Advective Component Research Articles

A novel bicompartmental mathematical model of glioblastoma multiforme.

Glioblastoma multiforme (GBM) is the most common primary CNS neoplasm, and continues to have a dismal prognosis. A widely-used approach to the mathematical modeling of GBM involves utilizing a reaction-diffusion model of cell density as a function of space and time, which accounts for both the infiltrative nature of the tumor using a diffusion term, and the proliferation of tumor cells using a proliferation term. The current paper extends the standard models by incorporating an advection term to account for the so-called 'cell streaming' which is often seen with GBM, where some of the tumor cells seem to stream widely along the white matter pathways. The current paper introduces a bicompartmental GBM model in the form of coupled partial differential equations with a component of dispersive cells. The parameters needed for this model are explored. It is shown that this model can account for the rapid distant dispersal of GBM cells in the CNS, as well as such phenomena as multifocal gliomas with tumor foci distant from the core tumor site. The model suggests a higher percentage of tumor cells below the threshold of MRI images in comparison to the standard model. By incorporating an advection component, the proposed model is able to account for phenomena such as multicentric gliomas and rapid distant dispersion of a small fraction of tumor cells throughout the CNS, features important to the prognosis of GBM, but not easily accounted for by current models.

Heat and salinity budgets at the Stratus mooring in the southeast Pacific

The surface layer of the southeast Pacific Ocean (SEP) requires an input of cold, fresh water to balance heat gain, and evaporation from air-sea fluxes. Models typically fail to reproduce the cool sea surface temperatures (SST) of the SEP, limiting our ability to understand the variability of this climatically important region. We estimate the annual heat budget of the SEP for the period 2004–2009, using data from the upper 250 m of the Stratus mooring, located at 85°W 20°S, and from Argo floats. The surface buoy measures meteorological conditions and air-sea fluxes; the mooring line is heavily instrumented, measuring temperature, salinity, and velocity at more than 15 depth levels. We use a new method for estimating the advective component of the heat budget that combines Argo profiles and mooring velocity data, allowing us to calculate monthly profiles of heat advection. Averaged over the 6 year study period, we estimate a cooling advective heat flux of −41 ± 29 W m−2, accomplished by a combination of the mean gyre circulation, Ekman transport, and eddies. This compensates for warming fluxes of 32 ± 4 W m−2 due to air-sea fluxes and 7 ± 9 W m−2 due to vertical mixing and Ekman pumping. A salinity budget exhibits a similar balance, with advection of freshwater (−60 psu m) replenishing the freshwater lost through evaporation (47 psu m) and Ekman pumping (14 psu m).

Climatological monthly heat and freshwater flux estimates on a global scale from Argo

AbstractThe global pattern of climatological monthly heat and freshwater fluxes at the ocean surface is estimated using Argo temperature and salinity profile data for the period 2004–2013. Temperature or salinity changes are calculated in a volume of water above an isopycnal that is below the mixed layer and not subject to mixed‐layer entrainment. Horizontal advection components from geostrophic velocity and from Ekman transport, based on wind stress, are also included. The climatological monthly heat or freshwater flux at the ocean surface is estimated as the sum of advective and time tendency contributions. The air‐sea flux estimates from Argo are described in global maps and basin‐wide integrals, in comparison to atmospheric reanalysis data and to air‐sea flux products based on observations. This ocean‐based estimate of surface fluxes is consistent with property variations in the subsurface ocean and indicates greater amplitude for the climatological monthly heat flux values in the subtropics compared to other products. Similarly, the combination of Argo freshwater flux and reanalysis evaporation, suggests greater amplitude for climatological monthly precipitation in the tropics.

Comparison of heuristic and empirical approaches for estimating reference evapotranspiration from limited inputs in Iran

Accurate estimation of reference evapotranspiration (ET0) values is of crucial importance in hydrology, agriculture and agro-meteorology issues. The present study reports a comprehensive comparison of empirical and semi empirical ET0 equations with the corresponding Heuristic Data Driven (HDD) models in a wide range of weather stations in Iran. Artificial Neural Networks (ANNs), Adaptive Neuro-Fuzzy Inference System (ANFIS), Support Vector Machine (SVM) and Gene Expression Programming (GEP) techniques are applied for modeling ET0 values considering different data management scenarios, and compared with corresponding Hargreaves–Samani (HS), Makkink (MK), Priestley–Taylor (PT), and Turc (T) ET0 models as well as their linear and non-linear calibrated versions along with the regression-based Copais algorithm. The obtained results confirm the superiority of GEP-based models. Further, the HDD models generally outperform the applied empirical models. Among the empirical models, the calibrated HS model found to give the most accurate results in all local and pooled scenarios, followed by the Copais and the calibrated PT models. In both local and pooled applications, the calibrated HS equation should be applied when no training data are available for the use of HDD models. The best results of the models correspond to the humid regions, while the arid regions provide the poorest estimates. This may be attributed to higher ET0 values associated with these stations and the high advective component of these locations.

Gross Moist Stability and MJO Simulation Skill in Three Full-Physics GCMs

Abstract Previous studies have demonstrated a link between gross moist stability (GMS) and intraseasonal variability in theoretical and reduced-complexity models. In such simplified models, MJO-like moisture modes—convectively coupled tropical disturbances akin to the MJO whose formation and dynamics are linked to moisture perturbations—develop only when GMS is either negative or “effectively” negative when considering additional sources of moist entropy. These simplified models typically use a prescribed, time-independent GMS value. Limited work has been done to assess GMS and its connection to intraseasonal variability in full-physics general circulation models (GCMs). The time-mean and intraseasonal behavior of normalized GMS (NGMS) are examined in three pairs of GCMs to elucidate the possible importance of NGMS for the MJO. In each GCM pair, one member produces weak intraseasonal variability, while the other produces robust MJOs because of a change in the treatment of deep convection. A strong linear correlation between time-mean NGMS and MJO simulation skill is observed, such that GCMs with less positive NGMS produce improved MJO eastward propagation. The reduction in time-mean NGMS is primarily due to a sharp drop to negative values in the NGMS component related to vertical advection, while the horizontal advection component has a less clear relationship with MJO simulations. Intraseasonal fluctuations of anomalous NGMS modulate the magnitude of background NGMS but generally do not change the sign of background NGMS. NGMS declines ahead of peak MJO rainfall and increases during and after heaviest precipitation. Total NGMS fluctuates during MJO passage but remains positive, suggesting that other sources of moist entropy are required to generate an effectively negative NGMS.

Methods and uncertainties in the experimental assessment of horizontal advection

The eddy covariance technique is prone to underestimating the net ecosystem CO2 exchange under stable atmospheric conditions, which mostly occur at night time when other terms of the CO2 mixing ratio conservation equation (i.e. advection) may become significant. Given the potential large impact of night-time flux measurements on the estimation of the ecosystem carbon budget, it is important to develop reliable methodologies for the assessment of advective fluxes. Accurate CO2 concentration gradient measurements are needed for a precise estimation of the advection components. For this purpose a novel measurement system, designed to overcome some of the key issues of CO2 concentration measurements, has been developed and deployed at the IT-Ren eddy covariance site (Renon, BZ, Italy). In particular, the system is optimized for minimizing both the spatial and temporal uncertainty of the CO2 concentration gradients by adopting buffer volumes, a ramified sampling scheme, and a rapid switch between lines.Different configurations of the measurement system were used to quantify the uncertainty of horizontal concentration gradients and to disentangle its sources. The discrete temporal sampling was the major source of uncertainty, accounting for 54% of the total uncertainty, while spatial sampling accounts for 39% of the total uncertainty in stable conditions and for 35% in unstable conditions, with the remaining uncertainty being explained by the accuracy of the instrumental set-up (analyser, pumps and valves) (7% and 11% for stable and unstable atmospheric conditions, respectively, corresponding to ∼0.2ppm). Finally, we investigated the effect of buffer volumes on the uncertainty generated by a discrete temporal sampling in the estimation of horizontal advection. The use of volumes with a mean residence time equal to the turn-over time of the manifold reduced by half the standard deviation in the time series of horizontal advection (from 3.8 to 1.8μmolm−2s−1). The measurement system in its final configuration is currently used to quantify storage and advective fluxes at the site.

Predicting reference evapotranspiration for screenhouse-grown crops

The purpose of the study is to estimate the reference evapotranspiration of screenhouse-grown crops (ETo,in) from routine outside weather data and main screenhouse characteristics. To this aim, all the microclimatic variables required to calculate ETo,in by means of the standard FAO-56 Penman–Monteith formula were measured under three cultivated (sweet-pepper, spring–summer cycle) screenhouses for a two months period observation (Aug–Sept 2012) in a Mediterranean climate (Eastern Central Greece). The screenhouses differed in transmittance to solar radiation (τ) and wind ratio (ω=ratio of inside-to-outside wind speed): (i) a pearl insect-proof screen (IP-1, τ≈0.76, ω≈0.19), (ii) a white insect proof screen (IP-2, τ≈0.58, ω≈0.20), and (iii) a green shade-screen (GS, τ≈0.56 and ω≈0.43). We quantified and analysed at daily scale the evolution of the radiative (ETrad,in) and advective (ETadv,in) components of ETo,in, ETrad,in and ETadv,in were expressed as a function of the corresponding outside values (ETrad,out and ETadv,out) through two reduction ratios (ζrad=ETrad,in/ETrad,out and ζadv=ETadv,in/ETadv,out). ζrad and ζadv could be expressed as linear functions of τ and ω respectively. Based on this finding, we proposed an additive model of the form ETo,in=ζrad ETrad,out+ζadv ETadv,out. The predictive performance of the model was fair (RMSE=0.11mmday−1). The proposed model, based only on outside climate data and the knowledge of two screenhouse-related parameters, provides a straightforward way to estimate screenhouse ETo, a necessary step towards the determination of screenhouse-crops water requirements.

The Representation of Ocean Circulation and Variability in Thermodynamic Coordinates

Abstract The ocean’s circulation is analyzed in Absolute Salinity SA and Conservative Temperature Θ coordinates. It is separated into 1) an advective component related to geographical displacements in the direction normal to SA and Θ isosurfaces and 2) into a local component, related to local changes in SA–Θ values, without a geographical displacement. In this decomposition, the sum of the advective and local components of the circulation is equivalent to the material derivative of SA and Θ. The sum is directly related to sources and sinks of salt and heat. The advective component is represented by the advective thermohaline streamfunction . After removing a trend, the local component can be represented by the local thermohaline streamfunction . Here, can be diagnosed using a monthly averaged time series of SA and Θ from an observational dataset. In addition, and are determined from a coupled climate model. The diathermohaline streamfunction is the sum of and and represents the nondivergent diathermohaline circulation in SA–Θ coordinates. The diathermohaline trend, resulting from the trend in the local changes of SA and Θ, quantifies the redistribution of the ocean’s volume in SA–Θ coordinates over time. It is argued that the diathermohaline streamfunction provides a powerful tool for the analysis of and comparison among ocean models and observation-based gridded climatologies.

Fully coupled methods for multiphase morphodynamics

We present numerical methods for a system of equations consisting of the two dimensional Saint–Venant shallow water equations (SWEs) fully coupled to a completely generalized Exner formulation of hydrodynamically driven sediment discharge. This formulation is implemented by way of a discontinuous Galerkin (DG) finite element method, using a Roe Flux for the advective components and the unified form for the dissipative components. We implement a number of Runge–Kutta time integrators, including a family of strong stability preserving (SSP) schemes, and Runge–Kutta Chebyshev (RKC) methods. A brief discussion is provided regarding implementational details for generalizable computer algebra tokenization using arbitrary algebraic fluxes. We then run numerical experiments to show standard convergence rates, and discuss important mathematical and numerical nuances that arise due to prominent features in the coupled system, such as the emergence of nondifferentiable and sharp zero crossing functions, radii of convergence in manufactured solutions, and nonconservative product (NCP) formalisms. Finally we present a challenging application model concerning hydrothermal venting across metalliferous muds in the presence of chemical reactions occurring in low pH environments.

Seasonal variations in suspended-sediment dynamics in the tidal reach of an estuarine tributary

Abstract Quantifying sediment supply from estuarine tributaries is an important component of developing a sediment budget, and common techniques for estimating supply are based on gages located above tidal influence. However, tidal interactions near tributary mouths can affect the magnitude and direction of sediment supply to the open waters of the estuary. We investigated suspended-sediment dynamics in the tidal reach of Corte Madera Creek, an estuarine tributary of San Francisco Bay, using moored acoustic and optical instruments. Flux of both water and suspended-sediment were calculated from observed water velocity and turbidity for two periods in each of wet and dry seasons during 2010. During wet periods, net suspended-sediment flux was seaward; tidally filtered flux was dominated by the advective component. In contrast, during dry periods, net flux was landward; tidally filtered flux was dominated by the dispersive component. The mechanisms generating this landward flux varied; during summer we attributed wind–wave resuspension in the estuary and subsequent transport on flood tides, whereas during autumn we attributed increased spring tide flood velocity magnitude leading to local resuspension. A quadrant analysis similar to that employed in turbulence studies was developed to summarize flux time series by quantifying the relative importance of sediment transport events. These events are categorized by the direction of velocity (flood vs. ebb) and the magnitude of concentration relative to tidally averaged conditions (relatively turbid vs. relatively clear). During wet periods, suspended-sediment flux was greatest in magnitude during relatively turbid ebbs, whereas during dry periods it was greatest in magnitude during relatively turbid floods. A conceptual model was developed to generalize seasonal differences in suspended-sediment dynamics; model application to this study demonstrated the importance of few, relatively large events on net suspended-sediment flux. These results suggest that other estuarine tributaries may alternate seasonally as sediment sinks or sources, leading to the conclusion that calculations of estuary sediment supply from local tributaries that do not account for tidal reaches may be overestimates.

Solute Mass Transfer Effects in Two‐Dimensional Dual‐Permeability Modeling of Bromide Leaching From a Tile‐Drained Field

Preferential flow (PF) depends on processes and structures in soil at the small scale and can affect flow and transport processes at much larger scales. For studying PF processes, the discharge and solute effluent from subsurface drained experimental fields has frequently been used as a field‐integrated signal that included combined effects of macropore flow and lateral transport toward the drain. The objective of this study was to better understand effects of the mass transfer coefficients on bromide (Br) leaching in a two‐dimensional (2D) dual‐permeability concept. The Br leaching was simulated for data of a Br tracer irrigation experiment on a drained field (5000 m2 area) at Bokhorst (Germany), where soils developed from glacial till sediments. Flow and transport in 2D vertical cross‐sections was described using a numerical 2D dual‐permeability model. For applied Br, influx of Br only in the soil matrix (SM) domain, only in the preferential flow (PF) domain, and proportional to the water influx in both domains was considered to assess the impact of small‐scale redistribution processes occurring at the structured soil surface on field‐ and plot‐scale transport. Three values of the water and four of the solute mass transfer rate coefficients were tested to imitate local effects (e.g., of clay‐organic coatings) on the inter‐domain mass transfer. The local‐scale solute mass transfer between PF and SM domains had a clear impact on Br concentrations in drain effluent at the field scale; concentrations mainly increased more rapidly with smaller values of the diffusive mass transfer coefficient. In the 2D flow domain, representing the plot scale, mass transfer rates were temporally and spatially variable with varying importance of diffusive and advective components depending on the influx rates; local effects were still significant at the field scale. Small‐scale properties and processes such as domain‐specific infiltration and mass transfer in structured soil seem important for improving the description of larger‐scale flow and transport processes.

Eddy parameterization challenge suite I: Eady spindown

The first set of results in a suite of eddy-resolving Boussinesq, hydrostatic simulations is presented. Each set member consists of an initially linear stratification and shear as in the Eady problem, but this profile occupies only a limited region of a channel and is allowed to spin-down via baroclinic instability. The diagnostic focus is on the spatial structure and scaling of the eddy transport tensor, which is the array of coefficients in a linear flux–gradient relationship. The advective (antisymmetric) and diffusive (symmetric) components of the tensor are diagnosed using passive tracers, and the resulting diagnosed tensor reproduces the horizontal transport of the active tracer (buoyancy) to within ±7% and the vertical transport to within ±12%. The derived scalings are shown to be close in form to the standard Gent–McWilliams (antisymmetric) and Redi diffusivity (symmetric) tensors with a magnitude that varies in space (concentrated in the horizontal and vertical near the center of the frontal shear) and time as the eddies energize. The Gent–McWilliams eddy coefficient is equal to the Redi isopycnal diffusivity to within ±6%, even as these coefficients vary with depth. The scaling for the magnitude of simulation parameters is determined empirically to within ±28%. To achieve this accuracy, the eddy velocities are diagnosed directly and used in the tensor scalings, rather than assuming a correlation between eddy velocity and the mean flow velocity where ±97% is the best accuracy achievable. Plans for the next set of models in the challenge suite are described.

Modelling the Surface Heat Flow Distribution in the Area of Brandenburg (Northern Germany)

A lithosphere scale geological model has been used to determine the surface heat flow component due to conductive heat transport for the area of Brandenburg. The modelling results have been constrained by a direct comparison with available heat flow measurements. The calculated heat flow captures the regional trend in the surface heat flow distribution which can be related to existing thermal conductivity variations between the different sedimentary units. An additional advective component due to topography induced regional flow and focused flow within major fault zones should be considered to explain the spatial variation observed in the surface heat flow.

Impact of tides in a baroclinic circulation model of the Adriatic Sea

AbstractThe impact of tides in the circulation of the Adriatic Sea is investigated by means of a nested baroclinic numerical ocean model. Tides are introduced using a modified Flather boundary condition at the open edge of the domain. The results show that tidal amplitudes and phases are reproduced correctly by the baroclinic model and tidal harmonic constants errors are comparable with those resulting from the most consolidated barotropic models. Numerical experiments were conducted to estimate and assess the impact of (i) the modified Flather lateral boundary condition; (ii) tides on temperature, salinity, and stratification structures in the basin; and (iii) tides on mixing and circulation in general. Tides induce a different momentum advective component in the basin, which in turn produces a different distribution of water masses in the basin. Tides impact on mixing and stratification in the River Po region (northwestern Adriatic) and induce semidiurnal fluctuations of salinity and temperature, in all four seasons for the former and summer alone for the latter. A clear presence of internal tides was evidenced in the northern Adriatic Sea basin, corroborating previous findings.

Investigation of Large-Scale Atmospheric Moisture Budget and Land Surface Interactions over U.S. Southern Great Plains including for CLASIC (June 2007)

Abstract The atmospheric moisture budget and surface interactions for the southern Great Plains are evaluated for contrasting May–June periods (1998, 2002, 2006, and 2007) as background for the Cloud and Land Surface Interaction Campaign (CLASIC) of (wet) 7–30 June 2007. Budget components [flux divergence (MFD), storage change (dPW), and inflow (IF/A)] are estimated from North American Regional Reanalysis data. Precipitation (P) is calculated from NCEP daily gridded data, evapotranspiration (E) is obtained as moisture budget equation residual, and the recycling ratio (PE/P) is estimated using a new equation. Regional averages are presented for months and five daily P categories. Monthly budget results show that E and E − P are strongly positively related to P; E − P generally is positive and balanced by positive MFD that results from its horizontal velocity divergence component (HD, positive) exceeding its horizontal advection component (HA, negative). An exception is 2007 (CLASIC), when E − P and MFD are negative and supported primarily by negative HA. These overall monthly results characterize low P days (≤0.6 mm), including for nonanomalous 2007, but weaken as daily P approaches 4 mm. In contrast, for 4 < P ≤ 8 mm day−1 E − P and MFD are moderately negative and balanced largely by negative HD except in 2007 (negative HA). This overall pattern was accentuated (including for nonanomalous 2007) when daily P > 8 mm. Daily PE/P ratios are small and of limited range, with P category averages 0.15–0.19. Ratios for 2007 are above average only for daily P ≤ 4 mm. CLASIC wetness principally resulted from distinctive MFD characteristics. Solar radiation, soil moisture, and crop status/yield information document surface interactions.

Weakly Forced Mock Walker Cells

Abstract Mock Walker cells driven by weak sea surface temperature (SST) forcing are studied using planetary-scale cloud system–resolving simulations and a simplified framework that represents convection with its linear response functions and parameterizes the large-scale flow based on the gravity wave equation. For sinusoidal SST forcings of the same amplitude, as the horizontal domain size increases, the mock Walker cells strengthen substantially and shorter vertical scales in the vertical velocity profile diminish. This is explained by the fact that temperature anomalies required to sustain a vertical velocity profile of given amplitude are stronger in cases of larger horizontal and smaller vertical scales. Such temperature anomalies become significant at planetary scales so that properly accounting for the horizontal momentum balance, including convective momentum transport (CMT), becomes necessary, while a weak temperature gradient approach that neglects horizontal momentum balance is no longer adequate. The downward advection component of the CMT in particular is important for capturing a number of features of the mock Walker cells. The extent of convective organization also affects the mock Walker cell through its effects on the sensitivities of convective heating and moistening to temperature and moisture anomalies. For strongly organized convection with deep inflows, these sensitivities are consistent with a layer mode of convective overturning, instead of the parcel mode as in unorganized convection, resulting in a weaker second baroclinic component in the mock Walker cells.

Evaluation of evaporation estimation methods for a covered reservoir in a semi-arid climate (south-eastern Spain)

Summary The main purpose of this study was to evaluate different methods of evaporation estimation for covered water reservoirs. A reservoir equipped with a suspended cover was fully monitored to register the evaporation rate and microclimate below the cover. The datasets were used to evaluate the performance of commonly used evaporation methods, namely energy budget, mass-transfer, combination (Penman and FAO-56 Penman–Monteith) and floating class-A pan. The mass-transfer formula based on the Sherwood number proposed for free convection conditions, which were observed to prevail below the cover, supplied reasonably good estimates of covered reservoir evaporation and it is a good option from a practical point of view, with low input data requirements. Detailed input data and modifications in the calculation of energy fluxes are required to get good evaporation estimations of covered surfaces with the energy budget and FAO-56 Penman–Monteith methods. Besides, some of the standard meteorological input data (such as wind speed at 2 m height) cannot be registered below the cover. Penman equation presented a poor performance related to the overestimation of the advective component for free convection conditions. The pan evaporation was found to be substantially higher than the reservoir evaporation, due to the particular characteristics of the tank, that increased surface temperature and hence evaporation rate. A simplified empirical mass-transfer formula was also proposed to estimate evaporation of covered water bodies from the only knowledge of the surface-to-air mixing ratio gradient.

Estimation of hydrogen sulfide emission rates at several wastewater treatment plants through experimental concentration measurements and dispersion modeling

The management and operation of wastewater treatment plants (WWTP) usually involve the release into the atmosphere of malodorous substances with the potential to reduce the quality of life of people living nearby. In this type of facility, anaerobic degradation processes contribute to the generation of hydrogen sulfide (H2S), often at quite high concentrations; thus, the presence of this chemical compound in the atmosphere can be a good indicator of the occurrence and intensity of the olfactory impact in a specific area. The present paper describes the experimental and modelling work being carried out by CEAM-UMH in the surroundings of several wastewater treatment plants located in the Valencia Autonomous Community (Spain). This work has permitted the estimation of H2S emission rates at different WWTPs under different environmental and operating conditions. Our methodological approach for analyzing and describing the most relevant aspects of the olfactory impact consisted of several experimental campaigns involving intensive field measurements using passive samplers in the vicinity of several WWTPs, in combination with numerical simulation results from a diagnostic dispersion model. A meteorological tower at each WWTP provided the input values for the dispersion code, ensuring a good fit of the advective component and therefore more confidence in the modelled concentration field in response to environmental conditions. Then, comparisons between simulated and experimental H2S concentrations yielded estimates of the global emission rate for this substance at several WWTPs at different time periods. The results obtained show a certain degree of temporal and spatial (between-plant) variability (possibly due to both operational and environmental conditions). Nevertheless, and more importantly, the results show a high degree of uniformity in the estimates, which consistently stay within the same order of magnitude. Implications: Estimating emissions to the atmosphere is usually considered a complex task, especially when such discharge comes from diffuse or uncontrolled sources. In any approach to air quality control, just from the point of view of increasing knowledge or as a management problem in order to reduce present levels of pollution, accurate estimation of emission rates is revealed as a fundamental step. Evaluation from an indirect method provides a useful methodology in such cases. Combination of dispersion modeling with experimental air concentration measurements permits one to obtain a first estimation of H2S emission rates at several wastewater treatment plants. In a subsequent refinement of the process, the initial constant average emissions calculated were improved, leading to the formulation of a time-varying emission model, as a function of environmental quantities.

Development of the thermally affected zone (TAZ) around a groundwater heat pump (GWHP) system: A sensitivity analysis

Open-loop groundwater heat pumps (GWHPs) are considered one of the most energy efficient and environmentally friendly air-conditioning systems for temperate zones. A fundamental aspect in GWHP plant design is early evaluation of the thermally affected zone (TAZ) that develops around the injection well. This is particularly important to avoid interference with previously existing groundwater uses (wells) and subsurface underground structures. Numerical modelling is useful for delineating temperature anomalies. We carry out numerical simulations and a sensitivity analysis for the subsurface parameters affecting the TAZ. Using the simulation results we obtain a relative hierarchy of significance for the parameters with respect to the final result and then apply this analysis to an actual site. The results of the analysis indicate that the hydrodynamic parameters correlated with groundwater flow such as the hydraulic conductivity and the gradient are highly important, particularly those relating to the advective heat flow component.

Errors in the upstream mobility scheme for countercurrent two-phase flow in heterogeneous porous media

In reservoir simulation, the upstream mobility scheme is widely used for calculating fluid flow in porous media and has been shown feasible for flow when the porous medium is homogeneous. In the case of flow in heterogeneous porous media, the scheme has earlier been shown to give erroneous solutions in approximating pure gravity segregation. Here, we show that the scheme may exhibit larger errors when approximating flow in heterogeneous media for flux functions involving both advection and gravity segregation components. Errors have only been found in the case of countercurrent flow. The physically correct solution is approximated by an extension of the Godunov and Engquist–Osher flux. We also present a new finite volume scheme based on the local Lax–Friedrichs flux and test the performance of this scheme in the numerical experiments.