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Edwin L. Dunnavan
and
Alexander V. Ryzhkov

Abstract

This study derives simple analytical expressions for the theoretical height profiles of particle number concentrations (Nt ) and mean volume diameters (Dm ) during the steady-state balance of vapor growth and collision–coalescence with sedimentation. These equations are general for both rain and snow gamma size distributions with size-dependent power-law functions that dictate particle fall speeds and masses. For collision–coalescence only, Nt (Dm ) decreases (increases) as an exponential function of the radar reflectivity difference between two height layers. For vapor deposition only, Dm increases as a generalized power law of this reflectivity difference. Simultaneous vapor deposition and collision–coalescence under steady-state conditions with conservation of number, mass, and reflectivity fluxes lead to a coupled set of first-order, nonlinear ordinary differential equations for Nt and Dm . The solutions to these coupled equations are generalized power-law functions of height z for Dm (z) and Nt (z) whereby each variable is related to one another with an exponent that is independent of collision–coalescence efficiency. Compared to observed profiles derived from descending in situ aircraft Lagrangian spiral profiles from the CRYSTAL-FACE field campaign, these analytical solutions can on average capture the height profiles of Nt and Dm within 8% and 4% of observations, respectively. Steady-state model projections of radar retrievals aloft are shown to produce the correct rapid enhancement of surface snowfall compared to the lowest-available radar retrievals from 500 m MSL. Future studies can utilize these equations alongside radar measurements to estimate Nt and Dm below radar tilt elevations and to estimate uncertain microphysical parameters such as collision–coalescence efficiencies.

Significance Statement

While complex numerical models are often used to describe weather phenomenon, sometimes simple equations can instead provide equally good or comparable results. Thus, these simple equations can be used in place of more complicated models in certain situations and this replacement can allow for computationally efficient and elegant solutions. This study derives such simple equations in terms of exponential and power-law mathematical functions that describe how the average size and total number of snow or rain particles change at different atmospheric height levels due to growth from the vapor phase and aggregation (the sticking together) of these particles balanced with their fallout from clouds. We catalog these mathematical equations for different assumptions of particle characteristics and we then test these equations using spirally descending aircraft observations and ground-based measurements. Overall, we show that these mathematical equations, despite their simplicity, are capable of accurately describing the magnitude and shape of observed height and time series profiles of particle sizes and numbers. These equations can be used by researchers and forecasters along with radar measurements to improve the understanding of precipitation and the estimation of its properties.

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Ivo Pasmans
and
Alexander L. Kurapov

Abstract

Spurious long-distance correlations in estimates of the background error covariance can deteriorate the performance of ensemble-based data assimilation methods. In this study, a localization method, called Monte Carlo (MC) localization, is presented to remove these correlations. It is particularly useful for use in high-dimensional ensemble–variational data assimilation systems. In this method, raw ensemble members are truncated by multiplying them with functions having compact support. This creates a larger ensemble, in which points spaced farther apart than the size of the compact support have zero correlation. The localized background error covariance is then estimated as the sample covariance of this larger ensemble. It is hypothesized that this localized background error covariance can be approximated by the MC approximation method using a limited set of the truncated ensemble members. This hypothesis is tested here on a grid with 1001 grid points and assuming a Gaussian true background error covariance. It is found that the mean relative error has an upper bound that scales with the inverse square root of the number of truncated ensemble members. In the case studied the size of the support for which the localized background covariance best approximates the true background covariance increases with increasing number of raw ensemble members and is close to 4 times the standard deviation of the Gaussian when 20 raw ensemble members are used. In the Fourier space the localization manifests itself as a convolution resulting in smoothing of the power spectral density of the ensemble members.

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Pamela L. Heinselman
and
Alexander V. Ryzhkov

Abstract

This study describes, illustrates, and validates hail detection by a simplified version of the National Severe Storms Laboratory’s fuzzy logic polarimetric hydrometeor classification algorithm (HCA). The HCA uses four radar variables: reflectivity, differential reflectivity, cross-correlation coefficient, and “reflectivity texture” to classify echoes as rain mixed with hail, ground clutter–anomalous propagation, biological scatterers (insects, birds, and bats), big drops, light rain, moderate rain, and heavy rain. Diagnostic capabilities of HCA, such as detection of hail, are illustrated for a variety of storm environments using polarimetric radar data collected mostly during the Joint Polarimetric Experiment (JPOLE; 28 April–13 June 2003). Hail classification with the HCA is validated using 47 rain and hail reports collected by storm-intercept teams during JPOLE. For comparison purposes, probability of hail output from the Next-Generation Weather Radar Hail Detection Algorithm (HDA) is validated using the same ground truth. The anticipated polarimetric upgrade of the Weather Surveillance Radar-1988 Doppler network drives this direct comparison of performance. For the four examined cases, contingency table statistics show that the HCA outperforms the HDA. The superior performance of the HCA results primary from the algorithm’s lack of false alarms compared to the HDA. Statistical significance testing via bootstrapping indicates that differences in the probability of detection and critical success index between the algorithms are statistically significant at the 95% confidence level, whereas differences in the false alarm rate and Heidke skill score are statistically significant at the 90% confidence level.

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Alexander V. Wilchinsky
and
Daniel L. Feltham

Abstract

In this note, the authors discuss the contribution that frictional sliding of ice floes (or floe aggregates) past each other and pressure ridging make to the plastic yield curve of sea ice. Using results from a previous study that explicitly modeled the amount of sliding and ridging that occurs for a given global strain rate, it is noted that the relative contribution of sliding and ridging to ice stress depends upon ice thickness. The implication is that the shape and size of the plastic yield curve is dependent upon ice thickness. The yield-curve shape dependence is in addition to plastic hardening/weakening that relates the size of the yield curve to ice thickness. In most sea ice dynamics models the yield-curve shape is taken to be independent of ice thickness. The authors show that the change of the yield curve due to a change in the ice thickness can be taken into account by a weighted sum of two thickness-independent rheologies describing ridging and sliding effects separately. It would be straightforward to implement the thickness-dependent yield-curve shape described here into sea ice models used for global or regional ice prediction.

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Alexander V. Wilchinsky
and
Daniel L. Feltham

Abstract

The mixing of floes of different thickness caused by repeated deformation of the ice cover is modeled as diffusion, and the mass balance equation for sea ice accounting for mass diffusion is developed. The effect of deformational diffusion on the ice thickness balance is shown to reach 1% of the divergence effect, which describes ridging and lead formation. This means that with the same accuracy the mass balance equation can be written in terms of mean velocity rather than mean mass-weighted velocity, which one should correctly use for a multicomponent fluid such as sea ice with components identified by floe thickness. Mixing (diffusion) of sea ice also occurs because of turbulent variations in wind and ocean drags that are unresolved in models. Estimates of the importance of turbulent mass diffusion on the dynamic redistribution of ice thickness are determined using empirical data for the turbulent diffusivity. For long-time-scale prediction (≫5 days), where unresolved atmospheric motion may have a length scale on the order of the Arctic basin and the time scale is larger than the synoptic time scale of atmospheric events, turbulent mass diffusion can exceed 10% of the divergence effect. However, for short-time-scale prediction, for example, 5 days, the unresolved scales are on the order of 100 km, and turbulent diffusion is about 0.1% of the divergence effect. Because inertial effects are small in the dynamics of the sea ice pack, diffusive momentum transfer can be disregarded.

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Alexander V. Wilchinsky
and
Daniel L. Feltham

Abstract

Descent and spreading of high salinity water generated by salt rejection during sea ice formation in an Antarctic coastal polynya is studied using a hydrostatic, primitive equation three-dimensional ocean model called the Proudman Oceanographic Laboratory Coastal Ocean Modeling System (POLCOMS). The shape of the polynya is assumed to be a rectangle 100 km long and 30 km wide, and the salinity flux into the polynya at its surface is constant. The model has been run at high horizontal spatial resolution (500 m), and numerical simulations reveal a buoyancy-driven coastal current. The coastal current is a robust feature and appears in a range of simulations designed to investigate the influence of a sloping bottom, variable bottom drag, variable vertical turbulent diffusivities, higher salinity flux, and an offshore position of the polynya. It is shown that bottom drag is the main factor determining the current width. This coastal current has not been produced with other numerical models of polynyas, which may be because these models were run at coarser resolutions. The coastal current becomes unstable upstream of its front when the polynya is adjacent to the coast. When the polynya is situated offshore, an unstable current is produced from its outset owing to the capture of cyclonic eddies. The effect of a coastal protrusion and a canyon on the current motion is investigated. In particular, due to the convex shape of the coastal protrusion, the current sheds a dipolar eddy.

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Alexander V. Wilchinsky
and
Daniel L. Feltham

ABSTRACT

A rheological model of sea ice is presented that incorporates the orientational distribution of ice thickness in leads embedded in isotropic floe ice. Sea ice internal stress is determined by coulombic, ridging and tensile failure at orientations where corresponding failure criteria are satisfied at minimum stresses. Because sea ice traction increases in thinner leads and cohesion is finite, such failure line angles are determined by the orientational distribution of sea ice thickness relative to the imposed stresses. In contrast to the isotropic case, sea ice thickness anisotropy results in these failure lines becoming dependent on the stress magnitude. Although generally a given failure criteria type can be satisfied at many directions, only two at most are considered. The strain rate is determined by shearing along slip lines accompanied by dilatancy and closing or opening across orientations affected by ridging or tensile failure. The rheology is illustrated by a yield curve determined by combining coulombic and ridging failure for the case of two pairs of isotropically formed leads of different thicknesses rotated with regard to each other, which models two events of coulombic failure followed by dilatancy and refreezing. The yield curve consists of linear segments describing coulombic and ridging yield as failure switches from one lead to another as the stress grows. Because sliding along slip lines is accompanied by dilatancy, at typical Arctic sea ice deformation rates a one-day-long deformation event produces enough open water that these freshly formed slip lines are preferential places of ridging failure.

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Richard C. Alexander
and
Robert L. Mobley

Abstract

Climatological monthly ocean-surface temperatures obtained from the National Center for Atmospheric Research and from Fleet Numerical Weather Central are merged and interpolated onto a 1° global grid. Monthly distributions of the main ice packs of the Arctic and Antarctic are digitized from Fleet Weather Facility ice charts and Navy atlases, and are incorporated into the global arrays. Machine-analyzed maps of the resulting distributions for the months of January, March, May, July, September and November are presented to indicate the seasonal variations of temperature and ice extent.

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S. E. Perkins
and
L. V. Alexander

Abstract

Despite their adverse impacts, definitions and measurements of heat waves are ambiguous and inconsistent, generally being endemic to only the group affected, or the respective study reporting the analysis. The present study addresses this issue by employing a set of three heat wave definitions, derived from surveying heat-related indices in the climate science literature. The definitions include three or more consecutive days above one of the following: the 90th percentile for maximum temperature, the 90th percentile for minimum temperature, and positive extreme heat factor (EHF) conditions. Additionally, each index is studied using a multiaspect framework measuring heat wave number, duration, participating days, and the peak and mean magnitudes. Observed climatologies and trends computed by Sen's Kendall slope estimator are presented for the Australian continent for two time periods (1951–2008 and 1971–2008). Trends in all aspects and definitions are smaller in magnitude but more significant for 1951–2008 than for 1971–2008. Considerable similarities exist in trends of the yearly number of days participating in a heat wave and yearly heat wave frequency, suggesting that the number of available heat wave days drives the number of events. Larger trends in the hottest part of a heat wave suggest that heat wave intensity is increasing faster than the mean magnitude. Although the direct results of this study cannot be inferred for other regions, the methodology has been designed as such that it is widely applicable. Furthermore, it includes a range of definitions that may be useful for a wide range of systems impacted by heat waves.

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Alexander Lowag
,
Michael L. Black
, and
Matthew D. Eastin

Abstract

Hurricane Bret underwent a rapid intensification (RI) and subsequent weakening between 1200 UTC 21 August and 1200 UTC 22 August 1999 before it made landfall on the Texas coast 12 h later. Its minimum sea level pressure fell 35 hPa from 979 to 944 hPa within 24 h. During this period, aircraft of the National Oceanic and Atmospheric Administration (NOAA) flew several research missions that sampled the environment and inner core of the storm. These datasets are combined with gridded data from the National Centers for Environmental Prediction (NCEP) Global Model and the NCEP–National Center for Atmospheric Research (NCAR) reanalyses to document Bret’s atmospheric and oceanic environment as well as their relation to the observed structural and intensity changes. Bret’s RI was linked to movement over a warm ocean eddy and high sea surface temperatures (SSTs) in the Gulf of Mexico coupled with a concurrent decrease in vertical wind shear. SSTs at the beginning of the storm’s RI were approximately 29°C and steadily increased to 30°C as it moved to the north. The vertical wind shear relaxed to less than 10 kt during this time. Mean values of oceanic heat content (OHC) beneath the storm were about 20% higher at the beginning of the RI period than 6 h prior. The subsequent weakening was linked to the cooling of near-coastal shelf waters (to between 25° and 26°C) by prestorm mixing combined with an increase in vertical wind shear. The available observations suggest no intrusion of dry air into the circulation core contributed to the intensity evolution. Sensitivity studies with the Statistical Hurricane Intensity Prediction Scheme (SHIPS) model were conducted to quantitatively describe the influence of environmental conditions on the intensity forecast. Four different cases with modified vertical wind shear and/or SSTs were studied. Differences between the four cases were relatively small because of the model design, but the greatest intensity changes resulted for much cooler prescribed SSTs. The results of this study underscore the importance of OHC and vertical wind shear as significant factors during RIs; however, internal dynamical processes appear to play a more critical role when a favorable environment is present.

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