Upper-boundary Condition Research Articles

A Multilayer Upper-Boundary Condition for Longwave Radiative Flux to Correct Temperature Biases in a Mesoscale Model

Abstract An upper-level cold bias in potential temperature tendencies of 10 K day−1, strongest at the top of the model, is observed in Weather Research and Forecasting (WRF) model forecasts. The bias originates from the Rapid Radiative Transfer Model longwave radiation physics scheme and can be reduced substantially by 1) modifying the treatment within the scheme by adding a multilayer buffer between the model top and top of the atmosphere and 2) constraining stratospheric water vapor to remain within the estimated climatology in the stratosphere. These changes reduce the longwave heating rate bias at the model top to ±0.5 K day−1. Corresponding bias reductions are also seen, particularly near the tropopause.

A general analytical solution for flow to a single horizontal well by Fourier and Laplace transforms

The objective of this paper is to present an analytical solution for describing the head distribution in an unconfined aquifer with a single pumping horizontal well parallel to a fully penetrating stream. The Laplace-domain solution is developed by applying Fourier sine, Fourier and Laplace transforms to the governing equation as well as the associated initial and boundary conditions. The time-domain solution is obtained after taking the inverse Laplace transform along with the Bromwich integral method and inverse Fourier and Fourier sine transforms. The upper boundary condition of the aquifer is represented by the free surface equation in which the second-order slope terms are neglected. Based on the solution and Darcy’s law, the equation representing the stream depletion rate is then derived. The solution can simulate head distributions in an aquifer infinitely extending in horizontal direction if the well is located far away from the stream. In addition, the solution can also simulate head distributions in confined aquifers if specific yield is set zero. It is shown that the solution can be applied practically to evaluate flow to a horizontal well.

SELF-CONSISTENT MODEL ATMOSPHERES AND THE COOLING OF THE SOLAR SYSTEM'S GIANT PLANETS

We compute grids of radiative–convective model atmospheres for Jupiter, Saturn, Uranus, and Neptune over a range of intrinsic fluxes and surface gravities. The atmosphere grids serve as an upper boundary condition for models of the thermal evolution of the planets. Unlike previous work, we customize these grids for the specific properties of each planet, including the appropriate chemical abundances and incident fluxes as a function of solar system age. Using these grids, we compute new models of the thermal evolution of the major planets in an attempt to match their measured luminosities at their known ages. Compared to previous work, we find longer cooling times, predominantly due to higher atmospheric opacity at young ages. For all planets, we employ simple "standard" cooling models that feature adiabatic temperature gradients in the interior H/He and water layers, and an initially hot starting point for the calculation of subsequent cooling. For Jupiter, we find a model cooling age ∼10% longer than previous work, a modest quantitative difference. This may indicate that the hydrogen equation of state used here overestimates the temperatures in the deep interior of the planet. For Saturn, we find a model cooling age ∼20% longer than previous work. However, an additional energy source, such as that due to helium phase separation, is still clearly needed. For Neptune, unlike in work from the 1980s and 1990s, we match the measured Teff of the planet with a model that also matches the planet's current gravity field constraints. This is predominantly due to advances in the high-pressure equation of state of water. This may indicate that the planet possesses no barriers to efficient convection in its deep interior. However, for Uranus, our models exacerbate the well-known problem that Uranus is far cooler than calculations predict, which could imply strong barriers to interior convective cooling. The atmosphere grids are published here as tables, so that they may be used by the wider community.

SOSA – a new model to simulate the concentrations of organic vapours and sulphuric acid inside the ABL – Part 1: Model description and initial evaluation

Abstract. Chemistry in the atmospheric boundary layer (ABL) is controlled by complex processes of surface fluxes, flow, turbulent transport, and chemical reactions. We present a new model SOSA (model to simulate the concentration of organic vapours and sulphuric acid) and attempt to reconstruct the emissions, transport and chemistry in the ABL in and above a vegetation canopy using tower measurements from the SMEAR II at Hyytiälä, Finland and available soundings data from neighbouring meteorological stations. Using the sounding data for upper boundary condition and nudging the model to tower measurements in the surface layer we were able to get a reasonable description of turbulence and other quantities through the ABL. As a first application of the model, we present vertical profiles of organic compounds and discuss their relation to newly formed particles.

Flow‐Induced Polymer Degradation During Ink‐Jet Printing

We report for the first time evidence of flow-induced polymer degradation during inkjet printing for both poly(methyl methacrylate) (PMMA) and polystyrene (PS) in good solvent. This has significance for the deposition of functional and biological materials. Polymers having Mw either less than 100 kDa or greater than approximately 1,000 kDa show no evidence of molecular weight degradation. The lower boundary condition is a consequence of low Deborah Number De imposed by the printhead geometry and the upper boundary condition due to visco-elastic damping. For intermediate molecular weights the effect is greatest at high elongational strain rate and low solution concentration with higher polydispersity polymers being most sensitive to molecular weight degradation. For low polydispersity samples, PDi ≤ 1.3, chain breakage is essentially centro-symmetric induced either by turbulance or overstretching when the strain rate increases well beyond a critical value, that is the stretching rate is high enough to exceed the rate of relaxation. For higher polydispersity samples chain breakage is consistent with almost random scission along the chain, inferring that the forces required to break the chain are additionally transmitted either by valence bonds, i.e. network chains and junctions or discrete entanglements rather than solely by hydrodynamic interaction.

Propagation of linear surface air temperature trends into the terrestrial subsurface

Previous studies have tested the long‐term coupling between air and terrestrial subsurface temperatures working under the assumption that linear trends in surface air temperature should be equal to those measured at depth within the subsurface. A one‐dimensional model of heat conduction is used to show that surface trends are attenuated as a function of depth within conductive media on time scales of decades to centuries, therefore invalidating the above assumption given practical observational constraints. The model is forced with synthetic linear temperature trends as the time‐varying upper boundary condition; synthetic trends are either noise free or include additions of Gaussian noise at the annual time scale. It is shown that over a 1000 year period, propagating surface trends are progressively damped with depth in both noise‐free and noise‐added scenarios. Over shorter intervals, the relationship between surface and subsurface trends is more variable and is strongly impacted by annual variability (i.e., noise). Using output from the FOR1 millennial simulation of the GKSS ECHO‐G General Circulation Model as a more realistic surface forcing function for the conductive model, it is again demonstrated that surface trends are damped as a function of depth within the subsurface. Observational air and subsurface temperature data collected over 100 years in Armagh, Ireland, and 29 years in Fargo, North Dakota, are also analyzed and shown to have subsurface temperature trends that are not equal to the surface trend. While these conductive effects are correctly accounted for in inversions of borehole temperature profiles in paleoclimatic studies, they have not been considered in studies seeking to evaluate the long‐term coupling between air and subsurface temperatures by comparing trends in their measured time series. The presented results suggest that these effects must be considered and that a demonstrated trend equivalency in air and subsurface temperatures is inconclusive regarding their long‐term tracking.

An analytical solution for tidal fluctuations in unconfined aquifers with a vertical beach

The perturbation technique has been commonly used to develop analytical solutions for simulating the dynamic response of tidal fluctuations in unconfined aquifers. However, the solutions obtained from the perturbation method might result in poor accuracy for the case of the perturbation parameter being not small enough. In this paper, we develop a new analytical model for describing the water table fluctuations in unconfined aquifers, based on Laplace and Fourier transforms. In the new approach, the mean sea level is used as the initial condition and a free surface equation, neglecting the second‐order slope terms, as the upper boundary condition. Numerical results show that the present solution agrees well with the finite different model with the second‐order surface terms. Unlike Teo et al.'s (2003) approximation which restricts on the case of shallow aquifers, the present model can be applied to most of the tidal aquifers except for the very shallow one. In addition, a large‐time solution in terms of sine function is provided and examined graphically with four different tidal periods.

Slab- and height-resolving models of the tropical cyclone boundary layer. Part II: Why the simulations differ

Depth-averaged, or slab, models of the tropical cyclone boundary layer have had important practical uses in engineering design and climatological risk-assessment studies and as components of tropical cyclone potential-intensity models. In Part I of this article, such models were compared with a fully height-resolving model, and it was shown that there are substantial differences in the simulations. This second part determines the reasons for these differences. The main tool used is a new model, which parametrizes the vertical structure of the boundary layer and thereby allows more accurate calculation of the surface drag and nonlinear terms. It is more accurate than the slab model, but of similar computational cost. This model, and hybrids of it and the slab model, are used to determine the consequences of the approximations in slab models. It was indicated in Part I and is confirmed here that the excessively strong inflow and too great departure of the boundary-layer mean winds from gradient balance in the slab model are due to excessive surface drag. The tendency of slab models to produce quasi-inertial oscillations is shown to be due to the inaccurate treatment of the vertically averaged nonlinear terms in the momentum equations. In particular, these oscillations are shown not to be due to the improper specification of the upper boundary condition as has recently been argued by Smith and Vogl. The considerable deficiencies of slab models of the tropical cyclone boundary layer are therefore inherent to their formulation. It is further shown that the dynamics leading to supergradient flow are different in the slab model and in the height-resolving model. The possible uses of linearized versions of the slab model are briefly considered. Copyright © 2010 Royal Meteorological Society

Damping rates of p-modes by an ensemble of randomly distributed thin magnetic flux tubes

AbstractThe magnetohydrodynamic (MHD) sausage tube waves are excited in the magnetic flux tubes by p-mode forcing. These tube waves thus carry energy away from the p-mode cavity which results in the deficit of incident p-mode energy. We calculate the loss of incident p-mode energy as a damping rate of f- and p-modes. We calculate the damping rates of f- and p-modes by a model Sun consisting of an ensemble of many thin magnetic flux tubes with varying plasma properties and distributions. Each magnetic flux tube is modelled as axisymmetric, vertically oriented and untwisted. We find that the magnitude and the form of the damping rates are sensitive to the plasma-β of the tubes and the upper boundary condition used.

Expansion of magnetic flux concentrations: a comparison of Hinode SOT data and models

Context: The expansion of network magnetic fields with height is a fundamental property of flux tube models. A rapid expansion is required to form a magnetic canopy. Aims: We characterize the observed expansion properties of magnetic network elements and compare them with the thin flux tube and sheet approximations, as well as with magnetoconvection simulations. Methods: We used data from the Hinode SOT NFI NaD1 channel and spectropolarimeter to study the appearance of magnetic flux concentrations seen in circular polarization as a function of position on the solar disk. We compared the observations with synthetic observables from models based on the thin flux tube approximation and magnetoconvection simulations with two different upper boundary conditions for the magnetic field (potential and vertical). Results: The observed circular polarization signal of magnetic flux concentrations changes from unipolar at disk center to bipolar near the limb, which implies an expanding magnetic field. The observed expansion agrees with expansion properties derived from the thin flux sheet and tube approximations. Magnetoconvection simulations with a potential field as the upper boundary condition for the magnetic field also produce bipolar features near the limb while a simulation with a vertical field boundary condition does not. Conclusions: The near-limb apparent bipolar magnetic features seen in high-resolution Hinode observations can be interpreted using a simple flux sheet or tube model. This lends further support to the idea that magnetic features with vastly varying sizes have similar relative expansion rates. The numerical simulations presented here are less useful in interpreting the expansion since the diagnostics we are interested in are strongly influenced by the choice of the upper boundary condition for the magnetic field in the purely photospheric simulations.

Low-Level Wind Field Climatology over the La Plata River Region Obtained with a Mesoscale Atmospheric Boundary Layer Model Forced with Local Weather Observations

Abstract A primitive equation, dry, hydrostatic, and incompressible mesoscale boundary layer model is used to simulate the high-horizontal-resolution low-level wind field “climatology” over the La Plata River region in South America. The horizontal model domain has 79 × 58 points (350 km × 316 km), with a horizontal resolution of 0.05°. The model climatological field is the ensemble result of a series of daily forecasts obtained by forcing the model with limited local observations. Each ensemble member produces a daily forecast that participates in the definition of the wind climatology with a probability calculated with the local observations. The upper boundary condition is taken from the only local radiosonde observation, and the lower boundary condition consists of a surface heating function calculated with the temperature observations of the surface weather stations in the region. The study, conducted during the period of 1959–84, reveals an overall good agreement between the observed and the modeled surface wind climatological fields at five weather stations in the region. The model represents very well the differences in the wind speed magnitudes and predominant wind direction sectors throughout a region that displays a strong sea–land-breeze daily cycle. The average root-mean-square value of the model relative error is 31% for wind direction and 23% for wind speed. Model errors vary throughout the day with the minimum in the morning and afternoon and the maximum at night. The seasonal climatology shows the minimum wind direction error in winter and the maximum error in summer, whereas the wind speed errors reveal no seasonality. The annual wind direction error is very similar to the winter minimum error. The conclusion of the study is that the proposed ensemble mean method is useful for synthesizing high-resolution climatological low-level wind fields over regions with a strong diurnal cycle of surface thermal contrasts and a limited number of available weather stations.

Coupling between internal and surface waves

In a fluid system in which two immiscible layers are separated by a sharp free interface, there can be strong coupling between large amplitude nonlinear waves on the interface and waves in the overlying free surface. We study the regime where long waves propagate in the interfacial mode, which are coupled to a modulational regime for the free- surface mode. This is a system of Boussinesq equations for the internal mode, coupled to the linear Schrodinger equations for wave propagation on the free surface, and respectively a version of the Korteweg-de Vries equation for the internal mode in case of unidirectional motions. The perturbation methods are based on the Hamiltonian formulation for the original system of irrotational Euler's equations, as described in (Benjamin and Bridges, J Fluid Mech 333:301-325, 1997, Craig et al., Comm Pure Appl Math 58:1587-1641, 2005a, Zakharov, J Appl Mech Tech Phys 9:190-194, 1968), using the perturbation theory for the modulational regime that is given in (Craig et al. to appear). We focus in particular on the situation in which the internal wave gives rise to localized bound states for the Schrodinger equation, which are interpreted as surface wave patterns that give a charac- teristic signature of the presence of an internal wave soliton. We also comment on the discrepancies between the free interface-free surface cases and the approximation of the upper boundary condition by a rigid lid.

A stabilization algorithm for geodynamic numerical simulations with a free surface

Geodynamic processes are in many cases coupled to surface processes such as erosion of mountains or deposition of sediments in basins. Numerical models that study the effect of such surface processes on the dynamics of the lithosphere use either a self-consistent free surface approach or approximate it by adding a weak, low density “air” layer on top of the model domain. A main problem with such setups, however, is that they are numerically unstable, which is caused by the fact that the density difference that drives geodynamic processes (∼30–100 kg/m 3) is much smaller than the density difference between rocks and air (∼3000 kg/m 3). In order to retain isostatic balance, one should thus employ a time step that is at least 30 times smaller than in models with a free slip upper boundary condition, which makes such models computationally very expensive. Here we describe a new free surface stabilization approach (FSSA) that largely overcomes this time step restriction. In this work, we apply the stabilization technique to consistent free surface models utilizing a finite element discretization. The approach is based on the observation that most geodynamical simulations perform time-dependent simulations by solving the static Stokes equations and then updating the material or temperature fields in a separate step. If, however, the time-dependency of these quantities is taken into account during the discretization of the momentum equations, additional surface traction terms appear in the weak form of the FE formulation. These terms, which depend on the employed time step and velocity, essentially correct for the change of forces in an element due to advection or distortion of every element. By time-discretizing them, they act as a stabilizing term that largely increases the time steps that can be employed (by a factor 20–100 depending on the time stepping criteria that is used). We illustrate the accuracy and power of this method with examples of a free surface Rayleigh–Taylor instability and with a free subduction experiment.

Variability of saturated hydraulic conductivities in the agriculturallycultivated soils

The knowledge of the moisture conditions in a variably saturated zone of soil and their management is one of the main possibilities that allow the agronomists to raise significantly the fertility of soils. A progressive scientific method for describing the moisture conditions in a variably saturated zone uses a numerical simulation on a mathematical model. The accuracy of the outputs from the model (i.e. moisture profiles) depends mainly, besides the physical and mathematical structures of the model, on the accuracy of the input data. The upper boundary condition comprises the climate and phenological parameters. The initial condition is represented by the moisture profile at the beginning of the simulation and by the main hydrophysical properties of the soil. One of the main hydrophysical properties of soil is the value of the saturated hydraulic conductivity (<I>K</I>). This study is aimed at the determination of its temporal variability, keeping in mind also its areal one (with respect to the sampling data from various verticals). Several methods exist for the determination of the <I>K </I>values. In this study, a laboratory method with the falling head method (<I>K</I><SUB>labor</SUB>) was used. The areal-temporal variability of the <I>K</I><SUB>labor</SUB> values was evaluated for the vegetation period of the year 2003 on the locality Most pri Bratislave.

Estimation of actual evapotranspiration of Mediterranean perennial crops by means of remote-sensing based surface energy balance models

Abstract. Actual evapotranspiration from typical Mediterranean crops has been assessed in a Sicilian study area by using surface energy balance (SEB) and soil-water balance models. Both modelling approaches use remotely sensed data to estimate evapotranspiration fluxes in a spatially distributed way. The first approach exploits visible (VIS), near-infrared (NIR) and thermal (TIR) observations to solve the surface energy balance equation whereas the soil-water balance model uses only VIS-NIR data to detect the spatial variability of crop parameters. Considering that the study area is characterized by typical spatially sparse Mediterranean vegetation, i.e. olive, citrus and vineyards, alternating bare soil and canopy, we focused the attention on the main conceptual differences between one-source and two-sources energy balance models. Two different models have been tested: the widely used one-source SEBAL model, where soil and vegetation are considered as the sole source (mostly appropriate in the case of uniform vegetation coverage) and the two-sources TSEB model, where soil and vegetation components of the surface energy balance are treated separately. Actual evapotranspiration estimates by means of the two surface energy balance models have been compared vs. the outputs of the agro-hydrological SWAP model, which was applied in a spatially distributed way to simulate one-dimensional water flow in the soil-plant-atmosphere continuum. Remote sensing data in the VIS and NIR spectral ranges have been used to infer spatially distributed vegetation parameters needed to set up the upper boundary condition of SWAP. Actual evapotranspiration values obtained from the application of the soil water balance model SWAP have been considered as the reference to be used for energy balance models accuracy assessment. Airborne hyperspectral data acquired during a NERC (Natural Environment Research Council, UK) campaign in 2005 have been used. The results of this investigation seem to prove a slightly better agreement between SWAP and TSEB for some fields of the study area. Further investigations are programmed in order to confirm these indications.

The Steady‐State Analytical Solution of the Global Atmospheric Electricity Model on the Charging of Thunderstorms in Lower Atmosphere

AbstractGlobal atmospheric electricity model is the circuit between atmosphere and surface. In the lower atmosphere, the main sources of electric current within the model are thunderstorms, which are considered as vertical electric dipoles. Based on the current continuity equation, using spherical harmonic function expansion, with the lower boundary as the surface atmospheric electric potential and the upper boundary condition as the electric potential of the bottom of the ionosphere, and non‐homogeneous current source function of the vertical dipole assumptions for the charging of thunderstorms, we derive the steady‐state analytical solution of the global atmospheric electricity model in the lower atmosphere. It is proved that the solution can be written as the sum of limited polynomial series. The conclusions are consistent with the previous theoretical analysis and experimental observation. It is an improvement to the previous approximate solution, and the formula in this article can be used in numerical calculation and simulation of atmospheric electric parameters in the future.

Semi-analytical analysis of the response of the air temperature over the land surface to the global vegetation distribution

Response of the air temperature over the land surface to the global vegetation distribution is investigated, using a three-dimensional governing equation to simulate the steady, large-scale, limited amplitude perturbation of the free, inviscid and adiabatic atmosphere. The adoption of the static equation leads to a temperature governing equation in the terrain following coordinate. With the prescribed temperature as the upper boundary condition and the radiation balance as the lower boundary condition, the semi-analytical solution of the global circulation temperature can be calculated. In this article, only the air temperature (at 2 m height) over the land surface is analyzed, and the result suggests that this model can simulate the air temperature pattern over the land surface reasonably. A better simulation occurs when a simple feedback of the albedo on the temperature is included. Two sensitivity experiments are analyzed through this model. One suggests that the air temperature over the land surface descends obviously when the land surface is covered with ice all over, while another suggests that the air temperature rises a little when the land surface is covered with forest except the ice-covered area. This model appears to be a good tool to study the response of the air temperature to the vegetation distribution. Limitations of the model are also discussed.

Behavior of a shallow water table under periodic flow conditions

A new laboratory data set on the behavior of a shallow water table in a sand column aquifer subject to simple harmonic periodic forcing at its base is presented and discussed. The data are analyzed using the dynamic effective porosity, which is defined as the ratio of the rate of change in total moisture to the rate of change in water table elevation; thus, a reduction in this parameter means that the extent of moisture exchange has been reduced relative to a given water table fluctuation. The data show a clear decrease in the dynamic effective porosity with increasing proximity of the water table to the sand surface, which is consistent with previous research under a steadily rising or falling shallow water table. The observed reduction in moisture exchange due to shallowness of the water table has implications for periodic flow scenarios such as the propagation of water table waves in coastal and beach groundwater systems. That is, as moisture exchange is reduced, less work is being done by the flow, and thus, energy dissipation rates for shallow water tables will be reduced relative to the case of a deeper water table. At present no account of the influence of water table shallowness has been included in theories describing water table wave dispersion. The present experiments, in conjunction with the dynamic effective porosity concept, provide a framework in which this gap in knowledge can be further investigated. Additional experiments were designed such that the free surface transgressed the sand surface for part of the oscillation period to investigate the influence of meniscus formation and deformation at the sand surface on periodic flow dynamics. The observed behavior is consistent with previous observations of steady infiltration above shallow water tables, namely, a rapid drop (rise) in pore pressure with the onset of meniscus formation (deformation). A simple “wetting and drying” model is derived, accounting for the variation in effective porosity caused by the free surface transgressing the sand surface, which is shown to accurately capture the observed behavior. A finite element solution of the Richards equation in which the transient upper boundary condition is easily mimicked by means of a surface element with special storage features also shows excellent agreement with the observed data.

Convectively induced shear instability in large amplitude internal solitary waves

Laboratory study has been carried out to investigate the instability of an internal solitary wave of depression in a shallow stratified fluid system. The experimental campaign has been supported by theoretical computations and has focused on a two layered stratification consisting of a homogeneous dense layer below a linearly stratified top layer. The initial background stratification has been varied and it is found that the onset and intensity of breaking are affected dramatically by changes in the background stratification. Manifestations of a combination of shear and convective instability are seen on the leading face of the wave. It is shown that there is an interplay between the two instability types and convective instability induces shear by enhancing isopycnal compression. Variation in the upper boundary condition is also found to have an effect on stability. In particular, the implications for convective instability are shown to be profound and a dramatic increase in wave amplitude is seen for a fixed (as opposed to free) upper boundary condition.

Estimation of Unsaturated Flow Parameters Using GPR Tomography and Groundwater Table Data

Flow parameters in the vadose zone of an ice‐contact delta near Oslo's Gardermoen Airport were estimated by inverse flow modeling combining time‐lapse ground‐penetrating radar (GPR) travel‐time (TT) tomography and groundwater (GW) table data. Natural water infiltration from the 2006 snowmelt was used as the upper boundary condition in forward flow simulations. The lower boundary condition was the outflux of water from the vadose zone derived by time derivative of the GW table. The inverse flow modeling was done using different combinations of time‐lapse GPR TT tomography and time series of the level of the GW table. The purpose was to assess the improvements in parameter estimations and the information value of the different data sets. Flow parameters estimated by conditioning only on time‐lapse GPR TT tomography capture the development of the wet front but fail to simulate the GW table fluctuations. Inverse flow modeling conditioned on only the GW table did not simulate the wet front correctly but decreased the objective function better than conditioning on time‐lapse GPR data. If the inversion is conditioned on both time‐lapse GPR data and the GW table fluctuations, the final estimates of the flow parameters are close to the estimates from the inversion conditioned on only GW table data. This result was obtained because the moving GW table was monitored continuously in time while the GPR data were sampled only three times during the infiltration event; thus, observations of the GW table had higher weights in the objective function than did observations derived from GPR tomograms. Finally, we did forward flow modeling with the estimated parameter sets and compared the flow paths with an independent tracer experiment performed at the field site in 1999. The results showed that anisotropy in the intrinsic permeability was an important parameter that should be considered when simulating the flow paths. However, volumetric soil water content distribution is not strongly related to the anisotropy of intrinsic permeability. Therefore, anisotropy cannot be correctly estimated by inverse flow modeling conditioned on volumetric soil water content only.