Wind direction

Abstract: Review of several recent ocean surface wave models finds that while comprehensive in many regards, these spectral models do not satisfy certain additional, but fundamental, criteria. We propose that these criteria include the ability to properly describe diverse fetch conditions and to provide agreement with in situ observations of Cox and Munk [1954] and Jahne and Riemer [1990] and Hara et al. [1994] data in the high-wavenumber regime. Moreover, we find numerous analytically undesirable aspects such as discontinuities across wavenumber limits, nonphysical tuning or adjustment parameters, and noncentrosymmetric directional spreading functions. This paper describes a two-dimensional wavenumber spectrum valid over all wavenumbers and analytically amenable to usage in electromagnetic models. The two regime model is formulated based on the Joint North Sea Wave Project (JONSWAP) in the long-wave regime and on the work of Phillips [1985] and Kitaigorodskii [1973] at the high wavenumbers. The omnidirectional and wind-dependent spectrum is constructed to agree with past and recent observations including the criteria mentioned above. The key feature of this model is the similarity of description for the high- and low-wavenumber regimes; both forms are posed to stress that the air-sea interaction process of friction between wind and waves (i.e., generalized wave age, u/c) is occurring at all wavelengths simultaneously. This wave age parameterization is the unifying feature of the spectrum. The spectrum's directional spreading function is symmetric about the wind direction and has both wavenumber and wind speed dependence. A ratio method is described that enables comparison of this spreading function with previous noncentrosymmetric forms. Radar data are purposefully excluded from this spectral development. Finally, a test of the spectrum is made by deriving roughness length using the boundary layer model of Kitaigorodskii. Our inference of drag coefficient versus wind speed and wave age shows encouraging agreement with Humidity Exchange Over the Sea (HEXOS) campaign results.

Abstract: From observations of wind and of water surface elevation at 14 wave staffs in an array in Lake Ontario and in a large laboratory tank, the directional spectrum of wind-generated waves on deep water is determined by using a modification of Barber's (1963) method. Systematic investigations reveal the following: (a) the frequency spectrum in the rear face is inversely proportional to the fourth power of the frequency $\omega $, with the equilibrium range parameter and the peak enhancement factor clearly dependent on the ratio of wind speed to peak wave speed; (b) the angular spreading $\theta $ of the wave energy is of the form sech$^{2}$ ($\beta \theta $), where $\beta $ is a function of frequency relative to the peak; (c) depending on the gradient of the fetch, the direction of the waves at the spectral peak may differ from the mean wind direction by up to 50 degrees, but this observed difference is predictable by a similarity analysis; (d) under conditions of strong wind forcing, significant effects on the phase velocity caused by amplitude dispersion and the presence of bound harmonics are clearly observed and are in accordance with the Stokes theory, whereas (e) the waves under natural wind conditions show amplitude dispersion, but bound harmonics are too weak to be detected among the background of free waves.

Abstract: A numerical model of the coupled processes of tectonic deformation and surface erosion in convergent orogens is developed to investigate the nature of the interaction between these processes. Crustal deformation is calculated by a two-dimensional finite element model of deformation in response to subduction and accretion of continental crust. Erosion operates on the uplifted surface of this model through fluvial incision which is taken to be proportional to stream power. The relative importance of the tectonic and erosion processes is given by a dimensionless “erosion number” relating convergence velocity, rock erodibility, and precipitation rate. This number determines the time required for a system to reach steady state and the final topographic shape and size of a mountain belt. Fundamental characteristics of the model orogens include asymmetric topography with shallower slopes facing the subducting plate and an asymmetric pattern of exhumation with the deepest levels of exhumation opposite to subduction. These characteristics are modified when the regional climate exhibits a dominant wind direction and orographically enhanced precipitation on one side of the mountain belt. The two possible cases are dominant wind in the direction of motion of the subducting plate and dominant wind direction in the opposite direction of the subducting plate velocity. Models of the former case predict a broad zone of exhumation with maximum exhumation in the orogen interior. Models of the latter case predict a focused zone of exhumation at the margin of the orogen and, at high erosion number, a reversal in the topographic asymmetry. Natural examples of these two cases are presented. The Southern Alps of New Zealand exhibits the climate and exhumation asymmetry characteristic of wind in the direction opposite to motion of the subducting plate. The asymmetry of topography suggests that erosion is not efficient enough to have reversed the topographic asymmetry. The contrasting example of dominant wind in the direction of subduction motion is provided by the Olympic Mountains of Washington State. In this case, exhumation of deep levels of the Cascadia accretionary wedge shows a broad domal pattern consistent with the observed orographic precipitation.

Abstract: A theoretical model that describes the power of a scattered Global Positioning System (GPS) signal as a function of geometrical and environmental parameters has been developed. This model is based on a bistatic radar equation derived using the geometric optics limit of the Kirchhoff approximation. The waveform (i.e., the time-delayed power obtained in the delay-mapping technique) depends on a wave-slope probability density function, which in turn depends on wind. Waveforms obtained for aircraft altitudes and velocities indicate that altitudes within the interval 5-15 km are the best for inferring wind speed. In some regimes, an analytical solution for the bistatic radar equation is possible. This solution allows converting trailing edges of waveforms into a set of straight lines, which could be convenient for wind retrieval. A transition to satellite altitudes, together with satellite velocities, makes the peak power reduction and the Doppler spreading effect a significant problem for wind retrieval based on the delay-mapping technique. At the same time, different time delays and different Doppler shifts of the scattered GPS signal could form relatively small spatial cells on sea surface, suggesting mapping of the wave-slope probability distribution in a synthetic-aperture-radar (SAR) fashion. This may allow more accurate measurements of wind velocity and wind direction.