the effect of these characteristics and weir-gate geometry on discharge capacity. Interaction factor of combined side weir-gate is a function of the upstream Froude number, the ratio of gate opening to upstream flow depth, the ratio of distance between the top of the sluice gate and the weir crest to gate opening, the ratio of weir and gate length to upstream flow depth, and the ratio of weir and gate length to main channel width. Consequently, more discharge is passed through combined side weir-gate compared to side weir and sluice gates. The empirically derived equations for the discharge of combined side weir-gate show good compatibility with the experimental data.

Recent advances and opportunities in data assimilation for physics-based hydrological modeling

Data assimilation applications in integrated surface-subsurface hydrological models (ISSHMs) are generally limited to scales ranging from the hillslope to local or meso-scale catchments. This is because ISSHMs resolve hydrological processes in detail and in a physics-based fashion and therefore typically require intensive computational efforts and rely on ground-based observations with a small spatial support. At the other end of the spectrum, there is a vast body of literature on remote sensing data assimilation for land surface models (LSMs) at the continental or even global scale. In LSMs, some hydrological processes are usually represented with a coarse resolution and in empirical ways, especially groundwater lateral flows, which may be very important and yet often neglected. Starting from the review of some recent progress in data assimilation for physics-based hydrological models at multiple scales, we stress the need to find a common ground between ISSHMs and LSMs and suggest possible ways forward to advance the use of data assimilation in integrated hydrological models.

Study of hydraulic characteristics of trapezoidal piano key side weir using different approaches

Abstract Side weirs are widely used in hydraulic engineering applications. The studies on the subject have been generally focused on classical and labyrinth side weirs. However, the same is not true for piano key side weirs (PKSW) in a straight channel. The piano key weir (PKW) has high discharge capacity compared with classical weirs. In this study, the hydraulic characteristics of a trapezoidal piano key side weir (TPKSW) in straight channels were investigated experimentally. In all experiments, the hydraulic characteristics of nine TPKSW models were studied extensively using the De Marchi, Domínguez and Schmidt approaches in the subcritical flow regime, with Froude number range 0.12 < F1 < 0.87. The results show that a TPKSW provides better performance compared to traditional rectangular and triangular labyrinth side weirs. Specifically, for the 0.12 < F1 < 0.4 condition, the efficiencies of a TPKSW and trapezoidal labyrinth side weir are close to each other. A trapezoidal labyrinth side weir is more efficient than a TPKSW at larger Froude numbers. The discharge capacity of the TPKSW is 2.9 to 12 times higher than that of the rectangular side weir. Scatter diagrams were obtained for CPW and F1 numbers using various approaches available in the literature. The diagram generated by the De Marchi approach has much less scattering, compared to the diagrams generated by the Domínguez and Schmidt approaches. It has been determined that TPKSWs are an effective type of side weir in lateral flows. Lastly, an empirical equation was obtained for the discharge coefficient, which is in good agreement with the experimental data.

Explicitly modelling microtopography in permafrost landscapes in a land surface model (JULES vn5.4_microtopography)

Abstract. Microtopography can be a key driver of heterogeneity in the ground thermal and hydrological regime of permafrost landscapes. In turn, this heterogeneity can influence plant communities, methane fluxes, and the initiation of abrupt thaw processes. Here we have implemented a two-tile representation of microtopography in JULES (the Joint UK Land Environment Simulator), where tiles are representative of repeating patterns of elevation difference. Tiles are coupled by lateral flows of water, heat, and redistribution of snow, and a surface water store is added to represent ponding. Simulations are performed of two Siberian polygon sites, (Samoylov and Kytalyk) and two Scandinavian palsa sites (Stordalen and Iškoras). The model represents the observed differences between greater snow depth in hollows vs. raised areas well. The model also improves soil moisture for hollows vs. the non-tiled configuration (“standard JULES”) though the raised tile remains drier than observed. The modelled differences in snow depths and soil moisture between tiles result in the lower tile soil temperatures being warmer for palsa sites, as in reality. However, when comparing the soil temperatures for July at 20 cm depth, the difference in temperature between tiles, or “temperature splitting”, is smaller than observed (3.2 vs. 5.5 ∘C). Polygons display small (0.2 ∘C) to zero temperature splitting, in agreement with observations. Consequently, methane fluxes are near identical (+0 % to 9 %) to those for standard JULES for polygons, although they can be greater than standard JULES for palsa sites (+10 % to 49 %). Through a sensitivity analysis we quantify the relative importance of model processes with respect to soil moisture and temperatures, identifying which parameters result in the greatest uncertainty in modelled temperature. Varying the palsa elevation between 0.5 and 3 m has little effect on modelled soil temperatures, showing that using only two tiles can still be a valid representation of sites with a range of palsa elevations. Mire saturation is heavily dependent on landscape-scale drainage. Lateral conductive fluxes, while small, reduce the temperature splitting by ∼ 1 ∘C and correspond to the order of observed lateral degradation rates in peat plateau regions, indicating possible application in an area-based thaw model.