Turbulent Flux Divergence Research Articles

On the Estimation of Deep Atlantic Ventilation from Fossil Radiocarbon Records. Part II. (In)consistency with Modern Estimates

AbstractMeasurements of radiocarbon concentration (Δ14C) in fossil biogenic carbonates have been interpreted as reecting a reduced ventilation of the deep Atlantic during the last ice age. Here we evaluate the (in)consistency of an updated compilation of fossil Δ14C data for the last deglaciation with the abyssal circulation in the modern Atlantic. A 14C transport equation, in which the mean velocity field is a modern field estimate and turbulent flux divergence is treated as a random fluctuation, is fitted to deglacial Δ14C records by using recursive weighted least-squares. This approach allows us to interpret the records in terms of deviations from the modern flow with due regard for uncertainties in the fossil data, the 14C transport equation, and its boundary conditions.We find that the majority of fit residuals could be explained by uncertainties in fossil Δ14C data, for two distinct estimates of the modern flow and of the error variance in the boundary conditions. Thus, most, not all, deglacial data appear consistent with present-day ventilation rates. From 20 to 32% of the residuals exceed in magnitude the published errors in the fossil data by a factor of two. Residuals below 4000 m in the western North Atlantic are all negative, suggesting that deglacial Δ14C values from this region are too low to be explained by modern ventilation. Whilst deep water ventilation appeared different from today at some locations, a larger database and a better understanding of error (co)variances are needed to make reliable paleoceanographic inferences from fossil Δ14C records.

Erratum: ‘An easterly tip jet off Cape Farewell, Greenland. II: Simulations and dynamics’

The above article was originally published on Early View on 20 November 2009, and subsequently in volume 135 (issue 645), pp 1934–1949, DOI:10.1002/qj.531. There was an error in the sign of the turbulent flux-divergence term of the momentum budgets plotted in Figures 10, 11 and 12 of Outten et al. (2009). Consequently the momentum budget residual that is shown is also in error; it is too large by about an order of magnitude. Corrected versions of these figures are reproduced below and accompanied by these brief comments. The cross-jet (top) and along-jet (bottom) components of the momentum budget, in terms of force per unit mass (F/m), shown against distance along the jet locus. The forces shown are the advection (solid line), Coriolis (circles), pressure gradient (asterisks), viscous stress (squares) and turbulent momentum flux divergence (triangles). The residual is also shown (dashed line). The cross-jet components of the momentum budget shown over the region of imbalance. The forces shown are the Coriolis (circles), pressure gradient (asterisks), viscous stress (squares) and turbulent momentum flux divergence (triangles). The calculated centrifugal force is shown (diamonds) along with the residual (dashed line). The cross-jet components of the momentum budget for 13 January 2008 (top), 11 January 2008 (middle) and 10 February 2007 (bottom) are shown against distance along the jet locus. The forces shown in each plot are the advection (solid line), Coriolis (circles), pressure gradient (asterisks), viscous stress (squares) and turbulent momentum flux divergence (triangles). The residual is also shown (dashed lines). Following the sign correction the revised momentum budgets have a residual that is much smaller in magnitude and significantly smaller than that of the other forcing terms. This small remaining residual must be due to unaccounted-for contributions arising from differences between the momentum budget as we calculated it, see Outten et al. Eqs (1), (2) and (4), and the formulation used in the numerical model (the MetUM); for example, contributions from model diffusion. This was the explanation given for the residual in the original budgets (paragraph 3 on page 1945) and the discovery of a sign error does not make this incorrect. The large magnitude of the residual was a point of consternation in the original paper and was not fully explained but left to ‘further investigation’. It seems that further investigation is now not necessary. In the along-jet direction the change in the sign of the flux-divergence term means that this term now acts to decelerate the jet, which makes physical sense. In paragraph 2 of page 1946 there is a discussion of the turbulent flux divergence and, in particular, its ‘decrease in height’—this discussion is still valid if one regards it as pertaining to the magnitude of the flux divergence. Note the conclusions of the dynamical analysis are not made invalid by this error. However we would suggest a change in emphasis is warranted, away from the (now relatively small) residual and on to the (still important) turbulent flux-divergence term. In the Abstract of the original paper it was stated that: ‘Over the curved part of the locus, as the jet rounded Cape Farewell, a cross-jet residual suggests that the jet was unbalanced at the height of the jet core. This residual decreases with height so that an approximate gradient wind balance applies in the upper part of the jet.’ It would be more appropriate if this said: ‘Over the curved part of the locus, as the jet rounded Cape Farewell, a cross-jet turbulent flux divergence suggests that the jet was unbalanced at the height of the jet core. This flux divergence decreases in magnitude with height so that an approximate gradient wind balance applies in the upper part of the jet.’ We would like to apologise for this error and sincerely thank Dr William Ingram (Oxford University and Met Office Hadley Centre) for prompting a re-evaluation of the sign of the flux-divergence term, following a presentation of this work.

Direct advection measurements do not help to solve the night-time CO 2 closure problem: Evidence from three different forests

The ADVEX project involved conducting extensive advection measurements at three sites, each with a different topography. One goal of the project was to measure the [CO 2] balance under night-time conditions, in an attempt to improve NEE estimates. Four towers were arranged in a square around a main tower, with the sides of the square about 100 m long. Equipped with 16 sonic anemometers and [CO 2] sampling points, the towers were installed to measure vertical and horizontal advection of [CO 2]. Vertical turbulent fluxes were measured by an eddy covariance system at the top of the main tower. The results showed that horizontal advection varied greatly from site to site and from one wind sector to another, the highest values being reached when there were large friction velocities and fairly unstable conditions. There was less variation in vertical advection, the highest values being reached when there were low friction velocities and stable conditions. The night-time NEE estimates deduced from the mass balance were found to be incompatible with biologically driven fluxes because (i) they varied strongly from one wind sector to another and this variation could not be explained in terms of a response of the biologic flux to climate, (ii) their order of magnitude was not realistic and (iii) they still showed a trend vs. friction velocity. From a critical analysis of the measurement and data treatment we concluded that the causes of the problem are related to the representativeness of the measurement (control volume size, sampling resolution) or the hypotheses underlying the derivation of the [CO 2] mass balance (ignoring the horizontal turbulent flux divergence). This suggests that the improvement of eddy flux measurements by developing an advection completed [CO 2] mass balance at night would be practically difficult.

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.

Mesoscale moisture variability and its impact on energy transfer through the boundary layer

The impact of mesoscale moisture variability on the vertical energy transfer through a pre-frontal boundary layer is studied with NOPEX aircraft data. The moisture variability relates to a cold front that passed the area 2 1/2 hours after the observations. We find a density front ahead of the cold front. The large vertical divergence of the turbulent moisture flux in the surface layer is partly related to this moisture variability. Large scale horizontal advection contributes to the observed vertical turbulent flux divergence. The estimated horizontal mesoscale advection term in the budget of sensible heat and moisture is on average small but locally it can be large. This term acts to re-distribute moisture in the boundary layer and leads to sub-grid variations of relative humidity, which is an important quantity for boundary-layer cloud models. The distinct spatial variations of specific humidity are mainly related to synoptic forcing and not to heterogeneity in the surface energy balance.

Dynamical analyses of marine atmospheric boundary layer structure near the Gulf Stream oceanic front

AbstractThe effects of the sea surface temperature (s.s.t.) front at the edge of the Gulf Stream on the marine atmospheric boundary layer (MABL) are investigated using a numerical model to study the modification effects of an oceanic front on the MABL structure. The situation simulated is flow from over cold shelf water to over the warm water of the Gulf Stream. The initial temperature and humidity profiles of the air are specified to be near neutral over the cold water and are therefore typical of undisturbed conditions. The differential in s.s.t. across the oceanic front creates a horizontal variation in the surface perturbation pressure and the stability. The surface perturbation pressure and turbulent fluxes modulate the flow and produce horizontal variations in horizontal wind components with associated vertical motions. A thermally direct cell is produced as a result of the s.s.t. difference across the front. The isotherms slope upward towards the warm water. Entrainment of inversion layer air and upward vertical motion over the warm water cause the MABL to be deeper there. A layer of cloud forms over warm water and is associated with mixed layer deepening rather than lowering of the condensation level. Turbulent fluxes in the MABL show considerable spatial variation. Surface stress is much larger over the front and over the warm water than over the cold water. This is mostly caused by wind speed changes associated with the front. Changes in the drag coefficient due to changes in surface roughness and stability are much less important.Mean budgets for temperature and total water indicate that there is a balance between horizontal advection and turbulent flux divergence. The U momentum budget shows that once the geostrophic balance terms are subtracted, the balance is mainly between the pressure gradient force associated with the induced temperature field and turbulent friction, with horizontal advection and the Coriolis force acting on the geostrophic departure playing minor roles. The V momentum budget shows a balance between horizontal advection, Coriolis force and friction.Although there are few data for comparison, the results are in qualitative agreement with observations in the area. This study shows that the s.s.t. front at the Gulf Stream edge produces marked local changes in the nearby atmospheric surface layer.