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R. Meneghini and L. Liao

Abstract

Melting snow, graupel, and hail are often modeled as uniform mixtures of air–ice–water or ice–water. Two-layered models have also been proposed in which the particle consists of a dry snow or ice core surrounded by water or a wet snow mixture. For both types of particle models, the mixtures are characterized by effective dielectric constants. This information, along with particle shape, size, and orientation, provides the necessary data for calculating the scattering characteristics of the particles. The most commonly used formulas for the effective dielectric constant, ɛeff, are those of Maxwell Garnett and Bruggeman. To understand the applicability and limitations of these formulas, an expression for ɛeff is derived that depends on the mean internal electric fields within each component of the mixture. Using a conjugate gradient numerical method, the calculations are carried out for ice–water mixtures. Parameterization of the results in terms of the fractional water volume and the electromagnetic wavelength provides an expression for ɛeff for wavelengths between 3 and 28 mm. To circumvent the laborious task of parameterizing ɛeff with wavelength for air–ice–water mixtures, several approximate formulations are proposed. Tests of the accuracy of the formulas are made by calculating the mean and variance from different particle realizations and by comparison to a previous method. Tests of the applicability of the formulas for ɛeff are made by changing the shape, size, and orientations of the inclusions. While the formulas are adequate over a certain range of inclusion sizes and for a change in shape from cubic to spherical, they are not applicable to highly eccentric, aligned inclusions such as rods or plates.

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R. Meneghini and L. Liao

Abstract

One of the impediments to the interpretation of radar signatures from the melting layer is the uncertainty over the dielectric mixing formula for ice-water mixtures. In the commonly used Maxwell Garnett mixing formula, the dielectric constant for ice inclusions in a water matrix differs from that for water inclusions in an ice matrix for the same fraction of meltwater. While the choice of materials for the matrix and inclusion is clear for either small or large fractions of meltwater, it is not obvious how these are to be chosen in the intermediate ranges of melting. In this paper, cross sections derived from the various mixing formulas are compared to a conjugate gradient-fast Fourier transform numerical method. In the numerical method the particle is divided into equi-volume subcells in which the composition of the particle is controlled by assigning a probability of water to each subcell. For a uniform distribution of water and ice, where the probability of water in a subcell is independent of its location within the particle, the numerical results for fractional water contents of less than about 0.7 indicate that the scattering coefficients are closest to those predicted by the Maxwell Garnett mixing formula if an ice matrix with water inclusions is assumed. However, if the meltwater is highly concentrated near the boundary of the particle or if the fractional volume of water is greater than about 0.8, the Maxwell Garnett formula is in fair agreement with the numerical results, if the roles of ice and water are interchanged. A discussion of the relevance of these results to the modeling of melting snow aggregates and the interpretation of radar signatures of the bright band is given in the final section of the paper.

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R. Meneghini, L. Liao, and L. Tian

Abstract

The radar return powers from a three-frequency radar, with center frequency at 22.235 GHz and upper and lower frequencies chosen with equal water vapor absorption coefficients, can be used to estimate water vapor density and parameters of the precipitation. A linear combination of differential measurements between the center and lower frequencies on one hand and the upper and lower frequencies on the other provide an estimate of differential water vapor absorption. The coupling between the precipitation and water vapor estimates is generally weak but increases with bandwidth and the amount of non-Rayleigh scattering of the hydrometeors. The coupling leads to biases in the estimates of water vapor absorption that depend primarily on the phase state and the median mass diameter of the hydrometeors. For a down-looking radar, path-averaged estimates of water vapor absorption are possible under rain-free as well as raining conditions by using the surface returns at the three frequencies. Simulations of the water vapor attenuation retrieval show that the largest source of error typically arises from the variance in the measured radar return powers. Although the error can be mitigated by a combination of a high pulse repetition frequency, pulse compression, and averaging in range and time, the radar receiver must be stable over the averaging period. For fractional bandwidths of 20% or less, the potential exists for simultaneous measurements at the three frequencies with a single antenna and transceiver, thereby significantly reducing the cost and mass of the system.

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R. Meneghini, L. Liao, and G. M. Heymsfield

Abstract

An important objective in scatterometry is the estimation of near-surface wind speed and direction in the presence of rain. We investigate an attenuation correction method using data from the High-Altitude Imaging Wind and Rain Airborne Profiler (HIWRAP) dual-frequency scatterometer, which operates at Ku and Ka band with dual conical scans at incidence angles of 30° and 40°. The method relies on the fact that the differential normalized surface cross section, δσ 0 = σ 0(Ka) − σ 0(Ku), is relatively insensitive to wind speed and direction and that this quantity is closely related to the magnitude of the differential path attenuation, δA = A(Ka) − A(Ku), arising from precipitation, cloud, and atmospheric gases. As the method relies only on the difference between quantities measured in the presence and absence of rain, the estimates are independent of radar calibration error. As a test of the method’s accuracy, we make use of the fact that the radar rain reflectivities just above the surface, as seen along different incidence angles, are approximately the same. This yields constraint equations in the form of differences between pairs of path attenuations along different lines of sight to the surface. A second validation method uses the dual-frequency radar returns from the rain just above the surface where it can be shown that the difference between the Ku- and Ka-band-measured radar reflectivity factors provide an estimate of differential path attenuation. Comparisons between the path attenuations derived from the normalized surface cross section and those from these surface-independent methods generally show good agreement.

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R. Meneghini, L. Liao, and G. M. Heymsfield

Abstract

The High-Altitude Imaging Wind and Rain Airborne Profiler (HIWRAP) dual-frequency conically scanning airborne radar provides estimates of the range-profiled mean Doppler and backscattered power from the precipitation and surface. A velocity–azimuth display analysis yields near-surface estimates of the mean horizontal wind vector υ h in cases in which precipitation is present throughout the scan. From the surface return, the normalized radar cross section (NRCS) is obtained, which, by a method previously described, can be corrected for path attenuation. Comparisons between υ h and the attenuation-corrected NRCS are used to derive transfer functions that provide estimates of the wind vector from the NRCS data under both rain and rain-free conditions. A reasonably robust transfer function is found by using the mean NRCS (⟨NRCS⟩) over the scan along with a filtering of the data based on a Fourier series analysis of υ h and the NRCS. The approach gives good correlation coefficients between υ h and ⟨NRCS⟩ at Ku band at incidence angles of 30° and 40°. The correlation degrades if the Ka-band data are used rather than the Ku band.

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Jie Song, Ke Liao, Richard L. Coulter, and Barry M. Lesht

Abstract

A unique dataset obtained with combinations of minisodars and 915-MHz wind profilers at the Atmospheric Boundary Layer Experiments (ABLE) facility in Kansas was used to examine the detailed characteristics of the nocturnal low-level jet (LLJ). In contrast to instruments used in earlier studies, the ABLE instruments provide hourly, high-resolution vertical profiles of wind velocity from just above the surface to approximately 2 km above ground level (AGL). Furthermore, the 6-yr span of the dataset allowed the examination of interannual variability in jet properties with improved statistical reliability. It was found that LLJs occurred during 63% of the nighttime periods sampled. Although most of the observed jets were southerly, a substantial fraction (28%) was northerly. Wind maxima occurred most frequently at 200–400 m AGL, though some jets were found as low as 50 m, and the strongest jets tended to occur above 300 m. Comparison of LLJ heights at three locations within the ABLE domain and at one location outside the domain suggests that the jet is equipotential rather than terrain following. The occurrence of southerly LLJ varied annually in a way that suggests a connection between the tendency for jet formation and the large-scale circulation patterns associated with El Niño and La Niña, as well as with the Pacific decadal oscillation. Frequent and strong southerly jets that transport moisture downstream do not necessarily lead to more precipitation locally, however.

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Jiaying Zhang, Liao-Fan Lin, and Rafael L. Bras

Abstract

Hydrological applications rely on the availability and quality of precipitation products, especially model- and satellite-based products for use in areas without ground measurements. It is known that the quality of model- and satellite-based precipitation products is complementary: model-based products exhibit high quality during cold seasons while satellite-based products are better during warm seasons. To explore the complementary behavior of the quality of the precipitation products, this study uses 2-m air temperature as auxiliary information to evaluate high-resolution (0.1°/hourly) precipitation estimates from the Weather Research and Forecasting (WRF) Model and from the version 5 Integrated Multisatellite Retrievals for GPM (IMERG) algorithm (i.e., early and final runs). The products are evaluated relative to the reference NCEP Stage IV precipitation estimates over the central United States during August 2015–July 2017. Results show that the IMERG final-run estimates are nearly unbiased, while the IMERG early-run and the WRF estimates are positively biased. The WRF estimates exhibit high correlations with the reference data when the temperature falls below 280 K. The IMERG estimates, both early and final runs, do so when the temperature exceeds 280 K. Moreover, the complementary behavior of the WRF and the IMERG products conditioned on air temperature does not vary with either season or location.

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Liao-Fan Lin, Ardeshir M. Ebtehaj, Rafael L. Bras, Alejandro N. Flores, and Jingfeng Wang

Abstract

The objective of this study is to develop a framework for dynamically downscaling spaceborne precipitation products using the Weather Research and Forecasting (WRF) Model with four-dimensional variational data assimilation (4D-Var). Numerical experiments have been conducted to 1) understand the sensitivity of precipitation downscaling through point-scale precipitation data assimilation and 2) investigate the impact of seasonality and associated changes in precipitation-generating mechanisms on the quality of spatiotemporal downscaling of precipitation. The point-scale experiment suggests that assimilating precipitation can significantly affect the precipitation analysis, forecast, and downscaling. Because of occasional overestimation or underestimation of small-scale summertime precipitation extremes, the numerical experiments presented here demonstrate that the wintertime assimilation produces downscaled precipitation estimates that are in closer agreement with the reference National Centers for Environmental Prediction stage IV dataset than similar summertime experiments. This study concludes that the WRF 4D-Var system is able to effectively downscale a 6-h precipitation product with a spatial resolution of 20 km to hourly precipitation with a spatial resolution of less than 10 km in grid spacing—relevant to finescale hydrologic applications for the era of the Global Precipitation Measurement mission.

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Liao-Fan Lin, Ardeshir M. Ebtehaj, Alejandro N. Flores, Satish Bastola, and Rafael L. Bras

Abstract

This paper presents a framework that enables simultaneous assimilation of satellite precipitation and soil moisture observations into the coupled Weather Research and Forecasting (WRF) and Noah land surface model through variational approaches. The authors tested the framework by assimilating precipitation data from the Tropical Rainfall Measuring Mission (TRMM) and soil moisture data from the Soil Moisture Ocean Salinity (SMOS) satellite. The results show that assimilation of both TRMM and SMOS data can effectively improve the forecast skills of precipitation, top 10-cm soil moisture, and 2-m temperature and specific humidity. Within a 2-day time window, impacts of precipitation data assimilation on the forecasts remain relatively constant for forecast lead times greater than 6 h, while the influence of soil moisture data assimilation increases with lead time. The study also demonstrates that the forecast skill of precipitation, soil moisture, and near-surface temperature and humidity are further improved when both the TRMM and SMOS data are assimilated. In particular, the combined data assimilation reduces the prediction biases and root-mean-square errors, respectively, by 57% and 6% (for precipitation); 73% and 27% (for soil moisture); 17% and 9% (for 2-m temperature); and 33% and 11% (for 2-m specific humidity).

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Xun Jiang, Steven Pawson, Charles D. Camp, J. Eric Nielsen, Run-Lie Shia, Ting Liao, Varavut Limpasuvan, and Yuk L. Yung

Abstract

A principal component analysis (PCA) is applied to the Southern Hemisphere (SH) total column ozone following the method established for analyzing the data in the Northern Hemisphere (NH) in a companion paper. The interannual variability (IAV) of extratropical O3 in the SH is characterized by four main modes, which account for 75% of the total variance. The first two leading modes are approximately zonally symmetric and relate to the Southern Hemisphere annular mode and the quasi-biennial oscillation. The third and fourth modes exhibit wavenumber-1 structures. Contrary to the Northern Hemisphere, the third and fourth modes are not related to stationary waves. Similar results are obtained for the 30–100-hPa geopotential thickness. The decreasing O3 trend in the SH is captured in the first mode. The largest trend is at the South Pole, with value ∼−2 Dobson Units (DU) yr−1. Both the spatial pattern and trends in the column ozone are captured by the Goddard Earth Observation System chemistry–climate model (GEOS-CCM) in the SH.

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