Constant Pressure Surfaces Research Articles

A Constant Pressure Upper Boundary Formulation for Models Employing Height-Based Vertical Coordinates

Abstract For the numerical simulation of atmospheric flows that extend as high as the thermosphere, it is more appropriate to represent the upper boundary of the model domain as a material surface at constant pressure rather than one characterized by a rigid lid. Consequently, in adapting the Model for Prediction Across Scales (MPAS) for geospace applications, a modification of the height-based vertical coordinate is presented that permits the coordinate surfaces at upper levels to transition toward a constant pressure surface at the model’s upper boundary. This modification is conceptually similar to a terrain-following coordinate at low levels, but now modifies the coordinate surfaces at upper levels to conform to a constant pressure surface at the model top. Since this surface is evolving in time, the height of the upper boundary is adaptively adjusted to follow a designated constant pressure upper surface. This is accomplished by applying the hydrostatic equation to estimate the change in height along the boundary that is consistent with the vertical pressure gradient at the model top. This alteration in the vertical coordinate requires only minor modifications and little additional computational expense to the original height-based time-invariant terrain-following vertical coordinate employed in MPAS. The viability of this modified vertical coordinate formulation has been verified in a 2D prototype of MPAS for an idealized case of upper-level diurnal heating. Significance Statement Most atmospheric numerical models that use a height-based vertical coordinate employ a rigid lid at the top of the model domain. While a rigid lid works well for applications in the troposphere and stratosphere, it is not well suited for applications extending into the thermosphere where significant vertical expansion/contraction occurs due to deep heating/cooling of the atmosphere. This paper develops and tests a simple modification to the height-based coordinate formulation that allows the height of the upper boundary to adaptively follow a constant pressure surface. This added flexibility in the treatment of the upper domain boundary for height-based models may be particularly beneficial in facilitating their transition to a deep atmosphere configuration without significant retooling of the model numerics.

A Simulation Study on the Variation of Thermospheric O/N2 With Solar Activity

AbstractThe ratio of number density of atomic oxygen (O) to that of molecular nitrogen (N2) in the thermosphere (O/N2) on the constant pressure surface, which has complex temporal and spatial characteristics, is widely regarded as an important parameter connecting the terrestrial thermosphere and daytime ionosphere. Previous studies demonstrated that the thermospheric O/N2 increases with increasing solar activity, and the changes in O/N2 with solar activity show significant difference between winter and summer hemispheres. However, the root causes, which are responsible for the solar activity variation of O/N2, are not fully understood. In this study, the contributions of various physical and chemical processes on the response of O/N2 to the solar radiation change were quantitatively investigated through a series of controlled simulations from the Thermosphere Ionosphere Electrodynamics General Circulation Model. The simulation results suggested that the chemical processes lead to the increase of thermospheric O/N2 over the globe with increasing solar activity. The increase of O/N2 with solar activity is dominated by the enrichment of O abundance and the loss of N2 abundance in the lower and upper thermosphere, respectively. Moreover, the simulation results suggested that the stronger hemispheric asymmetry is attributed to the stronger thermospheric circulation, which changes the vertical advection of O/N2 through both direct and indirect effects.

К АППРОКСИМАЦИИ УРАВНЕНИЙ МОДЕЛИ ОБЛАЧНОЙ АТМОСФЕРЫ

A model of an ideal cloud atmosphere bounded from above by a free material constant-pressure surface is considered. It is assumed that the own volume of water vapor condensate is negligible, drops and crystals simultaneously exist as continuous fluids at positive and negative temperatures (°С), and saturated vapor pressure over the drop-crystal mixture depends on temperature alone. The velocity and temperature of condensate are the same as those for ambient air. The objective of the present paper is to approximate the equations of such model with a grid-characteristic method complemented with a correction of the finite-difference solution based on the integral conservation laws and on the rule of non-decreasing entropy. The applied correction is alternative to fulfilling the energy conservation law and the entropy rule. The patterns of calculated clouds generated when flowing over horizontally periodic terrain are given.

The Response of Middle Thermosphere (∼160 km) Composition to the November 20 and 21, 2003 Superstorm

AbstractTIMED/GUVI limb measurements and first‐principles simulations from the Thermosphere Ionosphere Electrodynamics Global Circulation Model (TIEGCM) are used to investigate thermospheric atomic oxygen (O) and molecular nitrogen (N2) responses in the middle thermosphere on a constant pressure surface (∼160 km) to the November 20 and 21, 2003 superstorm. The consistency between GUVI observations and TIEGCM simulated composition changes allows us to utilize TIEGCM outputs to investigate the storm‐time behaviors of O and N2 systematically. Diagnostic analysis shows that horizontal and vertical advection are the two main processes that determine the storm‐induced perturbations in the middle thermosphere. Molecular diffusion has a relatively smaller magnitude than the two advection processes, acting to compensate for the changes caused by the transport partly. Contributions from chemistry and eddy diffusion are negligible. During the storm initial and main phases, composition variations at high latitudes are determined by both horizontal and vertical advection. At middle‐low latitudes, horizontal advection is the main driver for the composition changes where O mass mixing ratio decreases (N2 mass mixing ratio increases); whereas horizontal and vertical advection combined to dominate the changes in the regions where increases ( decreases). Over the entire storm period, horizontal advection plays a significant role in transporting high‐latitude composition perturbations globally. Our results also demonstrate that storm‐time temperature changes are not the direct cause of the composition perturbations on constant pressure surfaces.

Stationary models of magnetized viscous tori around a Schwarzschild black hole

We present stationary solutions of magnetized, viscous thick accretion disks around a Schwarzschild black hole. We assume that the tori are not self-gravitating, are endowed with a toroidal magnetic field, and obey a constant angular momentum law. Our study focuses on the role of the black hole curvature in the shear viscosity tensor and in their potential combined effect on the stationary solutions. Those are built in the framework of a causality-preserving, second-order gradient expansion scheme of relativistic hydrodynamics in the Eckart frame description which gives rise to hyperbolic equations of motion. The stationary models are constructed by numerically solving the general relativistic momentum conservation equation using the method of characteristics. We place constraints in the range of validity of the second-order transport coefficients of the theory. Our results reveal that the effects of the shear viscosity and curvature are particularly noticeable only close to the cusp of the disks. The surfaces of constant pressure are affected by viscosity and curvature and the self-intersecting isocontour - the cusp - moves to smaller radii (i.e. towards the black hole horizon) as the effects become more significant. For highly magnetized disks the shift in the cusp location is smaller. Our findings might have implications on the dynamical stability of constant angular momentum tori which, in the inviscid case, are affected by the runaway instability.

A novel torque analysis method for drilling deep lunar soil by DEM

In order to solve the torque design problem of deep lunar soil sampling using drilling, a novel torque analysis method was presented based on discrete element model (DEM). This method includes three stages: drilling simulation of the bit and stem segment, resultant torque calculation, and predicted curve fitting. First, special drilling models were designed for a bit and stem separately. A high-density equivalent particle group, boundary vibration control, pre-drilling simulation and constant pressure surface control were designed for the bit and stem drilling modelling at different depths to ensure the rationality of the model. An example of the torque synthesis process was given, and the simulation time was analyzed. Finally, the simulation predicted torque curve was plotted and compared with the experimental curve. The experimental and simulation curves show that as the drilling depth increases, the torque increases approximately linearly first and then flattens out gradually after a depth of 1 m. The consistency between the two results indicated that the proposed method was validated. Using this method, engineers can take short time to analyze the torque and design basic parameters of the drill mechanism. The problem of high experimental cost and long simulation time in torque design is solved.

Different Peak Response Time of Daytime Thermospheric Neutral Species to the 27‐Day Solar EUV Flux Variations

AbstractPrevious work suggested that the peak response time of the mass densities of atomic oxygen (O) and molecular nitrogen (N2) in the thermosphere had more than a 1‐day difference relative to the peak of the 27‐day periodic variation of solar extreme ultraviolet (EUV) flux. In this study, we used the Thermosphere Ionosphere Electrodynamic General Circulation Model (TIEGCM) to explore the physical mechanisms responsible for the different peak response times of the daytime thermospheric neutral species. It was found that the peak response time of O or N2 mass density corresponds to the time of equilibrium between the contributions from the barometric effect and the change in its abundance. The peak response time of O is shorter than that of thermospheric temperature Tn, due to a dynamic change in the circulation that acts to cancel out the contribution from the barometric process prior to the peak of Tn. On the contrary, the change of N2 abundance contributes further to a decrease of N2 mass density on a constant pressure surface when the thermosphere is expanding. The change of chemical loss leads to a longer peak response time of N2 abundance than that due to barometric motion. Therefore, an equilibrium is reached after the barometric effect turns from expansion (contraction) to contraction (expansion), so that the peak response time of N2 is longer than that of Tn. Moreover, the meridional circulation in the thermosphere modulates the latitudinal dependence of the peak response time of thermospheric neutral species.

Demonstration and Evaluation of 3D Winds Generated by Tracking Features in Moisture and Ozone Fields Derived from AIRS Sounding Retrievals

For more than 15 years, polar winds from the Moderate Resolution Imaging Spectroradiometer (MODIS) imagery have been generated by the National Oceanic and Atmospheric Administration (NOAA) and the Cooperative Institute for Meteorological Satellite Studies (CIMSS). These datasets are a NOAA National Environmental Satellite, Data, and Information Service (NESDIS) operational satellite product that is used at more than 10 major numerical weather prediction (NWP) centers worldwide. The MODIS polar winds product is composed of both infrared window (IR-W) and water vapor (WV) tracked features. The WV atmospheric motion vectors (AMV) yield a better spatial distribution than the IR-W since both cloud and clear-sky features can be tracked in the WV images. As the new generation polar satellite-era begins with the Suomi National Polar-orbiting Partnership (S-NPP), there is currently no WV channel on the Visible/Infrared Imager/Radiometer Suite (VIIRS), resulting in a data gap with only IR-W derived AMVs possible. This scenario presents itself as an opportunity to evaluate hyperspectral infrared moisture retrievals from consecutive overlapping satellite polar passes to extract atmospheric motion from clear-sky regions on constant (and known) pressure surfaces, i.e., estimating winds in retrieval space rather than radiance space. Perhaps most significantly, this method has the potential to provide vertical wind profiles, as opposed to the current MODIS-derived single-level AMVs. In this study, the winds technique is applied to Atmospheric Infrared Sounder (AIRS) moisture retrievals from NASA’s Aqua satellite. The resulting winds are assimilated into the Goddard Earth Observing System Model, Version 5 (GEOS-5). The results are encouraging, as the AIRS retrieval polar AMVs have a similar quality as the MODIS AMVs and exhibit a positive impact in the hemispheric Day 4.5 to 6.5 forecasts for a one-month experiment in July 2012.

Practical gyrokinetics

Thousands of gyrokinetic papers have been published since the introduction of the gyrokinetic change of variables. The intent here is not to review the field, but rather the goal is to present a tutorial providing insight into why gyrokinetics is an appropriate description of turbulent transport. The focus is on turbulent transport in axisymmetric tokamaks, but many of the ideas and techniques are applicable to stellarators and other magnetic fusion devices with nested surfaces of constant pressure. Besides the origins of gyrokinetics and recent insights, gyrokinetic orderings and gyrokinetic variables are summarized. Then a compact, but careful, derivation of the simplest electrostatic gyrokinetic equation for tokamaks is presented, along with a brief mention of gyrokinetics for stellarators. The advantages of assuming scale separation between the finer spatial scales and faster time variation of the turbulence and the global behaviour and slow temporal evolution of the background are stressed. Moreover, the procedure for removing the adiabatic or Maxwell–Boltzmann response is emphasized. Scale separation allows the near Maxwellian behaviour of the background and the rapid variation of the turbulence to be described by separate, local gyrokinetic equations. The turbulent fluctuations are found by solving the nonlinear gyrokinetic equation for the non-adiabatic portion of the fluctuating distribution function. Also, generalizations of the gyrokinetic equation so that it retains electromagnetic and flow modifications are considered in detail along with some symmetry properties. In addition, ambipolarity, particle transport and heat transport are addressed, along with a discussion of the complications associated with describing momentum transport and profile evolution.

Temperature trends in Hawaiʻi: A century of change, 1917–2016

Based on a revised and extended multi‐station Hawaiʻi Temperature Index (HTI), the mean air temperature in the Hawaiian Islands has warmed significantly at 0.052°C/decade (p < 0.01) over the past 100 years (1917–2016). The year 2016 was the warmest year on record at 0.924°C above the 100‐year mean (0.202°C). During each of the last four decades, mean state‐wide positive air temperature anomalies were greater than those of any of the previous decades. Significant warming trends for the last 100 years are evident at low‐ (0.056°C/decade, p < 0.001) and high‐elevations (0.047°C/decade, p < 0.01). Warming in Hawai‘i is largely attributed to significant increases in minimum temperature (0.072°C/decade, p < 0.001) resulting in a corresponding downward trend in diurnal temperature range (−0.055°C/decade, p < 0.001) over the 100‐year period. Significant positive correlations were found between HTI, the Pacific Decadal Oscillation, and the Multivariate ENSO Index, indicating that natural climate variability has a significant impact on temperature in Hawaiʻi. Analysis of surface air temperatures from NCEP/NCAR reanalysis data for the region of Hawaiʻi over the last 69 years (1948–2016) and a mean atmospheric layer temperature time series calculated from radiosonde‐measured thickness (distance between constant pressure surfaces) data over the last 40 years (1977–2016) give results consistent with the HTI. Finally, we compare temperature trends for Hawaii's highest elevation station, Mauna Loa Observatory (3,397 m), to those on another mountainous subtropical island station in the Atlantic, Mt. Izaña Observatory (2,373 m), Tenerife, Canary Islands. Both stations sit above the local temperature inversion layer and have virtually identical significant warming trends of 0.19°C/decade (p < 0.001) between 1955 and 2016.

Hybrid Mass Coordinate in WRF-ARW and Its Impact on Upper-Level Turbulence Forecasting

Abstract Although a terrain-following vertical coordinate is well suited for the application of surface boundary conditions, it is well known that the influences of the terrain on the coordinate surfaces can contribute to increase numerical errors, particularly over steep topography. To reduce these errors, a hybrid sigma–pressure coordinate is formulated in the Weather Research and Forecasting (WRF) Model, and its effects are illustrated for both an idealized test case and a real-data forecast for upper-level turbulence. The idealized test case confirms that with the basic sigma coordinate, significant upper-level disturbances can be produced due to numerical errors that arise as the advection of strong horizontal flow is computed along coordinate surfaces that are perturbed by smaller-scale terrain influences. With the hybrid coordinate, this artificial noise is largely eliminated as the mid- and upper-level coordinate surfaces correspond much more closely to constant pressure surfaces. In real-data simulations for upper-level turbulence forecasting, the WRF Model using the basic sigma coordinate tends to overpredict the strength of upper-air turbulence over mountainous regions because of numerical errors arising as a strong upper-level jet is advected along irregular coordinate surfaces. With the hybrid coordinate, these errors are reduced, resulting in an improved forecast of upper-level turbulence. Analysis of kinetic energy spectra for these simulations confirms that artificial amplitudes in the smaller scales at upper levels that arise with the basic sigma coordinate are effectively removed when the hybrid coordinate is used.

Solitary water waves with discontinuous vorticity

We investigate the existence of solitary gravity waves traversing a two-dimensional body of water that is bounded below by a flat impenetrable ocean bed and above by a free surface of constant pressure. Our main interest is constructing waves of this form that exhibit a discontinuous distribution of vorticity. More precisely, this means that the velocity limits both upstream and downstream to a laminar flow that is merely Lipschitz continuous. We prove that, for any choice of background velocity with this regularity, there exists a global curve of solutions bifurcating from a critical laminar flow and including waves arbitrarily close to having stagnation points. Each of these waves has an axis of even symmetry, and the height of their streamlines above the bed decreases monotonically as one moves to the right of the crest.

Thermal removal of arsenic from copper concentrates: Three-dimensional isothermal predominance diagrams for the Cu-As-S-O system

The three-dimensional predominance volume diagrams (PVDs) for the system Cu-As-S-O were constructed at 900 K using PAs4O6 g, PO2 g, and PSO2 g as independent coordinates. The constant total pressure surface was used to identify the equilibrium phases that are stable at 0.25 atm total pressure. The isobaric surface superimposed on the predominance diagram provides useful insights into the roasting of complex copper sulfosalts such as enargite (Cu3AsS4) and tennantite (Cu12As4S13). There are nine interior invariant points each with four associated condensed phases at 900 K. The expanded diagrams showing the stability volumes of each individual phase are presented. According to the PVD for the Cu-As-S-O system, the transformation of enargite to copper sulfate follows the Cu3AsS4→CuS→CuSO4 or Cu3AsS4→Cu2S→ CuS→CuSO4 sequence when the pressure of As4O6 g is extremely low. At high As4O6 g pressures however, enargite can directly transform to copper sulfate.

On a Problem of Optimal Control of the Laminar Boundary Layer in Supersonic Flows on Constant-Pressure Surfaces

We consider the variational problem of Newtonian friction minimization that affects surfaces in supersonic flows at the constant velocity on the outer edge of the boundary layer.

Ideal relaxation of the Hopf fibration

Ideal magnetohydrodynamics relaxation is the topology-conserving reconfiguration of a magnetic field into a lower energy state where the net force is zero. This is achieved by modeling the plasma as perfectly conducting viscous fluid. It is an important tool for investigating plasma equilibria and is often used to study the magnetic configurations in fusion devices and astrophysical plasmas. We study the equilibrium reached by a localized magnetic field through the topology conserving relaxation of a magnetic field based on the Hopf fibration in which magnetic field lines are closed circles that are all linked with one another. Magnetic fields with this topology have recently been shown to occur in non-ideal numerical simulations. Our results show that any localized field can only attain equilibrium if there is a finite external pressure, and that for such a field a Taylor state is unattainable. We find an equilibrium plasma configuration that is characterized by a lowered pressure in a toroidal region, with field lines lying on surfaces of constant pressure. Therefore, the field is in a Grad-Shafranov equilibrium. Localized helical magnetic fields are found when plasma is ejected from astrophysical bodies and subsequently relaxes against the background plasma, as well as on earth in plasmoids generated by, e.g., a Marshall gun. This work shows under which conditions an equilibrium can be reached and identifies a toroidal depression as the characteristic feature of such a configuration.

Average field‐aligned ion velocity over the EISCAT radars

AbstractLong‐term measurements by the European Incoherent Scatter (EISCAT) radars at Tromsø (69.6°N, 19.2°E) and Svalbard (78.2°N, 16.0°E) are used to determine the climatology of the field‐aligned ion velocity in the F region ionosphere (175–475 km) at high latitudes. The average ion velocity is calculated at various altitudes and times of day. The magnitude of the average field‐aligned ion velocity is on the order of 10 m/s, similar to previous results at middle and low latitudes. The results obtained for the two radars are in good agreement. During daytime the direction of the average field‐aligned ion velocity changes from downward to upward around 350 km, while during nighttime it is upward at all heights. The reversal height of the daytime field‐aligned ion velocity depends on solar activity. It is elevated by more than 100 km during high solar flux periods compared to low solar flux periods. The Thermosphere Ionosphere Electrodynamics General Circulation Model reproduces the main features of the field‐aligned ion velocity climatology. The simulation results suggest that the plasma pressure gradient force and gravity force play a dominant role for the daytime field‐aligned ion motion. The height pattern of the field‐aligned ion velocity tends to be preserved in different solar activity conditions at constant pressure surfaces, but not at constant altitudes, which explains the observed dependence on solar activity. During nighttime, the effect of the neutral wind dominates the field‐aligned ion velocity.

Continuum Modeling of Steady Air Injection into Partially Saturated Soils

Proposed models and analytical solutions of steady one‐ and three‐dimensional (3D) air flow in partially saturated soil enable estimating air‐injection sources in unsaturated soils and optimizing their application. The 3D modeling offers six solutions for air injection from a point source located in a: (i) laterally unconfined domain and (ii) at the center of a cylindrically confined domain, in (a) an infinite, vertically unconfined domain, (b) a vertically semi‐infinite domain with a surface of constant pressure above the source, representing the effect of the atmosphere on air flow, and (c) with an impermeable surface below the source, representing the effect of a water table on the air flow. The 3D models were formulated using known mathematical solutions for water flow and adjusting them to describe air flow, assuming full analogy between the effect of gravitation on water flow to the effect of buoyancy on air flow. One‐dimensional air injection simulations based on two types of air‐permeability functions (a concaved exponential and a convex exponential) result in similar distributions of air pressure and capillary heads. Thus, the error caused by using the convex (of positive curvature) exponential function for linearizing the flow equation and for obtaining the 3D solutions is bounded, which justifies use of this function. Air flow patterns depend on a single soil characteristic parameter (α), indicative of the ratio between effects of buoyancy and capillary forces driving the air; high values indicate more upwardly oriented flow. The proposed analysis can be used for decision making regarding locations and depths of air‐injection sources for aeration in the vadose zone. Based on the air pressure distribution and the streamlines outlined by the relevant solutions we conclude that the effect of the water table below the source on air flow is negligible, especially in cylindrical confinements. Furthermore, the effect of the atmosphere on air flow in a cylindrical domain is also negligible. The proposed models are applicable especially when the air‐pressure gradient in the soil is relatively small, and the effect of air compressibility is negligible.

Composition and physical properties of the Asian Tropopause Aerosol Layer and the North American Tropospheric Aerosol Layer.

Recent studies revealed layers of enhanced aerosol scattering in the upper troposphere and lower stratosphere over Asia (Asian Tropopause Aerosol Layer (ATAL)) and North America (North American Tropospheric Aerosol Layer (NATAL)). We use a sectional aerosol model (Community Aerosol and Radiation Model for Atmospheres (CARMA)) coupled with the Community Earth System Model version 1 (CESM1) to explore the composition and optical properties of these aerosol layers. The observed aerosol extinction enhancement is reproduced by CESM1/CARMA. Both model and observations indicate a strong gradient of the sulfur-to-carbon ratio from Europe to the Asia on constant pressure surfaces. We found that the ATAL is mostly composed of sulfates, surface-emitted organics, and secondary organics; the NATAL is mostly composed of sulfates and secondary organics. The model also suggests that emission increases in Asia between 2000 and 2010 led to an increase of aerosol optical depth of the ATAL by 0.002 on average which is consistent with observations.Key Points The Asian Tropopause Aerosol Layer is composed of sulfate, primary organics, and secondary organics The North American Tropospheric Aerosol Layer is mostly composed of sulfate and secondary organics Aerosol Optical Depth of Asian Tropopause Aerosol Layer increases by 0.002 from 2000 to 2010

Atmospheric Kinetic Energy Spectra from Global High-Resolution Nonhydrostatic Simulations

Abstract Kinetic energy (KE) spectra derived from global high-resolution atmospheric simulations from the Model for Prediction Across Scales (MPAS) are presented. The simulations are produced using quasi-uniform global Voronoi horizontal meshes with 3-, 7.5-, and 15-km mean cell spacings. KE spectra from the MPAS simulations compare well with observations and other simulations in the literature and possess the canonical KE spectra structure including a very-well-resolved shallow-sloped mesoscale region in the 3-km simulation. There is a peak in the vertical velocity variance at the model filter scale for all simulations, indicating the underresolved nature of updrafts even with the 3-km mesh. The KE spectra reveal that the MPAS configuration produces an effective model resolution (filter scale) of approximately 6Δx. Comparison with other published model KE spectra highlight model filtering issues, specifically insufficient filtering that can lead to spectral blocking and the production of erroneous shallow-sloped mesoscale tails in the KE spectra. The mesoscale regions in the MPAS KE spectra are produced without use of kinetic energy backscatter, in contrast to other results reported in the literature. No substantive difference is found in KE spectra computed on constant height or constant pressure surfaces. Stratified turbulence is not resolved with the vertical resolution used in this study; hence, the results do not support recent conjecture that stratified turbulence explains the mesoscale portion of the KE spectrum.

Present-day concepts of atmospheric frontogenesis. Part 1. Theoretical ideas

Presented is a review of quantitative characteristics of atmospheric frontogenesis that describe it as the process of variations of the vector of the horizontal temperature gradient (both in value and in direction) in an individual particle. The frontogenesis that strives for recovering the thermal wind balance disturbed in the case of inhomogeneous advection, generates vertical circulation which is both thermally direct (warm air ascends relative to cold air) and thermally opposite (upward motions in the cold air). Given are the expressions for computing frontogenesis using the data on temperature, pressure, and wind. Used is the resolution of the frontogenetic vector function into components along the isoline of potential temperature both on and across the constant-pressure surface. The first component describes the change in the temperature gradient vector due to the rotation of isotherms (rotational frontogenesis), and the second component, the variations of the absolute value of the gradient (scalar frontogenesis). Quantitative characteristics of frontogenesis are efficient diagnostic parameters both for understanding weather processes and weather forecast specification and for the verification and enhancement of numerical models.