Estimating Flow Using Tracers and Hydraulics in Synthetic Heterogeneous Aquifers

Regional ground water flow is most usually estimated using Darcy's law, with hydraulic conductivities estimated from pumping tests, but can also be estimated using ground water residence times derived from radioactive tracers. The two methods agree reasonably well in relatively homogeneous aquifers but it is not clear which is likely to produce more reliable estimates of ground water flow rates in heterogeneous systems. The aim of this paper is to compare bias and uncertainty of tracer and hydraulic approaches to assess ground water flow in heterogeneous aquifers. Synthetic two-dimensional aquifers with different levels of heterogeneity (correlation lengths, variances) are used to simulate ground water flow, pumping tests, and transport of radioactive tracers. Results show that bias and uncertainty of flow rates increase with the variance of the hydraulic conductivity for both methods. The bias resulting from the nonlinearity of the concentration–time relationship can be reduced by choosing a tracer with a decay rate similar to the mean ground water residence time. The bias on flow rates estimated from pumping tests is reduced when performing long duration tests. The uncertainty on ground water flow is minimized when the sampling volume is large compared to the correlation length. For tracers, the uncertainty is related to the ratio of correlation length to the distance between sampling wells. For pumping tests, it is related to the ratio of correlation length to the pumping test's radius of influence. In regional systems, it may be easier to minimize this ratio for tracers than for pumping tests.     

Soil creep and convex‐upward velocity profiles: theoretical and experimental investigation of disturbance‐driven sediment transport on hillslopes

The movement of unconsolidated materials near the Earth's surface is often driven by disturbances that occur at a range of spatial and temporal scales. The nature of these disturbances ranges from highly variable, such as tree turnover, to periodic and predictable, such as frost heave or creep. To explore the effect of probabilistic disturbances on surface processes, we formulated a granular creep model with analogy to rate process theory (RPT) used for chemical reactions. According to the theory, individual particles must be energized to a height greater than adjacent particles in order for grain dilation and transport to occur. The height of neighbouring particles (which is akin to activation energy in chemical reactions) varies with slope angle such that energy barriers get smaller in the downslope direction as slopes steepen. When slopes approach the friction‐limited angle of repose, the height of energy barriers approaches zero and grains ?ow in the absence of disturbance. An exponential function is used to describe the probability distribution of particle excitation height although alternative distributions are possible. We tested model predictions of granular dynamics in an experimental sandpile. In the sandpile, acoustic energy serves as the disturbance agent such that grains dilate and shear in response. Particle velocities are controlled by the frequency of energy pulses that result in grain displacement. Using tracer particles, we observed a convex‐upward velocity pro?le near the surface of the sandpile, consistent with predictions of our RPT‐based velocity model. In addition, we depth‐integrated the velocity model to predict how ?ux rates vary with inclination of the sandpile and observed non‐linear ?ux–gradient curves consistent with model predictions. By varying the acoustic energy level in the experimental sandpile, we documented changes in the rate of grain movement; similar changes in modelled velocities were achieved by varying the exponent of the particle excitation probability distribution. The general agreement between observed and modelled granular behaviour in our simple laboratory sandpile supports the utility of RPT‐based methods for modelling transport processes (e.g. soil creep, frost heave, and till deformation), thus enabling us to account for the probabilistic nature of disturbances that liberate sediment in natural landscapes. Copyright © 2004 John Wiley & Sons, Ltd.     

Deuterium tracing for the estimation of transpiration from trees Part 2. Estimation of transpiration rates and transpiration parameters using a time-averaged deuterium tracing method

A method for estimating transpiration rates and transpiration parameters, including the surface resistance term in the Penman-Monteith evaporation equation, from deuterium tracing experiments, where the samples were chemically time-averaged, is described. With this method only one deuterium tracer concentration analysis is required per tree compared with 90 using an earlier method. The calculation of surface resistance through solution of the convolution integral of the transpiration rate and the tracer concentration-time curve is described and the sensitivity of the surface resistance estimate to the flow parameters is investigated using as an example observations made on a 3-year-old plantation of Eucalyptus tereticornis growing in Karnataka, Southern India.     

Numerical modelling of circulation and dispersion processes in Boulogne-sur-Mer harbour (Eastern English Channel): sensitivity to physical forcing and harbour design

The MARS-3D model in conjunction with the particle tracking module Ichthyop is used to study circulation and tracer dynamics under a variety of forcing conditions in the eastern English Channel, and in the Boulogne-sur-Mer harbour (referred to hereafter as BLH). Results of hydrodynamic modelling are validated against the tidal gauge data, VHF radar surface velocities and ADCP measurements. Lagrangian tracking experiments are performed with passive particles to study tracer dispersal along the northern French coast, with special emphasis on the BLH. Simulations revealed an anticyclonic eddy generated in the harbour at rising tide. Tracers, released during flood tide at the Liane river mouth, move northward with powerful clockwise rotating current. After the high water, the current direction changes to westward, and tracers leave the harbour through the open boundary. During ebb tide, currents convergence along the western open boundary but no eddy is formed, surface currents inside the harbour are much weaker and the tracer excursion length is small. After the current reversal at low water, particles are advected shoreward resulting in a significant increase of the residence time of tracers released during ebb tide. The effect of wind on particle dispersion was found to be particularly strong. Under strong SW wind, the residence time of particles released during flood tide increases from 1.5 to 6 days. For release during ebb tide, SW wind weakens the southward tidally induced drift and thus the residence time decreases. Similar effects are observed when the freshwater inflow to the harbour is increased from 2 to 10 m³/s during the ebb tide flow. For flood tide conditions, the effect of freshwater inflow is less significant. We also demonstrate an example of innovative coastal management targeted at the reduction of the residence time of the pathogenic material accidentally released in the harbour.     

Numerical modelling of circulation and dispersion processes in Boulogne-sur-Mer harbour (Eastern English Channel): sensitivity to physical forcing and harbour design

The MARS-3D model in conjunction with the particle tracking module Ichthyop is used to study circulation and tracer dynamics under a variety of forcing conditions in the eastern English Channel, and in the Boulogne-sur-Mer harbour (referred to hereafter as BLH). Results of hydrodynamic modelling are validated against the tidal gauge data, VHF radar surface velocities and ADCP measurements. Lagrangian tracking experiments are performed with passive particles to study tracer dispersal along the northern French coast, with special emphasis on the BLH. Simulations revealed an anticyclonic eddy generated in the harbour at rising tide. Tracers, released during flood tide at the Liane river mouth, move northward with powerful clockwise rotating current. After the high water, the current direction changes to westward, and tracers leave the harbour through the open boundary. During ebb tide, currents convergence along the western open boundary but no eddy is formed, surface currents inside the harbour are much weaker and the tracer excursion length is small. After the current reversal at low water, particles are advected shoreward resulting in a significant increase of the residence time of tracers released during ebb tide. The effect of wind on particle dispersion was found to be particularly strong. Under strong SW wind, the residence time of particles released during flood tide increases from 1.5 to 6 days. For release during ebb tide, SW wind weakens the southward tidally induced drift and thus the residence time decreases. Similar effects are observed when the freshwater inflow to the harbour is increased from 2 to 10 m³/s during the ebb tide flow. For flood tide conditions, the effect of freshwater inflow is less significant. We also demonstrate an example of innovative coastal management targeted at the reduction of the residence time of the pathogenic material accidentally released in the harbour.

     

Experimental study of fly-ash migration by using magnetic method

Several studies have shown that magnetic measurements can be used in assessing soil contamination due to atmospheric deposition of pollutants. Reliable spatial mapping of magnetic susceptibility of soils assumes high temporal stability of deposited particles, accumulated in top-soil horizons. One of the main methodological concerns is whether the migration of deposited anthropogenic ferrimagnetic particles may bias the measured values. Measurements carried out on high-porosity (sandy) soils, or on soils with a very variable water regime may yield inconsistent values of top-soil magnetic susceptibility as the indicator of contamination. This study focuses on the laboratory examination of migration of fly ashes from a coal-burning power plant in sands of different porosity and under a simulated rain regime. Columns of sand of different grain sizes, placed in plastic cylinders, were contaminated on the surface by the fly ash. The vertical migration of magnetic particles was monitored using measurements of magnetic susceptibility with an SM400 Kappameter. Calibration measurements in the water environment showed an erroneous performance and resulted in the technical improvement of the used susceptibility meter (Model 2009). Our results show that the vertical distribution of flyash particles deposited on fine sand is very stable even after repeated rain simulation. The peak value of magnetic susceptibility is located in a stable position a few millimeters under the surface. Hence, standard top-soil magnetic mapping is in such a case reliable and fully representative. Contrary to that, in case of coarse sand, the peak value of magnetic susceptibility migrates by more than 10 cm. The results will be further used for numerical modeling of contaminant transport in porous media.     

The mobilization and deposition of mud deposits in a coastal plain estuary

Muddy sediments with their potential for containing contaminants are commonly deposited and remobilized by tidal currents in estuarine environments. We examined the mobilization and subsequent redeposition of mud in a coastal plain estuary located in the southeastern United States. Time-series data for salinity, suspended sediment concentrations and quality (percent organic matter and pigment concentrations) were obtained over a 13-hour tidal cycle. We found that fast-settling mud particles are found during the highest tidal current speeds. Particle quality analyses suggest that all the material is of similar origin, and that phaeopigment can be used as a tracer of particles in this system. These particles settle onto the bed when current speeds approach slack conditions. We speculate that the quantity of mud mobilized during neap tide is less than during spring tide resulting in an opportunity for the mud to partially consolidate on the bottom and be removed from resuspension. We further speculate that the muddy sediments are mainly derived from fringing marshes in this estuary.     

Assessment of magnetite as a magnetic tracer for sediments in the study of ephemeral gully erosion: Conditioning factors of magnetic susceptibility

In gully erosion, the detached soil can be transported over long distances along the landscape. The eroded material can be redistributed and/or deposited on the soil surface along the landscape and then eventually be buried by newly eroded and deposited sediment. There can be significant variability of the soil conditions (e.g., texture and moisture content) over which the eroded material travels. The eroded material can be detected through the use of magnetic tracers attached to or mixed with the eroded soil. In this study we evaluated the degree to which the magnetic signal of the magnetite is conditioned by (i) burial depth of tracer, (ii) condition of soil covering the tracer and (iii) tracer concentration. In the laboratory containers were filled with a specific soil. In the filling process, a 0.5-cm layer of a soil–magnetite mixture was interspersed in the soil profile at a certain depth. Experiments encompassed three different soil–tracer concentrations (1000:1, 200:1, 100:1), four burial depths of tracer (0 cm, 3 cm, 5 cm and 10 cm from soil surface), and two different soils. In each case, the magnetic susceptibility was measured with a susceptometer. Experiments were repeated with different soil moisture contents. If the tracer is located under the soil surface, a minimum soil–tracer concentration of 200:1 is required for its correct detection. The intensity of the magnetic signal decreases dramatically with the vertical distance of the tracer from the soil surface. The maximum detection depth for the tracer's magnetic signal is strongly dependent on the natural magnetic susceptibility of the soil, which masks the tracer's signal. Variation in soil moisture content does not significantly affect the magnetic signal. For extensive field studies, the soil–tracer volume to be handled would be very high and therefore, it is necessary to explore new tracer application techniques.     

A Straightforward Random Walk Model for Fast Push‐Pull Tracer Test Evaluation

In this article, we present a straightforward random walk model for fast evaluation of push‐pull tracer tests. By developing an adaptive algorithm, we overcome the problem of manually defining how many particles have to be used to simulate the transport problem. Beside this, we validate the random walk model by evaluating a push‐pull tracer test with drift phase and confirm the results with MT3DMS. The random walk model took less than 1% of computational time of MT3DMS, thus allowing a remarkable faster evaluation of push‐pull tracer tests.     

The boundary layer of the residence time field

The residence time of a tracer in a control domain is usually computed by releasing tracer parcels and registering the time when each of these tracer parcels cross the boundary of the control domain. In this Lagrangian procedure, the particles are discarded or omitted as soon as they leave the control domain. In a Eulerian approach, the same approach can be implemented by integrating forward in time the advection–diffusion equation for a tracer. So far, the conditions to be applied at the boundary of the control domain were uncertain. We show here that it is necessary to prescribe that the tracer concentration vanishes at the boundary of the control domain to ensure the compatibility between the Lagrangian and Eulerian approaches. When we use the Constituent oriented Age and Residence time Theory (CART), this amounts to solving the differential equation for the residence time with boundary conditions forcing the residence time to vanish at the open boundaries of the control domain. Such boundary conditions are likely to induce the development of boundary layers (at outflow boundaries for the tracer concentration and at inflow boundaries for the residence time). The thickness of these boundary layers is of the order of the ratio of the diffusivity to the velocity. They can however be partly smoothed by tidal and other oscillating flows.     

Using a thermal tracer to estimate overland and rill flow velocities

Flow velocity is a basic hydraulic property of surface flows and its precise calculation is necessary for process based hydrological models, such as soil erosion and rill development models, as well as for modelling sediment and solute transport by runoff. This study presents a technique based on infrared thermography to visualize very shallow flows and allow a quantitative measurement of overland flow and rill flow velocities. Laboratory experiments were conducted to compare the traditional dye tracer technique with this new thermal tracer technique by injecting a combined tracer (heated dye) into shallow flowing surface water. The leading edge tracer velocities estimated by means of infrared video and by the usual real imaging video were compared. The results show that thermal tracers can be used to estimate both overland and rill flow velocities, since measurements are similar to those resulting from using dye tracers. The main advantage of using thermography was the higher visibility of the leading edge of the injected tracer compared with the real image videos. Copyright © 2013 John Wiley & Sons, Ltd.     

The effects of particle breakage and abrasion on the magnetic properties of two soils

As mineral magnetism is used as a tracer for sourcing river and dam sediments, changes in the magnetic properties that may occur during transport between the source and sink must be considered. Abrasion and breakage of particles will occur during transport. These processes were examined in simulation experiments with a granitic and a sedimentary soil. The effects of these processes on the magnetic properties of a granitic and a sedimentary soil were examined using a simulated breakage/abrasion experiment. Breakage and/or abrasion had substantial effects on the magnetic properties of both soils. All particle sizes were affected, but the magnitude varied through the size range of derived particles. The major effect was on the concentration of magnetic minerals, with differences between the concentrations in particle sizes of the original material and those generated by the experiments being as much as 20 times. The effect on the granite soil was to reduce the concentrations, i.e. derived material was less than original material; whereas for the sedimentary soil the derived particles had higher concentrations. The effect on magnetic grain size, as indicated by the magnetic ratios, was less than the effect on the mass magnetic properties, but still substantial for some ratios for some sizes. © 1998 John Wiley & Sons, Ltd.     

Using atmospheric tracers to reduce uncertainty in groundwater recharge areas

A Monte Carlo-based approach to assess uncertainty in recharge areas shows that incorporation of atmospheric tracer observations (in this case, tritium concentration) and prior information on model parameters leads to more precise predictions of recharge areas. Variance-covariance matrices, from model calibration and calculation of sensitivities, were used to generate parameter sets that account for parameter correlation and uncertainty. Constraining parameter sets to those that met acceptance criteria, which included a standard error criterion, did not appear to bias model results. Although the addition of atmospheric tracer observations and prior information produced similar changes in the extent of predicted recharge areas, prior information had the effect of increasing probabilities within the recharge area to a greater extent than atmospheric tracer observations. Uncertainty in the recharge area propagates into predictions that directly affect water quality, such as land cover in the recharge area associated with a well and the residence time associated with the well. Assessments of well vulnerability that depend on these factors should include an assessment of model parameter uncertainty. A formal simulation of parameter uncertainty can be used to delineate probabilistic recharge areas, and the results can be expressed in ways that can be useful to water-resource managers. Although no one model is the correct model, the results of multiple models can be evaluated in terms of the decision being made and the probability of a given outcome from each model.     

Interstitial flow through preferential flow paths in the hyporheic zone of the Oberer Seebach,Austria

We investigated interstitial flow velocities in the Oberer Seebach, Austria, with NaCl tracer injections at a sediment depth of 30 cm to estimate the hydraulic conditions experienced by invertebrates inhabiting the hyporheic zone. Flow velocity measured with tracers is taken as travel time of the water along a straight line between injection and sampling points, although the water flows around sediment particles, and thus travels a somewhat longer distance. From sections of stream sediment in which the interstitial spaces were replaced by concrete, we estimated that this difference amounts, on average, to 27% and used this factor to correct the results of our velocity measurements. Corrected interstitial water velocities ranged from 0.01 to 1.32 cm s^-1 and were independent of surface discharge. We also studied spatial flow patterns in the bed sediments with long-term tracer injections. The three-dimensional distribution of tracer concentrations 24 hours after the start of the injection indicated that interstitial water preferentially flows in a complex network of areas of high hydraulic connectivity. Reynolds numbers for flow in the hyporheic pore space ranged from 0.1 to 489, implying that the flow environment varies from laminar up to the zone of transition to turbulent flow. Therefore, invertebrates may have a size-related active choice of areas where either friction drag or pressure drag predominates. The consequence of flow patterns, such as those observed in our study, is that small-scale variability of hydraulic conditions may be an important determinant of the patchy invertebrate distribution in bed sediments.     

Surface particle sizes on armoured gravel streambeds: effects of supply and hydraulics

Most gravel‐bed streams exhibit a surface armour in which the median grain size of the surface particles is coarser than that of the subsurface particles. This armour has been interpreted to result when the supply of sediment is less than the ability of the stream to move sediment. While there may be certain sizes in the bed for which the supply is less than the ability of the stream to transport these sizes, for other sizes of particles the supply may match or even exceed the ability of the channel to transport these particles. These sizes of particles are called ‘supply‐limited’ and ‘hydraulically limited’ in their transport, respectively, and can be differentiated in dimensionless sediment transport rating curves by size fractions. The supply‐ and hydraulically limited sizes can be distinguished also by comparing the size of particles of the surface and subsurface. Those sizes that are supply‐limited are winnowed from the bed and are under‐represented in the surface layer. Progressive truncation of the surface and subsurface size distributions from the ?ne end and recalculation until the size distributions are similar (collapse), establishes the break between supply‐ and hydraulically limited sizes. At sites along 12 streams in Idaho ranging in drainage area from about 100 to 4900 km², sediment transport rating curves by size class and surface and subsurface size distributions were examined. The break between sizes that were supply‐ and hydraulically limited as determined by examination of the transport rate and surface and subsurface size distributions was similar. The collapse size as described by its percentile in the cumulative size distribution averaged D₃₆ of the surface and D₇₃ of the subsurface. The discharge at which the collapse size began to move averaged 88 per cent of bankfull discharge. The collapse size decreased as bed load yield increased and increased with the degree of selective transport. Copyright © 2003 John Wiley & Sons, Ltd.     

The influence of channel morphology on bedload path lengths: Insights from a survival process model

Tracer studies are a commonly used tool to develop and test Einstein-type stochastic bedload transport models. The movements of these tracers are controlled by many factors including grain characteristics, hydrologic forcing, and channel morphology. Although the influence of these sediment storage zones related to morphological features (e.g., bars, pools, riffles) have long been observed to “trap” bedload particles in transport, this influence has not been adequately quantified. In this paper we explore the influence of channel morphology on particle travel distances through the development of a Bayesian survival process model. This model simulates particle path length distributions using a location-specific “trapping probability” parameter (p_i ), which is estimated using the starting and ending locations of bedload tracers. We test this model using a field tracer study from Halfmoon Creek, Colorado. We find that (1) the model is able to adequately recreate the observed multi-modal path length distributions, (2) particles tend to accumulate in trapping zones, especially during large floods, and (3) particles entrained near a trapping zone will travel a shorter distance than one that is further away. Particle starting positions can affect path lengths by as much as a factor of two, which we confirm by modelling “starting-location-specific” path length probability distributions. This study highlights the importance of considering both tracer locations and channel topography in examinations of field tracer studies. © 2020 John Wiley & Sons, Ltd.     

Quantification of river water infiltration in shallow aquifers using acesulfame and anthropogenic gadolinium

This study has investigated the use of the artificial sweetener acesulfame and the magnetic resonance imaging contrast agent gadolinium as quantitative tracers for river water infiltration into shallow groundwater. The influence of a river on alluvial groundwater in a subalpine catchment in western Europe has been assessed using the ‘classical’ hydrochemical tracer chloride and the trace contaminants acesulfame and anthropogenic gadolinium. Mixing ratios for riverine bank filtrate with ambient groundwater and the uncertainties associated with the temporal and spatial tracer variability were calculated using acesulfame and gadolinium and compared with those obtained using chloride. The temporal variability of tracer concentrations in river water of gadolinium (standard deviation SD: 63%) and acesulfame (SD: 71%) both exceeded that of chloride (SD: 27%), and this was identified as the main source of uncertainty in the mixing analysis. Similar spatial distributions were detected in the groundwater for chloride and gadolinium, but not for acesulfame. Mixing analyses using acesulfame resulted in calculated mixing ratios that differed from those obtained using gadolinium and chloride by up to 83% and 92%, respectively. At the investigated site, which had oxic conditions and moderate temperatures, acesulfame was found to be a less reliable tracer than either gadolinium or chloride, probably because of natural attenuation and input from other sources. There was no statistically significant difference between the mixing ratios obtained using chloride or gadolinium, the mixing ratios obtained using gadolinium were 40–50% lower than those obtained using chloride. This is mainly due to a bias of the mean gadolinium concentration in river water towards higher values. In view of the uncertainties of the two tracers, neither could be preferred over the other for the quantification of bank filtrate in groundwater. At this specific site gadolinium was able to reliably identify river water infiltration and was a more precise tracer than chloride at low mixing ratios (<20%), because of the exclusive occurrence of gadolinium in river water and its high dynamic range. Copyright © 2015 John Wiley & Sons, Ltd.     

无参考序列条件下地面气温观测资料城市化偏差订正方法：以北京站为例

本文以北京气象站长期地面气温观测资料为例,发展了一种无早期参考序列条件下城镇站城市化偏差评价和订正方法.首先对北京站逐月平均最高、最低气温资料进行质量控制和均一化处理,并借助卫星遥感亮度温度资料遴选附近乡村站;然后利用最近3年逐时地面气温资料,计算观象台和5个乡村站各月平均地面气温的差值,把其作为北京站1915-2012年期间的城市化累积影响;最后假设城市化累积影响在整个研究时期呈匀速增长,采用线性订正法对地面月平均气温序列中的城市化偏差进行订正.分析表明：资料均一化处理后,北京站近百年最高、最低和平均气温多年平均值有所下降,气温日较差则有所提高,但三种年平均气温序列增温趋势和年平均气温日较差序列下降趋势有所增强.北京站年平均最低气温、平均气温和气温日较差序列中均存在较大的城市化累积影响,其中最低气温和平均气温四个季节均为正值,冬季最大,秋季次之,夏季最小,四季和年平均气温日较差均为较大的负值.订正城市化偏差后,最低气温和平均气温增加速率均明显下降,年平均气温日较差下降趋势则明显变弱.     

An analysis of soil crust strength in relation to potential abrasion by saltating particles

Wind erosion depends on the ease with which particles can be detached from the soil surface, but suitable tests to characterize this property are not available. Two possible methods to determine surface soil strength in the field were therefore compared on a range of artificially ‘crusted’ surfaces. These were made by spraying or tension wetting aggregates (10–2, 2–0.5 and <0.5 mm) from a structurally unstable sandy loam, followed by drying. Each test involved measuring the force exerted on a probe driven at a steady rate into the surface, using either a flat-tipped 0.6 mm diameter penetrometer or a flat-ended cylindrical punch with inner and outer diameters of 5 and 6 mm, respectively. Both probes showed that crusts could be produced reproducibly. Depending on the probe and aggregate size, penetration mainly occurred either as a result of aggregates being deflected out of the pathway of the probe or by genuine rupture of aggregates or of the crusted surface. The penetrometer, because it was comparable to the size of sand grains, gave results that can be used to characterize surface erodibility to saltating particles. The punch gave results that would be unsuitable for this purpose, as would other strength tests that are on too large a scale. Penetrometer results were analyzed to calculate the energy required for penetration. It was thus possible to demonstrate that only the spray-wetted fine aggregates had a surface that could undergo large-scale rupture by saltating sand grains. For all other surfaces, saltating particles would be unable to supply sufficient energy to rupture aggregates or the crusted surface. Erosion could only occur by a slower process of abrasion in which smaller particles or aggregates are chipped away from the surface. However, it is shown that saltating particles could rupture the interaggregate bonding in the 2–0.5 mm aggregate surfaces, thus permitting creep. An alternative and potentially simpler way of characterizing surface erodibility by using a surface modulus of elasticity is also discussed. Our results demonstrate that the small diameter penetrometer is a promising technique for characterizing erodibility of aggregated and crusted surfaces. © 1997 by John Wiley & Sons, Ltd.     

A velocity projection framework for inferring shallow water currents from surface tracer fields

To the extent that sea surface temperature and colors can be considered passive tracers, their motions can be tracked to estimate the current velocities, or a conservation equation can be invoked to relate their temporal variations to the velocities. We investigate the latter, the so-called tracer inversion problem, with a particular focus on (1) the conditions under which the problem can be rendered over-determined for least squares solutions, (2) the possibility of using the tracer conservation equation within the “velocity projection” framework to estimate subsurface current profiles in shallow coastal waters, and (3) the accuracy of the tracer inversion calculation in terms of the data resolution and noise. The velocity projection framework refers to relating surface motion, either measured directly or made visible by tracers, to the subsurface current motion through the equations of motion. The accuracy of the tracer inversion calculation is quantified in terms of the spatial and temporal resolution of the tracer distribution. In the presence of irreducible tracer noise, the accuracy of the inversion rapidly degrades, and it is shown that the inversion with velocity projection can help improve accuracy. The tracer inversion method developed in this study is applied to the satellite sea surface temperature data, and the velocity result is compared to the velocity measurements made with the shore-based HF Coastal Current Radar. The potential of improving the velocity estimation with the present approach is indicated.