Tracer Cloud Research Articles

A Study of Tracer Distribution Parameter Estimation from Sparse Samples

Abstract How do design parameters such as the spacing of sampling stations affect the quality of information obtained from atmospheric dispersion experiments? In large-scale experiments such as the Cross-Appalachian Tracer Experiment (CAPTEX) and the Across North America Tracer Experiment (ANATEX), the average crosswind spacing between surface sampling stations Δy may be of the same order as, or greater than, the tracer cloud width parameter σy. For such sparse samplings, investigated are the errors in estimating five parameters of the crosswind distribution of tracer dosage or concentration: the crosswind integrated dosage (M); the centroid coordinate (ȳ); the lateral dispersion parameter (σy); the skewness (S); and the kurtosis (K). These are examined as functions of the ratio of σy to Δy, the nonuniformity of station spacing, and the location of ȳ relative to the nearest sampling station. Tracer experiments are simulated with the Gaussian distribution model, as well as a non-Gaussian model consisting o...

On the nature of the dispersive flux in saturated heterogeneous porous media

A method is presented for evaluating the mean transport of a tracer in saturated heterogeneous porous media when the hydraulic conductivity can be represented by a stochastic process; no assumption concerning stationarity of the concentration field is made. The analysis results in a transform‐space solution for the dispersive flux associated with the mean concentration in a mean uniform flow field when the tracer is conservative. For a pulse input of tracer, general forms for the first four moments in the longitudinal direction are presented; these forms are solved for specific cases of interest. A general form for the global dispersive flux, associated with mean transport, is presented for the case where local dispersion, relative to the length scale of heterogeneity, is negligible. The global dispersive flux takes the form of a convolution, over time, of the concentration gradient weighted by the correlation function of the velocity field; in large time, this integral asymptotically approaches a classical Fickian form. The convolution formulation of the global flux manifests itself in early time in the form of non‐Gaussian behavior of the mean tracer concentration. Beyond a travel distance equivalent to approximately 20 length scales of the hydraulic conductivity process, Gaussian behavior of the mean tracer cloud dominates.

Dilution Discharge Measurement During Flood Wave

A severe restriction to dilution discharge measurements is that they are to be applied to steady-flow conditions only. Using a computational model, dilution discharge measurements by constant-rate injection are simulated during unsteady-flow conditions caused by a Gaussian flood wave propagating down a prismatic channel with rectangular cross section. The accuracy of the discharge measurement is deduced from the computational results. The main source causing discrepancies between the actual and measured discharges is the difference in propagation velocities of the tracer cloud and the flood wave. Correction procedures are recommended, since maximum inaccuracies can easily be larger by an order of magnitude than inaccuracies during steady flow conditions.

The along-wind diffusion of the tracer cloud in finite release experiments.

The along-wind elongation of the tracer plume was observed in the medium-range atmospheric diffusion experiments with finite release time of air tracer substance. Since the elongated portion of a detached plume pursues the same course in the treatment of along-wind diffusion as an instantaneous puff, the along-wind diffusion parameter σx was estimated from the time variation of concentration in the elongated portion of the detached plume. This was compared with σx from other equivalent range experiments after grouping under stable, near neutral, and unstable classifications of atmospheric stability. In stable condition, a slight tendency to smaller σx values was recognized, but distinct dependency of σx growth on stability was not observed. Furthermore, consideration was taken of the valuation of time average concentration relating to the tracer release time, sampling time, and total time of tracer cloud passage. The method of evaluating the average concentration was considered, and it was made clear that the method was available for any sampling mode.

Truncation Effects on Estimated Parameters of Tracer Distributions Sampled on Finite Domains

Abstract Methods are presented and demonstrated for compensating for the apparent effect of truncation of the sampled crosswind distribution of a tracer, at either or both boundaries of a surface sampling grid downwind from the point of release. Errors and correction on estimates of the apparent vertical mixing depth, h, the location of the centroid of the crosswind distribution ȳ, and the crosswind dispersion parameter, σy are those which would apply to a truncated Gaussian distribution having the observed moments (zeroth, first and second). For truncation on only one side of the tracer cloud, a linear relationship between certain measurable quantities based on moments of partial distributions is used to derive the parameters of a best-fit truncated Gaussian distribution by linear regression. The methods are illustrated by an example from the Cross Appalachian Tracer Experiment and by a Gaussian simulation.

Horizontal diffusivity in a small, ice‐covered lake1

A horizontal eddy diffusivity (Kx) value of 0.47 cm2 · s‒1 was calculated from tracer cloud expansion data from a previous experiment in which a 24Na solution was introduced as a point source under ice cover in Tub Lake, Wisconsin. This Kx value, the first from a lake where surface wind stress was not a factor, is lower than any lake Kx previously reported. The constancy of Kx found for the 48‐h period of monitoring implied mixing eddy lengths <1.6 m, the diffusion cloud size found at first monitoring. Surface seiches or convective flows appeared to be probable sources of mixing energy.

Dispersivity and velocity relationship from laboratory and field experiments

Laboratory test results on longitudinal dispersion of soluble material in loose rocks with artificially composed or natural grain-size distributions are compared with one another and with results of field tests. In this way it can be demonstrated that it is quite possible to translate laboratory results to field conditions, if sedimentological properties of the loose materials are comparable, if bedding (geological interfaces) runs parallel to the flow direction and is hydraulically ineffective, and if distances between injection and detection are about less than 50 m. Transverse dispersion is difficult to determine. At first approximation the width of tracer cloud from a line injection was determined and the aperture angle of the resultant cloud calculated. The laboratory and field experiments showed an aperture angle of about 5° on distances between 10 and 2500 m.

A field study of longitudinal dispersion

The results of a comprehensive longitudinal dispersion experiment in a stream with an irregular, sinuous pattern are presented. The time-spread of tracer clouds was found to increase at a rate between [Formula: see text] as found for uniform prismatic channels, and x as found for highly irregular mountain streams. This ‘intermediate’ dispersive state is thought to be related to the stream’s degree of nonuniformity. The accuracy of one-dimensional approaches is considered, as is the applicability of a similarity analysis. A new definition of a 'mixing' length, based upon the condition of identical but shifted concentration–time curves, is proposed.

Satellite-Tracked Cumulus Velocities

Velocities of tracer clouds have been computed by NOAA, NASA, Stanford Research Institute, University of Wisconsin, University of Chicago, and others. Despite the fact that their methods and inherent computation speeds are different from each other, the present state-of-the-art permits the computations with 1 m s−1 speed and 4° direction in standard deviation. Such an accuracy in the cloud velocity is satisfactory for most practical purposes. The research presented in this paper warns that we have to exercise extreme caution in converting cloud velocities into winds. The motion of fair-weather cumuli obtained by tracking their shadows over Springfield, Mo., revealed that the standard deviation in the individual cloud motion is several times the tracking error. The motion of over-ocean cumuli near Barbados clearly indicated the complicated nature of cumulus velocities. Analysis of whole-sky images obtained near Tampa, Fla., failed to show significant continuity and stability of cumulus plumes, less than 0.3 mi in diameter. Cumulus turrets 0.3 to 2 mi in size appear to be the best target to infer the mean wind within the sub cloud layers. Cumulus or stratocumulus cells consisting of multi-turrets do not always move with wind. The addition and deletion of turrets belonging to a specific cell appear to be the cause of the erratic motion of a tracer cell. It may be concluded that the accuracy of wind estimates is unlikely to be better than 2 m s−1 unless the physical and dynamical characteristics of cumulus motion is further investigated.

Lagrangian similarity theory applied to diffusion in the planetary boundary layer

A similarity theory is developed to describe diffusion of a cloud of passive material in a neutral barotropic steady-state boundary layer of the Earth's atmosphere. It is suggested that a characteristic length scale U */f is relevant in the diffusion process when the diffusing cloud mixes well into the depth of the boundary layer. For an atmosphere having an effective upper bound for vertical spread, an expression for the trajectory of the centroid of the diffusing cloud is derived. The theoretically computed vertical spread is compared with experimental data on diffusion of tracer cloud over rough (urban) and smooth terrains.

Longitudinal Dispersion in Sinuous Channels

The longitudinal spreading of tracer solution and the distribution of velocity are investigated experimentally in a laboratory flume having a series of 13 uniform bends in alternating directions. Viewing the tracer cloud as a whole, the dispersion process behaves like a one-dimensional diffusion process, as in a straight channel. The dispersion coefficient is larger, and the initial convective period is shorter than in an equivalent straight channel. From the perspective of a single cross section, however, the process is periodic. The convective dispersion coefficient attains a maximum at about the middle of each bend, a minimum between bends, and lags the mean square velocity deviation by about a quarter of a bend. Analysis of the flume data together with available river data indicates that the dispersion coefficient tends to increase with increasing radius of curvature, and decrease with increasing bend length and depth.