Representation Of Fluxes Research Articles

Deep Learned Process Parameterizations Provide Better Representations of Turbulent Heat Fluxes in Hydrologic Models

AbstractDeep learning (DL) methods have shown great promise for accurately predicting hydrologic processes but have not yet reached the complexity of traditional process‐based hydrologic models (PBHM) in terms of representing the entire hydrologic cycle. The ability of PBHMs to simulate the hydrologic cycle makes them useful for a wide range of modeling and simulation tasks, for which DL methods have not yet been adapted. We argue that we can take advantage of each of these approaches by embedding DL methods into PBHMs to represent individual processes. We demonstrate that this is viable by developing DL‐based representations of turbulent heat fluxes and coupling them into the Structure for Unifying Multiple Modeling Alternatives (SUMMA), a modular PBHM modeling framework. We developed two DL parameterizations and integrated them into SUMMA, resulting in a one‐way coupled implementation which relies only on model inputs and a two‐way coupled implementation, which also incorporates SUMMA‐derived model states. Our results demonstrate that the DL parameterizations are able to outperform calibrated standalone SUMMA benchmark simulations. Further we demonstrate that the two‐way coupling can simulate the long‐term latent heat flux better than the standalone benchmark and one‐way coupled configuration. This shows that DL methods can benefit from PBHM information, and the synergy between these modeling approaches is superior to either approach individually.

Modifications to the K-Profile Parameterization with Nondiffusive Fluxes for Langmuir Turbulence

AbstractThe K-profile parameterization (KPP) is a common method to model turbulent fluxes in regional and global oceanic models. Many versions of KPP exist in the oceanic sciences community, and one of their main differences is how they take the effects of nonbreaking waves into account. Although there is qualitative consensus that nonbreaking waves enhance vertical mixing due to the ensuing Langmuir circulations, there is no consensus on the quantitative aspects and modeling approach. In this paper we use a recently developed method to estimate both components of KPP (the diffusive term, usually called local, and the nondiffusive component, usually called nonlocal) based on numerically simulated turbulent fluxes without any a priori assumptions about their scaling or their shape. Through this method we show that the cubic shape usually used in KPP is not optimal for wavy situations and propose new ones. Furthermore, we show that the formulation for the nondiffusive fluxes, which currently only depend on the presence of surface buoyancy fluxes, should also take wave effects into account. We also investigate how the application of these changes to KPP improves the representation of turbulent fluxes in a diagnostic approach when compared with previous models.

Comparing i-Tree Eco Estimates of Particulate Matter Deposition with Leaf and Canopy Measurements in an Urban Mediterranean Holm Oak Forest.

Trees and urban forests remove particulate matter (PM) from the air through the deposition of particles on the leaf surface, thus helping to improve air quality and reduce respiratory problems in urban areas. Leaf deposited PM, in turn, is either resuspended back into the atmosphere, washed off during rain events or transported to the ground with litterfall. The net amount of PM removed depends on crown and leaf characteristics, air pollution concentration, and weather conditions, such as wind speed and precipitation. Many existing deposition models, such as i-Tree Eco, calculate PM2.5 removal using a uniform deposition velocity function and resuspension rate for all tree species, which vary based on leaf area and wind speed. However, model results are seldom validated with experimental data. In this study, we compared i-Tree Eco calculations of PM2.5 deposition with fluxes determined by eddy covariance assessments (canopy scale) and particulate matter accumulated on leaves derived from measurements of vacuum/filtration technique as well as scanning electron microscopy combined with energy-dispersive X-ray spectroscopy (leaf scale). These investigations were carried out at the Capodimonte Royal Forest in Naples. Modeled and measured fluxes showed good overall agreement, demonstrating that net deposition mostly happened in the first part of the day when atmospheric PM concentration is higher, followed by high resuspension rates in the second part of the day, corresponding with increased wind speeds. The sensitivity analysis of the model parameters showed that a better representation of PM deposition fluxes could be achieved with adjusted deposition velocities. It is also likely that the standard assumption of a complete removal of particulate matter, after precipitation events that exceed the water storage capacity of the canopy (Ps), should be reconsidered to better account for specific leaf traits. These results represent the first validation of i-Tree Eco PM removal with experimental data and are a starting point for improving the model parametrization and the estimate of particulate matter removed by urban trees.

The value of ASCAT soil moisture and MODIS snow cover data for calibrating a conceptual hydrologic model

Abstract. Recent advances in soil moisture remote sensing have produced satellite data sets with improved soil moisture mapping under vegetation and with higher spatial and temporal resolutions. In this study, we evaluate the potential of a new, experimental version of the Advanced Scatterometer (ASCAT) soil water index data set for multiple objective calibrations of a conceptual hydrologic model. The analysis is performed in 213 catchments in Austria for the period 2000–2014. An HBV (Hydrologiska Byråns Vattenbalansavdelning)-type hydrologic model is calibrated based on runoff data, ASCAT soil moisture data, and Moderate Resolution Imaging Spectroradiometer (MODIS) snow cover data for various calibration variants. Results show that the inclusion of soil moisture data in the calibration mainly improves the soil moisture simulations, the inclusion of snow data mainly improves the snow simulations, and the inclusion of both of them improves both soil moisture and snow simulations to almost the same extent. The snow data are more efficient at improving snow simulations than the soil moisture data are at improving soil moisture simulations. The improvements of both runoff and soil moisture model efficiencies are larger in low elevation and agricultural catchments than in others. The calibrated snow-related parameters are strongly affected by including snow data and, to a lesser extent, by soil moisture data. In contrast, the soil-related parameters are only affected by the inclusion of soil moisture data. The results indicate that the use of multiple remote sensing products in hydrological modeling can improve the representation of hydrological fluxes and prediction of runoff hydrographs at the catchment scale.

Scale-Similarity Subgrid-Scale Turbulence Closure for Supercell Simulations at Kilometer-Scale Resolutions: Comparison against a Large-Eddy Simulation

Abstract In numerical simulations of deep convection at kilometer-scale horizontal resolutions, in-cloud subgrid-scale (SGS) turbulence plays an important role in the transport of heat, moisture, and other scalars. By coarse graining a 50 m high-resolution large-eddy simulation (LES) of an idealized supercell storm to kilometer-scale grid spacings ranging from 250 m to 4 km, the SGS fluxes of heat, moisture, cloud, and precipitating water contents are diagnosed a priori. The kilometer-scale simulations are shown to be within the “gray zone” as in-cloud SGS turbulent fluxes are comparable in magnitude to the resolved fluxes at 4 km spacing, and do not become negligible until ~500 m spacing. Vertical and horizontal SGS fluxes are of comparable magnitudes; both exhibit nonlocal characteristics associated with deep convection as opposed to local gradient-diffusion type of turbulent mixing. As such, they are poorly parameterized by eddy-diffusivity-based closures. To improve the SGS representation of turbulent fluxes in deep convective storms, a scale-similarity LES closure is adapted to kilometer-scale simulations. The model exhibits good correlations with LES-diagnosed SGS fluxes, and is capable of representing countergradient fluxes. In a posteriori tests, supercell storms simulated with the refined similarity closure model at kilometer-scale resolutions show better agreement with the LES benchmark in terms of SGS fluxes than those with a turbulent-kinetic-energy-based gradient-diffusion scheme. However, it underestimates the strength of updrafts, which is suggested to be a consequence of the model effective resolution being lower than the native grid resolution.

DeepFlux for Skeleton Detection in the Wild

The medial axis, or skeleton, is a fundamental object representation that has been extensively used in shape recognition. Yet, its extension to natural images has been challenging due to the large appearance and scale variations of objects and complex background clutter that appear in this setting. In contrast to recent methods that address skeleton extraction as a binary pixel classification problem, in this article we present an alternative formulation for skeleton detection. We follow the spirit of flux-based algorithms for medial axis recovery by training a convolutional neural network to predict a two-dimensional vector field encoding the flux representation. The skeleton is then recovered from the flux representation, which captures the position of skeletal pixels relative to semantically meaningful entities (e.g., image points in spatial context, and hence the implied object boundaries), resulting in precise skeleton detection. Moreover, since the flux representation is a region-based vector field, it is better able to cope with object parts of large width. We evaluate the proposed method, termed DeepFlux, on six benchmark datasets, consistently achieving superior performance over state-of-the-art methods. Finally, we demonstrate an application of DeepFlux, augmented with a skeleton scale estimation module, to detect objects in aerial images. This combination yields results that are competitive with models trained specifically for object detection, showcasing the versatility and effectiveness of mid-level representations in high-level tasks. An implementation of our method is available at https://github.com/YukangWang/DeepFlux .

Ocean-Land Atmosphere Model (OLAM) performance for major extreme meteorological events near the coastal region of southern Brazil

Coastal regions are generally densely populated and have become highly vulnerable to the occurrence of extreme events. In recent years, Brazil’s southern coastal region has been affected by several different extreme weather events that have caused coastal flooding, with economic losses as well as fatalities. Understanding and improving the predictability of these events has become a major issue for the local population. In this study, state-of-the-art numerical modeling was applied to this region to assess the ability of the Ocean-Land Atmosphere Model to represent major extreme events. The model was applied to the region with a high-resolution grid refinement technique capable of simultaneously representing global and local atmospheric phenomena. The main events that affected Brazil’s southern coastal region between 2000 and 2018 were identified and then simulated. All selected events were associated with cyclonic and/or anticyclonic systems near the coastal region of the study area. Those systems were responsible for bringing heavy rain, strong winds and sea level rise, causing impacts for the coastal region. The results of the numerical simulations were compared with observational data to evaluate model performance. The model simulated well the air temperature and wind fields. Correlation values for sea level pressure were high despite a maximum positive bias of approximately 2 hPa. Precipitation presented a negative bias for most events. Finally, the results show that the methodology allowed for a detailed representation of sensible and latent heat fluxes for the region, allowing a better representation of local mesoscale features.

Modelling and parametrization of the convective flow over leads in sea ice and comparison with airborne observations

AbstractA non‐eddy‐resolving microscale model is applied to simulate convection over three different leads (elongated channels in sea ice), which were observed by aircraft over the Arctic Marginal Ice Zone in 2013. The study aims to evaluate the quality of a local and a non‐local turbulence parametrization. The latter represents a lead‐width‐dependent approach for the turbulent fluxes designed for idealised conditions of a lead‐perpendicular, near‐neutral inflow in an atmospheric boundary layer (ABL) capped by a strong inversion at around 250 to 350 m height. The observed cases considered here are also characterised by an almost lead‐perpendicular flow but, in comparison to the idealised conditions, our analysis covers effects in stable inflow conditions and a much shallower ABL. The model simulations are initialised with observed surface parameters and upwind profiles, and the results are compared with measurements obtained above and downwind of the leads. The basic observed features related to the lead‐generated convection can be reproduced with both closures, but the observed plume inclination and vertical entrainment near the inversion layer by the penetrating plume are underestimated. The advantage of the non‐local closure becomes obvious by the more realistic representation of regions with observed vertical entrainment or where the observations hint at counter‐gradient transport. It is shown by comparison with the observations that results obtained with the non‐local closure can be further improved by including the determination of a fetch‐dependent inversion height and by specifying a parameter determining the plume inclination as a function of the upwind ABL stratification. Both effects improve the representation of fluxes, boundary‐layer warming, and vertical entrainment. The model is also able to reproduce the observed vanishing of a weak low‐level jet over the lead, but its downwind regeneration and related momentum transport are not always well captured, irrespective of the closure used.

Assessment of CMIP6 models' skill for tropical Indian Ocean sea surface temperature variability

AbstractThe present study examines the ability of Coupled Model Inter‐comparison Project phase 6 (CMIP6) models in representing the dominant modes of tropical Indian Ocean (TIO) sea surface temperature (SST) variability on the interannual and decadal time scale. Historical simulations from 27 CMIP6 models are assessed against Extended Reconstructed SST over the period of 1854 to 2014. Spectrum analysis reveals that many models reproduce interannual and decadal variability of TIO SST but underestimate the amplitude of variability with some disparity in the periodicity. All models can reproduce the dominant basin‐wide mode of interannual and decadal variability of TIO SST reasonably well. Skill score analysis of TIO SST variability reveals that KACE‐1‐0‐G has highest skill, followed by FGOALS‐f3‐L, EC‐Earth3‐Veg‐LR, ACCESS‐ESM1‐5, CanESM5‐CanOE on the interannual timescale and FGOALS‐f3‐L, CanESM5‐CanOE, KACE‐1‐0‐G and CanESM5, respectively, showed highest skills for decadal variability. It is found that variations in radiation and latent heat flux are primarily responsible for interannual variability in TIO SST, the basin‐wide warming, in the observations. Taylor diagram analysis reveals that all the models exhibit better skill for the radiative flux; however, skill for the latent heat and momentum flux varies from model to model. It is important to note that the models in which the latent heat flux and zonal wind are better represented have produced better TIO SST variability compared to other models. A higher discrepancy in latent heat and zonal momentum flux leads to improper wind‐evaporation‐SST and wind‐circulation‐SST feedback, which in turn restricts the model skill. Besides, model that has realistic central and eastern Pacific SST variability show better skill for TIO SST variability in both interannual and decadal time scales. The present study advocates that better representation of latent heat flux and zonal wind in coupled models is important for the accurate simulation of interannual and decadal variability in TIO SST.

Flexible vector-based spatial configurations in land models

Abstract. Land models are increasingly used in terrestrial hydrology due to their process-oriented representation of water and energy fluxes. A priori specification of the grid size of the land models is typically defined based on the spatial resolution of forcing data, the modeling objectives, the available geospatial information, and computational resources. The variability of the inputs, soil types, vegetation covers, and forcing is masked or aggregated based on the a priori grid size. In this study, we propose an alternative vector-based implementation to directly configure a land model using unique combinations of land cover types, soil types, and other desired geographical features that have hydrological significance, such as elevation zone, slope, and aspect. The main contributions of this paper are to (1) implement the vector-based spatial configuration using the Variable Infiltration Capacity (VIC) model; (2) illustrate how the spatial configuration of the model affects simulations of basin-average quantities (i.e., streamflow) as well as the spatial variability of internal processes (snow water equivalent, SWE, and evapotranspiration, ET); and (3) describe the work and challenges ahead to improve the spatial structure of land models. Our results show that a model configuration with a lower number of computational units, once calibrated, may have similar accuracy to model configurations with more computational units. However, the different calibrated parameter sets produce a range of, sometimes contradicting, internal states and fluxes. To better address the shortcomings of the current generation of land models, we encourage the land model community to adopt flexible spatial configurations to improve model representations of fluxes and states at the scale of interest.

Building and Urban Cooling Performance Indexes of Wetted and Green Roofs—A Case Study under Current and Future Climates

We developed and studied key performance indexes and representations of energy simulation heat fluxes to evaluate the performance of the evaporative cooling process as a passive cooling technique for a commercial building typology. These performance indexes, related to indoor thermal comfort, energy consumption and their interactions with their surrounding environments, contribute to understanding the interactions between the urban climate and building for passive cooling integration. We compare the performance indexes for current and future climates (2080), according to the highest emission scenario A2 of the Special Report on Emission Scenario (SRES). Specific building models were adapted with both green roof and wetted roof techniques. The results show that summer thermal discomfort will increase due to climate change and could become as problematic as winter thermal discomfort in a temperate climate. Thanks to evapotranspiration phenomena, the sensible heat contribution of the building to the urban heat island (UHI) is reduced for both current and future climates with a green roof. The performance of the vegetative roof is related to the water content of the substrate. For wetted roofs, the impacts on heat transferred to the surrounding environment are higher for a Mediterranean climate (Marseille), which is warmer and drier than the Paris climate studied (current and future climates). The impact on indoor thermal comfort depends on building insulation, as demonstrated by parametric studies, with higher effects for wetted roofs.

On the Effect of Angular and Spatial Discretization on Perturbation Calculations

In this article, different angular flux discretization options, namely discrete ordinates representation and spherical harmonics expansion are compared from the viewpoint of the accuracy of perturbation calculations. The PARTISN discrete ordinates neutron transport solver was coupled with the SEnTRi code, developed at BME, in order to perform perturbation theory calculations in different types of geometry descriptions and angular representations. With the help of the implemented code, the effect of the angular and spatial discretization on the results of perturbation theory calculations was investigated. Exact matches were observed in Cartesian geometries with the direct perturbation method when the discrete ordinates angular representation was used, and small discrepancies were found when the spherical harmonics expansion was applied. In cylindrical geometries, slight differences were observed with both angular expansions, which originate from the nature of the adjoint transport operator in curvilinear coordinate systems. The differences can be reduced to a negligible level with increased expansion order in both cases. Small discrepancies can have a significant effect in sensitivity, uncertainty and transient calculations, which that for high accuracy calculation the discrete ordinates representation of the angular dependent flux should be used or sufficiently high expansion order with the spherical harmonics must be applied.

Simulation of the GOx/GCH4 Multi-Element Combustor Including the Effects of Radiation and Algebraic Variable Turbulent Prandtl Approaches

Multi-element thrusters operating with gaseous oxygen (GOX) and methane (GCH4) have been numerically studied and the results were compared to test data from the Technical University of Munich (TUM). A 3D Reynolds Averaged Navier–Stokes Equations (RANS) approach using a 60° sector as a simulation domain was used for the studies. The primary goals were to examine the effect of the turbulent Prandtl number approximations including local algebraic approaches and to study the influence of radiative heat transfer (RHT). Additionally, the dependence of the results on turbulence modeling was studied. Finally, an adiabatic flamelet approach was compared to an Eddy-Dissipation approach by applying an enhanced global reaction scheme. The normalized and absolute pressures, the integral and segment averaged heat flux were taken as an experimental reference. The results of the different modeling approaches were discussed, and the best performing models were chosen. It was found that compared to other discussed approaches, the BaseLine Explicit Algebraic Reynolds Stress Model (BSL EARSM) provided more physical behavior in terms of mixing, and the adiabatic flamelet was more relevant for combustion. The effect of thermal radiation on the wall heat flux (WHF) was high and was strongly affected by spectral models and wall thermal emissivity. The obtained results showed good agreement with the experimental data, having a small underestimation for pressures of around 2.9% and a good representation of the integral wall heat flux.

Climate Response to Increasing Antarctic Iceberg and Ice Shelf Melt

AbstractMass loss from the Antarctic continent is increasing; however, climate models either assume a constant mass loss rate or return snowfall over land to the ocean to maintain equilibrium. Numerous studies have investigated sea ice and ocean sensitivity to this assumption and reached different conclusions, possibly due to different representations of melt fluxes. The coupled atmosphere–land–ocean–sea ice model, HadGEM3-GC3.1, includes a realistic spatial distribution of coastal melt fluxes, a new ice shelf cavity parameterization, and explicit representation of icebergs. This configuration makes it appropriate to revisit how increasing melt fluxes influence ocean and sea ice and to assess whether responses to melt from ice shelves and icebergs are distinguishable. We present results from simulated scenarios of increasing meltwater fluxes and show that these drive sea ice increases and, for increasing ice shelf melt, a decline in Antarctic Bottom Water formation. In our experiments, the mixed layer around the Antarctic coast deepens in response to rising ice shelf meltwater and shallows in response to stratification driven by iceberg melt. We find similar surface temperature and salinity responses to increasing meltwater fluxes from ice shelves and icebergs, but midlayer waters warm to greater depths and farther north when ice shelf melt is present. We show that as meltwater fluxes increase, snowfall becomes more likely at lower latitudes and Antarctic Circumpolar Current transport declines. These insights are helpful for interpretation of climate simulations that assume constant mass loss rates and demonstrate the importance of representing increasing melt rates for both ice shelves and icebergs.

High temperature oxidation and chromium volatilisation of AISI 430 stainless steel coated by Mn-Co and Mn-Co-Cu oxides for SOFC interconnect application

An AISI 430 stainless steel was coated by Mn-Co and Mn-Co-Cu oxides, then tested in O2-5%H2O at 800 °C. The coated samples had reduced rates of oxidation and Cr loss due to Cr-species volatilisation with the higher rates for the Mn-Co-Cu oxide coated steel due to more Cr diffusion to the coating layer. The measured rates of Cr loss were in the order of 10–11 g cm–2 s–1. The graphical representation of the mass flux of Cr loss as a function of water vapour content was proposed to help visualise the volatilisation effect.

Impacts of Ice-Shelf Melting on Water-Mass Transformation in the Southern Ocean from E3SM Simulations

AbstractThe Southern Ocean overturning circulation is driven by winds, heat fluxes, and freshwater sources. Among these sources of freshwater, Antarctic sea ice formation and melting play the dominant role. Even though ice-shelf melt is relatively small in magnitude, it is located close to regions of convection, where it may influence dense water formation. Here, we explore the impacts of ice-shelf melting on Southern Ocean water-mass transformation (WMT) using simulations from the Energy Exascale Earth System Model (E3SM) both with and without the explicit representation of melt fluxes from beneath Antarctic ice shelves. We find that ice-shelf melting enhances transformation of Upper Circumpolar Deep Water, converting it to lower density values. While the overall differences in Southern Ocean WMT between the two simulations are moderate, freshwater fluxes produced by ice-shelf melting have a further, indirect impact on the Southern Ocean overturning circulation through their interaction with sea ice formation and melting, which also cause considerable upwelling. We further find that surface freshening and cooling by ice-shelf melting cause increased Antarctic sea ice production and stronger density stratification near the Antarctic coast. In addition, ice-shelf melting causes decreasing air temperature, which may be directly related to sea ice expansion. The increased stratification reduces vertical heat transport from the deeper ocean. Although the addition of ice-shelf melting processes leads to no significant changes in Southern Ocean WMT, the simulations and analysis conducted here point to a relationship between increased Antarctic ice-shelf melting and the increased role of sea ice in Southern Ocean overturning.

Convective Boundary Layer Control of the Sea Surface Temperature in the Tropics

AbstractUsing successive versions of a global climate model, we show how convective transport to the free troposphere of the humidity evaporated at the surface or, reciprocally, entrainment of dry air from the free troposphere into the mixed layer, controls surface evaporative cooling and then sea surface temperature. This control is as important as the radiative effect of boundary layer clouds on radiation. Those aspects are shown to be improved when activating a mass flux representation of the organized structures of the convective boundary layer coupled to eddy diffusion, the so‐called “thermal plume model,” leading to an increased near‐surface drying compared to the use of turbulent diffusion alone. Controlling detrainment by air properties from just above the boundary layer allows the thermal plume model to be valid for both cumulus and stratocumulus regimes, improving the contrast in near‐surface humidity between the trade winds region and East Tropical oceans. Using pairs of stand‐alone atmospheric simulations forced by sea surface temperature and of coupled atmosphere‐ocean simulations, we show how the improvement of the surface fluxes that arise from this improved physics projects into an improvement of the representation of sea surface temperature patterns in the coupled model, and in particular into a reduction of the East Tropical Ocean warm bias. The work presented here led to the bias reduction in sea surface temperature in the Institute Pierre Simon Laplace coupled model, IPSL‐CM6A, developed recently for the 6th phase of the Coupled Model Intercomparison Project, CMIP6.

Evaluation of the Bulk Mass Flux Formulation Using Large-Eddy Simulations

Abstract In this study, bulk mass flux formulations for turbulent fluxes are evaluated for shallow and deep convection using large-eddy simulation data. The bulk mass flux approximation neglects two sources of variability: the interobject variability due to differences between the average properties of different cloud objects, and the intraobject variability due to perturbations within each cloud object. Using a simple cloud–environment decomposition, the interobject and intraobject contributions to the heat flux are comparable in magnitude with that from the bulk mass flux approximation, but do not share a similar vertical distribution, and so cannot be parameterized with a rescaling method. A downgradient assumption is also not appropriate to parameterize the neglected flux contributions because a nonnegligible part is associated with nonlocal buoyant structures. A spectral analysis further suggests the presence of fine structures within the clouds. These points motivate investigations in which the vertical transports are decomposed based on the distribution of vertical velocity. As a result, a “core-cloak” conceptual model is proposed to improve the representation of total vertical fluxes, composed of a strong and a weak draft for both the updrafts and downdrafts. It is shown that the core-cloak representation can well capture the magnitude and vertical distribution of heat and moisture fluxes for both shallow and deep convection.

Mass transfer in irrigated plane-parallel channels for cocurrent laminar flow of liquid and gas

Isothermal absorption of components from dilute gaseous mixtures by falling film of liquids in irrigated plane-parallel channels for co-current laminar flows of liquid and gas were modeled taking into account the processes occurring at the gas entrance. A solution was obtained in the form of analytical expression and reduced to the solution of particular limited problems for the cases when the resistance is concentrated within the gas or the liquid. For visual representation of fluxes the plane of hydrodynamic parameters was suggested. The calculations can be carried out inside of a limited area of the plane. Outside of the area, some simplifications can be adopted: (a) mass transfer resistance is concentrated in a gas or in a liquid and (b) the concentration changes in transversal directions can be neglected or there is a boundary diffusion layer in the gas or the liquid. It was shown that in calculating of the process of gas cooling by the transversal temperature gradients in the liquid can be neglected. The restrictions on temperature difference at the entrance were found, according to them the corresponding thermophysical coefficients can be assumed to be constants and the heat exchange can be calculated using the relationships derived for isothermal absorption. The method can be applied to a wide class of problems which can be reduced to solving of convection diffusion equations with more difficult interphase boundary conditions. Compared to existing numerical and analytical methods, our approach advantage is in its simplicity, visual representation, and shorter computation time.

Discontinuous Galerkin discretization for two-equation turbulence closure model

Accurate representation of vertical turbulent fluxes is crucial for numerical ocean modeling, both in global and coastal applications. The state-of-the-art approach is to use two-equation turbulence closure models which introduces two dynamic equations to the system. Solving these equations numerically, however, is challenging due to the strict requirement of positivity of the turbulent quantities (e.g., turbulence kinetic energy and its dissipation rate), and the non-linear source terms that may render the numerical system unstable. In this paper, we present a Discontinuous Galerkin (DG) finite element discretization of the Generic Length Scale (GLS) equations designed to be incorporated in a DG coastal ocean model, Thetis. To ensure numerical stability, the function space for turbulent quantities must be chosen carefully. In this work, we propose to use zeroth degree elements for the turbulent quantities and linear discontinuous elements for the tracers and velocity. The spatial discretization is completed with a positivity preserving semi-implicit time integration scheme. We validate the implementation with standard turbulence closure model benchmarks and an idealized estuary simulation. Finally, we use the full three-dimensional model to simulate the Columbia River plume. The results confirm that the coupled model generates realistic vertical mixing, and remains stable under strongly stratified conditions and strong tidal forcing. River plume characteristics are well captured.