Mountain ordering: A method for classifying mountains based on their morphometry

A new method for classifying mountain morphology, ‘mountain ordering,’ is proposed, and quantitative expressions for various morphological parameters of two ordered mountains in northern Japan were obtained using this method. Mountain order was defined in terms of the closed contour lines on a topographic map. A set of closed, concentric contour lines defines a first-order mountain. Higher-order mountains can be defined as a set of closed contour lines that contain lower-order mountains and that have only one closed contour line for each elevation; they are identified as m + 1th-order mountains, where m represents the order of the enclosed, lower-order mountains. The geomorphometry for a mountain ordered according to this definition permits the identification of systematic relationships between various morphological parameters. The relationships between mountain order and these morphological parameters follow a form similar to that of Horton's laws, and permit the calculation of the ratios of number, area and height; these parameters are sufficient to express the magnitude of a mountain's dissection. The size–frequency distribution for area and height shows self-similarity for ordered mountains, and determines their fractal dimensions. Furthermore, the relationship between area and height, which has the form of a power function, describes the relief structure of ordered mountains. Copyright © 1999 John Wiley & Sons, Ltd.     

Convective destabilization of a thickened continental lithosphere

Removal or delamination of the lithospheric mantle in a late stage of mountain building is a process often invoked to explain syn orogenic extension, high temperature metamorphism, magmatism and uplift. One mechanism that could explain the lithospheric root detachment is the development of convective instabilities within the peridotitic lithosphere due to its high density. This mechanism is studied by two-dimensional convective numerical simulations in the simple case of a strongly temperature dependent viscous rheology appropriate for upper mantle rocks. We neglect here the weakening effect of a brittle rheology and of a crustal layer, and therefore we did not model tectonic deformations. Depending on the upper mantle viscosity and activation energy, a 300 km thick root can be inferred to be either indefinitely stable or to thicken with time or to thin with time. When the lithosphere is initially thicker than its equilibrium thickness, the convective flow at the base and on the sides of the lithospheric root is strong enough to cancel downwards heat conduction and to progressively remove the root. This flow is due to the finite density perturbations induced by the topography of the isotherms on the base and at the sides of the root. We derive two general parameterizations of the convective removal duration as a function of the equilibrium thickness, the thickening factor, the root width, and the rheological temperature scale. Using these relationships, and assuming that the lithospheric equilibrium thickness is about 100 km, the removal duration of a 250 km thick root ranges from 55 to 750 Myr depending on the root width. It is too small to explain the long term stability of cratonic lithospheric root, but too long to explain any sudden change in the stress and strain states in mountain belts development.     

Frequency shift of acoustic gravity waves in a stratified,isothermal, turbulent atmosphere

We study the modification of the frequency of small amplitude acoustic gravity waves which propagate in an isothermal turbulent atmosphere that is stratified by a homogeneous gravitational field. Using a Green's function method, the dispersion relation for the frequency of the waves is formulated as an integral eigenvalue equation and it is solved by perturbation techniques. We draw the following main conclusions: (a) for an arbitrary turbulent correlation spectrum the dispersion relation has a root with a negative imaginary part in the unphysical Riemann sheet of the dispersion function, leading to wave attenuation, much in the same way as it happens for Landau damping; (b) the real part of this root differs from the frequency of an acoustic gravity wave propagating in a nonturbulent medium and, for all forms of the turbulent correlation spectrum, the absolute value of this difference increases if gravity increases; (c) for a Gaussian turbulent correlation spectrum, this difference is always positive; (d) conversely if this frequency difference is known from observations, the auto-correlation function of the temperature fluctuations can be calculated through a simple inversion formula.     

Gamma random field simulation by a covariance matrix transformation method

In studies involving environmental risk assessment, Gaussian random field generators are often used to yield realizations of a Gaussian random field, and then realizations of the non-Gaussian target random field are obtained by an inverse-normal transformation. Such simulation process requires a set of observed data for estimation of the empirical cumulative distribution function (ECDF) and covariance function of the random field under investigation. However, if realizations of a non-Gaussian random field with specific probability density and covariance function are needed, such observed-data-based simulation process will not work when no observed data are available. In this paper we present details of a gamma random field simulation approach which does not require a set of observed data. A key element of the approach lies on the theoretical relationship between the covariance functions of a gamma random field and its corresponding standard normal random field. Through a set of devised simulation scenarios, the proposed technique is shown to be capable of generating realizations of the given gamma random fields.     

Statistical equilibrium distributions of baroclinic vortices in a rotating two-layer model at low Froude numbers

The point-vortex equilibrium statistical model of two-layer baroclinic quasigeostrophic vortices in an unbounded f-plane is examined. A key conserved quantity, angular momentum, serves to confine the vortices to a compact domain, thereby justifying the statistical mechanics model, and also eliminating the need for boundary conditions in a practical method for its resolution. The Metropolis method provides a fast and efficient algorithm for solving the mean field non-linear elliptic PDEs of the equilibrium statistical theory. A verification of the method is done by comparison with the exact Gaussian solution at the no interaction limit of zero inverse temperature. The numerical results include a geophysically and computationally relevant power law for the radii at which the most probable vortex distribution is non-vanishing: For fixed total circulation, and fixed average angular momentum, the radii of both layers are proportional to the square root of the inverse temperature β. By changing the chemical potentials μ of the runs, one is able to model the most probable vorticity distributions for a wide range of total circulation and energy. The most probable vorticity distribution obtained at low positive temperatures are consistently close to a radially symmetric flat-top profiles. At high temperatures, the radially symmetric vorticity profiles are close to the Gaussian distribution.     

Classifying wave forecasts with model-based Geostatistics and the Aitchison distribution

This paper proposes a non-parametric method of classification of maps (i.e., variable fields such as wave energy maps for the Western Mediterranean Sea) into a set of D typical regimes (calm, E-, SW- or N/NW-wind dominated storms, the 4 synoptic situations more often occurring in this region). Each map in the training set is described by its values at P measurement points and one of these regime classes. A map is thus identified as a labelled point in a P-dimensional feature space, and the problem is to find a discrimination rule that may be used for attaching a classification probability to future unlabelled maps. The discriminant model proposed assumes that some log-contrasts of these classification probabilities form a Gaussian random field on the feature space. Then, available data (labelled maps of the training set) are linked to these latent probabilities through a multinomial model. This model is quite common in model-based Geostatistics and the Gaussian process classification literature. Inference is here approximated numerically using likelihood based techniques. The multinomial likelihood of labelled features is combined in a Bayesian updating with the Gaussian random field, playing the role of prior distribution. The posterior corresponds to an Aitchison distribution. Its maximum posterior estimates are obtained in two steps, exploiting several properties of this family. The first step is to obtain the mode of this distribution for labelled features, by solving a mildly non-linear system of equations. The second step is to propagate these estimates to unlabelled features, with simple kriging of log-contrasts. These inference steps can be extended via Markov-chain Monte Carlo (MCMC) sampling to a hierarchical Bayesian problem. This MCMC sampling can be improved by further exploiting the Aitchison distribution properties, though this is only outlined here. Results for the application case study suggest that E- and N/NW-dominated storms can be successfully discriminated from calm situations, but not so easily distinguished from each other.     

NMR Logging to Estimate Hydraulic Conductivity in Unconsolidated Aquifers

Nuclear magnetic resonance (NMR) logging provides a new means of estimating the hydraulic conductivity (K) of unconsolidated aquifers. The estimation of K from the measured NMR parameters can be performed using the Schlumberger‐Doll Research (SDR) equation, which is based on the Kozeny–Carman equation and initially developed for obtaining permeability from NMR logging in petroleum reservoirs. The SDR equation includes empirically determined constants. Decades of research for petroleum applications have resulted in standard values for these constants that can provide accurate estimates of permeability in consolidated formations. The question we asked: Can standard values for the constants be defined for hydrogeologic applications that would yield accurate estimates of K in unconsolidated aquifers? Working at 10 locations at three field sites in Kansas and Washington, USA, we acquired NMR and K data using direct‐push methods over a 10‐ to 20‐m depth interval in the shallow subsurface. Analysis of pairs of NMR and K data revealed that we could dramatically improve K estimates by replacing the standard petroleum constants with new constants, optimal for estimating K in the unconsolidated materials at the field sites. Most significant was the finding that there was little change in the SDR constants between sites. This suggests that we can define a new set of constants that can be used to obtain high resolution, cost‐effective estimates of K from NMR logging in unconsolidated aquifers. This significant result has the potential to change dramatically the approach to determining K for hydrogeologic applications.     

Comparison of root water uptake functions to simulate surface energy fluxes within a deep‐rooted desert shrub ecosystem

Root water uptake (RWU) is a unique process whereby plants obtain water from soil, and it is essential for plant survival. The mechanisms of RWU are well understood, but their parameterization and simulation in current Land Surface Models (LSMs) fall short of the requirements of modern hydrological and climatic modelling research. Though various RWU functions have been proposed for potential use in LSMs, none was proven to be applicable for dryland ecosystems where drought was generally the limiting factor for ecosystem functioning. This study investigates the effect of root distribution on the simulated surface energy fluxes by incorporating the observed vertical root distribution. In addition, three different RWU functions were integrated into the Common Land Model (CLM) in place of the default RWU function. A comparison of the modified model's results with the measured surface energy fluxes measured by eddy covariance techniques in a Central Asian desert shrub ecosystem showed that both RWU function and vertical root distribution were able to significantly impact turbulent fluxes. Parameterizing the root distribution based on in‐situ measurement and replacing the default RWU function with a revised version significantly improved the CLM's performance in simulating the latent and sensible heat fluxes. Sensitivity analysis showed that varying the parameter values of the revised RWU function did not significantly impact the CLM's performance, and therefore, this function is recommended for use in the CLM in Central Asian desert ecosystems and, possibly, other similar dryland ecosystems. Copyright © 2013 John Wiley & Sons, Ltd.     

A diffusion approximation for a network of reservoirs with power law release rule

A diffusion approximation for a network of continuous time reservoirs with power law release rules is examined. Under a mild assumption on the inflow processes, we show that for physically reasonable values of the power law constants, the system of processes converges to a multi-dimensional Gaussian diffusion process. We also illustrate how the limiting Gaussian process may be used to compute approximations to the original system of reservoirs. In addition, we study the quality of our approximations by comparing them to results obtained by simulations of the original watershed model. The simulations offer support for the use of the approximation developed here.     

Elastic properties of saturated porous rocks with aligned fractures

Elastic properties of fluid saturated porous media with aligned fractures can be studied using the model of fractures as linear-slip interfaces in an isotropic porous background. Such a medium represents a particular case of a transversely isotropic (TI) porous medium, and as such can be analyzed with equations of anisotropic poroelasticity. This analysis allows the derivation of explicit analytical expressions for the low-frequency elastic constants and anisotropy parameters of the fractured porous medium saturated with a given fluid. The five elastic constants of the resultant TI medium are derived as a function of the properties of the dry (isotropic) background porous matrix, fracture properties (normal and shear excess compliances), and fluid bulk modulus. For the particular case of penny-shaped cracks, the expression for anisotropy parameter ε has the form similar to that of Thomsen [Geophys. Prospect. 43 (1995) 805]. However, contrary to the existing view, the compliance matrix of a fluid-saturated porous-fractured medium is not equivalent to the compliance matrix of any equivalent solid medium with a single set of parallel fractures. This unexpected result is caused by the wave-induced flow of fluids between pores and fractures.     

Biomechanical effects of trees in an old‐growth temperate forest

The role of biomechanical effects of trees (BETs) in ecosystem and landscape dynamics is poorly understood. In this study, we aim to (i) describe a widely applicable methodology for quantifying the main BETs in soil, and (ii) analyze the actual frequencies, areas and soil volumes associated with these effects in a mountain temperate old‐growth forest. The research took place in the Boubínský Primeval Forest in the Czech Republic; this forest reserve, predominated by Fagus sylvatica L. and Picea abies (L.) Karst., is among the oldest protected areas in Europe. We evaluated the effects of 4000 standing and lying trees in an area of 10.2 ha from the viewpoint of the following features: tree uprooting, root mounding, bioprotection, trunk baumsteins (rock fragments displaced by trunk growth), root baumsteins, stump hole infilling, trunk and root systems displacements, depressions formed after trunk fall, stemwash, and trunkwash. BETs were recorded in 59% of standing and 51% of lying dead trees (excluding the pervasive soil displacement by thickening trunks and roots and the infilling of decayed stumps). Approximately one tenth of the trees showed simultaneous bioprotective and bioerosion effects. Different tree species and size categories exhibited significantly different biomechanical effects. A bioprotective function was the most frequent phenomenon observed, while treethrows prevailed from the viewpoint of areas and soil volumes affected. The total area influenced by the BETs was 342 m² ha^?1. An additional 774 m² ha^?1 were occupied by older treethrow pit‐mounds with already decayed uprooted trunks. The total volume of soil associated with the studied phenomena was 322 m³ ha^?1, and apart from treethrows, volumes of the living and decaying root systems and bioprotective functions predominated. Other processes were not so frequent but still significant for biogeomorphology. Copyright © 2017 John Wiley & Sons, Ltd.     

Examination and parameterization of the root water uptake model from stem water potential and sap flow measurements

A simple field‐based method for directly parameterizing root water uptake models is proposed. Stem psychrometers and sap flow meters are used to measure stem water potential and plant transpiration rate continuously and simultaneously. Predawn stem water potential is selected as a surrogate for root zone soil water potential to examine and parameterize the root water uptake–water stress response functions. The method is applied to two drooping sheoak (Allocasuarina verticillata) trees for a period of 80 days, covering both a dry season and a wet season. The results indicate that the S‐shape function is more appropriate than the Feddes piecewise linear function for drooping sheoak to represent the effect of soil moisture stress on its root water uptake performance. Besides, the water stress function is found to be not only a function of soil moisture but also dependent of the atmospheric demand. As a result, the water stress function is corrected for the effect of atmospheric conditions. Copyright © 2012 John Wiley & Sons, Ltd.     

Correction of TRMM 3B43 monthly precipitation data over the mountainous areas of Peru during the period 1998–2007

In an attempt to estimate the spatial and temporal behaviour of rainfall over the mountainous areas of the Peruvian Andes, a new in situ monthly rainfall dataset has been collected (1998–2007) and compared with Tropical Rainfall Measuring Mission (TRMM) 3B43 monthly precipitation data for regions located above 3000 m. The reliability of the TRMM 3B43 data varies depending on the root mean squared error ratio (%RMSE) and correlation coefficient. Because of the discrepancy between the two datasets, the use of additive and multiplicative correction models is proposed for the TRMM 3B43 data. In the Peruvian mountain ranges, these correction models better approximate TRMM rainfall monthly values, as already verified for annual values. Copyright © 2011 John Wiley & Sons, Ltd.     

Impact of climate change on runoff from a mid‐latitude mountainous catchment in central Japan

Hydrologic balance in high‐altitude, mid‐latitude mountain areas is important in terms of the water resources available to associated lowlands. This study examined how current and historical shifts in precipitation (P) patterns and concurrent increases in temperature (T) affected runoff (Q) and other hydrologic components in a mid‐latitude mountain catchment of central Japan, using a combination of long‐term data and a simplified hydrologic model, along with their stochastic treatment. The availability of intensive meteorological and hydrological data from the period 1997–2001 allowed the derivation of key relationships for the current climate that tie the forcing term to the parameters or state variables. By using the data recorded in the period 1965–2001, the force for driving the historical simulation was generated. Based on this model and historical shifts in P and T, the probability density functions of Q (pdf(Q)) was computed. A main novelty in this study is that such a stochastic representation, which is useful for considering the influence of projected shifts in environmental factors on the hydrologic budget, was provided. Despite the large increase in the rate of T in winter and spring, pdf(Q) in spring and summer varied appreciably during the time studied mainly because of an increase in snowmelt. An interannual change in whole‐year Q was robust to shifts in T because while Q in spring increased, in summer it decreased, implying a crucial effect of global warming on mountain hydrologic regimes is change in the timing of Q. Copyright © 2009 John Wiley & Sons, Ltd.     

Electromagnetic fields of a vertical magnetic dipole above a laterally inhomogeneous thin layer of conductive overburden

An analytical formulation is developed for the resultant electromagnetic field of an oscillating vertical magnetic dipole located over a thin conductive sheet of infinite extent. The sheet is characterized by a conductivity-thickness product or conductance d that may be a function of the horizontal coordinates. The system of integral equations arising in the general formulation is simplified greatly when azimuthal symmetry prevails. Numerical results for a Gaussian variation of d in the radial direction are presented for the case of a symmetrically located source. These results are for the fields at the level of the source dipole over the conductive sheet. It is shown that the quadrature response of the sheet is enhanced when there is rapid variation of the conductance. The null in the resultant wave tilt is also found to be shifted toward the direction of increasing conductance.     

Dynamic response and optimal design of structures with large mass ratio TMD

This paper investigates the dynamic behavior and the seismic effectiveness of a non‐conventional Tuned Mass Damper (TMD) with large mass ratio. Compared with conventional TMD, the device mass is increased up to be comparable with the mass of the structure to be protected, aiming at a better control performance. In order to avoid the introduction of an excessive additional weight, masses already present on the structure are converted into tuned masses, retaining structural or architectural functions beyond the mere control function. A reduced order model is introduced for design purposes and the optimal design of a large mass ratio TMD for seismic applications is then formulated. The design method is specifically developed to implement High‐Damping Rubber Bearings (HDRB) to connect the device mass to the main structure, taking advantage of combining stiffness and noticeable damping characteristics. Ground acceleration is modeled as a Gaussian random process with white noise power spectral density. A numerical searching technique is used to obtain the optimal design parameter, the frequency ratio alpha, which minimizes the root‐mean‐square displacement response of the main structure. The study finally comprises shaking table tests on a 1:5 scale model under a wide selection of accelerograms, both artificial and natural, to assess the seismic effectiveness of the proposed large mass ratio TMD. Copyright © 2011 John Wiley & Sons, Ltd.     

BAYESIAN ESTIMATION IN SEISMIC INVERSION. PART II: UNCERTAINTY ANALYSIS1

A parameter estimation or inversion procedure is incomplete without an analysis of uncertainties in the results. In the fundamental approach of Bayesian parameter estimation, discussed in Part I of this paper, the a posteriori probability density function (pdf) is the solution to the inverse problem. It is the product of the a priori pdf, containing a priori information on the parameters, and the likelihood function, which represents the information from the data. The maximum of the a posteriori pdf is usually taken as a point estimate of the parameters. The shape of this pdf, however, gives the full picture of uncertainty in the parameters. Uncertainty analysis is strictly a problem of information reduction. This can be achieved in several stages. Standard deviations can be computed as overall uncertainty measures of the parameters, when the shape of the a posteriori pdf is not too far from Gaussian. Covariance and related matrices give more detailed information. An eigenvalue or principle component analysis allows the inspection of essential linear combinations of the parameters. The relative contributions of a priori information and data to the solution can be elegantly studied. Results in this paper are especially worked out for the non-linear Gaussian case. Comparisons with other approaches are given. The procedures are illustrated with a simple two-parameter inverse problem.     

Simulating soil‐water movement under a hedgerow surrounding a bottomland reveals the importance of transpiration in water balance

The objective of this study was to quantify components of the water balance related to root‐water uptake in the soil below a hedgerow. At this local scale, a two‐dimensional (2D) flow domain in the x–z plane 6 m long and 1·55 m deep was considered. An attempt was made to estimate transpiration using a simulation model. The SWMS‐2D model was modified and used to simulate temporally and spatially heterogeneous boundary conditions. A function with a variable spatial distribution of root‐water uptake was considered, and model calibration was performed by adjusting this root‐water uptake distribution. Observed data from a previous field study were compared against model predictions. During the validation step, satisfactory agreement was obtained, as the difference between observed and modelled pressure head values was less than 50 cm for 80% of the study data. Hedge transpiration capacity is a significant component of soil‐water balance in the summer, when predicted transpiration reaches about 5·6 mm day^?1. One of the most important findings is that hedge transpiration is nearly twice that of a forest canopy. In addition, soil‐water content is significantly different whether downslope or upslope depending on the root‐water uptake. The high transpiration rate was mainly due to the presence of a shallow water table below the hedgerow trees. Soil‐water content was not a limiting factor for transpiration in this context, as it could be in one with a much deeper water table. Hedgerow tree transpiration exerts a strong impact not only on water content within the vadose zone but also on the water‐table profile along the transect. Results obtained at the local scale reveal that the global impact of hedges at the catchment scale has been underestimated in the past. Transpiration rate exerts a major influence on water balance at both the seasonal and annual scales for watersheds with a dense network of hedgerows. Copyright © 2007 John Wiley & Sons, Ltd.     

2D共炮时间域高斯波束偏移

针对传统射线方法在奇异区成像精度不高,而2D频率域高斯波束叠前深度偏移需要计算成像点处每个频率的格林函数,影响计算效率的问题,本文通过使用复走时代替实走时,改变频率域下成像公式的积分顺序,给出了在时间域下进行高斯波束偏移的方法和计算公式.本文使用复杂数值模型验证了2D时间域高斯波束叠前偏移方法的正确性,并同传统射线偏移成像结果做了对比.对比结果表明时间域高斯波束偏移在成像精度上优于传统射线偏移.     

The hydrological significance of mountains: a regional case study,the Ebro River basin,northeast Iberian Peninsula

Abstract

This study evaluated the hydrological significance of mountain regions, comparing them with the lowlands of the Ebro River basin (northeast Iberian Peninsula). It was based on records obtained from measuring stations. An altitude of 1000 m above mean sea level was adopted as the criterion for distinguishing between lowland and mountain areas. We analysed 12 sub-basins whose rivers flow directly into the River Ebro, and which covered 66% of the total surface area, 91% of the mountain area and accounted for 77% of total annual runoff. For the River Ebro basin, we found that the mean precipitation depth, the runoff volume per unit of surface area, and the runoff coefficient were all greater in the mountains than in the adjacent lowlands, with respective differences of 70%, 180% and 60%. These results and the particular fragility of the Mediterranean mountain ecosystems confirm the mountain regions of the Ebro basin as strategic zones for hydrological and territorial planning.

Citation López, R. & Justribó, C. (2010) The hydrological significance of mountains: a regional case study, the Ebro River basin, northeast Iberian Peninsula. Hydrol. Sci. J. 55(2), 223–233.