Outlier Problem in Evaluating Similarity Functions in the Stable Atmospheric Boundary Layer

The gradient-based similarity approach removes turbulent fluxes as governing parameters and replaces them with vertical gradients of mean wind speed and potential temperature. As a result, the gradient Richardson number, Ri, appears as a stability parameter instead of the Monin–Obukhov stability parameter z/L (L is the Obukhov length). The gradient-based scaling is more appropriate for moderate and very stable conditions when the gradients are large and their errors are relatively small whereas z/L becomes ambiguous in these conditions because turbulent fluxes are small. However, the gradient-based formulation is faced with a problem related to the influence of Ri outliers: outliers with high values of Ri can exist in conditions that are really near-neutral. These outliers are mapped into the very stable range in plots in which Ri is the independent variable and may lead to spurious dependencies for bin-averaged data (spurious bin-averaging). This effect is quite large for functions that are steep for the gradient-based scaling. The present study uses the Surface Heat Budget of the Arctic Ocean (SHEBA) data to examine the problem and proposes two methods, conditional analysis and independent binning, to limit the influence of outliers on bin-averaging. A disadvantage of the conditional analysis is associated with eliminating outliers based on criteria that could be considered as subjective. The independent bin-averaging method does not have this disadvantage, but the scatter of the bin-averaged points is higher than for the conditional analysis, rendering data analysis and interpretation difficult.     

Modelling Flow Routing in Permafrost Landscapes with TWI: An Evaluation against Site‐Specific Wetness Measurements

In northern peatlands the thawing of permafrost increasing the active layer depth and changing the hydrology may lead to feedbacks in the climate system through changes in the biogeochemistry of carbon. We are examining this association on the Stordalen peatland complex in subarctic Sweden by analyzing a DEM derived from LiDAR‐data and the calculated TWI. The DEM, with a spatial resolution of 1 m, and the TWI are evaluated against two seasons of water level measurements from 30 sites in the peatland. The TWI is calculated with a form‐based flow routing algorithm which produces a natural flow routing pattern. In permafrost wetlands the topography is the major driver and is very important even though its magnitude is low. Site‐specific wetness (SSW) measurements from the sites were compared with the different peatland types that occur in the study area, i.e. fen, internal fen and palsa. The results showed a strong correlation between the TWI and the palsa. The TWI was better at describing general patterns than site‐specific hydrology. The evaluation of spatial patterns of TWI against SSW reveal the resolution required to develop the technique to be useful for climate change studies.     

A solubility and surface complexation study of a non-stoichiometric hydroxyapatite

The dissolution and surface complexation of a non-stoichiometric hydroxyapatite (Ca_8.4(HPO₄)_1.6(PO₄)_4.4(OH)_0.4), (HAP) was studied in the pH range 3.5-10.5, at 25 °C in 0.1 M Na(Cl). The results from well-equilibrated batch experiments, potentiometric titrations, and zeta-potential measurements were combined with information provided by Attenuated Total Reflectance Fourier Transform Infrared (ATR-FTIR) spectroscopy and X-ray Photoelectron Spectroscopy (XPS). The information from the analyses was used to design an equilibration model that takes into account dissolution, surface potential, solution and surface complexation, as well as possible phase transformations. The results from the XPS measurements clearly show that the surface of the mineral has a different composition than the bulk and that the Ca/P ratio of the surface layer is 1.4 ± 0.1. This ratio was also found in solution in the batches equilibrated at low pH where the dominating reaction is dissolution. In the batches equilibrated at near neutral pH values, however, the Ca/P ratio in solution attains values as high as 25, which is due to re-adsorption of phosphate ions to the HAP surface. The total concentration of protons as well as the total concentration of dissolved calcium and phosphate in solution were used to calculate a model for the dissolution and surface complexation of HAP. The constant capacitance model was applied in designing the following surface complexation model:

     

A multi‐method field experiment to determine local groundwater flow in a glacier forefield

We implemented multiple independent field techniques to determine the direction and velocity of groundwater flow at a specific stream reach in a glacier forefield. Time‐lapse experiments were conducted using two electrical resistivity tomography (ERT) lines installed in a cross pattern. A circular array of groundwater tubes was also installed to monitor groundwater flow via discrete salt injections. Both inter‐borehole and ERT results confirmed this stream section as a losing reach and enabled quantification of the flow direction. Both techniques yielded advection velocities varying between 5.7 and 21.8 m/day. Estimates of groundwater flow direction and velocity indicated that groundwater infiltrates from the stream nearby and not from the adjacent lateral moraine. Groundwater age estimated from radon concentration measurements supported this hypothesis. Despite uncertainties inherent to each of the methods deployed, the combination of multiple field techniques allowed drawing consistent conclusions about local groundwater flow. We thus regard our multi‐method approach as a reliable way to characterize the two‐dimensional groundwater flow at sites where more invasive groundwater investigation techniques are difficult to carry out and local heterogeneities can make single measurements unreliable. Copyright © 2014 John Wiley & Sons, Ltd.     

Turbulent measurements in the stable atmospheric boundary layer during SHEBA: ten years after

This paper surveys results of the comprehensive turbulent measurements in the stable boundary layer (SBL) made over the Arctic pack ice during the Surface Heat Budget of the Arctic Ocean experiment (SHEBA) in the Beaufort Gyre from October 1997 through September 1998. Turbulent fluxes and mean meteorological data were continuously measured and reported hourly at five levels on a 20-m main SHEBA tower. Eleven months of measurements during SHEBA cover a wide range of stability conditions, from the weakly unstable regime to very stable stratification, and allow studying the SBL in detail. A brief overview of the SBL regimes, the flux-profile relationships, the turbulent Prandtl number, and other parameters obtained during SHEBA is given. The traditional Monin—Obukhov approach, z-less scaling, and gradient-based scaling are evaluated and discussed based on the data from SHEBA.     

Ab initio study of the composition dependence of the pressure-induced spin crossover in perovskite (Mg1 − x,Fex)SiO3

We present ab initio calculations of the zero-temperature iron high- to low-spin crossover in (Mg_1 ? xFe_x)SiO₃ perovskite at pressures relevant to Earth's lower mantle. Equations of state are fit for a range of compositions and used to predict the Fe spin transition pressure and associated changes in volume and bulk modulus. We predict a dramatic decrease in transition pressure as Fe concentration increases. This trend is contrary to that seen in ferropericlase, and suggests the energetics for spin crossover is highly dependent on the structural environment of Fe. Both Local Density Approximation (LDA) and Generalized Gradient Approximation (GGA) exchange-correlation methods are used, and both methods reproduce the same compositional trends. However, GGA gives a significantly higher transition pressure than LDA. The spin transition is made easier by the decreasing spin-flip energy with pressure but is also driven by the change in volume from high to low spin. Volume trends show that high-spin Fe²⁺ is larger than Mg²⁺ even under pressure, but low-spin Fe²⁺ is smaller at ambient conditions and approximately the same size as Mg²⁺ under high pressure, indicating that low-spin Fe²⁺ is less compressible than high-spin Fe²⁺. We find large changes between high- and low-spin in the slope of volume with Fe concentration. Although these changes are small in absolute magnitude for small Fe content, they are still important when measured per Fe and could be relevant for calculating partitioning coefficients in the lower mantle.     

The Critical Richardson Number and Limits of Applicability of Local Similarity Theory in the Stable Boundary Layer

Measurements of atmospheric turbulence made over the Arctic pack ice during the Surface Heat Budget of the Arctic Ocean experiment (SHEBA) are used to determine the limits of applicability of Monin–Obukhov similarity theory (in the local scaling formulation) in the stable atmospheric boundary layer. Based on the spectral analysis of wind velocity and air temperature fluctuations, it is shown that, when both the gradient Richardson number, Ri, and the flux Richardson number, Rf, exceed a ‘critical value’ of about 0.20–0.25, the inertial subrange associated with the Richardson–Kolmogorov cascade dies out and vertical turbulent fluxes become small. Some small-scale turbulence survives even in this supercritical regime, but this is non-Kolmogorov turbulence, and it decays rapidly with further increasing stability. Similarity theory is based on the turbulent fluxes in the high-frequency part of the spectra that are associated with energy-containing/flux-carrying eddies. Spectral densities in this high-frequency band diminish as the Richardson–Kolmogorov energy cascade weakens; therefore, the applicability of local Monin–Obukhov similarity theory in stable conditions is limited by the inequalities Ri < Ri _cr and Rf < Rf _cr. However, it is found that Rf _cr  =  0.20–0.25 is a primary threshold for applicability. Applying this prerequisite shows that the data follow classical Monin–Obukhov local z-less predictions after the irrelevant cases (turbulence without the Richardson–Kolmogorov cascade) have been filtered out.     

Stable Boundary-Layer Scaling Regimes: The Sheba Data

Turbulent and mean meteorological data collected at five levels on a 20-m tower over the Arctic pack ice during the Surface Heat Budget of the Arctic Ocean experiment (SHEBA) are analyzed to examine different regimes of the stable boundary layer (SBL). Eleven months of measurements during SHEBA cover a wide range of stability conditions, from the weakly unstable regime to very stable stratification. Scaling arguments and our analysis show that the SBL can be classified into four major regimes: (i) surface-layer scaling regime (weakly stable case), (ii) transition regime, (iii) turbulent Ekman layer, and (iv) intermittently turbulent Ekman layer (supercritical stable regime). These four regimes may be considered as the basic states of the traditional SBL. Sometimes these regimes, especially the last two, can be markedly perturbed by gravity waves, detached elevated turbulence (‘upside down SBL’), and inertial oscillations. Traditional Monin–Obukhov similarity theory works well in the weakly stable regime. In the transition regime, Businger–Dyer formulations work if scaling variables are re-defined in terms of local fluxes, although stability function estimates expressed in these terms include more scatter compared to the surface-layer scaling. As stability increases, the near-surface turbulence is affected by the turning effects of the Coriolis force (the turbulent Ekman layer). In this regime, the surface layer, where the turbulence is continuous, may be very shallow (< 5 m). Turbulent transfer near the critical Richardson number is characterized by small but still significant heat flux and negligible stress. The supercritical stable regime, where the Richardson number exceeds a critical value, is associated with collapsed turbulence and the strong influence of the earth’s rotation even near the surface. In the limit of very strong stability, the stress is no longer a primary scaling parameter.