Unusually high differential attenuation at C band: Results from a two-year analysis of the French Trappes polarimetric radar data

The differential phase (ΦDP) measured by polarimetric radars is recognized to be a very good indicator of the path integrated by rain. Moreover, if a linear relationship is assumed between the specific differential phase (KDP) and the specific attenuation (AH) and specific differential attenuation (ADP), then attenuation can easily be corrected. The coefficients of proportionality, γH and γDP, are, however, known to be dependent in rain upon drop temperature, drop shapes, drop size distribution, and the presence of large drops causing Mie scattering. In this paper, the authors extensively apply a physically based method, often referred to as the “Smyth and Illingworth constraint,” which uses the constraint that the value of the differential reflectivity ZDR on the far side of the storm should be low to retrieve the γDP coefficient. More than 30 convective episodes observed by the French operational C-band polarimetric Trappes radar during two summers (2005 and 2006) are used to document the variability of γDP with respect to the intrinsic three-dimensional characteristics of the attenuating cells. The Smyth and Illingworth constraint could be applied to only 20% of all attenuated rays of the 2-yr dataset so it cannot be considered the unique solution for attenuation correction in an operational setting but is useful for characterizing the properties of the strongly attenuating cells. The range of variation of γDP is shown to be extremely large, with minimal, maximal, and mean values being, respectively, equal to 0.01, 0.11, and 0.025 dB °−1. Coefficient γDP appears to be almost linearly correlated with the horizontal reflectivity (ZH), differential reflectivity (ZDR), and specific differential phase (KDP) and correlation coefficient (ρHV) of the attenuating cells. The temperature effect is negligible with respect to that of the microphysical properties of the attenuating cells. Unusually large values of γDP, above 0.06 dB °−1, often referred to as “hot spots,” are reported for 15%—a nonnegligible figure—of the rays presenting a significant total differential phase shift (ΔϕDP > 30°). The corresponding strongly attenuating cells are shown to have extremely high ZDR (above 4 dB) and ZH (above 55 dBZ), very low ρHV (below 0.94), and high KDP (above 4° km−1). Analysis of 4 yr of observed raindrop spectra does not reproduce such low values of ρHV, suggesting that (wet) ice is likely to be present in the precipitation medium and responsible for the attenuation and high phase shifts. Furthermore, if melting ice is responsible for the high phase shifts, this suggests that KDP may not be uniquely related to rainfall rate but can result from the presence of wet ice. This hypothesis is supported by the analysis of the vertical profiles of horizontal reflectivity and the values of conventional probability of hail indexes.

Radar scattering from ice aggregates using the horizontally aligned oblate spheroid approximation

The assumed relationship between ice particle mass and size is profoundly important in radar retrievals of ice clouds, but, for millimeter-wave radars, shape and preferred orientation are important as well. In this paper the authors first examine the consequences of the fact that the widely used ‘‘Brown and Francis’’ mass–size relationship has often been applied to maximumparticle dimension observed by aircraftDmax rather than to the mean of the particle dimensions in two orthogonal directions Dmean, which was originally used by Brown and Francis. Analysis of particle images reveals that Dmax ’ 1.25Dmean, and therefore, for clouds for which this mass–size relationship holds, the consequences are overestimates of ice water content by around 53% and of Rayleigh-scattering radar reflectivity factor by 3.7 dB. Simultaneous radar and aircraft measurements demonstrate that much better agreement in reflectivity factor is provided by using this mass–size relationship with Dmean. The authors then examine the importance of particle shape and fall orientation for millimeter-wave radars. Simultaneous radar measurements and aircraft calculations of differential reflectivity and dual-wavelength ratio are presented to demonstrate that ice particles may usually be treated as horizontally aligned oblate spheroids with an axial ratio of 0.6, consistent with them being aggregates. An accurate formula is presented for the backscatter cross section apparent to a vertically pointing millimeter-wave radar on the basis of a modified version of Rayleigh–Gans theory. It is then shown that the consequence of treating ice particles as Mie-scattering spheres is to substantially underestimate millimeter-wave reflectivity factor when millimeter-sized particles are present, which can lead to retrieved ice water content being overestimated by a factor of 4.h

The formation of ice in a long-lived supercooled layer cloud

This article focuses on the characteristics of persistent thin single-layer mixed-phase clouds. We seek to answer two important questions: (i) how does ice continually nucleate and precipitate from these clouds, without the available ice nuclei becoming depleted? (ii) how do the supercooled liquid droplets persist in spite of the net flux of water vapour to the growing ice crystals? These questions are answered quantitatively using in situ and radar observations of a long-lived mixed-phase cloud layer over the Chilbolton Observatory. Doppler radar measurements show that the top 500 m of cloud (the top 250 m of which is mixed-phase, with ice virga beneath) is turbulent and well-mixed, and the liquid water content is adiabatic. This well-mixed layer is bounded above and below by stable layers. This inhibits entrainment of fresh ice nuclei into the cloud layer, yet our in situ and radar observations show that a steady flux of ≈100 m−2s−1 ice crystals fell from the cloud over the course of ∼1 day. Comparing this flux to the concentration of conventional ice nuclei expected to be present within the well-mixed layer, we find that these nuclei would be depleted within less than 1 h. We therefore argue that nucleation in these persistent supercooled clouds is strongly time-dependent in nature, with droplets freezing slowly over many hours, significantly longer than the few seconds residence time of an ice nucleus counter. Once nucleated, the ice crystals are observed to grow primarily by vapour deposition, because of the low liquid water path (21 g m−2) yet vapour-rich environment. Evidence for this comes from high differential reflectivity in the radar observations, and in situ imaging of the crystals. The flux of vapour from liquid to ice is quantified from in situ measurements, and we show that this modest flux (3.3 g m−2h−1) can be readily offset by slow radiative cooling of the layer to space.

Rayleigh scattering by hexagonal ice crystals and the interpretation of dual-polarisation radar measurements

Dual-polarisation radar measurements provide valuable information about the shapes and orientations of atmospheric ice particles. For quantitative interpretation of these data in the Rayleigh regime, common practice is to approximate the true ice crystal shape with that of a spheroid. Calculations using the discrete dipole approximation for a wide range of crystal aspect ratios demonstrate that approximating hexagonal plates as spheroids leads to significant errors in the predicted differential reflectivity, by as much as 1.5 dB. An empirical modification of the shape factors in Gans's spheroid theory was made using the numerical data. The resulting simple expressions, like Gans's theory, can be applied to crystals in any desired orientation, illuminated by an arbitrarily polarised wave, but are much more accurate for hexagonal particles. Calculations of the scattering from more complex branched and dendritic crystals indicate that these may be accurately modelled using the new expression, but with a reduced permittivity dependent on the volume of ice relative to an enclosing hexagonal prism.

Polarimetric X-band weather radar measurements in the tropics: radome and rain attenuation correction

A polarimetric X-band radar has been deployed during one month (April 2011) for a field campaign in Fortaleza, Brazil, together with three additional laser disdrometers. The disdrometers are capable of measuring the raindrop size distributions (DSDs), hence making it possible to forward-model theoretical polarimetric X-band radar observables at the point where the instruments are located. This setup allows to thoroughly test the accuracy of the X-band radar measurements as well as the algorithms that are used to correct the radar data for radome and rain attenuation. For the campaign in Fortaleza it was found that radome attenuation dominantly affects the measurements. With an algorithm that is based on the self-consistency of the polarimetric observables, the radome induced reflectivity offset was estimated. Offset corrected measurements were then further corrected for rain attenuation with two different schemes. The performance of the post-processing steps was analyzed by comparing the data with disdrometer-inferred polarimetric variables that were measured at a distance of 20 km from the radar. Radome attenuation reached values up to 14 dB which was found to be consistent with an empirical radome attenuation vs. rain intensity relation that was previously developed for the same radar type. In contrast to previous work, our results suggest that radome attenuation should be estimated individually for every view direction of the radar in order to obtain homogenous reflectivity fields.

Differential optical densities of intraretinal spaces

PURPOSE: To test the hypothesis that hyporeflective spaces in the neuroretina found on optical coherence tomography (OCT) examination have different optical reflectivities according to whether they are associated with exudation or degeneration. METHODS: Retrospective analysis of eyes with idiopathic perifoveal telangiectasia (IPT), diabetic macular edema (DME), idiopathic central serous chorioretinopathy (CSC), retinitis pigmentosa (RP), or cone dystrophy (CD) and eyes of healthy control subjects. OCT scans were performed. Raw scan data were exported and used to calculate light reflectivity profiles. Reflectivity data were acquired by projecting three rectangular boxes, each 50 pixels long and 5 pixels wide, into the intraretinal cystoid spaces, centrally onto unaffected peripheral RPE, and onto the prefoveolar vitreous. Light reflectivity in the retinal pigment epithelium (RPE), vitreous, and intraretinal spaces for the different retinal conditions and control subjects were compared. RESULTS: Reflectivities of the vitreous and the RPE were similar among the groups. Hyporeflective spaces in eyes with exudation (DME, RP, and CSC) had higher reflectivity compared with the mean reflectivity of the vitreous, whereas the cystoid spaces in the maculae of the eyes without exudation (CD and IPT) had a lower reflectivity than did the normal vitreous. CONCLUSIONS: Analysis of the light reflectivity profiles may be a tool to determine whether the density of hyporeflective spaces in the macula is greater or less than that of the vitreous, and may be a way to differentiate degenerative from exudative macular disease.

Systemic Granulomatous Diseases Associated With Multiple Palpable Masses That May Involve The Breast: Case Presentation And An Approach To The Differential Diagnosis.

Palpable mass is a common complaint presented to the breast surgeon. It is very uncommon for patients to report breast mass associated with palpable masses in other superficial structures. When these masses are related to systemic granulomatous diseases, the diagnosis and initiation of specific therapy can be challenging. The purpose of this paper is to report a case initially assessed by the breast surgeon and ultimately diagnosed as granulomatous variant of T-cell lymphoma, and discuss the main systemic granulomatous diseases associated with palpable masses involving the breast.

Water Stress Reveals Differential Antioxidant Responses Of Tolerant And Non-tolerant Sugarcane Genotypes.

The biochemical responses of the enzymatic antioxidant system of a drought-tolerant cultivar (IACSP 94-2094) and a commercial cultivar in Brazil (IACSP 95-5000) grown under two levels of soil water restriction (70% and 30% Soil Available Water Content) were investigated. IACSP 94-2094 exhibited one additional active superoxide dismutase (Cu/Zn-SOD VI) isoenzyme in comparison to IACSP 95-5000, possibly contributing to the heightened response of IACSP 94-2094 to the induced stress. The total glutathione reductase (GR) activity increased substantially in IACSP 94-2094 under conditions of severe water stress; however, the appearance of a new GR isoenzyme and the disappearance of another isoenzyme were found not to be related to the stress response because the cultivars from both treatment groups (control and water restrictions) exhibited identical changes. Catalase (CAT) activity seems to have a more direct role in H2O2 detoxification under water stress condition and the shift in isoenzymes in the tolerant cultivar might have contributed to this response, which may be dependent upon the location where the excessive H2O2 is being produced under stress. The improved performance of IACSP 94-2094 under drought stress was associated with a more efficient antioxidant system response, particularly under conditions of mild stress.

Enhanced D1 And D2 Inhibitions Induced By Low-frequency Trains Of Conditioning Stimuli: Differential Effects On H- And T-reflexes And Possible Mechanisms.

Mechanically evoked reflexes have been postulated to be less sensitive to presynaptic inhibition (PSI) than the H-reflex. This has implications on investigations of spinal cord neurophysiology that are based on the T-reflex. Preceding studies have shown an enhanced effect of PSI on the H-reflex when a train of ~10 conditioning stimuli at 1 Hz was applied to the nerve of the antagonist muscle. The main questions to be addressed in the present study are if indeed T-reflexes are less sensitive to PSI and whether (and to what extent and by what possible mechanisms) the effect of low frequency conditioning, found previously for the H-reflex, can be reproduced on T-reflexes from the soleus muscle. We explored two different conditioning-to-test (C-T) intervals: 15 and 100 ms (corresponding to D1 and D2 inhibitions, respectively). Test stimuli consisted of either electrical pulses applied to the posterior tibial nerve to elicit H-reflexes or mechanical percussion to the Achilles tendon to elicit T-reflexes. The 1 Hz train of conditioning electrical stimuli delivered to the common peroneal nerve induced a stronger effect of PSI as compared to a single conditioning pulse, for both reflexes (T and H), regardless of C-T-intervals. Moreover, the conditioning train of pulses (with respect to a single conditioning pulse) was proportionally more effective for T-reflexes as compared to H-reflexes (irrespective of the C-T interval), which might be associated with the differential contingent of Ia afferents activated by mechanical and electrical test stimuli. A conceivable explanation for the enhanced PSI effect in response to a train of stimuli is the occurrence of homosynaptic depression at synapses on inhibitory interneurons interposed within the PSI pathway. The present results add to the discussion of the sensitivity of the stretch reflex pathway to PSI and its functional role.

An Extension of the Invariance Principle for a Class of Differential Equations with Finite Delay

An extension of the uniform invariance principle for ordinary differential equations with finite delay is developed. The uniform invariance principle allows the derivative of the auxiliary scalar function V to be positive in some bounded sets of the state space while the classical invariance principle assumes that. V <= 0. As a consequence, the uniform invariance principle can deal with a larger class of problems. The main difficulty to prove an invariance principle for functional differential equations is the fact that flows are defined on an infinite dimensional space and, in such spaces, bounded solutions may not be precompact. This difficulty is overcome by imposing the vector field taking bounded sets into bounded sets.

EXISTENCE RESULTS FOR NEUTRAL INTEGRO-DIFFERENTIAL EQUATIONS WITH UNBOUNDED DELAY

In this paper we discuss the existence of mild, strict and classical solutions for a class of abstract integro-differential equations in Banach spaces. Some applications to ordinary and partial integro-differential equations are considered.

Existence Results for Abstract Partial Neutral Integro-differential Equation with Unbounded Delay

In this paper we study the existence and regularity of mild solutions for a class of abstract partial neutral integro-differential equations with unbounded delay.

GLOBAL SOLUTIONS FOR ABSTRACT FUNCTIONAL DIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS

In this paper we study the existence of global solutions for a class of abstract functional differential equation with nonlocal conditions. An application is considered.

Weighted S-Asymptotically omega-Periodic Solutions of a Class of Fractional Differential Equations

We study the existence of weighted S-asymptotically omega-periodic mild solutions for a class of abstract fractional differential equations of the form u' = partial derivative (alpha vertical bar 1)Au + f(t, u), 1 < alpha < 2, where A is a linear sectorial operator of negative type.

EXISTENCE RESULTS FOR ABSTRACT NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS

In this paper we discuss the existence of solutions for a class of abstract partial neutral functional differential equations.