Scaling Properties of Biologically Active Scalar Concentration Fluctuations in the Atmospheric Surface Layer over a Managed Peatland

The higher-order scalar concentration fluctuation properties are examined in the context of Monin–Obukhov similarity theory for a variety of greenhouse gases that have distinct and separate source/sink locations along an otherwise ideal micrometeorological field site. Air temperature and concentrations of water vapour, carbon dioxide and methane were measured at high frequency (10 Hz) above a flat and extensive peat-land soil in the San Joaquin–Sacramento Delta (California, USA) area, subjected to year-round grazing by beef cattle. Because of the heterogeneous distribution of the sources and sinks of CO₂ and especially CH₄ emitted by cattle, the scaling behaviour of the higher-order statistical properties diverged from predictions based on a balance between their production and dissipation rate terms, which can obtained for temperature and H₂O during stationary conditions. We identify and label these departures as ‘exogenous’ because they depend on heterogeneities and non-stationarities induced by boundary conditions on the flow. Spectral analysis revealed that the exogenous effects show their signatures in regions with frequencies lower than those associated with scalar vertical transport by turbulence, though the two regions may partially overlap in some cases. Cospectra of vertical fluxes appear less influenced by these exogenous effects because of the modulating role of the vertical velocity at low frequencies. Finally, under certain conditions, the presence of such exogenous factors in higher-order scalar fluctuation statistics may be ‘fingerprinted’ by a large storage term in the mean scalar budget.     

Dispersion of a Point-Source Release of a Passive Scalar Through an Urban-Like Array for Different Wind Directions

The dispersion of a point-source release of a passive scalar in a regular array of cubical, urban-like, obstacles is investigated by means of direct numerical simulations. The simulations are conducted under conditions of neutral stability and fully rough turbulent flow, at a roughness Reynolds number of Re _τ  = 500. The Navier–Stokes and scalar equations are integrated assuming a constant rate release from a point source close to the ground within the array. We focus on short-range dispersion, when most of the material is still within the building canopy. Mean and fluctuating concentrations are computed for three different pressure gradient directions (0°, 30°, 45°). The results agree well with available experimental data measured in a water channel for a flow angle of 0°. Profiles of mean concentration and the three-dimensional structure of the dispersion pattern are compared for the different forcing angles. A number of processes affecting the plume structure are identified and discussed, including: (i) advection or channelling of scalar down ‘streets’, (ii) lateral dispersion by turbulent fluctuations and topological dispersion induced by dividing streamlines around buildings, (iii) skewing of the plume due to flow turning with height, (iv) detrainment by turbulent dispersion or mean recirculation, (v) entrainment and release of scalar in building wakes, giving rise to ‘secondary sources’, (vi) plume meandering due to unsteady turbulent fluctuations. Finally, results on relative concentration fluctuations are presented and compared with the literature for point source dispersion over flat terrain and urban arrays.     

Surface turbulent flux measurements over the Loess Plateau for a semi-arid climate change study

In order to provide high quality data for climate change studies, the data quality of turbulent flux measurements at the station of SACOL (Semi-Arid Climate & Environment Observatory of Lanzhou University), which is located on a semi-arid grassland over the Loess Plateau in China, has been analyzed in detail. The effects of different procedures of the flux corrections on CO₂, momentum, and latent and sensible heat fluxes were assessed. The result showed that coordinate rotation has a great influence on the momentum flux but little on scalar fluxes. For coordinate rotation using the planar fit method, different regression planes should be determined for different wind direction sectors due to the heterogeneous nature of the ground surface. Sonic temperature correction decreased the sensible heat flux by about 9%, while WPL correction (correction for density fluctuations) increased the latent heat flux by about 10%. WPL correction is also particularly important for CO₂ fluxes. Other procedures of flux corrections, such as the time delay correction and frequency response correction, do not significantly influence the turbulent fluxes. Furthermore, quality tests on stationarity and turbulence development conditions were discussed. Parameterizations of integral turbulent characteristics (ITC) were tested and a specific parameterization scheme was provided for SACOL. The ITC test on turbulence development conditions was suggested to be applied only for the vertical velocity. The combined results of the quality tests showed that about 62%–65% of the total data were of high quality for the latent heat flux and CO₂ flux, and as much as about 76% for the sensible heat flux. For the momentum flux, however, only about 35% of the data were of high quality.     

Local and Global Similarity in Turbulent Transfer of Heat, Water Vapour, And CO 2 in the Dynamic Convective Sublayer Over a Suburban Area

We investigated the ‘local’ and ‘global’ similarity of vertical turbulent transfer of heat, water vapour, and CO₂ within an urban surface layer. The results were derived from field measurements in a residential area of Tokyo, Japan during midday on fair-weather days in July 2001. In this study, correlation coefficients and quadrant analysis were used for the evaluation of ‘global’ similarity and wavelet analysis was employed for investigating ‘local’ similarity. The correlation coefficients indicated that the transfer efficiencies of water vapour and CO₂ were generally smaller than that of heat. Using wavelet analysis, we found that heat is always efficiently transferred by thermal and organized motions. In contrast, water vapour and CO₂, which are passive quantities, were not transferred as efficiently as heat. The quadrant analyses showed that the heat transfer by ejection exceeded that by sweep, and the ratios of ejection to sweep for water vapour and CO₂ transfer were less than that for heat. This indicated that heat is more efficiently transferred by upward motions and supported the findings from wavelet analysis. The differences of turbulent transfer between heat and both CO₂ and water vapour were probably caused both by the active role of temperature and the heterogeneity in the source distribution of scalars     

A New Method for the Determination of Area-Averaged Turbulent Surface Fluxes from Low-Level Flights Using Inverse Models

The low-level flight method (LLF) has been combined with linear inverse models (IM) resulting in an LLF+IM method for the determination of area-averaged turbulent surface fluxes. With this combination, the vertical divergences of the turbulent latent and sensible heat fluxes were calculated from horizontal flights. The statistical errors of the derived turbulent surface fluxes were significantly reduced. The LLF+IM method was tested both in numerical and field experiments. Large-eddy simulations (LES) were performed to compare ‘true’ flux profiles with ‘measurements’ of simulated flights in an idealised convective boundary layer. Small differences between the ‘true’ and the ‘measured’ fluxes were found, but the vertical flux divergences were correctly calculated by the LLF+IM method. The LLF+IM method was then applied to data collected during two flights with the Helipod, a turbulence probe carried by a helicopter, and with the research aircraft Do 128 in the LITFASS-98 field campaign. The derived surface fluxes were compared with results from eddy-covariance surface stations and with large-aperture scintillometer data. The comparison showed that the LLF+IM method worked well for the sensible heat flux at 77 and 200 m flight levels, and also for the latent heat flux at the lowest level. The model quality control indicated failures for the latent heat flux at the 200 m level (and higher), which were probably due to large moisture fluctuations that could not be modelled using linear assumptions. Finally the LLF+IM method was applied to more than twenty low-level flights from the LITFASS-2003 experiment. Comparison with aggregated surface flux data revealed good agreement for the sensible heat flux but larger discrepancies and a higher statistical uncertainty for the latent heat flux     

Turbulent carbon exchange in very stable conditions

Turbulent fluxes obtained using the conventional eddy covariance approach result in erratic results with large time fluctuations in extremely stable conditions. This can limit efforts to estimate components of the nocturnal energy budget and respiratory CO₂ fluxes. Well-organized fluxes that show a clear dependence on turbulent intensity were obtained when multiresolution decomposition was used to estimate turbulent exchanges. CO₂, heat and water vapour fluxes were observed at a site in the eastern Amazon basin that had been cleared for agricultural purposes. Temporal scales of the carbon transfer were determined and shown to be similar to those of latent heat, but as much as three times larger than those of sensible heat. CO₂ eddy diffusivities at the temporal scales on which most of the vertical CO₂ exchange occurs are shown to be 50 times larger than the eddy diffusivity for heat. A process associated with the vertical scale of the scalar accumulation layer is suggested to explain these different scales and turbulent diffusivities of carbon and sensible heat transfer. For an appreciable range of turbulence intensities, the observed vertical turbulent carbon exchange is insufficient to account for the locally respired CO₂ estimated independently. Evidence that shallow drainage currents may account for this is given.     

On the relationship between the eddy covariance,the turbulent flux,and surface exchange for a trace gas such as CO<Subscript>2</Subscript>

In the context of CO₂ surface exchange estimation, an analysis combining the basic principles of diffusion and scalar conservation shows that the mixing ratio is the appropriate variable both for defining the (eddy covariance) turbulent flux and also for expressing the relationship between the turbulent flux and surface exchange in boundary-layer budget equations. Other scalar intensity variables sometimes chosen, both the CO₂ density and molar fraction, are susceptible to the influence of surface exchange of heat and water vapour. The application of a hypsometric analysis to the boundary-layer “control volume” below the tower measurement height reveals flaws in previously applied approaches: (a) incompressibility cannot be assumed to simplify mass conservation (the budget in terms of CO₂ density); (b) compressibility alone makes the analysis of mass conservation vulnerable to uncertainties associated with resultant non-zero vertical velocities too small to measure or model over real terrain; and (c) the WPL (Webb et al. (1980) Quart J Roy Meteorol Soc 106:85–100) “zero dry air flux” assumption is invalidated except at the surface boundary. Nevertheless, the definition and removal of the WPL terms do not hinge upon this last assumption, and so the turbulent CO₂ flux can be accurately determined by eddy covariance using gas analysers of either open- or closed-path design. An appendix discusses the necessary assumptions and appropriate interpretations for deriving the WPL terms.     

Influence of Nocturnal Low-level Jets on Eddy-covariance Fluxes over a Tall Forest Canopy

Observations of low-level jets (LLJs) at the Howland AmeriFlux site in the USA and the jet’s impact on nocturnal turbulent exchange and scalar fluxes over a tall forest canopy are discussed. Low-frequency motions and turbulent bursts characterize moderately strong LLJs, whereas low-frequency motions are suppressed during periods with strong LLJs and enhanced shear. An analysis based on the shear-sheltering hypothesis seeks to elucidate the effect of LLJs on flux measurements. In the absence of shear sheltering, large eddies penetrate the roughness sublayer causing enhanced mixing while during periods with shear sheltering, mixing is reduced. In the absence of the latter, ‘upside-down’ eddies are primarily responsible for the enhanced velocity variances, scalar and momentum fluxes. The integral length scales over the canopy are greater than the canopy height. The variance spectra and cospectra from the wavelet analysis indicate that large eddies (spatial scale greater than the low-level jet height) interact with active canopy-scale turbulence, contributing to counter-gradient scalar fluxes.     

How Well Can We Measure the Vertical Wind Speed? Implications for Fluxes of Energy and Mass

Sonic anemometers are capable of measuring the wind speed in all three dimensions at high frequencies (10–50 Hz), and are relied upon to estimate eddy-covariance-based fluxes of mass and energy over a wide variety of surfaces and ecosystems. In this study, wind-velocity measurement errors from a three-dimensional sonic anemometer with a non-orthogonal transducer orientation were estimated for over 100 combinations of angle-of-attack and wind direction using a novel technique to measure the true angle-of-attack and wind speed within the turbulent atmospheric surface layer. Corrections to the vertical wind speed varied from −5 to 37% for all angles-of-attack and wind directions examined. When applied to eddy-covariance data from three NOAA flux sites, the wind-velocity corrections increased the magnitude of CO₂ fluxes, sensible heat fluxes, and latent heat fluxes by ≈11%, with the actual magnitude of flux corrections dependent upon sonic anemometer, surface type, and scalar. A sonic anemometer that uses vertically aligned transducers to measure the vertical wind speed was also tested at four angles-of-attack, and corrections to the vertical wind speed measured using this anemometer were within ±1% of zero. Sensible heat fluxes over a forest canopy measured using this anemometer were 15% greater than sensible heat fluxes measured using a sonic anemometer with a non-orthogonal transducer orientation. These results indicate that sensors with a non-orthogonal transducer orientation, which includes the majority of the research-grade three-dimensional sonic anemometers currently in use, should be redesigned to minimize sine errors by measuring the vertical wind speed using one pair of vertically aligned transducers.     

Methodological Development of the Conditional Sampling Method. Part II: Quality Control Criteria of Relaxed Eddy Accumulation Flux Measurements

Determination of biosphere–atmosphere exchanges requires accurate quantification of the turbulent fluxes of energy and of a wide variety of trace gases. Relaxed Eddy Accumulation (REA) is a method that has received increasing attention in recent years, because it does not require any rapid sensor for the scalar measurements as the Eddy Correlation method (EC) does. As in all micrometeorological studies, REA measurements in the atmospheric surface layer are valid under some restrictive conditions so as to be representative of a specific ecosystem. These conditions are the homogeneity of the underlying surface, stationary and horizontally homogeneous turbulence. For most experiments these conditions are not fully satisfied. Data uncertainties can also be related to not fulfilling the method principles or to the technical characteristics of the REA system itself. In order to assess REA measurement quality, a methodological approach of data analysis is developed in this study. This methodological analysis is based on the establishment of criteria for data quality control. A set of them, deduced from the mean and turbulent flow, are called ‘Dynamic criteria’ and are designated to control the stationarity and homogeneity of the w function and the validation of Taylor’s hypothesis. A second set (‘REA operational criteria’) is designed to check the sampling process and, more precisely, the homogeneity of the negative and positive selection process throughout the sampling period. A third set of criteria (‘Chemical scalar criteria’) concerns the scalar measurements. Results of the criteria application to data measured at two different experimental sites are also presented. Cut-off limits of criteria are defined based on their statistical distribution and shown to be specific for each site. Strictness of each criterion, defined by the percentage of flagged samples, is analysed in conjunction with the meteorological conditions and atmospheric stability. It is found that flagged samples mainly correspond to neutral and stable nocturnal conditions. During daytime, nearly free convection conditions can also yield poor quality data.     

Horizontal and Vertical Turbulent Fluxes Forced by a Gravity Wave Event in the Nocturnal Atmospheric Surface Layer Over the Amazon Forest

A nocturnal gravity wave was detected over a south-western Amazon forest during the Large-Scale Biosphere–Atmosphere experiment in Amazonia (LBA) in the course of the dry-to-wet season campaign on October 2002. The atmospheric surface layer was stably stratified and had low turbulence activity, based on friction velocity values. However, the passage of the wave, an event with a period of about 180–300 s, caused negative turbulent fluxes of carbon dioxide (CO₂) and positive sensible heat fluxes, as measured by the eddy-covariance system at 60 m (≈30 m above the tree tops). The evolution of vertical profiles of air temperature, specific humidity and wind speed during the wave movement revealed that cold and drier air occupied the sub-canopy space while high wind speeds were measured above the vegetation. The analysis of wind speed and scalars high frequency data was performed using the wavelet technique, which enables the decomposition of signals in several frequencies allowed by the data sampling conditions. The results showed that the time series of vertical velocity and air temperature were −90° out of phase during the passage of the wave, implying no direct vertical transport of heat. Similarly, the time series of vertical velocity and CO₂ concentration were 90° out of phase. The wave was not directly associated with vertical fluxes of this variable but the mixing induced by its passage resulted in significant exchanges in smaller scales as measured by the eddy-covariance system. The phase differences between horizontal velocity and both air temperature and CO₂ concentration were, respectively, zero and 180°, implying phase and anti-phase relationships. As a result, the wave contributed to positive horizontal fluxes of heat and negative horizontal fluxes of carbon dioxide. Such results have to be considered in nocturnal boundary-layer surface-atmosphere exchange schemes for modelling purposes.     

Variance Method to Determine Turbulent Fluxes of Momentum And Sensible Heat in The Stable Atmospheric Surface Layer

Evidence is presented that in the stable atmospheric surface layer turbulent fluxes of heat and momentum can be determined from the standard deviations of longitudinal wind velocity and temperature, σ _u and σ _T respectively, measured at a single level. An attractive aspect of this method is that it yields fluxes from measurements that can be obtained with two-dimensional sonic anemometers. These instruments are increasingly being used at official weather stations, where they replace the standard cup anemometer–wind vane system. With methods such as the one described in this note, a widespread, good quality, flux network can be established, which would greatly benefit the modelling community. It is shown that a ‘variance’ dimensionless height (ζ _σ) defined from σ _u and σ _T is highly related to the ‘conventional’ dimensionless stability parameter ζ=z/L, where z is height and L is the Obukhov length. Empirical functions for ζ _σ are proposed that allow direct calculation of heat and momentum fluxes from σ _u and σ _T. The method performs fairly well also during a night of intermittent turbulence.     

Estimating the components of the sensible heat budget of a tall forest canopy in complex terrain

Ultrasonic wind measurements, sonic temperature and air temperature data at two heights in the advection experiment MORE II were used to establish a complete budget of sensible heat including vertical advection, horizontal advection and horizontal turbulent flux divergence. MORE II took place at the long-term Carbo-Europe IP site in Tharandt, Germany. During the growing period of 2003 three additional towers were established to measure all relevant parameters for an estimation of advective fluxes, primarily of CO₂. Additionally, in relation to other advection experiments, a calculation of the horizontal turbulent flux divergence is proposed and the relation of this flux to atmospheric stability and friction velocity is discussed. In order to obtain a complete budget, different scaling heights for horizontal advection and horizontal turbulent flux divergence are tested. It is shown that neglecting advective fluxes may lead to incorrect results. If advective fluxes are taken into account, the sensible heat budget based upon vertical turbulent flux and storage change only, is reduced by approximately 30%. Additional consideration of horizontal turbulent flux divergence would in turn add 5–10% to this sum (i.e., the sum of vertical turbulent flux plus storage change plus horizontal and vertical advection). In comparison with available energy horizontal advection is important at night whilst horizontal turbulent flux divergence is rather insignificant. Obviously, advective fluxes typically improve poor nighttime energy budget closure and might change ecosystem respiration fluxes considerably.     

Spectral Structure of Small-Scale Turbulent and Mesoscale Fluxes in the Atmospheric Boundary Layer over a Thermally Inhomogeneous Land Surface

Spectral analysis was performed on aircraft observations of a convective boundary layer (CBL) that developed over a thermally inhomogeneous, well-marked mesoscale land surface. The observations, part of the GAME-Siberia experiment, were recorded between April and June 2000 over the Lena River near Yakutsk City. A special integral parameter termed the ‘reduced depth of the CBL’ was used to scale the height of the mixed layer with variable depth. Analysis of wavelet cospectra and spectra facilitated the separation of fluxes and other variables into small-scale turbulent fluctuations (with scales less than the reduced depth of the CBL, approximately 2 km) and mesoscale fluctuations (up to 20 km). This separation approach allows for independent exploration of the scales. Analyses showed that vertical distributions obeyed different laws for small-scale fluxes and mesoscale fluxes (of sensible heat, water vapour, momentum and carbon dioxide) and for other variables (wind speed and air temperature fluctuations, coherence and degree of anisotropy). Vertical profiles of small-scale turbulent fluxes showed a strong decay that differed from generally accepted similarity models for the CBL. Vertical profiles of mesoscale fluxes and other variables clearly showed sharp inflections at the same relative (with respect to the reduced depth of the CBL) height of approximately 0.55 in the CBL. Conventional similarity models for sensible heat fluxes describe both small-scale turbulent and mesoscale flows. The present results suggest that mesoscale motions that reach up to the relative level of 0.55 could be initiated by thermal surface heterogeneity. Entrainment between the upper part of the CBL and the free atmosphere may cause mesoscale motions in that region of the CBL.     

Dissimilarity of Scalar Transport in the Convective Boundary Layer in Inhomogeneous Landscapes

A land-surface model (LSM) is coupled with a large-eddy simulation (LES) model to investigate the vegetation-atmosphere exchange of heat, water vapour, and carbon dioxide (CO₂) in heterogeneous landscapes. The dissimilarity of scalar transport in the lower convective boundary layer is quantified in several ways: eddy diffusivity, spatial structure of the scalar fields, and spatial and temporal variations in the surface fluxes of these scalars. The results show that eddy diffusivities differ among the three scalars, by up to 10–12%, in the surface layer; the difference is partly attributed to the influence of top-down diffusion. The turbulence-organized structures of CO₂ bear more resemblance to those of water vapour than those of the potential temperature. The surface fluxes when coupled with the flow aloft show large spatial variations even with perfectly homogeneous surface conditions and constant solar radiation forcing across the horizontal simulation domain. In general, the surface sensible heat flux shows the greatest spatial and temporal variations, and the CO₂ flux the least. Furthermore, our results show that the one-dimensional land-surface model scheme underestimates the surface heat flux by 3–8% and overestimates the water vapour and CO₂ fluxes by 2–8% and 1–9%, respectively, as compared to the flux simulated with the coupled LES-LSM.     

Spectra of CO<Subscript>2</Subscript> and Water Vapour in the Marine Atmospheric Surface Layer

Spectra of CO₂ and water vapour fluctuations from measurements made in the marine atmospheric surface layer have been analyzed. A normalization of spectra based on Monin–Obukhov similarity theory, originally developed for wind speed and temperature, has been successfully extended also to CO₂ and humidity spectra. The normalized CO₂ spectra were observed to have somewhat larger contributions from low frequencies compared to humidity spectra during unstable stratification. However, overall, the CO₂ and humidity spectra showed good agreement as did the cospectra of vertical velocity with water vapour and CO₂ respectively. During stable stratification the spectra and cospectra displayed a well-defined spectral gap separating the mesoscale and small-scale turbulent fluctuations. Two-dimensional turbulence was suggested as a possible source for the mesoscale fluctuations, which in combination with wave activity in the vertical wind is likely to explain the increase in the cospectral energy for the corresponding frequency range. Prior to the analysis the turbulence time series of the density measurements were converted to time series of mixing ratios relative to dry air. Some differences were observed when the spectra based on the original density measurements were compared to the spectra based on the mixing ratio time series. It is thus recommended to always convert the density time series to mixing ratio before performing spectral analysis.     

An Analysis and Implications of Alternative Methods of Deriving the Density (WPL) Terms for Eddy Covariance Flux Measurements

We explore some of the underlying assumptions used to derive the density or WPL terms (Webb et al. (1980) Quart J Roy Meteorol Soc 106:85–100) required for estimating the surface exchange fluxes by eddy covariance. As part of this effort we recast the origin of the density terms as an assumption regarding the density fluctuations rather than as a (dry air) flux assumption. This new approach, which is similar to the expansion/compression approach of Liu (Boundary-Layer Meteorol 115:151–168, 2005), eliminates the dry-air mean advective vertical velocity from the development of the WPL terms and allows us to directly compare Liu’s assumptions for deriving the WPL terms with the analogous assumptions appropriate to the original expression of the WPL terms. We suggest, (i) that the main difference between these two approaches lies in the interpretation of the turbulent exchange flux, and (ii) that the original WPL formulation is the more appropriate approach. Given the importance of the WPL terms to accurate and reliable measurements of surface exchange fluxes, a careful analysis of their origins and their proper mathematical expression and interpretation is warranted.     

A Simple Method of Estimating Scalar Fluxes Over Forests

A simple aerodynamic-variance method is proposed to fill gaps in continuous CO₂ flux measurements in rainy conditions, when open-path analysers do not function. The method requires turbulent conditions (friction velocity greater than 0.1 ms^–1), and uses measurements of mean wind speed, and standard deviations of temperature and CO₂ concentration fluctuations to complement, and at times replace, eddy-covariance measurements of friction velocity, sensible heat flux and CO₂ flux. Friction velocity is estimated from the mean wind speed with a flux-gradient relationship modified for the roughness sublayer. Since normalised standard deviations do not follow Monin-Obukhov similarity theory in the roughness sublayer, a simple classification scheme according to the scalar turbulence scale was used. This scheme is shown to produce sensible heat and CO₂ flux estimates that are well correlated with the measured values.     

Two climatic states and feedbacks on thermohaline circulation in an Earth system model of intermediate complexity

The McGill Paleoclimate Model-2 (MPM-2) is employed to study climate–thermohaline circulation (THC) interactions in a pre -industrial climate, with a special focus on the feedbacks on the THC from other climate system components. The MPM-2, a new version of the MPM, has an extended model domain from 90S to 90N, active winds and no oceanic heat and freshwater flux adjustments. In the MPM-2, there are mainly two stable modes for the Atlantic meridional overturning circulation (MOC) under the ‘present-day’ forcing (present-day solar forcing and the pre-industrial atmospheric CO₂ level of 280 ppm). The ‘on’ mode has an active North Atlantic deep water formation, while the ‘off’ mode has no such deep water formation. By comparing the ‘off’ mode climate state with its ‘on’ mode analogue, we find that there exist many large differences between the two climate states, which originate from large changes in the oceanic meridional heat transports. By suppressing or isolating each process associated with a continental ice sheet over North America, sea ice, the atmospheric hydrological cycle and vegetation, feedbacks from these components on the Atlantic MOC are investigated. Sensitivity studies investigating the role of varying continental ice growth and sea ice meridional transport in the resumption of the Atlantic MOC are also carried out. The results show that a fast ice sheet growth and an enhanced southward sea ice transport significantly favor the resumption of the Atlantic MOC in the MPM-2. In contrast to this, the feedback from the atmospheric hydrological cycle is a weak positive one. The vegetation-albedo feedback could enhance continental ice sheet growth and thus could also favor the resumption of the Atlantic MOC. However, before the shut-down of the Atlantic MOC, feedbacks from these components on the Atlantic MOC are very weak.