Vertical Density Variations Research Articles

Variación longitudinal en densidad, resistencia a flexión y rigidez de la madera 'de seda' persa

Vertical variation of density, flexural strength and stiffness of Persian silk woodThe aim of this research was to investigate the effects of longitudinal position (stem height) and heart-sapwood on density, modulus of elasticity (MOE) and modulus of rupture (MOR) in bending for Persian silk wood (Albizzia julibrissin). Five normal trees were selected from the Guilan region, Iran. Samples for testing were prepared at four stem height levels (5%, 25%, 50% and 75% of total stem height) in both positions along radial direction (heartwood and sapwood). Analysis of variance results (Anova) indicated that the effects of longitudinal position (stem height) and heartwood-sapwood on the wood density, MOE and MOR were significant. The mean of wood density, MOE and MOR along longitudinal position from base to top decreased with height. The mean of wood density, MOR and MOE in sapwood are lower compared to the corresponding values for heartwood. The relationship between wood density and mechanical strength properties were analyzed by regression models. A positive correlation was found between wood density with MOE and MOR in both heartwood and sapwood.

Modeling wave attenuation induced by the vertical density variations of vegetation

A phase-averaged model, SWAN, and a phase-resolving RANS-type numerical model, NHWAVE, were compared to previously reported physical model data to evaluate the effectiveness of these models in simulating the attenuation of irregular waves propagating over emergent vegetation with variations in stem heights. The physical model was conducted with two treatments of vegetation, one with a uniform stem height and the other with different heights approximating a linear distribution in stem density over the vertical. The number of stems in the second treatment was doubled so that the total projected area over the vertical was the same between the two tests. The drag coefficients CD used by SWAN-SL (single-layer in SWAN), SWAN-ML (multi-layer in SWAN) and NHWAVE to model the presence of the vegetation were calibrated separately against the physical model data after removing the effects of bottom and sidewall friction. Although it was expected that every model would have to be recalibrated for a given wave condition and water depth due to the dependence of CD on the Keulegan–Carpenter number, this paper showed that it was also necessary to recalibrate CD in SWAN-SL for a given wave condition and water depth when the two different vegetation treatments were applied. Conversely, it was shown that the CD values in NHWAVE and SWAN-ML changed very little between the two treatments, highlighting the utility of a layered SWAN and RANS model for estimating wave attenuation when the aboveground biomass is no longer uniform over the vertical. The vertical structure of vegetation-induced turbulent kinetic energy, eddy viscosity and dissipation rate were investigated numerically using NHWAVE.

A discontinuous Galerkin method for two-layer shallow water equations

In this paper, we study a discontinuous Galerkin method to approximate solutions of the two-layer shallow water equations on non-flat topography. The layers can be formed in the shallow water model based on the vertical variation of water density which in general depends on the water temperature and salinity. For a water body with equal density the model reduces to the canonical single-layer shallow water equations. Thus, for a model with equal density on flat bottom, the method is equivalent to the discontinuous Galerkin method for conservation laws. The considered method is a stable, highly accurate and locally conservative finite element method whose approximate solutions are discontinuous across inter-element boundaries; this property renders the method ideally suited for the hp-adaptivity. Several numerical results illustrate the performance of the method and confirm its capability to solve two-layer shallow water flows including tidal conditions on the water free-surface and bed frictions on the bottom topography.

Constraining the thick disc formation scenario of the Milky Way

We study the shape of the thick disc using photometric data at high and intermediate latitudes from SDSS and 2MASS surveys. We use the population synthesis approach using an ABC-MCMC method to characterize the thick disc shape, scale height, scale length, local density and flare, and we investigate the extend of the thick disc formation period by simulating several formation episodes. We find that the vertical variation in density is not exponential, but much closer to an hyperbolic secant squared. Assuming a single formation epoch, the thick disc is better fitted with a sech2 scale height of 470 pc and a scale length of 2.3 kpc. However if one simulates two successive formation episodes, mimicking an extended formation period, the older episode has a higher scale height and a larger scale length than the younger episode, indicating a contraction during the collapse phase. The scale height decreases from 800 pc to 340 pc, and the scale length from 3.2 kpc to 2 kpc. The star formation increases from the old episode to the young one. During the fitting process, the halo parameters are also determined. The constraint on the halo shows that a transition between a inner and outer halo, if exists, cannot be at a distance of less than about 30 kpc, which is the limit of our investigation using turnoff halo stars. Finally, we show that extrapolating the thick disc towards the bulge region explains well the stellar populations observed there, that there is no longer need to invoke a classical bulge. To explain these results, the most probable scenario for the thick disc is that it formed while the Galaxy was gravitationally collapsing from well mixed gas-rich giant clumps sustained by high turbulence which awhile prevent a thin disc to form, as proposed by Bournaud et al. (2009). This scenario explains the observations in the thick disc region as well as in the bulge region. (abridged)

Nonlinear and dispersive free surface waves propagating over fluids with weak vertical and horizontal density variation

AbstractWe consider the change in fluid density in a depth-integrated long-wave model. By allowing horizontal and vertical variation of fluid density, a depth-integrated model for long gravity waves over a variable-density fluid has been developed, where density change effects are included as correction terms. In particular, a two-layer fluid system is chosen to represent vertical density variations, where interfacial wave effects on the free surface are accounted for through direct inclusion of the velocity component of the interfacial wave. For the numerical implementation of the model, a finite-volume scheme coupled with an approximate Riemann solver is adopted for leading-order terms while cell-centred finite-volume methods are utilized for others. Numerical tests in which the density field is configured to vary either horizontally or vertically have been performed to verify the model. For horizontal variation of fluid density, a pneumatic breakwater system is simulated and fair agreement is observed between computed and measured data, indicating that the current induced by the upward bubble flux is responsible for wave attenuation to some degree. To investigate the effects of internal motion on the free surface, a two-layer fluid system with monochromatic internal wave motion is tested numerically. Simulated results agree well with the measured and analytical data. Lastly, nonlinear interactions between external- and internal-mode surface waves are studied numerically and analytically, and the model is shown to have nonlinear accuracy limitations similar to existing Boussinesq-type models.

The compressional beta effect: A source of zonal winds in planets?

Giant planets like Jupiter and Saturn feature strong zonal wind patterns on their surfaces. Although several different mechanisms that may drive these jets have been proposed over the last decades, the origin of the zonal winds is still unclear. Here, we explore the possibility that the interplay of planetary rotation with the compression and expansion of the convecting fluid can drive multiple deep zonal jets by a compressional Rhines-type mechanism, as originally proposed by Ingersoll and Pollard (Ingersoll, A.P., Pollard, D. [1982]. Icarus 52(1), 62–80). In a certain limit, this deep mechanism is shown to be mathematically analogous to the classical Rhines mechanism possibly operating at cloud level. Jets are predicted to occur on a compressional Rhines length lR=(2Ω〈Hρ-1〉vjet-1)-1/2, where Ω is the angular velocity, 〈Hρ-1〉 is the mean inverse density scale height and vjet is the typical jet velocity. Two-dimensional numerical simulations using the anelastic approximation reveal that this mechanism robustly generates jets of the predicted width, and that it typically dominates the dynamics in systems deeper than O(lR). Potential vorticity staircases are observed to form spontaneously and are typically accompanied by unstably stratified buoyancy staircases. The mechanism only operates at large rotation rates, exceeding those typically reached in three-dimensional simulations of deep convection in spherical shells. Applied to Jupiter and Saturn, the compressional Rhines scaling reasonably fits the available observations. Interestingly, even weak vertical density variations such as those in the Earth core can give rise to a large number of jets, leading to fundamentally different flow structures than predicted by the Boussinesq models typically used in this context.

A new fast methodology to estimate the density of frozen materials by means of common offset GPR data

Abstract We propose a methodology to estimate the density of frozen media (snow, firn and ice) using common offset (CO) GPR data. The technique is based on reflection amplitude analysis to calculate the series of reflection coefficients used to estimate the dielectric permittivity of each layer. We determine the vertical density variations for all the GPR traces by applying an empirical equation. We are thus able to infer the nature of frozen materials, from fresh snow to firn and ice. The proposed technique is critically evaluated and validated on synthetic data and further tested on real data of the Glacier of Mt. Canin (South-Eastern Alps). Despite the simplifying hypotheses and the necessary approximations, the average values of density for different levels are calculated with acceptable accuracy. The resulting large-scale density data are fundamental to estimate the water equivalent (WE), which is an essential parameter to determine the actual water mass within a certain frozen volume. Moreover, this analysis can help to find and locate debris or moraines embedded within the ice bodies.

Density and undrained shear strength of bed sediment from ND-CPT

The density and the undrained shear strength (s u) of bed sediments at either side of the Isahaya Bay dike in the Ariake Sea, Japan, were investigated using nuclear density cone penetration tests (ND-CPTs). The nuclear density cone penetrometer (ND-CP) was operated from a boat, conducting 71 ND-CPTs. Furthermore, 26 undisturbed samples were obtained for soil density and s u measurements to calibrate the ND-CPT data. The results show that the density and s u obtained from in situ with the ND-CPTs agree well with those from the laboratory tests on undisturbed samples, and the obtained density profiles show good repeatability. The vertical variation in density and s u of the bed sediment can be obtained from the ND-CPT results. The relations between the density and s u show that s u increases with an increase in density, but that this relation is site specific. The values of s u show an exponentially growing trend and the values of log s u show a linearly increasing trend with density. The vertical distribution of the bed sediments can be described using the density values obtained with the ND-CPT.

Canopy vertical heterogeneity plays a critical role in reflectance simulation

An explicit analytical model for calculating vegetation canopy reflectance, the multiple-layer canopy radiative transfer model (MRTM), has been developed in this paper. The model is based on radiative transfer theory by separating the roles of incident direct and diffuse radiation and radiation singly and multiply scattered by foliage. Specifically, the vertical heterogeneity of biophysical and biochemical parameters within the canopy was carefully treated in the model. This model was validated with field measurements from a deciduous forest canopy. The results proved that the model could reproduce the measured reflectance quite well. In addition, the performance of MRTM was found to be superior in comparison to other canopy models such as PROSAIL, ACRM and FRT. The significant effect of vertical heterogeneity on the canopy reflectance was clearly identified by different scenarios, which indicates that the influence of vertical variation in leaf area density and leaf chlorophyll, water, and dry matter contents cannot be neglected, especially when the total LAI is large. If such influences are ignored, significant biases in the estimated canopy reflectance can be expected. Since this multiple-layer model is a hybrid one that offers efficient calculation, it could serve as a primary model to develop more accurate reflectance models for inhomogeneous forests at plot and regional scales in future studies.

Geothermal studies of the Outokumpu Deep Drill Hole, Finland: Vertical variation in heat flow and palaeoclimatic implications

Detailed geothermal studies of deep drill holes provide insights to heat transfer processes in the crust, and allow separation of different factors involved, such as palaeoclimatic and structural conductive effects as well as advective fluid flow effects. We present high resolution geothermal results of the 2516 m deep Outokumpu Deep Drill Hole in eastern Finland drilled in 2004–2005 into a Palaeoproterozoic formation with metasedimentary rocks, ophiolite-derived altered ultramafic rocks and pegmatitic granite. The down-hole temperatures have been logged five times after end of drilling and extend to day 948 after drilling. The hole is completely cored (79% core coverage) and thermal conductivity measurements were done at 1 m intervals. The geothermal results on temperature gradient, thermal conductivity and heat flow density yield an exceptionally detailed data set and indicate a significant vertical variation in gradient and heat flow density. Heat flow density increases from about 28 – 32 mW m −2 in the uppermost 1000 m to 40–45 mW m −2 at depths exceeding 2000 m. The estimated undisturbed surface heat flow value is 42 mW m −2. We present results on forward and inverse transient conductive models which suggest that the vertical variation in heat flow can mostly be attributed to a palaeoclimatic effect due to ground surface temperature (GST) variations during the last 100,000 years. The modeling suggests that the average GST was about −3 to −4 °C during the Weichselian glaciation. Holocene GST values are within ±2° from the present average GST in Outokumpu (5 °C). The topographic hydraulic heads and hydraulic conductivity of crystalline rocks are low which suggests that advective heat transfer in the formation is not significant. The slow replacement of fresh flushing water by saline formation fluids is observed in the hole, but it does not generate significant thermal disturbances in the logs. On the other hand, free sluggish thermal convection is present in the large diameter (22 cm) borehole, and temperature variations in the range of few mK to 0.01 K occur over times of minutes to tens of minutes. Theory suggests that convection cells are about as tall as the drill hole diameter, and thus the free convection is expected to generate only local thermal ‘noise’ not affecting the general geothermal results.

The formation and evolution of stratification during transient mixing ventilation

We investigate the buoyancy-driven ventilation of an enclosed volume of buoyant fluid, which is connected to the exterior through two openings at the top of the enclosure. An exchange flow becomes established, with outflow through one opening being matched by an equal and opposite inflow through the other vent. The inflowing flux of dense exterior fluid develops a turbulent buoyant plume, which mixes with the interior fluid as it cascades to the base of the fluid volume. An upward return flow gradually stratifies the confined volume of fluid, with a first front of relatively dense plume fluid advancing to the top of the space. Initially, the exchange flow is steady, but as the first front rises above the inflow opening, the flow rate wanes. The initial development of the exchange flow and interior stratification follows the classical filling box work of Baines & Turner (J. Fluid Mech., vol. 37, 1969, p. 51), with a plume of constant buoyancy flux. Once the first front exits the space, the volume flux rapidly asymptotes to the form Q = Q0(τ/(τ+t)) from the initial value Q0, where τ is the buoyancy-driven draining time, based on the initial density contrast with the environment. The vertical structure of the interior density stratification asymptotes to a profile of constant shape whose amplitude decays in time as (τ/(τ+t))2, and we identify conditions under which the vertical variation in density is comparable to the difference between mean interior density and the exterior. This generalises the analysis presented by Linden, Lane-Serff & Smeed (J. Fluid Mech., vol. 212, 1990, p. 309), who assumed that the interior fluid is well mixed. New laboratory experiments of the process are shown to be consistent with our predictions of the evolution of the flow, the interior stratification and the migration of contaminants. We also develop our analysis for situations where there are multiple stacks and show how this improves the mixing efficiency for a given ventilation flow. The model has relevance for the design of transient mixing ventilation in a building, especially when the effect of vertical stratification is important for ensuring thermal comfort.

LSTRKFALTG – A forward modeling program to compute theoretical gravity anomalies of strike limited listric fault structures with prescribed vertical variation in density

A method to compute the gravity anomalies of strike limited listric fault structures among which the density contrast varies continuously with depth is presented along with a program, LSTRKFALTG. The expression for the gravity anomaly due to a listric fault structure having finite strike length is derived in the space domain using both analytical and numerical approaches. The main program is supported with a subroutine SIMP. Calculation of gravity anomalies at different offsets across a synthetic fault structure reveals the fact that the offset of the profile controls the magnitude of the gravity anomaly. Sample input and output data files pertaining to a synthetic fault model are presented. The validity and efficacy of the method is demonstrated with a real field example.

Relative contribution of temperature and salinity to ocean acoustic reflectivity

Marine seismic data display laterally coherent reflectivity from the water column that is attributed to fine‐scale oceanic layering. The amplitude of the different reflections is the expression of acoustic impedance contrasts between neighbouring water masses, and therefore water reflectivity maps the ocean's vertical sound speed and density (i.e., temperature and salinity) variations. Here we determine the relative contribution of each parameter by computing the temperature and salinity partial derivatives of sound speed and density, and using them to estimate reflection coefficients from a real oceanographic dataset. The results show that the mean contribution of density variations is 5–10%, while 90–95% is due to sound speed variations. On average, 80% of reflectivity comes from temperature contrasts. Salinity contribution averages 20%, but it is highly variable and reaches up to 40% in regions prone to diffusive convection such as the top of the Mediterranean Undercurrent in the Gulf of Cadiz.

Intratree vertical variation of fruit density and the nature of contest competition in frugivores

Recently, we demonstrated that the highest densities of fruit pulp are located in the uppermost zones of tree crowns. Since heterogeneous distributions of depletable food is theorized to foster contest competition, we tested three hypotheses involving rank differences among species of arboreal frugivores: (1) In the absence of competitors, species tend to feed in higher strata of tree crowns; (2) interspecific contest competition occurs through monopolization and usurpation of feeding sites in these higher strata; and (3) subordinate species decrease their feeding height and ingestion rate when dominants enter the food patch. To test these hypotheses, we observed chimpanzees (Pan troglodytes), red-tailed monkeys (Cercopithecus ascanius), blue monkeys (Cercopithecus mitis), and gray-cheeked mangabeys (Lophocebus albigena) in Kibale National Park, Uganda. We found that: (1) all four primates fed preferentially in upper tree crowns when alone, (2) dominant species monopolized and aggressively usurped the upper crown when co-feeding with subordinates and the latter retreated below the middle of tree crowns, (3) in the presence of dominant species, subordinate species showed lower standardized feeding height and modified their food intake rates, while dominants were not affected by the subordinate species, (4) subordinates moved down at the arrival of and up at the departure of dominants, and (5) the presence of folivores in the tree did not affect the feeding height of a frugivore, even through folivores were socially dominant. Contrary to expectations, we found that red-tailed monkeys decreased their movements between successive fruits that they ate in the presence of blue monkeys compared to when they were feeding alone, perhaps to avoid disturbing dominants and attracting aggression or because they ingested more semi-ripe and green unripe fruits, i.e., more food of lower quality.

Chromospheric magnetic field and density structure measurements using hard X-rays in a flaring coronal loop

Aims. A novel method of using hard X-rays as a diagnostic for chromospheric density and magnetic structures is developed to inf er sub-arcsecond vertical variation of magnetic flux tube size and neutral gas density. Methods. Using Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) X-ray data and the newly developed X-ray visibilities forward fitting technique we find the FWHM and ce ntroid positions of hard X-ray sources with sub-arcsecond r esolution (∼ 0.2 ′′ ) for a solar limb flare. We show that the height variations of t he chromospheric density and the magnetic flux densities can be found with unprecedented vertical resolution of∼ 150 km by mapping 18-250 keV X-ray emission of energetic electrons propagating in the loop at chromospheric heights of 400-1500 km. Results. Our observations suggest that the density of the neutral gas is in good agreement with hydrostatic models with a scale height of around 140± 30 km. FWHM sizes of the X-ray sources decrease with energy suggesting the expansion (fanning out) of magnetic flux tube in the chromosphere with height. The magnetic scale height B(z) (dB/dz) −1 is found to be of the order of 300 km and strong horizontal magnetic field is associated with noticeable flux tube expansion at a height of∼ 900 km.

Vertical variation of particle speed and flux density in aeolian saltation: Measurement and modeling

Particle dynamics in aeolian saltation has been studied in a boundary layer wind tunnel above beds composed of quartz grains having diameters of either 242 μm or 320 μm. The cross section of the tunnel is 600 mm × 900 mm, and its thick boundary layer allows precise estimation of the fluid friction speed. Saltation is modeled using a numerical saltation model, and predicted grain speeds agree fairly well with experimental results obtained from laser‐Doppler anemometry. The use of laser‐Doppler anemometry to study aeolian saltation is thoroughly discussed and some pitfalls are identified. At 80 mm height the ratio between air speed and grain speed is about 1.1 and from there it increases toward the bed so that at 5 mm it is about 2.0. All grain speed profiles converge toward a common value of about 1 m/s at 2−3 mm height. Moreover, the estimated launch velocity distributions depend only very weakly on the friction speed in contrast to what has often been assumed in the literature. Flux density profiles measured with a laser‐Doppler appear to be similar to most other density profiles measured with vertical array compartment traps; that is, two exponential segments will fit data between heights from a few millimeters to 100−200 mm. The experimental flux density profiles are found to agree well with model predictions. Generally, validation rates are low from 30 to 50% except at the highest level of 80 mm, where they approach 80%. When flux density profiles based on the validated data are used to estimate the total mass transport rate results are in fair agreement with measured transport rates except for conditions near threshold where as much as 50% difference is observed.

Numerical Study of the Response of an Atmospheric Surface Layer to a Spatially Nonuniform Plant Canopy

High-accuracy large-eddy simulations of neutral atmospheric surface-layer flow over a gapped plant canopy strip have been performed. Subgrid-scale (SGS) motions are parameterized by the Sagaut mixed length SGS model, with a modification to compute the SGS characteristic length self-adaptively. Shaw’s plant canopy model, taking the vertical variation of leaf area density into account, is applied to study the response of the atmospheric surface layer to the gapped dense forest strip. Differences in the region far away from the gap and in the middle of the gap are investigated, according to the instantaneous velocity magnitude, the zero-plane displacement, the potential temperature and the streamlines. The large-scale vortex structure, in the form of a roll vortex, is revealed in the region far away from the gap. The nonuniform spatial distribution of plants appears to cause the formation of the coherent structure. The roll vortex starts in the wake of the canopy, and results in strong fluctuations throughout the entire canopy region. Wind sweeps and ejections in the plant canopy are also attributed to the large vortex structure.

Internal tides modelling in the bay of Biscay. Comparisons with observations

An Isopycnic Coordinate Ocean Model is used to represent the three-dimensional propagation of internal tides in the Bay of Biscay. The model is forced by the semi-diurnal tidal waves M2, S2, N2 and K2. A high resolution topography of French and Iberian continental slopes preserves the shape of the main canyons, which are areas of internal tide generation. Hydrological and velocity data collected during a French Naval experiment in 1994 are compared with the model results. Near the generation area, the vertical distribution of the internal tide amplitude, associated with a vertical shear of baroclinic tidal currents, is in agreement with the observations. Moreover, at most locations, the increase in the baroclinic current modelled near the bottom depth matches the data. This increase is related to the distribution of the internal tide amplitude along the ray slope defined by c( z ) = ( w 2 - f 2 /N where w is the tidal frequency, f the Coriolis parameter and N(z) the buoyancy frequency. In most of the data/model comparisons, the vertical density variation in the deep layers shows a difference in phase in agreement with the ray theory. Over the abyssal plain, high horizontal shears of surface current are modelled at mid-bay, i.e. in areas where the internal wave energy coming from the deep ocean encounters the seasonal thermocline. However, the location of these areas is very sensitive to the initial vertical density profile: the three-dimensional variation of the density must be introduced in the initial conditions to improve the model results.

Effects of temporal dynamics and vertical structure of the seagrassZostera caulescenson distribution and recruitment of the epifaunal encrusting bryozoaMicroporella trigonellata

AbstractSeagrass is an ephemeral habitat for epifaunal sessile invertebrates attaching on seagrass leaves, and spatial and temporal dynamics of seagrasses strongly affect the distribution of epifauna.Zostera caulescensMiki, a seagrass species endemic to Japan, provides a complex habitat for epifauna with two types of shoots: vegetative, less than 1 m tall, and flowering, 5–7 m tall. We conducted monthly field observations and a manipulative field experiment to investigate the effects of the seagrass vertical structure and its temporal variation on the distribution and recruitment of the encrusting bryozoanMicroporella trigonellata. The density ofM. trigonellataon the leaves of flowering shoots, located at the seagrass canopy, varied temporally, reaching maximum in summer and minimum in winter. In contrast,M. trigonellatadensity on the leaves of vegetative shoots near the sea floor was consistently low throughout the study period. Early recruit bryozoans also showed this temporal and vertical variation in density; thus spatial and temporal variation in recruitment determined the distribution of the whole colonies. The field experiment revealed that the recruitment rate ofM. trigonellatawas significantly higher at the higher position of the water column (3 m above the sea floor) than at the lower position (0.5 m) in June. However, the recruitment rate was higher at the lower position in October when most of the flowering shoots started falling down. The temporal change in bryozoan habitat selection is considered to be adaptive to maintain their population on the seagrass leaves that show complex temporal dynamics.

Gravity and density variations of the tilted Tottabetsu plutonic complex, Hokkaido, northern Japan: implications for subsurface intrusive structure and pluton development

Abstract An exposed cross section of the tilted Tottabetsu plutonic complex allows direct evaluation of its original 2-D cross-sectional shape and pretilting vertical density variations in both the pluton and the country rocks, which serves as a strong constraint in gravity modeling that complements information on the ’missing’ pretilting horizontal dimension of this tilted pluton. The pluton is stratified with the uppermost thin granitic unit (≈1-km thick) and the underlying thick gabbro-diorite units (≈9-km thick) that preserve a stratigraphic record of numerous hotter replenishments in the form of alternation of originally horizontal mafic sheets and cumulate layers. Both the pluton and the country rocks show systematic density increase with pretilting crustal depth, but density contrast of the pluton with the country rocks varies between each unit. The 2-D cross-sectional shape and gravity analysis revealed that the pluton had a vertically-elongated shape with vertical side walls before tilting. The vertical side walls, together with the stack of the originally horizontal sheets and cumulate layers, suggests that the pluton grew only vertically by piston mechanism. The very thick, exposed cross section provides unequivocal evidence for development of such a pluton with this unusual shape and mass distribution, which has been inferred elsewhere only by some geophysical studies.