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.

Evaluation of two "integrated" polarimetric Quantitative Precipitation Estimation (QPE) algorithms at C-band

Two so-called “integrated” polarimetric rate estimation techniques, ZPHI (Testud et al., 2000) and ZZDR (Illingworth and Thompson, 2005), are evaluated using 12 episodes of the year 2005 observed by the French C-band operational Trappes radar, located near Paris. The term “integrated” means that the concentration parameter of the drop size distribution is assumed to be constant over some area and the algorithms retrieve it using the polarimetric variables in that area. The evaluation is carried out in ideal conditions (no partial beam blocking, no ground-clutter contamination, no bright band contamination, a posteriori calibration of the radar variables ZH and ZDR) using hourly rain gauges located at distances less than 60 km from the radar. Also included in the comparison, for the sake of benchmarking, is a conventional Z = 282R1.66 estimator, with and without attenuation correction and with and without adjustment by rain gauges as currently done operationally at Météo France. Under those ideal conditions, the two polarimetric algorithms, which rely solely on radar data, appear to perform as well if not better, pending on the measurements conditions (attenuation, rain rates, …), than the conventional algorithms, even when the latter take into account rain gauges through the adjustment scheme. ZZDR with attenuation correction is the best estimator for hourly rain gauge accumulations lower than 5 mm h−1 and ZPHI is the best one above that threshold. A perturbation analysis has been conducted to assess the sensitivity of the various estimators with respect to biases on ZH and ZDR, taking into account the typical accuracy and stability that can be reasonably achieved with modern operational radars these days (1 dB on ZH and 0.2 dB on ZDR). A +1 dB positive bias on ZH (radar too hot) results in a +14% overestimation of the rain rate with the conventional estimator used in this study (Z = 282R^1.66), a -19% underestimation with ZPHI and a +23% overestimation with ZZDR. Additionally, a +0.2 dB positive bias on ZDR results in a typical rain rate under- estimation of 15% by ZZDR.

Proposed design for an ultrasonic optical force-feedback microphone

We discuss a novel approach that would lead to the development of an ultrasonic optical force-feedback measurement microphone.

Performance limitations of piezoelectric and force feedback electrostatic transducers in different applications

Current limitations in piezoelectric and electrostatic transducers are discussed. A force-feedback electrostatic transducer capable of operating at bandwidths up to 20 kHz is described. Advantages of the proposed design are a linearised operation which simplifies the feedback control aspects and robustness of the performance characteristics to environmental perturbations. Applications in nanotechnology, optical sciences and acoustics are discussed.

Propagation of errors from a null balance terahertz reflectometer to a sample's relative water content

The THz water content index of a sample is defined and advantages in using such metric in estimating a sample's relative water content are discussed. The errors from reflectance measurements performed at two different THz frequencies using a quasi-optical null-balance reflectometer are propagated to the errors in estimating the sample water content index.

A simple fluid cell for the study of aqueous solutions using THz time-domain spectroscopy

We describe a fluid cell for the measurement of aqueous solutions of biomolecules adapted particularly for the requirements of THz time-domain spectroscopy. The design is simple, requires small-volume samples, avoids cross-contamination and is inexpensive.

Sub-surface terahertz imaging through uneven surfaces: visualizing Neolithic wall paintings in Çatalhöyük

Pulsed terahertz imaging is being developed as a technique to image obscured mural paintings. Due to significant advances in terahertz technology, portable systems are now capable of operating in unregulated environments and this has prompted their use on archaeological excavations. August 2011 saw the first use of pulsed terahertz imaging at the archaeological site of Çatalhöyük, Turkey, where mural paintings dating from the Neolithic period are continuously being uncovered by archaeologists. In these particular paintings the paint is applied onto an uneven surface, and then covered by an equally uneven surface. Traditional terahertz data analysis has proven unsuccessful at sub-surface imaging of these paintings due to the effect of these uneven surfaces. For the first time, an image processing technique is presented, based around Gaussian beam-mode coupling, which enables the visualization of the obscured painting.

Terahertz deconvolution

The ability to retrieve information from different layers within a stratified sample using terahertz pulsed reflection imaging and spectroscopy has traditionally been resolution limited by the pulse width available. In this paper, a deconvolution algorithm is presented which circumvents this resolution limit, enabling deep sub-wavelength and sub-pulse width depth resolution. The algorithm is explained through theoretical investigation, and demonstrated by reconstructing signals reflected from boundaries in stratified materials that cannot be resolved directly from the unprocessed time-domain reflection signal. Furthermore, the deconvolution technique has been used to recreate sub-surface images from a stratified sample: imaging the reverse side of a piece of paper.

One-port de-embedding technique for the quasi-optical characterization of integrated components

We describe a one-port de-embedding technique suitable for the quasi-optical characterization of terahertz integrated components at frequencies beyond the operational range of most vector network analyzers. This technique is also suitable when the manufacturing of precision terminations to sufficiently fine tolerances for the application of a TRL de-embedding technique is not possible. The technique is based on vector reflection measurements of a series of easily realizable test pieces. A theoretical analysis is presented for the precision of the technique when implemented using a quasi-optical null-balanced bridge reflectometer. The analysis takes into account quantization effects in the linear and angular encoders associated with the balancing procedure, as well as source power and detector noise equivalent power. The precision in measuring waveguide characteristic impedance and attenuation using this de-embedding technique is further analyzed after taking into account changes in the power coupled due to axial, rotational, and lateral alignment errors between the device under test and the instruments' test port. The analysis is based on the propagation of errors after assuming imperfect coupling of two fundamental Gaussian beams. The required precision in repositioning the samples at the instruments' test-port is discussed. Quasi-optical measurements using the de-embedding process for a WR-8 adjustable precision short at 125 GHz are presented. The de-embedding methodology may be extended to allow the determination of S-parameters of arbitrary two-port junctions. The measurement technique proposed should prove most useful above 325 GHz where there is a lack of measurement standards.

Multivariate analysis of the dielectric response of materials modeled using networks of resistors and capacitors

We discuss the modeling of dielectric responses of electromagnetically excited networks which are composed of a mixture of capacitors and resistors. Such networks can be employed as lumped-parameter circuits to model the response of composite materials containing conductive and insulating grains. The dynamics of the excited network systems are studied using a state space model derived from a randomized incidence matrix. Time and frequency domain responses from synthetic data sets generated from state space models are analyzed for the purpose of estimating the fraction of capacitors in the network. Good results were obtained by using either the time-domain response to a pulse excitation or impedance data at selected frequencies. A chemometric framework based on a Successive Projections Algorithm (SPA) enables the construction of multiple linear regression (MLR) models which can efficiently determine the ratio of conductive to insulating components in composite material samples. The proposed method avoids restrictions commonly associated with Archie’s law, the application of percolation theory or Kohlrausch-Williams-Watts models and is applicable to experimental results generated by either time domain transient spectrometers or continuous-wave instruments. Furthermore, it is quite generic and applicable to tomography, acoustics as well as other spectroscopies such as nuclear magnetic resonance, electron paramagnetic resonance and, therefore, should be of general interest across the dielectrics community.