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NASA NTRS1987

The effect of wind and currents on gas exchange in an estuarine system

The objectives were to develop a non-volatile tracer to use in gas exchange experiments in laterally unconfined systems and to study applications of deliberate tracers in limnology and oceanography. Progress was made on both fronts but work on the development of the non-volatile tracer proved to be more difficult and labor intensive that anticipated so no field experiments using non-volatile tracers was performed as yet. In the search for a suitable non-volatile tracer for an ocean scale gas exchange experiment a tracer was discovered which does not have the required sensitivity for a large scale experiment, but is very easy to analyze and will be well suited for smaller experiments such as gas exchange determinations on rivers and streams. Sulfur hexafluoride, SF6, was used successfully as a volatile tracer along with tritium as a non-volatile tracer to study gas exchange rates from a primary stream. This is the first gas exchange experiment in which gas exchange rates were determined on a head water stream where significant groundwater input occurs along the reach. In conjunction with SF6, Radon-222 measurements were performed on the groundwater and in the stream. The feasibility of using a combination of SF6 and radon is being studied to determine groundwater inputs and gas exchange of rates in streams with significant groundwater input without using a non-volatile tracer.

Broecker, W. S.↗

NASA NTRS2019

Large-Scale Transport into the Arctic: The Roles of the Midlatitude Jet and the Hadley Cell

Transport from the Northern Hemisphere (NH) midlatitudes to the Arctic plays a crucial role in determining the abundance of trace gases and aerosols that are important to Arctic climate via impacts on radiation and chemistry. Here we examine this transport using an idealized tracer with a fixed lifetime and predominantly midlatitude land-based sources in models participating in the Chemistry Climate Model Initiative (CCMI). We show that there is a 25%-45% difference in the Arctic concentrations of this tracer among the models. This spread is correlated with the spread in the location of the Pacific jet, as well as the spread in the location of the Hadley Cell (HC) edge, which varies consistently with jet latitude. Our results suggest that it is likely that the HC-related zonal-mean meridional transport rather than the jet-related eddy mixing is the major contributor to the inter-model spread in the transport of land-based tracers into the Arctic. Specifically, in models with a more northern jet, the HC generally extends further north and the tracer source region is mostly covered by surface southward flow associated with the lower branch of the HC, resulting in less efficient transport poleward to the Arctic. During boreal summer, there are poleward biases in jet location in free-running models, and these models likely underestimate the rate of transport into the Arctic. Models using specified dynamics do not have biases in the jet location, but do have biases in the surface meridional flow, which may result in differences in transport into the Arctic. In addition to the land-based tracer, the midlatitude-to-Arctic transport is further examined by another idealized tracer with zonally uniform sources. With equal sources from both land and ocean, the inter-model spread of this zonally uniform tracer is more related to variations in parameterized convection over oceans rather than variations in HC extent, particularly during boreal winter. This suggests that transport of land-based and oceanic tracers or aerosols towards the Arctic differs in pathways and therefore their corresponding inter-model variabilities result from different physical processes.

chemistry climate models↗

NASA NTRS1986

Numerical advection by conservation of second-order moments

A new, accurate, and nondiffusive method for three-dimensional advection of trace species is presented. The method preserves tracer structures by conserving the second-order moments of the spatial distribution of tracer during advection. Upstream transport and second-order tracer distribution are described, and the moments of the tracer distribution about the center of a grid box are formally defined and related to the polynomial distribution. Formulas are presented which describe how the moments of a grid box are decomposed into a unique set of moments centered about each subbox and how they are reassembled into new grid boxes. A one-dimensional example if tracer transport is given, and limits necessary to maintain positive tracer concentrations are derived. The accuracy and stability of this method are analytically examined, and numerical experiments testing the effective resolution are presented. The method is compared with other methods for numerical advection of tracers.

Prather, M. J.↗

NASA NTRS1998

A Lagrangian View of Stratospheric Trace Gas Distributions

As a result of photochemistry, some relationship between the stratospheric age-of-air and the amount of tracer contained within an air sample is expected. The existence of such a relationship allows inferences about transport history to be made from observations of chemical tracers. This paper lays down the conceptual foundations for the relationship between age and tracer amount, developed within a Lagrangian framework. In general, the photochemical loss depends not only on the age of the parcel but also on its path. We show that under the "average path approximation" that the path variations are less important than parcel age. The average path approximation then allows us to develop a formal relationship between the age spectrum and the tracer spectrum. Using the relation between the tracer and age spectra, tracer-tracer correlations can be interpreted as resulting from mixing which connects parts of the single path photochemistry curve, which is formed purely from the action of photochemistry on an irreducible parcel. This geometric interpretation of mixing gives rise to constraints on trace gas correlations, and explains why some observations are do not fall on rapid mixing curves. This effect is seen in the ATMOS observations.

Schoeberl, M. R.↗

NASA NTRS2011

Evaluation of Convective Transport in the GEOS-5 Chemistry and Climate Model

The NASA Goddard Earth Observing System (GEOS-5) Chemistry and Climate Model (CCM) consists of a global atmospheric general circulation model and the combined stratospheric and tropospheric chemistry package from the NASA Global Modeling Initiative (GMI) chemical transport model. The subgrid process of convective tracer transport is represented through the Relaxed Arakawa-Schubert parameterization in the GEOS-5 CCM. However, substantial uncertainty for tracer transport is associated with this parameterization, as is the case with all global and regional models. We have designed a project to comprehensively evaluate this parameterization from the point of view of tracer transport, and determine the most appropriate improvements that can be made to the GEOS-5 convection algorithm, allowing improvement in our understanding of the role of convective processes in determining atmospheric composition. We first simulate tracer transport in individual observed convective events with a cloud-resolving model (WRF). Initial condition tracer profiles (CO, CO2, O3) are constructed from aircraft data collected in undisturbed air, and the simulations are evaluated using aircraft data taken in the convective anvils. A single-column (SCM) version of the GEOS-5 GCM with online tracers is then run for the same convective events. SCM output is evaluated based on averaged tracer fields from the cloud-resolving model. Sensitivity simulations with adjusted parameters will be run in the SCM to determine improvements in the representation of convective transport. The focus of the work to date is on tropical continental convective events from the African Monsoon Multidisciplinary Analyses (AMMA) field mission in August 2006 that were extensively sampled by multiple research aircraft.

Pickering, Kenneth E.↗

NASA NTRS2010

An Aircraft-Based Upper Troposphere Lower Stratosphere O3, CO, and H2O Climatology for the Northern Hemisphere

We present a climatology of O3, CO, and H2O for the upper troposphere and lower stratosphere (UTLS), based on a large collection of high ]resolution research aircraft data taken between 1995 and 2008. To group aircraft observations with sparse horizontal coverage, the UTLS is divided into three regimes: the tropics, subtropics, and the polar region. These regimes are defined using a set of simple criteria based on tropopause height and multiple tropopause conditions. Tropopause ]referenced tracer profiles and tracer ]tracer correlations show distinct characteristics for each regime, which reflect the underlying transport processes. The UTLS climatology derived here shows many features of earlier climatologies. In addition, mixed air masses in the subtropics, identified by O3 ]CO correlations, show two characteristic modes in the tracer ]tracer space that are a result of mixed air masses in layers above and below the tropopause (TP). A thin layer of mixed air (1.2 km around the tropopause) is identified for all regions and seasons, where tracer gradients across the TP are largest. The most pronounced influence of mixing between the tropical transition layer and the subtropics was found in spring and summer in the region above 380 K potential temperature. The vertical extent of mixed air masses between UT and LS reaches up to 5 km above the TP. The tracer correlations and distributions in the UTLS derived here can serve as a reference for model and satellite data evaluation

Tilmes, S.↗

NASA NTRS2017

Multi-Model Impacts of Climate Change on Pollution Transport from Global Emission Source Regions

The impacts of climate change on tropospheric transport, diagnosed from a carbon monoxide (CO)-like tracer species emitted from global CO sources, are evaluated from an ensemble of four chemistry-climate model (CCMs) contributing to the Atmospheric Chemistry and Climate Model Intercomparison Project (ACCMIP). Model time-slice simulations for present-day and end of the 21st century conditions were performed under the Representative Concentrations Pathways (RCP) climate scenario RCP 8.5. All simulations reveal a strong seasonality in transport, especially over the tropics. The highest CO-tracer mixing ratios aloft occur during boreal winter when strong vertical transport is co-located with biomass burning emission source regions. A consistent and robust decrease in future CO-tracer mixing ratios throughout most of the troposphere, especially in the tropics, and an increase around the tropopause is found across the four CCMs in both winter and summer. Decreases in CO-tracer mixing ratios in the tropical troposphere are associated with reduced convective mass fluxes in this region, which in turn may reflect a weaker Hadley Cell circulation in the future climate. Increases in CO-tracer mixing ratios near the tropopause are largely attributable to a rise in tropopause height, although a poleward shift in the midlatitude jets may also play an important role in the extra-tropical upper troposphere. An increase in CO-tracer mixing ratios also occurs near the Equator, centred over EquatorialCentral Africa, extending from the surface to the mid troposphere which is most likely related to localised decreases in convection in the vicinity of the Intertropical Convergence Zone, resulting in larger CO-tracer mixing ratios over biomass burning regions and smaller mixing ratios downwind.

Tropospheric Transport↗

NASA NTRS2021

Summertime Transport Pathways from Different Northern Hemisphere Regions into the Arctic

Trace gases and aerosols play an important role in Arctic chemistry and climate. As most Arctic tracers and aerosols are transported from midlatitude source regions, long-range transport into the Arctic is one of the key factors to understand the current and future states of Arctic climate. While previous studies have investigated the airmass fraction and transit time distribution in the Arctic, the actual transport pathways and their underlying dynamics and efficiencies are yet to be understood. In this study, we implement a large ensemble of idealized tagged pulse passive tracers in the Whole Atmosphere Community Climate Model version 5 to identify and analyze summertime transport pathways from different Northern Hemisphere surface regions into the Arctic. Three different transport pathways are identified as those associated with fast, intermediate and slow time scales. Midlatitude tracers can be transported into the Arctic in the troposphere via the fast transport pathway (~8 days), which moves tracers northward from the source region mainly through transient eddies. For the intermediate transport pathway, which happens on 1~3 weeks’ time scales, midlatitude tracers are first zonally transported by the jet stream, and then advected northward into the Arctic over Alaska and northern North Atlantic. Tropical and subtropical tracers are transported into the Arctic lower stratosphere via the slow transport pathway (1~3 months), as the tracers are lifted upward into the tropical and subtropical lower stratosphere, and then transported into the Arctic following the isentropic surfaces.

Trace gases↗

NASA NTRS2003

Large-scale Stratospheric Transport Processes

The PI has undertaken a theoretical analysis of the existence and nature of compact tracer-tracer relationships of the kind observed in the stratosphere, augmented with three-dimensional model simulations of stratospheric tracers (the latter being an extension of modeling work the group did during the SOLVE experiment). This work achieves a rigorous theoretical basis for the existence and shape of these relationships, as well as a quantitative theory of their width and evolution, in terms of the joint tracer-tracer PDF distribution. A paper on this work is almost complete and will soon be submitted to Rev. Geophys. We have analyzed lower stratospheric water in simulations with an isentropic-coordinate version of the MATCH transport model which we recently helped to develop. The three-dimensional structure of lower stratospheric water, in particular, attracted our attention: dry air is, below about 400K potential temperature, localized in the regions of the west Pacific and equatorial South America. We have been analyzing air trajectories to determine how air passes through the tropopause cold trap. This work is now being completed, and a paper will be submitted to Geophys. Res. Lett. before the end of summer. We are continuing to perform experiments with the 'MATCH' CTM, in both sigma- and entropy-coordinate forms. We earlier found (in collaboration with Dr Natalie Mahowald, and as part of an NSF-funded project) that switching to isentropic coordinates made a substantial improvement to the simulation of the age of stratospheric air. We are now running experiments with near-tropopause sources in both versions of the model, to see if and to what extent the simulation of stratosphere-troposphere transport is dependent on the model coordinate. Personnel Research is supervised by the PI, Prof. Alan Plumb. Mr William Heres conducts the tracer modeling work and performs other modeling tasks. Two graduate students, Ms Irene Lee and Mr Michael Ring, have been participating in the research.

Plumb, R. Alan↗

NASA NTRS2017

Biogeochemical Protocols and Diagnostics for the CMIP6 Ocean Model Intercomparison Project (OMIP)

The Ocean Model Intercomparison Project (OMIP) focuses on the physics and biogeochemistry of the ocean component of Earth system models participating in the sixth phase of the Coupled Model Intercomparison Project (CMIP6). OMIP aims to provide standard protocols and diagnostics for ocean models, while offering a forum to promote their common assessment and improvement. It also offers to compare solutions of the same ocean models when forced with reanalysis data (OMIP simulations) vs. when integrated within fully coupled Earth system models (CMIP6). Here we detail simulation protocols and diagnostics for OMIP's biogeochemical and inert chemical tracers. These passive-tracer simulations will be coupled to ocean circulation models, initialized with observational data or output from a model spin-up, and forced by repeating the 1948-2009 surface fluxes of heat, fresh water, and momentum. These so-called OMIP-BGC simulations include three inert chemical tracers (CFC-11, CFC-12, SF [subscript] 6) and biogeochemical tracers (e.g., dissolved inorganic carbon, carbon isotopes, alkalinity, nutrients, and oxygen). Modelers will use their preferred prognostic BGC model but should follow common guidelines for gas exchange and carbonate chemistry. Simulations include both natural and total carbon tracers. The required forced simulation (omip1) will be initialized with gridded observational climatologies. An optional forced simulation (omip1-spunup) will be initialized instead with BGC fields from a long model spin-up, preferably for 2000 years or more, and forced by repeating the same 62-year meteorological forcing. That optional run will also include abiotic tracers of total dissolved inorganic carbon and radiocarbon, CTabio and 14CTabio, to assess deep-ocean ventilation and distinguish the role of physics vs. biology. These simulations will be forced by observed atmospheric histories of the three inert gases and CO2 as well as carbon isotope ratios of CO2. OMIP-BGC simulation protocols are founded on those from previous phases of the Ocean Carbon-Cycle Model Intercomparison Project. They have been merged and updated to reflect improvements concerning gas exchange, carbonate chemistry, and new data for initial conditions and atmospheric gas histories. Code is provided to facilitate their implementation.

Carbon↗

NASA NTRS1967

Chemical Method of Urine Volume Measurement

A system has been developed and qualified as flight hardware for the measurement of micturition volumes voided by crewmen during Gemini missions. This Chemical Urine Volume Measurement System (CUVMS) is used for obtaining samples of each micturition for post-flight volume determination and laboratory analysis for chemical constituents of physiological interest. The system is versatile with respect to volumes measured, with a capacity beyond the largest micturition expected to be encountered, and with respect to mission duration of inherently indefinite length. The urine sample is used for the measurement of total micturition volume by a tracer dilution technique, in which a fixed, predetermined amount of tritiated water is introduced and mixed into the voided urine, and the resulting concentration of the tracer in the sample is determined with a liquid scintillation spectrometer. The tracer employed does not interfere with the analysis for the chemical constituents of the urine. The CUVMS hardware consists of a four-way selector valve in which an automatically operated tracer metering pump is incorporated, a collection/mixing bag, and tracer storage accumulators. The assembled system interfaces with a urine receiver at the selector valve inlet, sample bags which connect to the side of the selector valve, and a flexible hose which carries the excess urine to the overboard drain connection. Results of testing have demonstrated system volume measurement accuracy within the specification limits of +/-5%, and operating reliability suitable for system use aboard the GT-7 mission, in which it was first used.

QUANTITATIVE ANALYSIS↗

NASA NTRS1998

NO(x) Concentrations in the Upper Troposphere as a Result of Lightning

Upper tropospheric NO(x) controls, in part, the distribution of ozone in this greenhouse-sensitive region of the atmosphere. Many factors control NO(x) in this region. As a result it is difficult to assess uncertainties in anthropogenic perturbations to NO from aircraft, for example, without understanding the role of the other major NO(x) sources in the upper troposphere. These include in situ sources (lightning, aircraft), convection from the surface (biomass burning, fossil fuels, soils), stratospheric intrusions, and photochemical recycling from HNO3. This work examines the separate contribution to upper tropospheric "primary" NO(x) from each source category and uses two different chemical transport models (CTMS) to represent a range of possible atmospheric transport. Because aircraft emissions are tied to particular pressure altitudes, it is important to understand whether those emissions are placed in the model stratosphere or troposphere and to assess whether the models can adequately differentiate stratospheric air from tropospheric air. We examine these issues by defining a point-by-point "tracer tropopause" in order to differentiate stratosphere from troposphere in terms of NO(x) perturbations. Both models predict similar zonal average peak enhancements of primary NO(x) due to aircraft (approx. = 10-20 parts per trillion by volume (pptv) in both January and July); however, the placement of this peak is primarily in a region of large stratospheric influence in one model and centered near the level evaluated as the tracer tropopause in the second. Below the tracer tropopause, both models show negligible NO(x) derived directly from the stratospheric source. Also, they predict a typically low background of 1 - 20 pptv NO(x) when tropospheric HNO3 is constrained to be 100 pptv of HNO3. The two models calculate large differences in the total background NO(x) (defined as the source of NO(x) from lightning + stratosphere + surface + HNO3) when using identical loss frequencies for NO(x). This difference is primarily due to differing treatments of vertical transport. An improved diagnosis of this transport that is relevant to NO(x) requires either measurements of a surface-based tracer with a substantially shorter lifetime than Rn-222 or diagnosis and mapping of tracer correlations with different source signatures. Because of differences in transport by the two models we cannot constrain the source of NO(x) from lightning through comparison of average model concentrations with observations of NO(x).

Penner, Joyce E.↗

NASA NTRS1999

Statistical Perspectives on Stratospheric Transport

Long-lived tropospheric source gases, such as nitrous oxide, enter the stratosphere through the tropical tropopause, are transported throughout the stratosphere by the Brewer-Dobson circulation, and are photochemically destroyed in the upper stratosphere. These chemical constituents, or "tracers" can be used to track mixing and transport by the stratospheric winds. Much of our understanding about the stratospheric circulation is based on large scale gradients and other spatial features in tracer fields constructed from satellite measurements. The point of view presented in this paper is different, but complementary, in that transport is described in terms of tracer probability distribution functions (PDFs). The PDF is computed from the measurements, and is proportional to the area occupied by tracer values in a given range. The flavor of this paper is tutorial, and the ideas are illustrated with several examples of transport-related phenomena, annotated with remarks that summarize the main point or suggest new directions. One example shows how the multimodal shape of the PDF gives information about the different branches of the circulation. Another example shows how the statistics of fluctuations from the most probable tracer value give insight into mixing between different regions of the atmosphere. Also included is an analysis of the time-dependence of the PDF during the onset and decline of the winter circulation, and a study of how "bursts" in the circulation are reflected in transient periods of rapid evolution of the PDF. The dependence of the statistics on location and time are also shown to be important for practical problems related to statistical robustness and satellite sampling. The examples illustrate how physically-based statistical analysis can shed some light on aspects of stratospheric transport that may not be obvious or quantifiable with other types of analyses. An important motivation for the work presented here is the need for synthesis of the large and growing database of observations of the atmosphere and the vast quantities of output generated by atmospheric models.

Sparling, L. C.↗

NASA NTRS1998

Ocean Turbulence V: Mesoscale Modeling in Level Coordinates. The Effect of Random Nature of Density

The main result of this paper is the derivation of a new expression for the tracer subgrid term in level coordinates S(l) to be employed in O-GCM. The novel feature is the proper account of the random nature of the density field which strongly affects the transformation from isopycnal to level coordinates of the variables of interest, velocity and tracer fields, their correlation functions and ultimately the subgrid terms. In deriving our result we made use of measured properties of vertical ocean turbulence. The major new results are: 1) the new subgrid expression is different from that of the heuristic GM model, 2) u++(tracer)=1/2u+(thickness), where u++ and u+ are the tracer and thickness bolus velocities. In previous models, u++ = u+, 2) the subgrid for a tracer tau is not the same as that for the density rho even when one accounts for the obvious absence of a diffusion term in the latter. The difference stems from a new treatment of the stochastic nature of the density, 3) the mesoscale diffusivity enters both locally and non-locally, as the integral over all z's from the bottom of the ocean to the level z.

Canuto, V. M.↗

NASA NTRS1999

Transport Experiments

MM II defined a series of experiments to better understand and characterize model transport and to assess the realism of this transport by comparison to observations. Measurements from aircraft, balloon, and satellite, not yet available at the time of MM I [Prather and Remsberg, 1993], provide new and stringent constraints on model transport, and address the limits of our transport modeling abilities. Simulations of the idealized tracers the age spectrum, and propagating boundary conditions, and conserved HSCT-like emissions probe the relative roles of different model transport mechanisms, while simulations of SF6 and C02 make the connection to observations. Some of the tracers are related, and transport diagnostics such as the mean age can be derived from more than one of the experiments for comparison to observations. The goals of the transport experiments are: (1) To isolate the effects of transport in models from other processes; (2) To assess model transport for realistic tracers (such as SF6 and C02) for comparison to observations; (3) To use certain idealized tracers to isolate model mechanisms and relationships to atmospheric chemical perturbations; (4) To identify strengths and weaknesses of the treatment of transport processes in the models; (5) To relate evaluated shortcomings to aspects of model formulation. The following section are included:Executive Summary, Introduction, Age Spectrum, Observation, Tropical Transport in Models, Global Mean Age in Models, Source-Transport Covariance, HSCT "ANOY" Tracer Distributions, and Summary and Conclusions.

Hall, Timothy M.↗

NASA NTRS2019

Emissions Relationships in Western Forest Fire Plumes: I. Reducing the Effect of Mixing Errors on Emission Factors

Studies of emission factors from biomass burning using aircraft data complement the results of lab studies and extend them to conditions of immense hot conflagrations. We illustrate and discuss emission relationships for 422 individual samples from many forest-fire plumes in the Western US. The samples are from two NASA investigations: ARCTAS (Arctic Research of the Composition of the Troposphere from Aircraft and Satellites) and SEAC4RS (Studies of Emissions and Atmospheric Composition, Clouds, and Climate Coupling by Regional Surveys). This work provides sample-by-sample enhancement ratios (EnRs) for 23 gases and particulate properties. Many EnRs provide candidates for emission ratios (ERs, corresponding to the EnR at the source) when the origin and degree of transformation is understood and appropriate. From these, emission factors (EFs) can be estimated when the fuel dry mass consumed is known or can be estimated using the carbon mass budget approach. This analysis requires understanding the interplay of mixing of the plume with surrounding air. Some initial examples emphasize that measured C(tot) = CO2 + CO in a fire plume does not necessarily describe the emissions of the total carbon liberated in the flames, C(burn). Rather, it represents C(tot) = C(burn) + C(bkgd), which includes possibly varying background concentrations for entrained air. Consequently, we present a simple theoretical description for plume entrainment for multiple tracers from flame to hundreds of kilometers downwind and illustrate some intrinsic linear behaviors. The analysis suggests a Mixed Effects Regression Emission Technique (MERET), which can eliminate occasional strong biases associated with the commonly used normalized excess mixing ratio (NEMR) method. MERET splits C(tot) to reveal C(burn) by exploiting the fact that C(burn) and all tracers respond linearly to dilution, while each tracer has consistent EnR behavior (slope of tracer concentration with respect to C(burn)). The two effects are separable. Two or three or preferably more emission indicators are required as a minimum; here we used ten. Limited variations in the EnRs for each tracer can be incorporated and the variations and co-variations analyzed. The percentage CO yield (or the modified combustion efficiency) plays some role. Other co-relationships involving nitrogen and organic classes are more prominent; these have strong relationships to the C(burn) to O3 emission relationship. In summary, MERET allows fine spatial resolution (EnRs for individual observations) and comparison of similar plumes distant in time and space. Alkene ratios provide us with an approximate photochemical timescale. This allows discrimination and definition, by fire situation, of ERs, allowing us to estimate emission factors.

Chatfield, Robert B.↗

NASA NTRS1980

Geological assessment probe

A probe is described which can be installed in a side hole that extends from a bore hole in the Earth, to assess the permeability of the strata surrounding the borehole. The probe is elongated and has a plurality of seals spaced therealong and sealed to the walls of the side hole to form a plurality of chambers sealed from one another. A tracer fluid injector on the probe can inject a tracer fluid into one of the chambers, while a tracer fluid detector located in another chamber can detect the tracer fluid, to thereby sense the permeability of the strata surrounding the side hole. The probe can include a train of modules, with each module having an inflatable packer which is inflated by the difference between the borehole pressure and the strata pressure.

Collins, E. R.↗

NASA NTRS1981

Parameterization of linear wave chemical transport in planetary atmospheres by eddy diffusion

Two-dimensional transport by linear waves is parameterized by wave velocity and temperature correlations and nonconservative properties of the atmosphere in a residual Eulerian framework. Explicit expressions derived for the eddy tracer flux vector are written in eddy diffusion tensor form, but it is demonstrated that strong coupling of chemistry and temperature through the rate constants, as is the case for ozone, requires additional terms proportional to the mixing ratio and not to its gradient. A variety of limiting cases are discussed. In the residual Eulerian framework the K(yz), K(zy) components are nonzero for a nonconservative atmosphere and/or a reactive tracer. Tracers have common transport coefficients in the limit where their chemistry is negligible in comparison to transience. It is shown that the usual one-dimensional vertical eddy diffusion continuity equation is rigorously valid only when the temperature dependence of the rate constants is negligible and the tracer has strong vertical stratification relative to its horizontal variability.

Strobel, D. F.↗