Large-Eddy Simulation of Stably-Stratified Flow Over a Steep Hill

Large-eddy simulation (LES) is used to simulate stably-stratified turbulent boundary-layer flow over a steep two-dimensional hill. To parametrise the subgrid-scale (SGS) fluxes of heat and momentum, three different types of SGS models are tested: (a) the Smagorinsky model, (b) the Lagrangian dynamic model, and (c) the scale-dependent Lagrangian dynamic model (Stoll and Porté-Agel, Water Resour Res 2006, doi:). Simulation results obtained with the different models are compared with data from wind-tunnel experiments conducted at the Environmental Flow Research Laboratory (EnFlo), University of Surrey, U.K. (Ross et al., Boundary-Layer Meteorol 113:427–459, 2004). It is found that, in this stably-stratified boundary-layer flow simulation, the scale-dependent Lagrangian dynamic model is able to account for the scale dependence of the eddy-viscosity and eddy-diffusivity model coefficients associated with flow anisotropy in flow regions with large mean shear and/or strong flow stratification. As a result, simulations using this tuning-free model lead to turbulence statistics that are more realistic than those obtained with the other two models.     

Coping with climate variability and climate change in La Ceiba,Honduras

La Ceiba, Honduras, a city of about 200,000 people, lies along the Caribbean Sea, nestled against a mountain range and the Rio Cangrejal. The city faces three flooding risks: routine flooding of city streets due to the lack of a stormwater drainage system; occasional major flooding of the Rio Cangrejal, which flows through the city; and flooding from heavy rainfall events and storm surges associated with tropical cyclones. In this study, we applied a method developed for the U.S. Agency for International Development and then worked with stakeholders in La Ceiba to understand climate change risks and evaluate adaptation alternatives. We estimated the impacts of climate change on the current flooding risks and on efforts to mitigate the flooding problems. The climate change scenarios, which addressed sea level rise and flooding, were based on the Intergovernmental Panel on Climate Change estimates of sea level rise (Houghton et al. 2001) and published literature linking changes in temperature to more intense precipitation (Trenberth et al., Bull Am Meteorol Soc, 84:1205–1217, 2003) and hurricanes (Knutson and Tuleya, J Clim, 17:3477–3495, 2004). Using information from Trenberth et al., Bull Am Meteorol Soc, 84:1205–1217, (2003) and Knutson and Tuleya, J Clim, 17:3477–3495, 2004, we scaled intense precipitation and hurricane wind speed based on projected temperature increases. We estimated the volume of precipitation in intense events to increase by 2 to 4% in 2025 and by 6 to 14% by 2050. A 13% increase in intense precipitation, the high scenario for 2050, could increase peak 5-year flood flows by about 60%. Building an enhanced urban drainage system that could cope with the estimated increased flooding would cost one-third more than building a system to handle current climate conditions, but would avoid costlier reconstruction in the future. The flow of the Rio Cangrejal would increase by one-third from more intense hurricanes. The costs of raising levees to protect the population from increased risks from climate change would be about $1 million. The coast west of downtown La Ceiba is the most vulnerable to sea level rise and storm surges. It is relatively undeveloped, but is projected to have rapid development. Setbacks on coastal construction in that area may limit risks. The downtown coastline is also at risk and may need to be protected with groins and sand pumping. Stakeholders in La Ceiba concluded that addressing problems of urban drainage should be a top priority. They emphasized improved management of the Rio Cangrejal watershed and improved storm warnings to cope with risks from extreme precipitation and cyclones. Adoption of risk management principles and effective land use management could also help reduce risks from current climate and climate change.     

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.     

Utility of Radiometric–aerodynamic Temperature Relations for Heat Flux Estimation

In many land-surface models using bulk transfer (one-source) approaches, the application of radiometric surface temperature observations in energy flux computations has given mixed results. This is due in part to the non-unique relationship between the so-called aerodynamic temperature, which relates to the efficiency of heat exchange between the land surface and overlying atmosphere, and a surface temperature measurement from a thermal-infrared radiometer, which largely corresponds to a weighted soil and canopy temperature as a function of radiometer viewing angle. A number of studies over the past several years using multi-source canopy models and/or experimental data have developed simplified methods to accommodate radiometric–aerodynamic temperature differences in one-source approaches. A recent investigation related the variability in the radiometric–aerodynamic relation to solar radiation using experimental data from a variety of landscapes, while another used a multi-source canopy model combined with measurements over a wide range in vegetation density to derive a relationship based on leaf area index. In this study, simulations by a detailed multi-source soil–plant–environment model, Cupid, which considers both radiative and turbulent exchanges across the soil–canopy–air interface, are used to explore the radiometric–aerodynamic temperature relations for a semi-arid shrubland ecosystem under a range of leaf area/canopy cover, soil moisture and meteorological conditions. The simulated radiometric-aerodynamic temperatures indicate that, while solar radiation and leaf area both strongly affect the magnitude of this temperature difference, the relationships are non-unique, having significant variability depending on local conditions. These simulations also show that soil–canopy temperature differences are highly correlated with variations in the radiometric–aerodynamic temperature differences, with the slope being primarily a function of leaf area. This result suggests that two-source schemes with reliable estimates of component soil and canopy temperatures and associated resistances may be better able to accommodate variability in the radiometric–aerodynamic relation for a wider range in vegetated canopy cover conditions than is possible with one-source schemes. However, comparisons of sensible heat flux estimates with Cupid using a simplified two-source model and a one-source model accommodating variability in the radiometric-aerodynamic relation based on vegetation density gave similar scatter. On the other hand, with experimental data from the shrubland site, the two-source model generally outperformed the one-source scheme. Clearly, vegetation density/leaf area has a major effect on the radiometric–aerodynamic temperature relation and must be considered in either one-source or two-source formulations. Hence these adjusted one-source models require similar inputs as in two-source approaches, but provide as output only bulk heat fluxes; this is not as useful for monitoring vegetation conditions.     

A Perspective on Thirty Years of the Webb,Pearman and Leuning Density Corrections

The density correction theory of Webb et al. (1980, Q J Roy Meteorol Soc 106: 85–100, hereafter WPL) is a principle underpinning the experimental investigation of surface fluxes of energy and masses in the atmospheric boundary layer. It has a long-lasting influence in boundary-layer meteorology and micrometeorology, and the year 2010 marks the 30th anniversary of the publication of the WPL theory. We provide here a critique of the theory and review the research it has spurred over the last 30 years. In the authors’ opinion, the assumption of zero air source at the surface is a fundamental novelty that gives the WPL theory its enduring vitality. Considerations of mass conservation show that, in a non-steady state, the WPL mean vertical velocity and the thermal expansion velocity are two distinctly different quantities of the flow. Furthermore, the integrated flux will suffer a systematic bias if the expansion velocity is omitted or if the storage term is computed from time changes in the CO₂ density. A discussion is provided on recent efforts to address several important practical issues omitted by the original theory, including pressure correction, unintentional alternation of the sampled air, and error propagation. These refinement efforts are motivated by the need for an unbiased assessment of the annual carbon budget in terrestrial ecosystems in the global eddy flux network (FluxNet).     

Impact of subgrid scale scheme on topography and landuse for better regional scale simulation of meteorological variables over the western Himalayas

An attempt is made to integrate subgrid scale scheme on the work of Dimri and Ganju (Pure Appl Geophys 167:1–24, 2007) to understand the overall nature of surface heterogeneity and landuse variability along with resolvable finescale micro/meso scale circulation over the Himalayan region, which is having different altitudes and orientations causing prevailing weather conditions to be complex. This region receives large amount of precipitation due to eastward moving low-pressure synoptic weather systems, called western disturbances, during winter season (December, January, February—DJF). Surface heterogeneity and landuse variability of the Himalayan region gives rise to numerous micro/meso scale circulation along with prevailing weather. Therefore, in the present work, a mosaic type parameterization of subgrid scale topography and landuse within a framework of a regional climate model (RegCM3) is extended to study interseasonal variability of surface climate during a winter season (October 1999–March 2000) of the work of Dimri and Ganju (Pure Appl Geophys 167:1–24, 2007). In this scheme, meteorological variables are disaggregated from the coarse grid to the fine grid, land surface calculations are then performed separately for each subgrid cell, and surface fluxes are calculated and reaggregated onto the coarse grid cell for input to the atmospheric model. By doing so, resolvable finescale structures due to surface heterogeneity and landuse variability at coarse grid are subjected to parameterize at regular finescale surface subgrid. Model simulations show that implementation of subgrid scheme presents more realistic simulation of precipitation and surface air temperature. Influence of topographic elevation and valleys is better represented in the scheme. Overall, RegCM3 with subgrid scheme provides more accurate representation of resolvable finescale atmospheric/surface circulations that results in explaining mean variability in a better way.     

Consequences of Uncertainties in CO<Subscript>2</Subscript> Density for Estimating Net Ecosystem CO<Subscript>2</Subscript> Exchange by Open-path Eddy Covariance

Errors in the estimation of CO₂ surface exchange by open-path eddy covariance, introduced during the removal of density terms [Webb et al. Quart J Roy Meteorol Soc 106:85–100, (1980) - WPL], can happen both because of errors in energy fluxes [Liu et al. Boundary-Layer Meteorol 120:65–85, (2006)] but also because of inaccuracies in other terms included in the density corrections, most notably due to measurements of absolute CO₂ density (ρ _c ). Equations are derived to examine the propagation of all errors through the WPL algorithm. For an open-path eddy covariance system operating in the Sierra de Gádor in south-east Spain, examples are presented of the inability of an unattended, open-path infrared gas analyzer (IRGA) to reliably report ρ _c and the need for additional instrumentation to determine calibration corrections. A sensitivity analysis shows that relatively large and systematic errors in net ecosystem exchange (NEE) can result from uncertainties in ρ _c in a semi-arid climate with large sensible heat fluxes (H _s ) and (wet) mineral deposition. When ρ_c is underestimated by 5% due to lens contamination, this implies a 13% overestimation of monthly CO₂ uptake.     

A Lagrangian Model to Predict the Modification of Near-Surface Scalar Mixing Ratios and Air–Water Exchange Fluxes in Offshore Flow

A model was developed to predict the modification with fetch in offshore flow of mixing ratio, air–water exchange flux, and near-surface vertical gradients in mixing ratio of a scalar due to air–water exchange. The model was developed for planning and interpretation of air–water exchange flux measurements in the coastal zone. The Lagrangian model applies a mass balance over the internal boundary layer (IBL) using the integral depth scale approach, previously applied to development of the nocturnal boundary layer overland. Surface fluxes and vertical profiles in the surface layer were calculated using the NOAA COARE bulk algorithm and gas transfer model (e.g., Blomquist et al. 2006, Geophys Res Lett 33:1–4). IBL height was assumed proportional to the square root of fetch, and estimates of the IBL growth rate coefficient, α, were obtained by three methods: (1) calibration of the model to a large dataset of air temperature and humidity modification over Lake Ontario in 1973, (2) atmospheric soundings from the 2004 New England Air Quality Study and (3) solution of a simplified diffusion equation and an estimate of eddy diffusivity from Monin–Obukhov similarity theory (MOST). Reasonable agreement was obtained between the calibrated and MOST values of α for stable, neutral, and unstable conditions, and estimates of α agreed with previously published parametrizations that were valid for the stable IBL only. The parametrization of α provides estimates of IBL height, and the model estimates modification of scalar mixing ratio, fluxes, and near-surface gradients, under conditions of coastal offshore flow (0–50 km) over a wide range in stability.     

Determining carbon isotope signatures from micrometeorological measurements: Implications for studying biosphere–atmosphere exchange processes

In recent years considerable effort has been focused on combining micrometeorological and stable isotope techniques to partition net fluxes and to study biosphere–atmosphere exchange processes. While much progress has been achieved over the last decade, some new issues are beginning to emerge as technological advances, such as laser spectroscopy, permit isotopic fluxes to be measured more easily and continuously in the field. Traditional investigations have quantified the isotopic composition of biosphere-atmosphere exchange by using the Keeling two-member mixing model (the classic Keeling plot). An alternative method, based on a new capacity to measure isotopic mixing ratios, is to determine the isotope composition of biosphere–atmosphere exchange from the ratio of flux measurements. The objective of this study was to critically evaluate these methods for quantifying the isotopic composition of ecosystem respiration (δ_R) over a period of three growing seasons (2003–2005) within a heterogeneous landscape consisting of C₃ and C₄ species. For C₄ canopies, the mixing model approach produced δ_R values that were 4–6‰ lower (isotopically lighter) than the flux-gradient method. The analyses presented here strongly suggest that differences between flux and concentration footprint functions are the main factor influencing the inequality between the mixing model and flux-gradient approaches. A mixing model approach, which is based on the concentration footprint, can have a source area influence more than 20-fold greater than the flux footprint. These results highlight the fact that isotopic flux partitioning is susceptible to problems arising from combining signals (concentration and fluxes) that represent very different spatial scales (footprint). This problem is likely to be most pronounced within heterogeneous terrain. However, even under ideal conditions, the mismatch between concentration and flux footprints could have a detrimental impact on isotopic flux partitioning where very small differences in isotopic signals must be resolved.     

Large-Eddy Simulation of Atmospheric Boundary-Layer Flow Over Fluvial-Like Landscapes Using a Dynamic Roughness Model

A recently developed dynamic surface roughness model (Anderson and Meneveau, J Fluid Mech 679:288–314, 2011) for large-eddy simulation (LES) of atmospheric boundary-layer flow over multi-scale topographies is applied to boundary-layer flow over several types of fluvial-like landscapes. The landscapes are generated numerically with simulation of a modified Kardar–Parisi–Zhang equation (Passalacqua et al., Water Resour Res 42:WOD611, 2006). These surfaces possess the fractal-like channel network and anisotropic features often found in real terrains. The dynamic model is shown to lead to accurate flow predictions when the surface-height distributions exhibit power-law scaling (scale invariance) in the prevalent mean flow direction. In those cases, the LES provide accurate predictions (invariant to resolution) of mean velocity profiles. Conversely, some resolution dependence is found for applications in which the landscape’s streamwise spectra do not exhibit pure power-law scaling near wavenumbers corresponding to the LES grid resolution.     

Resolved Versus Parametrized Boundary-Layer Plumes. Part II: Continuous Formulations of Mixing Rates for Mass-Flux Schemes

The conditional sampling of coherent structures in large-eddy simulations of the convective boundary layer (Couvreux et al. Boundary-layer Meteorol 134:441–458, 2010) is used to propose and evaluate formulations of fractional entrainment and detrainment rates for mass-flux schemes. The proposed formulations are physically-based and continuous from the surface to the top of clouds. Entrainment is related to the updraft vertical velocity divergence, while detrainment depends on the thermal vertical velocity, on buoyancy and on the moisture contrast between the mean plume and its environment. The proposed formulations are first directly evaluated in simulations of shallow clouds. They are then tested in single-column simulations with the thermal plume model, a mass-flux representation of boundary-layer thermals.     

Scalar Transport over Forested Hills

Numerical simulations of scalar transport in neutral flow over forested ridges are performed using both a 1.5-order mixing-length closure scheme and a large-eddy simulation. Such scalar transport (particularly of CO₂) has been a significant motivation for dynamical studies of forest canopy–atmosphere interactions. Results from the 1.5-order mixing-length simulations show that hills for which there is significant mean flow into and out of the canopy are more efficient at transporting scalars from the canopy to the boundary layer above. For the case with a source in the canopy this leads to lower mean concentrations of tracer within the canopy, although they can be very large horizontal variations over the hill. These variations are closed linked to flow separation and recirculation in the canopy and can lead to maximum concentrations near the separation point that exceed those over flat ground. Simple scaling arguments building on the analytical model of Finnigan and Belcher (Q J Roy Meteorol Soc 130:1–29, 2004) successfully predict the variations in scalar concentration near the canopy top over a range of hills. Interestingly this analysis suggests that variations in the components of the turbulent transport term, rather than advection, give rise to the leading order variations in scalar concentration. The scaling arguments provide a quantitative measure of the role of advection, and suggest that for smaller/steeper hills and deeper/sparser canopies advection will be more important. This agrees well with results from the numerical simulations. A large-eddy simulation is used to support the results from the mixing-length closure model and to allow more detailed investigation of the turbulent transport of scalars within and above the canopy. Scalar concentration profiles are very similar in both models, despite the fact that there are significant differences in the turbulent transport, highlighted by the strong variations in the turbulent Schmidt number both in the vertical and across the hill in the large-eddy simulation that are not represented in the mixing-length model.     

The correct form of the Webb,Pearman and Leuning equation for eddy fluxes of trace gases in steady and non-steady state,horizontally homogeneous flows

The original density corrections proposed by Webb et al. [Webb EK, Pearman GI, Leuning R (1980) Quart J Roy Meteorol Soc 106:85–100] for calculating the eddy fluxes of trace gases are shown to be correct for both steady and non-steady state, horizontally homogeneous flows. The revised theory replaces the original assumption of zero vertical flux of dry air with the requirement of no sources or sinks of dry air in the layer below the height of measurement.     

Consequences of Incomplete Surface Energy Balance Closure for CO2 Fluxes from Open-Path CO2/H2O Infrared Gas Analysers

We present an approach for assessing the impact of systematic biases in measured energy fluxes on CO₂ flux estimates obtained from open-path eddy-covariance systems. In our analysis, we present equations to analyse the propagation of errors through the Webb, Pearman, and Leuning (WPL) algorithm [Quart. J. Roy. Meteorol. Soc. 106, 85–100, 1980] that is widely used to account for density fluctuations on CO₂ flux measurements. Our results suggest that incomplete energy balance closure does not necessarily lead to an underestimation of CO₂ fluxes despite the existence of surface energy imbalance; either an overestimation or underestimation of CO₂ fluxes is possible depending on local atmospheric conditions and measurement errors in the sensible heat, latent heat, and CO₂ fluxes. We use open-path eddy-covariance fluxes measured over a black spruce forest in interior Alaska to explore several energy imbalance scenarios and their consequences for CO₂ fluxes.     

Shear-Stress Partitioning in Live Plant Canopies and Modifications to Raupach’s Model

The spatial peak surface shear stress t_S^￠￠{\tau _S^{\prime\prime}} on the ground beneath vegetation canopies is responsible for the onset of particle entrainment and its precise and accurate prediction is essential when modelling soil, snow or sand erosion. This study investigates shear-stress partitioning, i.e. the fraction of the total fluid stress on the entire canopy that acts directly on the surface, for live vegetation canopies (plant species: Lolium perenne) using measurements in a controlled wind-tunnel environment. Rigid, non-porous wooden blocks instead of the plants were additionally tested for the purpose of comparison since previous wind-tunnel studies used exclusively artificial plant imitations for their experiments on shear-stress partitioning. The drag partitioning model presented by Raupach (Boundary-Layer Meteorol 60:375–395, 1992) and Raupach et al. (J Geophys Res 98:3023–3029, 1993), which allows the prediction of the total shear stress τ on the entire canopy as well as the peak (t_S ^￠￠/t)^1/2{(\tau _S ^{\prime\prime}/\tau )^{1/2}} and the average (t_S^￠/t)^1/2{(\tau _S^{\prime}/\tau )^{1/2}} shear-stress ratios, is tested against measurements to determine the model parameters and the model’s ability to account for shape differences of various roughness elements. It was found that the constant c, needed to determine the total stress τ and which was unspecified to date, can be assumed a value of about c = 0.27. Values for the model parameter m, which accounts for the difference between the spatial surface average t_S^￠{\tau _S^{\prime}} and the peak t_S ^￠￠{\tau _S ^{\prime\prime}} shear stress, are difficult to determine because m is a function of the roughness density, the wind velocity and the roughness element shape. A new definition for a parameter a is suggested as a substitute for m. This a parameter is found to be more closely universal and solely a function of the roughness element shape. It is able to predict the peak surface shear stress accurately. Finally, a method is presented to determine the new a parameter for different kinds of roughness elements.     

The Apsley and Castro Limited-Length-Scale $${{k-\varepsilon}}$$ Model Revisited for Improved Performance in the Atmospheric Surface Layer

The limited-length-scale k-e{k-\varepsilon} model proposed by Apsley and Castro for the atmospheric boundary layer (Boundary-Layer Meteorol 83(1):75–98, 1997) is revisited with special attention given to its predictions in the constant-stress surface layer. The original model proposes a modification to the length-scale-governing e{\varepsilon} equation that ensures consistency with surface-layer scaling in the limit of small ℓ _m/ℓ _max (where ℓ _m is the mixing length and ℓ _max its maximum) and yet imposes a limit on ℓ _m as ℓ _m/ℓ _max approaches one. However, within the equilibrium surface layer and for moderate values of z/ℓ _max, the predicted profiles of velocity, mixing length, and dissipation rate using the Apsley and Castro model do not coincide with analytical solutions. In view of this, a general e{\varepsilon} transport equation is derived herein in terms of an arbitrary desired mixing-length expression that ensures exact agreement with corresponding analytical solutions for both neutral and stable stability. From this result, a new expression for C_e3{C_{\varepsilon3}} can be inferred that shows this coefficient tends to a constant only for limiting values of z/L; and, furthermore, that the values of C_e3{C_{\varepsilon3}} for z/L → 0 and z/L →∞ differ by a factor of exactly two.     

The Effect of Surface Heterogeneity on the Temperature–Humidity Correlation and the Relative Transport Efficiency

We derive a conceptual model of the flow over heterogeneous terrain consisting of patches with contrasting Bowen ratios. Upward moving eddies are assumed to carry heterogeneous properties, whereas downward moving eddies carry homogeneous properties. This results in a decorrelation of temperature and humidity as the contrast between the patches increases. We show that this model is able to reproduce the relationship developed by Lamaud and Irvine (Boundary-Layer Meteorol. 120:87–109, 2006). Some details differ from their expression but are in accordance with data obtained over African savannah. We extend the conceptual model to a combination of any scalars, not necessarily linked through the surface energy balance (as is the case for temperature and humidity). To this end we introduce a new parameter that describes the surface heterogeneity in surface fluxes. The results of the current model can be used to predict the discrepancy between similarity relationships for different scalars over heterogeneous terrain.     

Response of Southern Ocean circulation to global warming may enhance basal ice shelf melting around Antarctica

We investigate the large-scale oceanic features determining the future ice shelf–ocean interaction by analyzing global warming experiments in a coarse resolution climate model with a comprehensive ocean component. Heat and freshwater fluxes from basal ice shelf melting (ISM) are parameterized following Beckmann and Goosse [Ocean Model 5(2):157–170, 2003]. Melting sensitivities to the oceanic temperature outside of the ice shelf cavities are varied from linear to quadratic (Holland et al. in J Clim 21, 2008). In 1% per year CO₂-increase experiments the total freshwater flux from ISM triples to 0.09 Sv in the linear case and more than quadruples to 0.15 Sv in the quadratic case after 140 years at which 4 × 280 ppm = 1,120 ppm was reached. Due to the long response time of subsurface temperature anomalies, ISM thereafter increases drastically, if CO₂ concentrations are kept constant at 1,120 ppm. Varying strength of the Antarctic circumpolar current (ACC) is crucial for ISM increase, because southward advection of heat dominates the warming along the Antarctic coast. On centennial timescales the ACC accelerates due to deep ocean warming north of the current, caused by mixing of heat along isopycnals in the Southern Ocean (SO) outcropping regions. In contrast to previous studies we find an initial weakening of the ACC during the first 150 years of warming. This purely baroclinic effect is due to a freshening in the SO which is consistent with present observations. Comparison with simulations with diagnosed ISM but without its influence on the ocean circulation reveal a number of ISM-related feedbacks, of which a negative ISM-feedback, due to the ISM-related local oceanic cooling, is the dominant one.     

A Simple Model for the Vertical Transport of Reactive Species in the Convective Atmospheric Boundary Layer

We have developed a simple, steady-state, one-dimensional second-order closure model to obtain continuous profiles of turbulent fluxes and mean concentrations of non-conserved scalars in a convective boundary layer without shear. As a basic tool we first set up a model for conserved species with standard parameterizations. This leads to formulations for profiles of the turbulent diffusivity and the ratio of temperature-scalar covariance to the flux of the passive scalar. The model is then extended to solving, in terms of profiles of mean concentrations and fluxes, the NO _x –O₃ triad problem. The chemical reactions involve one first-order reaction, the destruction of NO₂ with decay time τ, and one second-order reaction, the destruction of NO and O₃ with the reaction constant k. Since the fluxes of the sum concentrations of NO _x = NO + NO₂ and O₃ + NO₂ turn out to be constant throughout the boundary layer, the problem reduces to solving two differential equations for the concentration and the flux of NO₂. The boundary conditions are the three surface fluxes and the fluxes at the top of the boundary layer, the last obtained from the entrainment velocity, and the concentration differences between the free troposphere and the top of the boundary layer. The equations are solved in a dimensionless form by using 1/(kτ) as the concentration unit, the depth h of the boundary layer as the length unit, the convective velocity scale w _* as the velocity unit, and the surface temperature flux divided by w _* as the temperature unit. Special care has been devoted to the inclusion of the scalar–scalar covariance between the concentrations of O₃ and NO. Sample calculations show that the fluxes of the reactive species deviate significantly from those of non-reactive species. Further, the diffusivities, defined by minus the flux divided by the concentration gradient may become negative for reactive species in contrast to those of non-reactive species, which in the present model are never negative.     

The Contribution of Variability of Lift-induced Upwash to the Uncertainty in Vertical Winds Determined from an Aircraft Platform

Aircraft-based vertical flux measurements fill a gap in the spatial domain for studies of biosphere–atmosphere exchange. To acquire valid flux data, a determination of the deviation from the mean vertical wind, w′, is essential. When using aircraft platforms, flux measurements are subject to systematic and random errors from airflow distortion caused by the lift-induced upwash ahead of the aircraft. Although upwash is typically considered to be a constant quantity over periods used for calculating fluxes, it can vary significantly over short (and longer) periods due to changes in aircraft lift. The characterization of such variations in upwash are of undeniable importance to flux measurements, especially when real-time computations of w′ are required. In this paper, the variability in upwash was compared to the calculated upwash from the model of Crawford et al. (Boundary-Layer Meteorol, 80:79–94, 1996) using data taken during a long-period (phugoid mode) free oscillation of the aircraft. The cyclic variation of lift during the free oscillation offers an ideal scenario in which to acquire in-flight data on the upwash that is present, as well as to test the capability of upwash correction models. Our results indicate that while this model corrects for much of the mean upwash, there can be significant variations in upwash on a time scale that is important to flux measurements. Our results suggest that use of the measured load factor could be an easily implemented operational constraint to minimize uncertainty in w′ due to changing upwash from changing aircraft lift. We estimate, using the phugoid data, and from variations in aircraft attitude and airspeed in flux-measurement configuration, that the uncertainty in w caused by variable upwash is approximately ± 0.05 m s⁻¹.