Zenith

About: Zenith is a research topic. Over the lifetime, 3678 publications have been published within this topic receiving 70654 citations.

Global mapping functions for the atmosphere delay at radio wavelengths

Abstract: I have developed expressions for calculating the ratios (mapping functions) of the “line of sight” hydrostatic and wet atmospheric path delays to their corresponding zenith delays at radio wavelengths for elevation angles down to 3°. The coefficients of the continued fraction representation of the hydrostatic mapping function depend on the latitude and height above sea level of the observing site and on the day of the year; the dependence of the wet mapping function is only on the site latitude. By comparing with mapping functions calculated from radiosonde profiles for sites at latitudes between 43°S and 75°N, the hydrostatic mapping function is seen to be more accurate than, and of comparable precision to, mapping functions currently in use, which are parameterized in terms of local surface meteorology. When the new mapping functions are used in the analysis of geodetic very long baseline interferometry (VLBI) data, the estimated lengths of baselines up to 10,400 km long change by less than 5 mm as the minimum elevation of included data is reduced from 12° to 3°. The independence of the new mapping functions from surface meteorology, while having comparable accuracy and precision to those that require such input, makes them particularly valuable for those situations where surface meteorology data are not available.

A Model for the Spectral Albedo of Snow. I: Pure Snow

Abstract: We present a method for calculating the spectral albedo of snow which can be used at any wavelength in the solar spectrum and which accounts for diffusely or directly incident radiation at any zenith angle. For deep snow, the model contains only one adjustable parameter, an effective grain size, which is close to observed grain sizes. A second parameter, the liquid-equivalent depth, is required only for relatively thin snow. In order for the model to make realistic predictions, it must account for the extreme anisotropy of scattering by snow particles. This is done by using the “delta-Eddington” approximation for multiple scattering, together with Mie theory for single scattering. The spectral albedo from 0.3 to 5 μm wavelength is examined as a function of the effective grain size, the solar zenith angle, the snowpack thickness, and the ratio of diffuse to direct solar incidence. The decrease in albedo due to snow aging can be mimicked by reasonable increases in grain size (50–100 μm for new snow...

Optical Properties of Snow

Abstract: Measurements of the dependence of snow albedo on wavelength, zenith angle, grain size, impurity content, and cloud cover can be interpreted in terms of single-scattering and multiple-scattering radiative transfer theory. Ice is very weakly absorptive in the visible (minimum absorption at λ = 0.46 µm) but has strong absorption bands in the near infrared (near IR). Snow albedo is therefore much lower in the near IR. The near-IR solar irradiance thus plays an important role in snowmelt and in the energy balance at a snow surface. The near-IR albedo is very sensitive to snow grain size and moderately sensitive to solar zenith angle. The visible albedo (for pure snow) is not sensitive to these parameters but is instead affected by snowpack thickness and parts-per-million amounts (or less) of impurities. Grain size normally increases as the snow ages, causing a reduction in albedo. If the grain size increases as a function of depth, the albedo may suffer more reduction in the visible or in the near IR, depending on the rate of grain size increase. The presence of liquid water has little effect per se on snow optical properties in the solar spectrum, in contrast to its enormous effect on microwave emissivity. Snow albedo is increased at all wavelengths as the solar zenith angle increases but is most sensitive around λ =1 µm. Many apparently conflicting measurements of the zenith angle dependence of albedo are difficult to interpret because of modeling error, instrument error, and inadequate documentation of grain size, surface roughness, and incident radiation spectrum. Cloud cover affects snow albedo both by converting direct radiation into diffuse radiation and also by altering the spectral distribution of the radiation. Cloud cover normally causes an increase in spectrally integrated snow albedo. Some measurements of spectral flux extinction in snow are difficult to reconcile with the spectral albedo measurements. The bidirectional reflectance distribution function which apportions the reflected solar radiation among the various reflection angles must be known in order to interpret individual satellite measurements. It has been measured at the snow surface and at the top of the atmosphere, but its dependence on wavelength, snow grain size, and surface roughness is still unknown. Thermal infrared emissivity of snow is close to 100% but is a few percent lower at large viewing angles than for overhead viewing. It is very insensitive to grain size, impurities, snow depth, liquid water content, or density. Solar reflectance and microwave emissivity are both sensitive to various of these snowpack parameters. However, none of these parameters can be uniquely determined by satellite measurements at a single wavelength; a multichannel method is thus necessary if they are to be determined by remote sensing.

GPS Meteorology: Mapping Zenith Wet Delays onto Precipitable Water

Abstract: Emerging networks of Global Positioning System (GPS) receivers can be used in the remote sensing of atmospheric water vapor. The time-varying zenith wet delay observed at each GPS receiver in a network can be transformed into an estimate of the precipitable water overlying that receiver. This transformation is achieved by multiplying the zenith wet delay by a factor whose magnitude is a function of certain constants related to the refractivity of moist air and of the weighted mean temperature of the atmosphere. The mean temperature varies in space and time and must be estimated a priori in order to transform an observed zenith wet delay into an estimate of precipitable water. We show that the relative error introduced during this transformation closely approximates the relative error in the predicted mean temperature. Numerical weather models can be used to predict the mean temperature with an rms relative error of less than 1%.