Ronald B. Smith

The Influence of Mountains on the Atmosphere

Publisher Summary The chapter reviews the meteorological phenomena that are associated with topography. The study of airflow past mountains is complicated by the wide range of scales that must be considered. The ratios of the mountain width to each of the natural length scales are important in determining the physical regime of the flow. This idea is emphasized in the chapter by treating the effects of boundary layers and buoyancy. The theory of two-dimensional mountain waves with the help of its governing equations is presented and the observations of mountain waves are presented. The chapter also examines the influence of the boundary layer on mountain flows and slope winds and mountain and valley winds. It considers the perturbation to the wind flow caused by a mountain of intermediate scale where the rotation of the Earth cannot be neglected. For this the flow near mesoscale and synoptic-scale mountains, quasi-geostrophic flow over a mountain, the effect of inertia on the flow over mesoscale mountains, and theories of lee cyclogenesis are discussed. Finally the chapter describes planetary-scale mountain waves; a vertically integrated model of topographically forced planetary waves; the vertical structure of planetary waves; models of stationary planetary waves allowing meridional propagation and lateral; and variation in the background wind.

Hyperspectral vegetation indices and their relationships with agricultural crop characteristics

The objective of this paper is to determine spectral bands that are best suited for characterizing agricultural crop biophysical variables. The data for this study comes from ground-level hyperspectral reflectance measurements of cotton, potato, soybeans, corn, and sunflower. Reflectance was measured in 490 discrete narrow bands between 350 and 1,050 nm. Observed crop characteristics included wet biomass, leaf area index, plant height, and (for cotton only) yield. Three types of hyperspectral predictors were tested: optimum multiple narrow band reflectance (OMNBR), narrow band normalized difference vegetation index (NDVI) involving all possible two-band combinations of 490 channels, and the soil-adjusted vegetation indices. A critical problem with OMNBR models was that of “over fitting” (i.e., using more spectral channels than experimental samples to obtain a highly maximum R2 value). This problem was addressed by comparing the R2 values of crop variables with the R2 values computed for random data of a large sample size. The combinations of two to four narrow bands in OMNBR models explained most (64% to 92%) of the variability in crop biophysical variables. The second part of the paper describes a rigorous search procedure to identify the best narrow band NDVI predictors of crop biophysical variables. Special narrow band lambda (λ1) versus lambda (λ2) plots of R2 values illustrate the most effective wavelength combinations (λ1 and λ2) and bandwidths (Δλ1 and Δλ2) for predicting the biophysical quantities of each crop. The best of these two-band indices were further tested to see if soil adjustment or nonlinear fitting could improve their predictive accuracy. The best of the narrow band NDVI models explained 64% to 88% variability in different crop biophysical variables. A strong relationship with crop characteristics is located in specific narrow bands in the longer wavelength portion of the red (650 nm to 700 nm), with secondary clusters in the shorter wavelength portion of green (500 nm to 550 nm), in one particular section of the near-infrared (900 nm to 940 nm), and in the moisture sensitive near-infrared (centered at 982 nm). This study recommends a 12 narrow band sensor, in the 350 nm to 1,050 nm range of the spectrum, for optimum estimation of agricultural crop biophysical information.

The MAP Special Observing Period

Intense weather over major mountain ranges such as the Alps brings a high cost to society in the form of floods, windstorms, and threats to aviation. The Mesoscale Alpine Programme (MAP; see Table 1 for a list of acronyms) is a measured response of the international atmospheric and hydrologic community to the challenge of improving the understanding and prediction of these events. It relies on intense international cooperation to assemble an alpine-scale dataset suitable to advance the basic knowledge and prediction techniques. The following scientific objectives for MAP were published in the MAP Design Proposal (Binder and Schär 1996).

Formation of folds, boudinage, and mullions in non-Newtonian materials

Previous work has suggested that the formation of folds, boudins, and mullions by creep is caused by the same general type of instability. The results of Newtonian flow models of this process compare poorly with observation, however. The study reported here extends the analysis to include a general class of non-Newtonian materials restricted only to being incompressible, anelastic (that is, without memory), isotropic, and homogeneous. Although the material is isotropic, the perturbation flow associated with growing structure is found to obey an anisotropic type of flow law. In a strain-rate softening material undergoing pure shear, resistance to additional normal straining is significantly reduced from the background level, whereas resistance to tangential straining is unchanged. This has a profound effect on the formation of geologic structures, increasing the growth rates and altering the dominant wavelengths. Non-Newtonian behavior turns out to be necessary for the formation of boudins and mullions and plays an important role, but not a necessary one, in the formation of folds.

On Severe Downslope Winds

Abstract Recent observations and numerical experiments indicate that during severe downslope windstorms, a large region of slow turbulent air develops in the middle and upper troposphere while strong winds plunge underneath. A mathematical model of this severe wind state is developed using Longs equation. This theory predicts the altitude of the turbulent air, the strength of the winds, and the mountain drag. In the presence of a wind reversal, the theory indicates which wind reversal altitudes will lead to windstorm conditions.

Shallow-water flow past isolated topography. Part I: Vorticity production and wake formation

Abstract The flow of a single layer of shallow water past high three-dimensional topography is studied in a nonrotating environment and in the absence of surface friction. The dimensionless parameters for this problem are the upstream Froude number, the dimensionless mountain height, and a dimensionless measure of the dissipation rate. In part I of this study, high-resolution numerical simulations are utilized to construct a regime diagram for steady left–right symmetric flow and for the domain of parameter space with subcritical upstream conditions. Three distinct regimes occur. They are characterized, respectively, by fore–aft symmetry, essentially inviscid dynamics, and entirely subcritical conditions (regime I); by transition to supercritical flow and the occurrence of a hydraulic jump over the lee slope (regime II); and by the inability of the flow to climb the mountain top resulting in flow separation (regime III). Regimes II and III are associated with a wake that entails significant potential vort...

A Linear Theory of Orographic Precipitation

A linear theory of orographic precipitation is developed, including airflow dynamics, condensed water advection, and downslope evaporation. The formulation extends the widely used ‘‘upslope’’ model. Vertically integrated steady-state governing equations for condensed water are solved using Fourier transform techniques. Closed form expressions are derived for special cases. For more general cases, the precipitation field is computed quickly by multiplying the terrain transform by a wavenumber-dependent transfer function. Five length scales are included in the model: mountain width, a buoyancy wave scale, the moist layer depth, and two condensed water advection distances. The efficiency of precipitation in the model is sensitive to the decay of the forced ascent through the moist layer and to the advection of condensed water downwind into the region of descent. The strong influence of horizontal scale on precipitation pattern and amount predicted by the model is discussed. The model is illustrated by applying it to the Olympic Mountains in Washington State.

Hydrostatic Airflow over Mountains

Publisher Summary This chapter describes the hydrostatic airflow over mountains. The flow of a density stratified fluid over an obstacle has been widely studied because of its application to atmospheric airflow over the irregular terrain of the earths surface. Theories of vertically propagating waves, wave breaking, flow splitting, and wake eddies are discussed. The knowledge of these phenomena is used to construct an approximate regime diagram depicting how the nature of mountain-induced flow disturbance depends on the control parameters of the problem. The starting point for the discussion is the set of governing equations for a stratified Boussinesq fluid. It is found that on the top, lateral, and downstream boundaries, radiation or free-advection conditions might have to replace decay conditions due to the lack of dissipative mechanisms in equations. It is found that the turbulence and dissipation associated with wave breaking can significantly alter the flow field everywhere, not just in the breaking region. The modifications to the regime diagram caused by vertical shear and vertical variations in static stability are also elaborated.

Unified theory of the onset of folding, boudinage, and mullion structure

A mathematical study of the flow of a layered fluid shows that homogeneous pure shear aligned with the bedding is a “possible” state of motion in the sense that it is an exact solution to the governing equation. In the case of a single layer of a Newtonian material between two thick layers of different viscosity, such a state of motion is unstable to small disturbances. The growing disturbances have foldlike or pinch-and-swell form, depending on whether the applied compression is parallel or perpendicular to the layering and on whether the layer is more or less resistant to deformation than the surrounding rock. The combination of these two factors gives four distinct cases. One of these, labeled inverse folding, is of no interest because its growth rate is too small. The other three cases correspond qualitatively to folding, boudinage, and mullions. This result suggests that these three geologic structures are caused by the same mechanism: a secondary flow driven by an interfacial discontinuity in normal stress.

THE TERRAIN-INDUCED ROTOR EXPERIMENT : A Field Campaign Overview Including Observational Highlights

Abstract The Terrain-Induced Rotor Experiment (T-REX) is a coordinated international project, composed of an observational field campaign and a research program, focused on the investigation of atmospheric rotors and closely related phenomena in complex terrain. The T-REX field campaign took place during March and April 2006 in the lee of the southern Sierra Nevada in eastern California. Atmospheric rotors have been traditionally defined as quasi-two-dimensional atmospheric vortices that form parallel to and downwind of a mountain ridge under conditions conducive to the generation of large-amplitude mountain waves. Intermittency, high levels of turbulence, and complex small-scale internal structure characterize rotors, which are known hazards to general aviation. The objective of the T-REX field campaign was to provide an unprecedented comprehensive set of in situ and remotely sensed meteorological observations from the ground to UTLS altitudes for the documentation of the spatiotem-poral characteristics ...