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At least 667 records · Page 37

Assembly and Delivery of Rabbit Capsules for Irradiation of Silicon Carbide Cladding Tube Specimens in the High Flux Isotope Reactor

Neutron irradiation of silicon carbide (SiC)-based fuel cladding under a high radial heat flux presents a critical challenge for SiC cladding concepts in light water reactors (LWRs). Fission heating in the fuel provides a high heat flux through the cladding, which, combined with the degraded thermal conductivity of SiC under irradiation, results in a large temperature gradient through the thickness of the cladding. The strong temperature dependence of swelling in SiC creates a complex stress profile in SiCbased cladding tubes as a result of differential swelling. The Nuclear Science User Facilities (NSUF) Program within the US Department of Energy Office of Nuclear Energy is supporting research efforts to improve the scientific understanding of the effects of irradiation on SiC cladding tubes. Ultimately, the results of this project will provide experimental validation of multi-physics models for SiC-based fuel cladding during LWR operation. The first objective of this project is to irradiate tube specimens using a previously developed design that allows for irradiation testing of miniature SiC tube specimens subjected to a high radial heat flux. The previous “rabbit” capsule design uses the gamma heating in the core of the High Flux Isotope Reactor (HFIR) to drive a high heat flux through the cladding tube specimens. A compressible aluminum foil allows for a constant thermal contact conductance between the cladding tubes and the rabbit housing despite swelling of the SiC tubes. To allow separation of the effects of irradiation from those due to differential swelling under a high heat flux, a new design was developed under the NSUF program. This design allows for irradiation of similar SiC cladding tube specimens without a high radial heat flux. This report briefly describes the irradiation experiment design concepts, summarizes the irradiation test matrix, and reports on the successful delivery of six rabbit capsules to the HFIR. Rabbits of both low and high heat flux configurations have been assembled, welded, evaluated, and delivered to the HFIR along with a complete quality assurance fabrication package. These rabbits contain a wide variety of specimens including monolith tubes, SiC fiber SiC matrix (SiC/SiC) composites, duplex specimens (inner composite, outer monolith), and specimens with a variety of metallic or ceramic coatings on the outer surface. The rabbits are targeted for insertion during HFIR cycle 475, which is scheduled for September 2017.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Observing Formation of Flux Rope by Tether-cutting Reconnection in the Sun

Tether-cutting reconnection is considered as one mechanism for the formation of a flux rope. It has been proposed for more than 30 years; however, so far, direct observations of it are very rare. In this Letter, we present observations of the formation of a flux rope via tether-cutting reconnection in NOAA AR 11967 on 2014 February 2 by combining observations with the New Vacuum Solar Telescope and the Solar Dynamic Observatory . The tether-cutting reconnection occurs between two sets of highly sheared magnetic arcades. Comprehensive observational evidence of the reconnection is as follows: changes of the connections between the arcades, brightenings at the reconnection site, hot outflows, formation of a flux rope, slow-rise motion of the flux rope, and flux cancelation. The outflows are along three directions from the reconnection site to the footpoints with the velocities from 24 ± 1 km s{sup −1} to 69 ± 5 km s{sup −1}. Additionally, it is found that the newly formed flux rope connects far footpoints and has a left-handed twisted structure with many fine threads and a concave-up-shape structure in the middle. All the observations are in agreement with the tether-cutting model and provide evidence that tether-cutting reconnection leads to the formation of the flux rope associated with flux shear flow and cancelation.

79 ASTRONOMY AND ASTROPHYSICS↗

Data from: Long-term nitrous oxide fluxes in annual and perennial agricultural and unmanaged ecosystems in the upper Midwest USA

Differences in soil nitrous oxide (N2O) fluxes among ecosystems are often difficult to evaluate and predict due to high spatial and temporal variabilities and few direct experimental comparisons. For 20 years, we measured N2O fluxes in 11 ecosystems in southwest Michigan USA: four annual grain crops (corn–soybean–wheat rotations) managed with conventional, no-till, reduced input, or biologically based/organic inputs; three perennial crops (alfalfa, poplar, and conifers); and four unmanaged ecosystems of different successional age including mature forest. Average N2O emissions were higher from annual grain and N-fixing cropping systems than from nonleguminous perennial cropping systems and were low across unmanaged ecosystems. Among annual cropping systems full-rotation fluxes were indistinguishable from one another but rotation phase mattered. For example, those systems with cover crops and reduced fertilizer N emitted more N2O during the corn and soybean phases, but during the wheat phase fluxes were ~40% lower. Likewise, no-till did not differ from conventional tillage over the entire rotation but reduced emissions ~20% in the wheat phase and increased emissions 30–80% in the corn and soybean phases. Greenhouse gas intensity for the annual crops (flux per unit yield) was lowest for soybeans produced under conventional management, while for the 11 other crop × management combinations intensities were similar to one another. Among the fertilized systems, emissions ranged from 0.30 to 1.33 kg N2O-N ha−1 yr−1 and were best predicted by IPCC Tier 1 and ΔEF emission factor approaches. Annual cumulative fluxes from perennial systems were best explained by soil inline image pools (r2 = 0.72) but not so for annual crops, where management differences overrode simple correlations. Daily soil N2O emissions were poorly predicted by any measured variables. Overall, long-term measurements reveal lower fluxes in nonlegume perennial vegetation and, for conservatively fertilized annual crops, the overriding influence of rotation phase on annual fluxes.

54 ENVIRONMENTAL SCIENCES↗

Lifecycle of updrafts and mass flux in isolated deep convection over the Amazon rainforest: insights from cell tracking

Long-term observations of deep convective cloud (DCC) vertical velocity and mass flux were collected during the Observations and Modelling of the Green Ocean Amazon (GoAmazon2014/5) experiment. Precipitation echoes from a surveillance weather radar near Manaus, Brazil, are tracked to identify and evaluate the isolated DCC lifecycle evolution during the dry and wet seasons. A radar wind profiler (RWP) provides precipitation and air motion profiles to estimate the vertical velocity, mass flux, and mass transport rates within overpassing DCC cores as a function of the tracked cell lifecycle stage. The average radar reflectivity factor (Z), DCC area (A), and surface rainfall rate (R) increased with DCC lifetime as convective cells were developing, reached a peak as the cells matured, and decreased thereafter as cells dissipated. As the convective cells mature, cumulative DCC properties exhibit stronger updraft behaviors with higher upward mass flux and transport rates above the melting layer (compared with initial and later lifecycle stages). In comparison, developing DCCs have the lowest Z associated with weak updrafts, as well as negative mass flux and transport rates above the melting layer. Over the DCC lifetime, the height of the maximum downward mass flux decreased, whereas the height of the maximum net mass flux increased. During the dry season, the tracked DCCs had higher Z, propagation speed, and DCC area, and were more isolated spatially compared with the wet season. Dry season DCCs exhibit higher Z, mass flux, and mass transport rate while developing, whereas wet season DCCs exhibit higher Z, mass flux, and mass transport rates at later stages.

54 ENVIRONMENTAL SCIENCES↗

Automatic high-frequency measurements of full soil greenhouse gas fluxes in a tropical forest

Measuring in situ soil fluxes of carbon dioxide (CO 2 ), methane(CH 4 ), and nitrous oxide (N 2 O) continuously at highfrequency requires appropriate technology. We tested the combination of acommercial automated soil CO 2 flux chamber system (LI-8100A) with a CH 4 and N 2 O analyzer (Picarro G2308) in a tropicalrainforest for 4 months. A chamber closure time of 2 min was sufficient fora reliable estimation of CO 2 and CH 4 fluxes (100 %and 98.5 % of fluxes were above minimum detectable flux – MDF,respectively). This closure time was generally not suitable for a reliableestimation of the low N 2 O fluxes in this ecosystem but wassufficient for detecting rare major peak events. A closure time of 25 minwas more appropriate for reliable estimation of most N 2 O fluxes(85.6 % of measured fluxes are above MDF ± 0.002 nmol m -2 s -1 ). Our study highlights the importance ofadjusted closure time for each gas.

54 ENVIRONMENTAL SCIENCES↗

A coupled ground heat flux–surface energy balance model of evaporation using thermal remote sensing observations

Abstract. One of the major undetermined problems in evaporation (ET) retrieval using thermal infrared remote sensing is the lack of a physically based ground heat flux (G) model and its integration within the surface energy balance (SEB) equation. Here, we present a novel approach based on coupling a thermal inertia (TI)-based mechanistic G model with an analytical surface energy balance model, Surface Temperature Initiated Closure (STIC, version STIC1.2). The coupled model is named STIC-TI. The model is driven by noon–night (13:30 and 01:30 local time) land surface temperature, surface albedo, and a vegetation index from MODIS Aqua in conjunction with a clear-sky net radiation sub-model and ancillary meteorological information. SEB flux estimates from STIC-TI were evaluated with respect to the in situ fluxes from eddy covariance measurements in diverse ecosystems of contrasting aridity in both the Northern Hemisphere and Southern Hemisphere. Sensitivity analysis revealed substantial sensitivity of STIC-TI-derived fluxes due to the land surface temperature uncertainty. An evaluation of noontime G (Gi) estimates showed 12 %–21 % error across six flux tower sites, and a comparison between STIC-TI versus empirical G models also revealed the substantially better performance of the former. While the instantaneous noontime net radiation (RNi) and latent heat flux (LEi) were overestimated (15 % and 25 %), sensible heat flux (Hi) was underestimated (22 %). Overestimation (underestimation) of LEi (Hi) was associated with the overestimation of net available energy (RNi−Gi) and use of unclosed surface energy balance flux measurements in LEi (Hi) validation. The mean percent deviations in Gi and Hi estimates were found to be strongly correlated with satellite day–night view angle difference in parabolic and linear pattern, and a relatively weak correlation was found between day–night view angle difference versus LEi deviation. Findings from this parameter-sparse coupled G–ET model can make a valuable contribution to mapping and monitoring the spatiotemporal variability of ecosystem water stress and evaporation using noon–night thermal infrared observations from future Earth observation satellite missions such as TRISHNA, LSTM, and SBG.

Bhattacharya, Bimal K.↗

On the predictability of turbulent fluxes from land: PLUMBER2 MIP experimental description and preliminary results

Accurate representation of the turbulent exchange of carbon, water, and heat between the land surface and the atmosphere is critical for modelling global energy, water, and carbon cycles in both future climate projections and weather forecasts. Evaluation of models' ability to do this is performed in a wide range of simulation environments, often without explicit consideration of the degree of observational constraint or uncertainty and typically without quantification of benchmark performance expectations. We describe a Model Intercomparison Project (MIP) that attempts to resolve these shortcomings, comparing the surface turbulent heat flux predictions of around 20 different land models provided with in situ meteorological forcing evaluated with measured surface fluxes using quality-controlled data from 170 eddy-covariance-based flux tower sites. Predictions from seven out-of-sample empirical models are used to quantify the information available to land models in their forcing data and so the potential for land model performance improvement. Sites with unusual behaviour, complicated processes, poor data quality, or uncommon flux magnitude are more difficult to predict for both mechanistic and empirical models, providing a means of fairer assessment of land model performance. When examining observational uncertainty, model performance does not appear to improve in low-turbulence periods or with energy-balance-corrected flux tower data, and indeed some results raise questions about whether the energy balance correction process itself is appropriate. In all cases the results are broadly consistent, with simple out-of-sample empirical models, including linear regression, comfortably outperforming mechanistic land models. In all but two cases, latent heat flux and net ecosystem exchange of CO 2 are better predicted by land models than sensible heat flux, despite it seeming to have fewer physical controlling processes. Land models that are implemented in Earth system models also appear to perform notably better than stand-alone ecosystem (including demographic) models, at least in terms of the fluxes examined here. The approach we outline enables isolation of the locations and conditions under which model developers can know that a land model can improve, allowing information pathways and discrete parameterisations in models to be identified and targeted for future model development.

54 ENVIRONMENTAL SCIENCES↗

The imprint of surface fluxes and transport on variations in total column carbon dioxide

New observations of the vertically integrated CO{sub 2} mixing ratio, <CO{sub 2}>, from ground-based remote sensing show that variations in <CO{sub 2}> are primarily determined by large-scale flux patterns. They therefore provide fundamentally different information than observations made within the boundary layer, which reflect the combined influence of large-scale and local fluxes. Observations of both <CO{sub 2}> and CO{sub 2} concentrations in the free troposphere show that large-scale spatial gradients induce synoptic-scale temporal variations in <CO{sub 2}> in the Northern Hemisphere midlatitudes through horizontal advection. Rather than obscure the signature of surface fluxes on atmospheric CO{sub 2}, these synoptic-scale variations provide useful information that can be used to reveal the meridional flux distribution. We estimate the meridional gradient in <CO{sub 2}> from covariations in <CO{sub 2}> and potential temperature, {theta}, a dynamical tracer, on synoptic timescales to evaluate surface flux estimates commonly used in carbon cycle models. We find that simulations using Carnegie Ames Stanford Approach (CASA) biospheric fluxes underestimate both the <CO{sub 2}> seasonal cycle amplitude throughout the Northern Hemisphere midlatitudes and the meridional gradient during the growing season. Simulations using CASA net ecosystem exchange (NEE) with increased and phase-shifted boreal fluxes better fit the observations. Our simulations suggest that climatological mean CASA fluxes underestimate boreal growing season NEE (between 45-65{sup o} N) by {approx}40%. We describe the implications for this large seasonal exchange on inference of the net Northern Hemisphere terrestrial carbon sink.

54 ENVIRONMENTAL SCIENCES↗

Upscaled diurnal cycles of land–atmosphere fluxes: a new global half-hourly data product

Interactions between the biosphere and the atmosphere can be well characterized by fluxes between the two. In particular, carbon and energy fluxes play a major role in understanding biogeochemical processes on an ecosystem level or global scale. However, the fluxes can only be measured at individual sites, e.g., by eddy covariance towers, and an upscaling of these local observations is required to analyze global patterns. Previous work focused on upscaling monthly, 8-day, or daily average values, and global maps for each flux have been provided accordingly. In this paper, we raise the upscaling of carbon and energy fluxes between land and atmosphere to the next level by increasing the temporal resolution to subdaily timescales. We provide continuous half-hourly fluxes for the period from 2001 to 2014 at 0.5° spatial resolution, which allows for analyzing diurnal cycles globally. The data set contains four fluxes: gross primary production (GPP), net ecosystem exchange (NEE), latent heat (LE), and sensible heat (H). We propose two prediction approaches for the diurnal cycles based on large-scale regression models and compare them in extensive cross-validation experiments using different sets of predictor variables. We analyze the results for a set of FLUXNET tower sites showing the suitability of our approaches for this upscaling task. Finally, we have selected one approach to calculate the global half-hourly data products based on predictor variables from remote sensing and meteorology at daily resolution as well as half-hourly potential radiation. In addition, we provide a derived product that only contains monthly average diurnal cycles, which is a lightweight version in terms of data storage that still allows studying the important characteristics of diurnal patterns globally. We recommend to primarily use these monthly average diurnal cycles, because they are less affected by the impacts of day-to-day variation, observation noise, and short-term fluctuations on subdaily timescales compared to the full half-hourly flux products. The global half-hourly data products are available at https://doi.org/10.17871/BACI.224 .

54 ENVIRONMENTAL SCIENCES↗

A global coupled Eulerian-Lagrangian model and 1 1 km CO2 surface flux dataset for high-resolution atmospheric CO2 transport simulations

Abstract. We designed a method to simulate atmospheric CO2 concentrations at several continuous observation sites around the globe using surface fluxes at a very high spatial resolution. The simulations presented in this study were performed using the Global Eulerian-Lagrangian Coupled Atmospheric model (GELCA), comprising a Lagrangian particle dispersion model coupled to a global atmospheric tracer transport model with prescribed global surface CO2 flux maps at a 1 1 km resolution. The surface fluxes used in the simulations were prepared by assembling the individual components of terrestrial, oceanic and fossil fuel CO2 fluxes. This experimental setup (i.e. a transport model running at a medium resolution, coupled to a high-resolution Lagrangian particle dispersion model together with global surface fluxes at a very high resolution), which was designed to represent high-frequency variations in atmospheric CO2 concentration, has not been reported at a global scale previously. Two sensitivity experiments were performed: (a) using the global transport model without coupling to the Lagrangian dispersion model, and (b) using the coupled model with a reduced resolution of surface fluxes, in order to evaluate the performance of Eulerian-Lagrangian coupling and the role of high-resolution fluxes in simulating high-frequency variations in atmospheric CO2 concentrations. A correlation analysis between observed and simulated atmospheric CO2 concentrations at selected locations revealed that the inclusion of both Eulerian-Lagrangian coupling and highresolution fluxes improves the high-frequency simulations of the model. The results highlight the potential of a coupled Eulerian-Lagrangian model in simulating high-frequency atmospheric CO2 concentrations at many locations worldwide. The model performs well in representing observations of atmospheric CO2 concentrations at high spatial and temporal resolutions, especially for coastal sites and sites located close to sources of large anthropogenic emissions. While this study focused on simulations of CO2 concentrations, the model could be used for other atmospheric compounds with known estimated emissions.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Empirical relationships between interplanetary conditions, magnetospheric flux transfer, and the AL index

Holzer and Slavin (1978) have found that the transfer of magnetic flux to and from the dayside magnetosphere as inferred from observed displacements of the magnetopause surface is correlated with both the magnitude of the auroral zone magnetic index AL and the incident flux of southward IMF. Empirical expressions specifying the rate at which magnetic flux is eroded in terms of interplanetary parameters and the rate of magnetic flux return as a function of AL have been developed. These relations are then used to predict magnetotail magnetic field enhancements from interplanetary and ground based data during an interval of substorm activity. The total magnetic flux in the tail is increased during intervals when the amount of flux transferred into its volume by dayside erosion exceeds the flux lost to the dayside by magnetospheric convection. Using Ogo-5 tail observations it is found for the sample events considered that these magnetic field enhancements can be described by empirical expressions for the magnetic flux transfer rates.

Slavin, J. A.↗

On the Global Distribution of Three-Dimensional Eliassen-Palm Fluxes by Stationary Waves

The global distribution of three dimensional EP fluxes is investigated by using statistics for Dec. 1980 to Feb. 1981 and June to August 1981 calculated from operational analyses. Results at 1000 and 150 mb are given. During the Northern Hemisphere (NH) winter strong upward fluxes can be seen at 1000 mb in the lee of the Himalayas and Rockies, windward of the Canadian Rockies in the east Pacific, to the north of the Atlantic stormtrack and over the west Pacific in a region of strong land sea thermal contrast. Upward fluxes also appear near the west coasts of the Southern Hemisphere (SH) subtropical continents regions of strong land sea thermal contrast. At 150 mb (Fig. 1b) the strongest upward flux now occurs south of Alaska. The horizontal fluxes imply poleward propagation from the convection over Indonesia to 20 N, a region where the assumptions underlying EP fluxes are not well met. Equatorward propagation dominates the NH midlatitude except over the Pacific. The fluxes given offer hints of the sources of stationary waves, but also show several puzzling features and a rather cavalier disregard of regions of easterly wind. The physical meaning and interpretation of three dimensional EP fluxes is not yet clear.

White, G. H.↗

Relationships of a growing magnetic flux region to flares

The evolution of flare sites at the boundaries of major new and growing magnetic flux regions within complexes of active regions has been analyzed using H-alpha images. A spectrum of possible relationships of growing flux regions to flares is described. An 'intimate' interaction between old and new flux and flare sites occurs at the boundaries of their regions. Forced or 'intimidated' interaction involves new flux pushing older, lower flux density fields toward a neighboring old polarity inversion line, followed by the occurrence of a flare. In 'influential' interaction, magnetic lines of force over an old polarity inversion line reconnect to new emerging flux, and a flare occurs when the magnetic field overlying the filament becomes too weak to prevent its eruption. 'Inconsequential' interaction occurs when a new flux region is too small or has the wrong orientation for creating flare conditions. 'Incidental' interaction involves a flare occurring without any significant relationship to new flux regions.

Martin, S. F.↗

Energetic particle characteristics of magnetotail flux ropes

During the recent ISEE-3 Geotail Mission three events have been identified from the magnetometer data which are consistent with a spacecraft crossing of a magnetotail flux rope. Energetic electron and proton observations obtained by the Max-Planck-Institut/University of Maryland sensor system during two of the possible flux rope events are presented. During one event remote sensing of the flux rope with energetic protons reveals that the flux rope is crossed by the spacecraft from south to north. This allows determination of the bandedness of the magnetic field twist and of the flux rope velocity relative to the spacecraft. A minimal flux rope radius of 3 earth radii is derived. Energetic proton intensity is highest just inside of the flux rope and decreases towards the core. Energetic electrons are streaming tailward near the outer boundary, indicating openness of the field lines, and are isotropic through the inner part of the flux rope.

Scholer, M.↗

Numerical study of the effects of boundary conditions on the measurement and calibration of gardon type heat flux sensors

To monitor the high-intensity heat flux conditions that occur in the space shuttle main engine (SSME), it is necessary to use specifically designed heat flux sensors. These sensors, which are of the Gardon-type, are exposed on the measuring face to high-intensity radiative and convective heat fluxes and on the other face to convective cooling. To improve the calibration and measurement accuracy of these gauges, researchers are studing the effect that the thermal boundary conditions have on gauge performance. In particular, they are studying how convective cooling effects the field inside the sensor and the measured heat flux. The first phase of this study involves a numerical study of these effects. Subsequent phases will involve experimental verification. A computer model of the heat transfer around a Garden-type heat flux sensor was developed. Two specific geometries are being considered are: (1) heat flux sensor mounted on a flat-plate; and (2) heat flux sensor mounted at the stagnation point of a circular cylinder. Both of these configurations are representative of the use of heat flux sensors in the components of the SSME. The purpose of the analysis is to obtain a temperature distribution as a function of the boundary conditions.

Krane, M.↗

Mass, heat and freshwater fluxes in the South Indian Ocean

Six hydrographic sections were used to examine the circulation and property fluxes in the South Indian Ocean from 10 to 32 deg S. The calculations were made by applying an inverse method to the data. In the interior of the South Indian Ocean, the geostrophic flow is generally northward. At 18 deg S, the northward interior mass flux is balanced by the southward Ekman mass flux at the surface, whereas at 32 deg S the northward interior mass flux is balanced by the southward mass flux of the Agulhas Current. There is a weak, southward mass flux of 6 x 10 to the 9th kg/s in the Mozambique Channel. The rate of water exchange between the Pacific Ocean and the Indian Ocean is dependent on the choice of the initial reference level used in the inverse calculation. The choice of 1500 m, the depth of the deep oxygen minimum, has led to a flux of water from the Pacific Ocean to the Indian Ocean at a rate of 6.6 x 10 to the 9th kg/s. Heat flux calculations indicate that the Indian Ocean is exporting heat to the rest of the world's oceans at a rate of -0.69 x 10 to the 15th W at 18 deg S and -0.25 x 10 to the 15th W at 32 deg S (negative values being southward).

Fu, Lee-Lueng↗

Measurement of local high-level, transient surface heat flux

This study is part of a continuing investigation to develop methods for measuring local transient surface heat flux. A method is presented for simultaneous measurements of dual heat fluxes at a surface location by considering the heat flux as a separate function of heat stored and heat conducted within a heat flux gage. Surface heat flux information is obtained from transient temperature measurements taken at points within the gage. Heat flux was determined over a range of 4 to 22 MW/sq m. It was concluded that the method is feasible. Possible applications are for heat flux measurements on the turbine blade surfaces of space shuttle main engine turbopumps and on the component surfaces of rocket and advanced gas turbine engines and for testing sensors in heat flux gage calibrators.

Liebert, Curt H.↗

Development of a two-dimensional zonally averaged statistical-dynamical model. III - The parameterization of the eddy fluxes of heat and moisture

A number of perpetual January simulations are carried out with a two-dimensional zonally averaged model employing various parameterizations of the eddy fluxes of heat (potential temperature) and moisture. The parameterizations are evaluated by comparing these results with the eddy fluxes calculated in a parallel simulation using a three-dimensional general circulation model with zonally symmetric forcing. The three-dimensional model's performance in turn is evaluated by comparing its results using realistic (nonsymmetric) boundary conditions with observations. Branscome's parameterization of the meridional eddy flux of heat and Leovy's parameterization of the meridional eddy flux of moisture simulate the seasonal and latitudinal variations of these fluxes reasonably well, while somewhat underestimating their magnitudes. New parameterizations of the vertical eddy fluxes are developed that take into account the enhancement of the eddy mixing slope in a growing baroclinic wave due to condensation, and also the effect of eddy fluctuations in relative humidity. The new parameterizations, when tested in the two-dimensional model, simulate the seasonal, latitudinal, and vertical variations of the vertical eddy fluxes quite well, when compared with the three-dimensional model, and only underestimate the magnitude of the fluxes by 10 to 20 percent.

Stone, Peter H.↗