Electrical Conductivity Probe Research Articles

Evaluation of a prototype variable frequency mode soil moisture and EC probe for its final development

AbstractA prototype dielectric probe developed by the Daiki Rika Kogyo Co., Ltd, Japan, was evaluated by controlled laboratory experiments. The probe simultaneously measures the real and imaginary parts of the dielectric permittivity, which are comparable to the measurements obtained with a vector network analyser (VNA) at frequencies ranging from 10 to 160 MHz. The probe accurately (±2% error) measures the real parts of the dielectric permittivity of oil–ethanol and ethanol–water mixtures over a wide range of real permittivities (3.26 ~ 79) at frequencies ranging from 70 to 90 MHz. The imaginary parts of the dielectric permittivity of aqueous solutions are related to the electrical conductivity (EC) through a unique rational model (±2.5% error) over 80–90 MHz. Dielectric measurements by probes at the desired frequencies can eliminate/reduce the limitations of fixed‐frequency measurements, such as the effects of EC, clay composition, porosity, and organic matter, of currently available probes.

Miniaturized device to measure urease activity in the soil interstitial fluid using wenner method

This paper presents a microdevice developed to measure the electrical conductivity of a liquid or a saturated porous medium using Wenner method. It is developed in the context of biocementation as soil improvement technique, which is used in Civil Engineering applications to produce calcium carbonate through bacterial or enzymatic activity, replacing the use of other binder materials such as cement or resins, and therefore reducing carbon footprint. The microdevice was used to measure urease activity in the soil interstitial fluid, to investigate if bacterial activity could be affected by the presence of the particles and tortuosity from pore geometry. Such analysis is important to understand biocementation mechanism inside the soil and helps to improve the design of such treatment solutions. The device is basically a squared reservoir printed in polypropylene using a 3D printing machine, incorporating stainless steel electrodes in its base. The electrical resistivity was computed adopting Wenner method, by connecting 4 PCB electrodes to a signal generator and an oscilloscope for measuring the voltage when a AC current of 1 mA was applied. Both square and sinusoidal waves with 5 kHz frequency were selected among other frequencies. The measurements were adjusted during the calibration of the microdevice, done using standard salt solutions with known electrical conductivity measured using an electrical conductivity probe. For the bacterial activity measurements, the bacterial and urea solutions were added to a uniform-graded size quarzitic sand (average diameter 0.3 mm) placed inside the microdevice and covering completely the electrodes. Bacterial activity was not affected by the presence of the sand, which confirms that this treatment is effective for this type of soils.

Online monitoring of continuous aqueous two-phase flotation (ATPF) for the development of an autonomous control strategy

Aqueous two-phase flotation (ATPF) is a separation technique for isolating biological products such as enzymes from crude complex biosuspensions. The continuous operation mode of ATPF allows high throughput while maintaining a high separation efficiency. In this work, a laboratory plant for continuous ATPF with integrated online measurement technology is presented and ATPF experiments with the model enzyme phospholipase A2 are performed. Three electrical conductivity probes allow real time and spatially resolved characterization of phase mixing in the flotation tank caused by rising bubbles. UV/Vis spectroscopy is used to measure the enzyme concentration online at the top phase outlet. The equilibrium concentrations in the top and bottom phase are linearly dependent on the feed concentration, revealing a constant partition coefficient. The experimental results of this work provide the basis for the development of an autonomous feedback controller for the continuous ATPF process.

Stratified water columns: homogenization and interface evolution

Stratified water columns are often found in lakes and oceans. Stratifications result from differences in density due to salt concentration, temperature, solid content and oxygenation. The stability of stratifications affects bioactivity, sedimentation, contaminant transport and environmental remediation. This study investigates the evolution of 6 stratified water columns created by differences in salinity, suspended minerals and the presence of a bottom heat source. We use acoustic wave reflection, photography, and both electrical conductivity and temperature profiles to track changes in stratification. Results show that multiple concurrent processes emerge across layers in otherwise quiescent water bodies. Dissimilar chemo-thermo conditions give rise to chemical and thermal diffusion, convection, and double-diffusion convection. When stratification involves suspended particles, interlayer processes include diffusiophoresis, flocculation/aggregation, sedimentation, osmosis, and chemo-consolidation; in this case, the specific surface and surface charge of suspended particles, and the salt concentration in contiguous layers determine aggregation-sedimentation-consolidation patterns. The interlayer transition zone acts as a high-pass filter that preferentially reflects low-frequency long-wavelength P-waves; invasive thermal and electrical conductivity probes provide complementary information and may identify stratification even when it is undetected by acoustic signals.

Automated Drift Compensation System for Electrical Conductivity and pH Probes in Hydroponic Systems

Highlights Used one- and two-point normalization to compensate for drifts in EC and pH probes in hydroponic systems. Developed automated sensor drift compensation systems for hydroponic systems. Evaluated the compensation systems for open- and closed-hydroponics. Application of the normalization methods increased the accuracy of the EC and pH measurements. Abstract. In hydroponic systems, the nutrient solutions are dispensed based on pH and electrical conductivity (EC) to ensure that the nutrient components in the solution are optimal for crop growth. However, the pH and EC probes may exhibit signal drifts when immersed in the solution for a considerable period, which deteriorate the measurement accuracy and the nutrient and water use efficiency. Notably, the existing hydroponic systems require manual calibration of the pH and EC probes and do not provide any information regarding their accuracy. Consequently, faults in the probes are challenging to detect. In this study, two types of automated drift compensation systems for EC and pH probes, based on one- and two-point normalization, were developed to accurately monitor changes in the pH and EC values in hydroponic solutions and enhance sensor management. The proposed framework can provide information regarding the drifts of the pH and EC probes through automated normalization solution measurements. The effectiveness of the developed system in scenarios involving plant growth with open and closed hydroponics was evaluated through comparison with a standard method involving sampling and laboratory analysis. The results indicated that the one-point normalization strategy had a simple structure and was effective in compensating drifted offsets of sensors. A two-point normalization strategy could effectively predict the sensor drifts as well as variations in the sensitivities, which could be used in the compensation processes. Application of the one-point normalization-based system increased the accuracy of the EC and pH measurements, with root mean square errors decreasing from 50 to 28.5 µS·cm-1 and 0.43 to 0.17 pH in the open hydroponic systems and from 68.7 to 38.3 µS·cm-1 and 0.15 to 0.11 pH in the closed systems, respectively. The two-point normalization-based system decreased the RMSEs from 44.6 to 33.4 µS·cm-1 and 0.55 to 0.20 pH for the EC and pH measurements, respectively. In addition, the decreased slope and coefficient of determination in the linear regression according to the system application proved the system can compensate for the drifts of the EC and pH probes. The proposed system provided accurate EC and pH measurements and sensor status information, promoting more efficient nutrient use and sensor maintenance. Keywords: Automation, Compensation, Drift, EC, Hydroponics, pH.

Feasibility studies on the detection of third phase formation in the solvent extraction equipment during reprocessing of fast reactor spent fuels

Fast reactor spent fuel plants reprocess plutonium rich fuel discharged from fast reactors. Centrifugal extractor or mixer settler solvent extraction equipments are employed for the selective recovery of nuclear grade uranium and plutonium from fission products. 30% (v/v) TBP/NPH is used as the solvent in PUREX process. Plutonium rich spent fuel has disadvantage of third phase formation during process upsets. Third phase can leads to flooding thereby prone for nuclear criticality or explosion hazard in evaporators. Hence, the solvent extraction equipments should be continuously monitored to detect onset of third phase. Studies are carried out by placing electrical conductivity probe in the organic outlet of a single stage mixer settler. This study measured electrical conductivity in different runs. 12 M feed nitric acid run and 15.8 M nitric acid feed acidity run indicated the conductivity at organic outlet is beyond 1035 μS/cm, indicated severe flooding as well as two phases in organic collecting container. Uranous in nitric acid run indicated when the A/O change was initiated loaded organic phase (8–11 μS/cm) conductivity at organic outlet decrease to 2.06 μS/cm as well when probe inserted at the organic and aqueous interface jumped to 190 μS/by forming Third phase. The results of this study indicated it is feasible to detect online of third phase in solvent extraction equipment such as mixer settler.

Self-Assembly of Angiotensin-Converting Enzyme Inhibitors Captopril and Lisinopril and Their Crystal Structures.

The peptide angiotensin-converting enzyme inhibitors captopril and lisinopril are unexpectedly shown to exhibit critical aggregation concentration (CAC) behavior through measurements of surface tension, electrical conductivity, and dye probe fluorescence. These three measurements provide similar values for the CAC, and there is also evidence from circular dichroism spectroscopy for a possible conformational change in the peptides at the same concentration. Cryogenic transmission electron microscopy indicates the formation of micelle-like aggregates above the CAC, which can thus be considered a critical micelle concentration, and the formation of aggregates with a hydrodynamic radius of ∼6–7 nm is also evidenced by dynamic light scattering. We also used synchrotron radiation X-ray diffraction to determine the single-crystal structure of captopril and lisinopril. Our results improve the accuracy of previous data reported in the literature, obtained using conventional X-ray sources. We also studied the structure of aqueous solutions containing captopril or lisinopril at high concentrations. The aggregation may be driven by intermolecular interactions between the proline moiety of captopril molecules or between the phenylalanine moiety of lisinopril molecules.

Modelling Shallow Groundwater Evaporation Rates from a Large Tank Experiment

A large tank (1.4 m x 4.0 m x 1.3 m) filled with medium-coarse sand was employed to measure evaporation rates from shallow groundwater at controlled laboratory conditions, to determine drivers and mechanisms. To monitor the groundwater level drawdown 12 piezometers were installed in a semi regular grid and equipped with high precision water level, temperature, and electrical conductivity (EC) probes. In each piezometer, 6 micro sampling ports were installed every 10 cm to capture vertical salinity gradients. Moreover, the soil water content, temperature and EC were measured in the unsaturated zone using TDR probes placed at 5, 20 and 40 cm depth. The monitoring started in February 2020 and lasted for 4 months until the groundwater drawdown became residual. To model the groundwater heads, temperature, and salinity variations SEAWAT 4.0 was employed. The calibrated model was then used to obtain the unknown parameters, such as: maximum evaporation rates (1.5-4.4 mm/d), extinction depth (0.90 m), mineral dissolution (5.0e-9 g/d) and evaporation concentration (0.35 g/L). Despite the drawdown was uniformly distributed, the increase of groundwater salinity was rather uneven, while the temperature increase mimicked the atmospheric temperature increase. The initial groundwater salinity and the small changes in the evaporation rate controlled the evapoconcentration process in groundwater, while the effective porosity was the most sensitive parameter. This study demonstrates that shallow groundwater evaporation from sandy soils can produce homogeneous water table drawdown but appreciable differences in the distribution of groundwater salinity.

New measurements on hydrodynamics in a gas–liquid–solid expanded bed

The solid holdup, in a 150mm-ID×2460mm-height gas–liquid–solid expanded bed with air, water and glass beads (the diameter of particles is 0.6–0.8mm) was firstly investigated based on the immersion-type online multiphase measuring instrument, and bubble behavior was studied via the BVW-2 double electrical conductivity probe. The effect of the superficial gas velocity and liquid velocity on the expanded ratio, the transition ratio, the bubble rising velocity, the gas holdup and the solid holdup was studied. It is discovered that compared with the gas velocity, the liquid velocity has stronger impact on the expanded ratio, but it is opposite for the transition ratio. The average gas holdup and solid holdup increase linearly as the superficial gas velocity goes up. Among it, the gas holdup increases greater in the center, while the solid holdup increases greater near the wall. Compared with it, when the superficial liquid velocity rises, the average gas holdup hardly changes, but the average solid holdup keeps decreasing, especially the solid holdup distributes flatter with the increase of the superficial liquid velocity.

Film formation and surface renewal on a rotating spoked disk for polymer devolatilization

The film flow and surface renewal of highly viscous liquid on a rotating spoked disk were investigated experimentally and numerically. In practical applications, the liquid is a polycarbonate melt with very high viscosity and Newtonian behavior at low shear rates. In the experiments, a maltose solution was used. The film thickness on the rotating disk was measured by an electrical conductivity probe. The Volume of Fluid (VOF) model combined with the sliding mesh method was used to simulate the film formation process. The simulated dimensionless film thickness and the film formation process agree well with the experimental results. The film flow and surface renewal under different operation conditions were evaluated. Gravity and viscous forces dominate the process with inertia playing a marginal role. A scraper was designed to intensify transfer processes on the film significantly.

Flow Regime Visualization and Identification of Air–Water Two-Phase Flow in a Horizontal Helically Coiled Rectangular Channel

Experiments of flow regime visualization and identification of air–water two-phase flow were conducted in a horizontal helically coiled rectangular channel. The test superficial liquid and gas velocities are 0.09–2 m/s and 0.18–16 m/s, respectively. Flow regimes were observed with a high-speed video camera and the corresponding local and average void fractions were measured with an electric conductivity probe method and with a quick-close valve method, respectively. Four main flow regimes including unsteady pulsating flow, bubbly flow, intermittent flow, and annular flow were observed. The bubbly flow identification criteria depend on more than 90% bubbles whose chord length was smaller than the channel equivalent diameter. The annular flow identification criteria is the local void fraction in the gas core larger than 0.97. Then the flow regimes and their transition mechanisms are analyzed. Furthermore, new transition criteria among these flow regimes have been proposed. The results show that the critical transition average void fraction from bubbly to intermittent flow is 0.23. A complete air–water flow regime map has been developed for the horizontal helically coiled rectangular channel and the map predicts the observed flow regimes well.

Two-phase interfacial structure of bubbly-to-slug transition flows in a 12.7 mm ID vertical tube

This experimental study focuses on the characteristics of air-water two-phase interfacial structure of bubbly-to-slug transition flow. Interfacial parameters including void fraction, interfacial area concentration, and bubble interfacial velocity are measured using four-sensor electrical conductivity probe on a 12.7 mm ID vertical tube. The tube size is approximately equal to the maximum distorted bubble size. Therefore, the bubbly-to-slug transition characteristics can be unique from in other sizes of tubes. Comparing with previous studies, this study provides an experimental database with a wide range of the bubbly-to-slug transition regime, with 4 different superficial liquid velocities (0.3, 0.5, 1.0, and 2.0 m/s) and void fraction ranging from 0.07 to 0.66. Experimental results show that the wall-peak void distribution does not appear in a small diameter tube under the bubbly-to-slug flow transition flow. The distribution is related to both void fraction and the relative bubble size to the tube size. In this sense, a new correlation of distribution parameter in the Drift Flux model is proposed based on the previous studies by Ishii, and Hibiki et al. This experimental study can be a good reference for the model development of flow regime transition and the Interfacial Area Transport Equation.

Two-phase interfacial area characteristics and transport under the transition from subcooled boiling to saturated boiling flows

This study focuses on the analysis of the transition from the subcooled boiling to saturated boiling flow. During this process, vapor generates drastically in a short developing length, which makes it difficult to predict the interfacial characteristics of two-phase flow. To investigate the characteristics of this process, experiments were performed in a vertical annulus with 19.1 mm inner diameter and 38.1 mm outer diameter. The two-phase interfacial parameters including time-averaged local vapor fraction, interfacial area concentration, and bubble interfacial velocity are obtained using high-temperature miniature four-sensor electrical conductivity probes. In this study, the conductivity probe signal is processed using the newly-developed signal processing algorithm developed for small spherical bubbles by Shen and Nakamura (2014) , instead of the algorithm used in the previous subcooled boiling experimental studies Ozar (2009) and Kumar et al. (2019), [3] for large bubbles developed by Kataoka et al. (1986). The flow conditions cover a wide range of inlet subcooling temperature at 12.9–21.2 °C, heat flux at 57.9–197.3 kW/m2, and inlet flow rate at 0.265–0.536 m/s. The vapor fractions are cross-validated with impedance void meter measurements. The state-of-art two-group interfacial area transport equations (IATE) [6], (Ozar, 2009) and (Brooks and Hibiki, 2016) is evaluated with the experimental data. The result shows that the two-group IATE gives fairly good predictions on the transition phenomena. Besides, a defect was identified in the condensation model (Park et al., 2007) used in IATE, which is the bubble boundary diameter classifying the two condensation mechanisms: heat-transfer-controlled and inertia-controlled condensation. A rigorous approach to estimate this boundary diameter is established in this study.

Experimental Methods for Investigation of Drilling Fluid Displacement in Irregular Annuli

Experimental methods are still indispensable for fluid mechanics research, despite advancements in the modelling and computer simulation field. Experimental data are vital for validating simulations of complex flow systems. However, measuring the flow in industrially relevant systems can be difficult for several reasons. Here we address flow measurement challenges related to cementing of oil wells, where main experimental issues are related to opacity of the fluids and the sheer size of the system. The main objective is to track the propagation of a fluid-fluid interface during a two-fluid displacement process, and thereby to characterize the efficiency of the displacement process. We describe the implementation and use of an array of electrical conductivity probes, and demonstrate with examples how the signals can be used to recover relevant information about the displacement process. To our knowledge this is the most extensive use of this measurement method for studying displacement in a large-scale laboratory setup. Optical measurements and visual observations are challenging and/or costly in such large-scale systems, but can still provide qualitative information as shown in this article. Using electrical conductivity probes is a robust and fairly low-cost experimental method for characterizing fluid-fluid displacement in large-scale systems.

Electric Conductivity Probes to Study Change in Degree of Saturation - Bench Top Laboratory Tests

Sand characteristics such as liquefaction susceptibility can be affected as a result of change in degree of saturation of sand. New liquefaction mitigation technique by inducing partial saturation in sands is introduced by Yegian et al in 2007[1]. This technique requires to monitor changes in degree of saturation of sand. By nature, changes in degree of saturation of sand can lead in changes in its electric conductivity. Electric conductivity is the property of a material that represents its ability to conduct electric current. Fully saturated sand can conduct electric current better than sand with lower degree of saturation. Therefore, the change in measured electric conductivity can be used to calculate the change in degree of saturation of sand. In 1942, Gus Archie [2] expressed that the electric conductivity of soil is a function of its porosity, degree of saturation, tortuosity and electric conductivity of pore fluid. Using Archie’s law electrical conductivity can be related to the degree of saturation in sands. Typically, electric conductivity probes and meters are instruments which are used to measure electric conductivity. Using electrical conductivity probes, sets of bench top tests were conducted on Ottawa sand to study the relation between degree of saturation and electric conductivity in sand. Partial saturation in sands were created by pouring dry sand into sodium percarbonate solution with a known initial concentration. By nature, sodium percarbonate in water, generates oxygen gas bubbles in time. The changes in electric conductivity in the specimen were measured using electric conductivity meters and probes. In addition, changes in degree of saturation of the specimen were measured using soil phase relations equations. Measured electric conductivity data and calculated degree of saturations were correlated to explore relation between electric conductivity and degree of saturation. This paper presents results of bench top tests, and suggests a relationship between, final degree of saturation of sand and initial concentration of sodium percarbonate solution

Relative Humidity on Mars: New Results From the Phoenix TECP Sensor.

In situ measurements of relative humidity (RH) on Mars have only been performed by the Phoenix (PHX) and Mars Science Laboratory (MSL) missions. Here we present results of our recalibration of the PHX thermal and electrical conductivity probe (TECP) RH sensor. This recalibration was conducted using a TECP engineering model subjected to the full range of environmental conditions at the PHX landing site in the Michigan Mars Environmental Chamber. The experiments focused on the warmest and driest conditions (daytime) because they were not covered in the original calibration (Zent et al., 2010, https://doi.org/10.1029/2009JE003420) and previous recalibration (Zent et al., 2016, https://doi.org/10.1002/2015JE004933). In nighttime conditions, our results are in excellent agreement with the previous 2016 recalibration, while in daytime conditions, our results show larger water vapor pressure values. We obtain vapor pressure values in the range ~0.005–1.4 Pa, while Zent et al. (2016, https://doi.org/10.1002/2015JE004933) obtain values in the range ~0.004–0.4 Pa. Our higher daytime values are in better agreement with independent estimates from the ground by the PHX Surface Stereo Imager instrument and from orbit by Compact Reconnaissance Imaging Spectrometer for Mars. Our results imply larger day‐to‐night ratios of water vapor pressure at PHX compared to MSL, suggesting a stronger atmosphere‐regolith interchange in the Martian arctic than at lower latitudes. Further, they indicate that brine formation at the PHX landing site via deliquescence can be achieved only temporarily between midnight and 6 a.m. on a few sols. The results from our recalibration are important because they shed light on the near‐surface humidity environment on Mars.

Interfacial area measurement with new algorithm for grouping bubbles by diameter

Many industrial systems make use of two-phase flows for processing or safety applications. Modeling these flows is essential for ensuring safety and engineering optimization. In general, these flows are modeled using the two-fluid model. Two key parameters in the two-fluid model are void fraction and interfacial area concentration. To improve model accuracy, the bubbles are typically broken up into groups based on transport properties and modeled separately. Such models must be validated using experimental data, which is often collected using intrusive probes such as electrical conductivity or optical void probes. Current algorithms for converting the signals from these instruments into void and interfacial area measurements struggled with missing interfaces due to signal rise and fall time. These types of instruments also use the chord length to classify the “group” of a bubble, which can lead to incorrect grouping behavior. In this paper, a new dynamic signal processing method and a grouping algorithm based on calculating bubble diameter have been introduced in an attempt to correct these inaccuracies. The ability of the new algorithm is to correctly identify smaller bubbles and to more accurately identify bubble signals is demonstrated by comparison of the output logic pulse for both the old and new algorithms with the same input signal. The new bubble size calculation means that a number of bubbles that were previously classified as “spherical/distorted” are now classified as “cap/slug/churn” bubbles. This leads to changes in average bubble properties. While these changes were expected in several cases, the increase was larger than the reported uncertainty of the instruments. This may indicate significant shortcomings in data analyzed using the previous algorithms. Additional data collection and analysis is required in order to evaluate this possibility. However, the new algorithm has a significant weakness: the bubble diameter calculation increases the computational t ime by an order of magnitude.

Experimental studies on hydrodynamic characteristics using an oblique plunging liquid jet

The present investigation is mainly concerned with experimental studies on the basic hydrodynamic characteristics of an oblique plunging liquid jet impinging on a liquid surface and resulting in air entrainment. To study the structure of a biphasic zone below the free surface of liquid, a needle type electrical conductivity probe has been indigenously designed and extensively used. For effective visualization of a two-phase flow field, a high-speed digital camera was utilized. With the aid of the above, the present study provides new methods and application of the phase detection probe to understand the physics of the plunging jet aeration system. This work, apart from the air entrainment characteristics, also investigates the geometry of the biphasic zone for the oblique plunging liquid jet. The experimental results were also compared with the existing correlations and are found to be in good agreement. Hence, this work contributes to the better understanding of the air entrainment process and bubble dispersion for the oblique plunging liquid jet system.

Emissions performance of high moisture wood fuels burned in a residential stove

A study has been made of the effect of fuel moisture content on emissions from a wood burning domestic stove. Two fuel types were studied: beech which is a hardwood, and spruce which is a softwood. The moisture contents investigated were for a freshly felled wood, a seasoned wood and a kiln dried wood. The effect of the moisture measurement method was considered using a commercial electrical conductivity probe moisture meter which was compared with laboratory analysis by drying in an oven at 105 °C. It was shown that the probe can significantly underestimate the actual moisture content in certain cases. Correlations were made of the burning rate, the Emission Factors for the formation of gaseous and particulate pollutants as a function of the moisture content. We also studied the ratio of Black Carbon to Total Carbon (BC/TC) to obtain information on the organic content of the particles. The NOX emissions from this type of stove were only dependent on the fuel-nitrogen content and not on the moisture content.

Hyporheic exchange in a gravel bed flume with and without traveling surface waves

Solute exchange between the pore water of a streambed and overlying flowing surface water can have important effects on the chemical mass balance and biological productivity in the aquatic environment. The base mechanism for driving this hyporheic exchange in a moving current is turbulence at the water- sediment interface and the water surface slope. Many previous studies have shown that the nature of the exchange can be significantly modified when spatial pressure variations, induced by standing surface waves or bed forms, are present in the system. In contrast to these studies, we consider how transient pressure variations induced by moving waves modify hypothetic exchange. This is achieved experimentally by using a vertical array of electrical conductivity probes to track the movement of a conservative solute tracer in the gravel bed of a recirculating laboratory flume under a variety of flow conditions. Our experimental observations indicate that the addition of traveling waves greatly increases the initial rate and depth of solute penetration into the bed. When the analytical solution of a one-dimensional (vertical) advection–dispersion model is fit to the experimental measurements it appears that the presence of traveling surface waves results in a more dispersive hyporheic transport. Through experimental observation, model fitting, and direct simulation we demonstrate that this apparent dispersion dominated transport is due to the vertical “pumping” of interstitial fluid in the presence of traveling surface waves. From these simulations we develop a relation that for a given set of flow and wave characteristics allows us to estimate the apparent dispersion due to traveling waves.