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Grant W. Petty and Wei Huang

Abstract

The four-parameter modified gamma distribution (MGD) is the most general mathematically convenient model for size distributions of particle types ranging from aerosols and cloud droplets or ice particles to liquid and frozen precipitation. The common three-parameter gamma distribution, the exponential distribution (e.g., Marshall–Palmer), and power-law distribution (e.g., Junge) are all special cases. Depending on the context, the particle “size” used in a given formulation may be the actual geometric diameter, the volume- or area-equivalent spherical diameter, the actual or equivalent radius, the projected or surface area, or the mass.

For microphysical and radiative transfer calculations, it is often necessary to convert from one size representation to another, especially when comparing or utilizing distribution parameters obtained from a variety of sources. Furthermore, when the mass scales with Db, with b < 3, as is typical for snow and ice and other particles having a quasi-fractal structure, an exponential or gamma distribution expressed in terms of one size parameter becomes an MGD when expressed in terms of another. The MGD model is therefore more fundamentally relevant to size distributions of nonspherical particles than is often appreciated.

The central purpose of this paper is to serve as a concise single-source reference for the mathematical properties of, and conversions between, atmospheric particle size distributions that can expressed as MGDs, including exponential and gamma distributions as special cases.

For illustrative purposes, snow particle size distributions published by Sekhon and Srivastava, Braham, and Field et al. are converted to a common representation and directly compared for identical snow water content, allowing large differences in their properties to be discerned and quantified in a way that is not as easily achieved without such conversion.

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Grant W. Petty and Wei Huang

Abstract

Coupled-dipole approximation (CDA) calculations of microwave extinction and radar backscatter are presented for nonhomogeneous (soft) ice spheres and for quasi-realistic aggregates of elementary ice crystal forms, including both simple needles and real dendrites. Frequencies considered include selections from the Dual-Frequency Precipitation Radar (DPR; 13.4 and 35.6 GHz) and the Global Precipitation Measurement (GPM) Microwave Imager (GMI; 18.7, 36.5, and 89.0 GHz), both slated for orbit on the GPM mission.

The computational method is first validated against Mie theory using dipole structures representing solid ice spheres as well as stochastically generated “soft” ice spheres of variable ice–air ratio. Neither the traditional Bruggeman nor Maxwell Garnett dielectric mixing formula is found to correctly predict the full range of CDA results for soft spheres. However, an excellent fit is found using the generalized mixing rule of Sihvola with ν = 0.85.

The suitability of the soft-sphere approximation for realistic aggregates is investigated, taking into account the spectral dependence of backscatter and/or extinction per unit mass at key DPR and GMI frequencies. Even when spheres of nonequal mass are considered, there is no single combination of fraction and mass that simultaneously captures all the relevant radiative properties. All four aggregate models do, however, exhibit a predictable power-law dependence of the mass extinction coefficient on the total particle mass. Dual-frequency mass extinction ratios are only very weakly dependent on particle masses; moreover, the ratio is found to be approximately proportional to frequency raised to the power 2.5.

The dual-frequency backscatter ratio is found to be a predictable function of the aggregate mass for particles smaller than 3 mg. Above this size, the ratio is strongly sensitive to aggregate shape, a finding that raises concerns about the utility of dual-frequency backscatter ratio measurements whenever larger particles might be present in a volume of air.

The validity of the Rayleigh–Gans approximation applied to radar backscatter from snow aggregates was also examined. Although the dual-frequency backscatter ratio was reasonably well reproduced, the absolute magnitude was not.

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Wei Wang and Rui Xin Huang

Abstract

Wind stress energy input through the surface ageostrophic currents is studied. The surface ageostrophic velocity is calculated using the classical formula of the Ekman spiral, with the Ekman depth determined from an empirical formula. The total amount of energy input over the global oceans for subinertial frequency is estimated as 2.4 TW averaged over a period from 1997 to 2002, or 2.3 TW averaged over a period from 1948 to 2002, based on daily wind stress data from NCEP–NCAR. Thus, in addition to the energy input to the near inertial waves of 0.5–0.7 TW reported by Alford and by Watanabe and Hibiya, the total energy input to the Ekman layer is estimated as 3 TW. This input is concentrated primarily over the Southern Ocean and the storm track in both the North Pacific and North Atlantic Oceans.

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Wei Wang and Rui Xin Huang

Abstract

Wind energy input into the ocean is primarily produced through surface waves. The total rate of this energy source, integrated over the World Ocean, is estimated at 60 TW, based on empirical formulas and results from a numerical model of surface waves. Thus, surface wave energy input is about 50 times the energy input to the surface geostrophic current and 20 times the total tidal dissipation rate. Most of the energy input is concentrated within the Antarctic Circumpolar Current.

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Chunyan Li, Wei Huang, and Brian Milan

Abstract

Atmospheric cold fronts provide recurring forcing for circulations and long-term transport in estuaries with microtides. Multiple horizontal ADCPs were used to obtain time series data from three inlets in Barataria Bay. The data cover a period of 51 atmospheric cold fronts between 2013 and 2015. The weather and subtidal ocean response are highly correlated in the “weather band” (3–7 days). The cold front–associated winds produce alternating flows into, out of, and then back into the bay, forming an asymmetric “M” for low-pass filtered flows. Results show that cold front–induced flows are the most important component in this region, and the flows can be predicted based on wind vector time series. Numerical simulations using a validated Finite-Volume Coastal Ocean Model (FVCOM) demonstrate that the wind-driven oscillations within the bay are consistent with the quasi-steady state with little influence of the Coriolis effect for cold front–related wind-driven flows. The four major inlets (from the southwest to the northeast) consistently carry 10%, 57%, 21%, and 12% of the tidal exchange of the bay, respectively. The subtidal exchange rates through them however fluctuate greatly with averages of 18% ± 13%, 35% ± 18%, 31% ± 16%, and 16% ± 9%, respectively. Several modes of exchange flows through the multiple inlets are found, consisting of the all-in and all-out mode (45% occurrence) under strong winds perpendicular to the coastline; the shallow-downwind, deep-upwind mode (41%), particularly during wind-relaxation periods; and the upwind-in and downwind-out mode (13%) under northerly or southerly winds. These modes are discussed with the low-pass filtered model results and verified by a forcing–response joint EOF analysis.

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Chuan Jiang Huang, Wei Wang, and Rui Xin Huang

Abstract

The circulation in the equatorial Pacific Ocean is studied in a series of numerical experiments based on an isopycnal coordinate model. The model is subject to monthly mean climatology of wind stress and surface thermohaline forcing. In response to decadal variability in the diapycnal mixing coefficient, sea surface temperature and other properties of the circulation system oscillate periodically. The strongest sea surface temperature anomaly appears in the geographic location of Niño-3 region with the amplitude on the order of 0.5°C, if the model is subject to a 30-yr sinusoidal oscillation in diapycnal mixing coefficient that varies between 0.03 × 10−4 and 0.27 × 10−4 m2 s−1. Changes in diapycnal mixing coefficient of this amplitude are within the bulk range consistent with the external mechanical energy input in the global ocean, especially when considering the great changes of tropical cyclones during the past decades. Thus, time-varying diapycnal mixing associated with changes in wind energy input into the ocean may play a nonnegligible role in decadal climate variability in the equatorial circulation and climate.

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Xiuhong Chen, Xianglei Huang, Norman G. Loeb, and Heli Wei

Abstract

The far-IR spectrum plays an important role in the earth’s radiation budget and remote sensing. The authors compare the near-global (80°S–80°N) outgoing clear-sky far-IR flux inferred from the collocated Atmospheric Infrared Sounder (AIRS) and Clouds and the Earth’s Radiant Energy System (CERES) observations in 2004 with the counterparts computed from reanalysis datasets subsampled along the same satellite trajectories. The three most recent reanalyses are examined: the ECMWF Interim Re-Analysis (ERA-Interim), NASA Modern-Era Retrospective Analysis for Research and Application (MERRA), and NOAA/NCEP Climate Forecast System Reanalysis (CFSR). Following a previous study by X. Huang et al., clear-sky spectral angular distribution models (ADMs) are developed for five of the CERES land surface scene types as well as for the extratropical oceans. The outgoing longwave radiation (OLR) directly estimated from the AIRS radiances using the authors’ algorithm agrees well with the OLR in the collocated CERES Single Satellite Footprint (SSF) dataset. The daytime difference is 0.96 ±2.02 W m−2, and the nighttime difference is 0.86 ±1.61 W m−2. To a large extent, the far-IR flux derived in this way agrees with those directly computed from three reanalyses. The near-global averaged differences between reanalyses and observations tend to be slightly positive (0.66%–1.15%) over 0–400 cm−1 and slightly negative (−0.89% to −0.44%) over 400–600 cm−1. For all three reanalyses, the spatial distributions of such differences show the largest discrepancies over the high-elevation areas during the daytime but not during the nighttime, suggesting discrepancies in the diurnal variation of such areas among different datasets. The composite differences with respect to temperature or precipitable water suggest large discrepancies for cold and humid scenes.

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Chunyan Li, Eddie Weeks, Wei Huang, Brian Milan, and Renhao Wu

Abstract

An unmanned surface vehicle (USV) was designed and constructed to operate continuously for covering both flood and ebb and preferably a complete tidal cycle (e.g., ~24 h) to measure the vertical profiles of horizontal flow velocity. It was applied in a tidal channel at Port Fourchon, Louisiana. A bottom-mounted ADCP was deployed for 515 days. The first EOF mode of the velocity profiles showed a barotropic type of flow that explained more than 98.2% of the variability. The second mode showed a typical estuarine flow with two layers, which explained 0.47% of the variability. Using a linear regression of the total transport from the USV with the vertically averaged velocity from the bottom-mounted ADCP, with an R-squared value of 98%, the total along-channel transport throughout the deployment was calculated. A low-pass filtering of the transport allowed for examining the impact of 76 events with cold, warm, or combined cold–warm fronts passing the area. The top seven most severe events were discussed, as their associated transports obviously stood out in the time series, indicating the importance of weather. It is shown that large-scale weather systems with frontal lines of ~1500–3000-km horizontal length scale control the subtidal transport in the area. Cold (warm) fronts tend to generate outward (inward) transports, followed by a rebound. The maximum coherence between the atmospheric forcing and the ocean response reached ~71%–84%, which occurred at about a frequency f of ~0.29 cycle per day or T of ~3.4 days in the period, consistent with the atmospheric frontal return periods (~3–7 days).

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XU ZHANG, YUHUA YANG, BAODE CHEN, and WEI HUANG

Abstract

The quantitative precipitation forecast in the 9 km operational modeling system (without the use of a convection parameterization scheme) at the Shanghai Meteorological Service (SMS) usually suffers from excessive precipitation at the grid scale and less-structured precipitation patterns. Two scale-aware convection parameterizations were tested in the operational system to mitigate these deficiencies. Their impacts on the warm-season precipitation forecast over China were analyzed in case studies and two-month retrospective forecasts. The results from case studies show that the importance of convection parameterization depends on geographical regions and weather regimes. Considering a proper magnitude of parameterized convection can produce more realistic precipitation distribution and reduce excessive grid-scale precipitation in southern China. In the northeast and southwest China, however, the convection parameterization plays an insignificant role in precipitation forecast because of strong synoptic-scale forcing. A statistical evaluation of the two-month retrospective forecasts indicates that the forecast skill for precipitation in the 9-km operational system is improved by choosing proper convection parameterization. This study suggests that improvement in contemporary convection parameterizations is needed for their usage for various meteorological conditions and reasonable partitioning between parameterized and resolved convection.

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Ling Ling Liu, Wei Wang, and Rui Xin Huang

Abstract

Wind stress and tidal dissipation are the most important sources of mechanical energy for maintaining the oceanic general circulation. The contribution of mechanical energy due to tropical cyclones can be a vitally important factor in regulating the oceanic general circulation and its variability. However, previous estimates of wind stress energy input were based on low-resolution wind stress data in which strong nonlinear events, such as tropical cyclones, were smoothed out.

Using a hurricane–ocean coupled model constructed from an axisymmetric hurricane model and a three-layer ocean model, the rate of energy input to the world’s oceans induced by tropical cyclones over the period from 1984 to 2003 was estimated. The energy input is estimated as follows: 1.62 TW to the surface waves and 0.10 TW to the surface currents (including 0.03 TW to the near-inertial motions). The rate of gravitational potential energy increase due to tropical cyclones is 0.05 TW. Both the energy input from tropical cyclones and the increase of gravitational potential energy of the ocean show strong interannual and decadal variability with an increasing rate of 16% over the past 20 years. The annual mean diapycnal upwelling induced by tropical cyclones over the past 20 years is estimated as 39 Sv (Sv ≡ 106 m3 s−1). Owing to tropical cyclones, diapycnal mixing in the upper ocean (below the mixed layer) is greatly enhanced. Within the regimes of strong activity of tropical cyclones, the increase of diapycnal diffusivity is on the order of (1 − 6) × 10−4 m2 s−1. The tropical cyclone–related energy input and diapycnal mixing may play an important role in climate variability, ecology, fishery, and environments.

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