Katabatic Flow: A Closed-Form Solution with Spatially-Varying Eddy Diffusivities

The Nieuwstadt closed-form solution for the stationary Ekman layer is generalized for katabatic flows within the conceptual framework of the Prandtl model. The proposed solution is valid for spatially-varying eddy viscosity and diffusivity (O’Brien type) and constant Prandtl number (Pr). Variations in the velocity and buoyancy profiles are discussed as a function of the dimensionless model parameters \(z_0 \equiv \hat{z}_0 \hat{N}^2 Pr \sin {(\alpha )} |\hat{b}_\mathrm{s} |^{-1}\) and \(\lambda \equiv \hat{u}_{\mathrm{ref}}\hat{N} \sqrt{Pr} |\hat{b}_\mathrm{s} |^{-1}\), where \(\hat{z}_0\) is the hydrodynamic roughness length, \(\hat{N}\) is the Brunt-Väisälä frequency, \(\alpha \) is the surface sloping angle, \(\hat{b}_\mathrm{s}\) is the imposed surface buoyancy, and \(\hat{u}_{\mathrm{ref}}\) is a reference velocity scale used to define eddy diffusivities. Velocity and buoyancy profiles show significant variations in both phase and amplitude of extrema with respect to the classic constant \(\textit{K}\) model and with respect to a recent approximate analytic solution based on the Wentzel-Kramers-Brillouin theory. Near-wall regions are characterized by relatively stronger surface momentum and buoyancy gradients, whose magnitude is proportional to \(z_0\) and to \(\lambda \). In addition, slope-parallel momentum and buoyancy fluxes are reduced, the low-level jet is further displaced toward the wall, and its peak velocity depends on both \(z_0\) and \(\lambda \).     

Verification of a One-Dimensional Model of $$\hbox {CO}_{2}$$ Atmospheric Transport Inside and Above a Forest Canopy Using Observations at the Norunda Research Station

A model of \(\hbox {CO}_{2}\) atmospheric transport in vegetated canopies is tested against measurements of the flow, as well as \(\hbox {CO}_{2}\) concentrations at the Norunda research station located inside a mixed pine–spruce forest. We present the results of simulations of wind-speed profiles and \(\hbox {CO}_{2}\) concentrations inside and above the forest canopy with a one-dimensional model of profiles of the turbulent diffusion coefficient above the canopy accounting for the influence of the roughness sub-layer on turbulent mixing according to Harman and Finnigan (Boundary-Layer Meteorol 129:323–351, 2008; hereafter HF08). Different modelling approaches are used to define the turbulent exchange coefficients for momentum and concentration inside the canopy: (1) the modified HF08 theory—numerical solution of the momentum and concentration equations with a non-constant distribution of leaf area per unit volume; (2) empirical parametrization of the turbulent diffusion coefficient using empirical data concerning the vertical profiles of the Lagrangian time scale and root-mean-square deviation of the vertical velocity component. For neutral, daytime conditions, the second-order turbulence model is also used. The flexibility of the empirical model enables the best fit of the simulated \(\hbox {CO}_{2}\) concentrations inside the canopy to the observations, with the results of simulations for daytime conditions inside the canopy layer only successful provided the respiration fluxes are properly considered. The application of the developed model for radiocarbon atmospheric transport released in the form of \(^{14}\hbox {CO}_{2}\) is presented and discussed.     

The Impact of the Afternoon Planetary Boundary-Layer Height on the Diurnal Cycle of CO and $$\hbox {CO}_{2}$$ Mixing Ratios at a Low-Altitude Mountaintop

Mountaintop trace-gas mixing ratios are often assumed to represent free atmospheric values, but are affected by valley planetary boundary-layer (PBL) air at certain times. We hypothesize that the afternoon valley–PBL height relative to the ridgetop is important in the diurnal cycle of mountaintop trace-gas mixing ratios. To investigate this, we use, (1) 4-years (1 January 2009–31 December 2012) of CO and \(\hbox {CO}_{2}\) mixing-ratio measurements and supporting meteorological observations from Pinnacles (\(38.61^{\circ }\hbox {N}\), \(78.35^{\circ }\hbox {W}\), 1017 m a.s.l.), which is a monitoring site in the Appalachian Mountains, (2) regional \(\hbox {O}_{3}\) mixing-ratio measurements, and (3) PBL heights determined from a nearby sounding station. Results reveal that the amplitudes of the diurnal cycles of CO and \(\hbox {CO}_{2}\) mixing ratios vary as a function of the daytime maximum valley–PBL height relative to the ridgetop. The mean diurnal cycle for the subset of days when the afternoon valley–PBL height is at least 400 m below the ridgetop shows a daytime CO mixing-ratio increase, implying the transport of PBL air from the valley to the mountaintop. During the daytime, on days when the PBL heights exceed the mountaintop, PBL dilution and entrainment cause CO mixing ratios to decrease. This decrease in CO mixing ratio, especially on days when PBL heights are at least 400 m above the ridgetop, suggests that measurements from these days can be used as with afternoon measurements from flat terrain in applications requiring regionally-representative measurements.     

Evaluation of Urban Local-Scale Aerodynamic Parameters: Implications for the Vertical Profile of Wind Speed and for Source Areas

Nine methods to determine local-scale aerodynamic roughness length \((z_{0})\) and zero-plane displacement \((z_{d})\) are compared at three sites (within 60 m of each other) in London, UK. Methods include three anemometric (single-level high frequency observations), six morphometric (surface geometry) and one reference-based approach (look-up tables). A footprint model is used with the morphometric methods in an iterative procedure. The results are insensitive to the initial \(z_{d}\) and \(z_{0}\) estimates. Across the three sites, \(z_{d}\) varies between 5 and 45 m depending upon the method used. Morphometric methods that incorporate roughness-element height variability agree better with anemometric methods, indicating \(z_{d}\) is consistently greater than the local mean building height. Depending upon method and wind direction, \(z_{0}\) varies between 0.1 and 5 m with morphometric \(z_{0}\) consistently being 2–3 m larger than the anemometric \(z_{0}\). No morphometric method consistently resembles the anemometric methods. Wind-speed profiles observed with Doppler lidar provide additional data with which to assess the methods. Locally determined roughness parameters are used to extrapolate wind-speed profiles to a height roughly 200 m above the canopy. Wind-speed profiles extrapolated based on morphometric methods that account for roughness-element height variability are most similar to observations. The extent of the modelled source area for measurements varies by up to a factor of three, depending upon the morphometric method used to determine \(z_{d}\) and \(z_{0}\).     

Observations of Atmospheric Methane and Carbon Dioxide Mixing Ratios: Tall-Tower or Mountain-Top Stations?

Mountain-top observations of greenhouse gas mixing ratios may be an alternative to tall-tower measurements for regional scale source and sink estimation. To investigate the equivalence or limitations of a mountain-top site as compared to a tall-tower site, we used the unique opportunity of comparing in situ measurements of methane (\(\hbox {CH}_{4}\)) and carbon dioxide (\(\hbox {CO}_{2}\)) mixing ratios at a mountain top (986 m above sea level, a.s.l.) with measurements from a nearby (distance 28.4 km) tall tower, sampled at almost the same elevation (1009 m a.s.l.). Special attention was given to, (i) how local wind statistics and greenhouse gas sources and sinks at the mountain top influence the observations, and (ii) whether mountain-top observations can be used as for those from a tall tower for constraining regional greenhouse gas emissions. Wind statistics at the mountain-top site are clearly more influenced by local flow systems than those at the tall-tower site. Differences in temporal patterns of the greenhouse gas mixing ratios observed at the two sites are mostly related to the influence of local sources and sinks at the mountain-top site. Major influences of local sources can be removed by applying a statistical filter (\(5{\mathrm{th}}\) percentile) or a filter that removes periods with unfavourable flow conditions. In the best case, the bias in mixing ratios between the mountain-top and the tall-tower sites after the application of the wind filter was \({-}0.0005\pm 0.0010\) ppm for methane (September, 0000–0400 UTC) and \(0.11\pm 0.18\) ppm for \(\hbox {CO}_{2}\) (February, 1200–1600 UTC). Temporal fluctuations of atmospheric \(\hbox {CH}_{4}\) and \(\hbox {CO}_{2}\) mixing ratios at both stations also showed good agreement (apart from \(\hbox {CO}_{2}\) during summertime) as determined by moving bi-weekly Pearson correlation coefficients (up to 0.96 for \(\hbox {CO}_{2}\) and 0.97 for \(\hbox {CH}_{4}\)). When only comparing mixing ratios minimally influenced by local sources (low bias and high correlation coefficients), our measurements indicate that mountain-top observations are comparable to tall-tower observations.     

Estimating Sediment Mass Fluxes on Surfaces Sheltered by Live Vegetation

We present a simple model based on already existing and widely used equations for estimating particle mass fluxes on surfaces sheltered by live vegetation. Wind-tunnel measurements of vertical profiles of mass flux in three different dense live plant canopies, and as a function of the spatially averaged skin friction velocity \({u_{\tau }}'\), provide the baseline set of data. For the bare-sand surface, the total mass flux Q shows the typical \(b({u_\tau }' - {u_{\tau t}}')^{3 }\) increase with increasing skin friction velocity \({u_{\tau }}'\), where b is a constant and \({u_{\tau t}}'\) is the threshold at the onset of particle erosion. Similar relations, however, with different values for b and \({u_{\tau t}}'\) compared to the bare-sand surface were found for experiments with 5.25 and 24.5 plants \(\hbox {m}^{-2}\) and can be explained by the spatial variations of \(u_{\tau }\) for the canopy cases. Based on the resulting parameters b and \({u_{\tau t}}'\), which are found to be functions of the roughness density \(\lambda \), we present a final simple relation \(Q(\lambda ,\, {u_{\tau }}')\) used for estimating the total mass flux for surfaces sheltered by live vegetation.     

Edge-to-Stem Variability in Wet-Canopy Evaporation From an Urban Tree Row

Evaporation from wet-canopy (\(E_\mathrm{C}\)) and stem (\(E_\mathrm{S}\)) surfaces during rainfall represents a significant portion of municipal-to-global scale hydrologic cycles. For urban ecosystems, \(E_\mathrm{C}\) and \(E_\mathrm{S}\) dynamics play valuable roles in stormwater management. Despite this, canopy-interception loss studies typically ignore crown-scale variability in \(E_\mathrm{C}\) and assume (with few indirect data) that \(E_\mathrm{S}\) is generally \({<}2\%\) of total wet-canopy evaporation. We test these common assumptions for the first time with a spatially-distributed network of in-canopy meteorological monitoring and 45 surface temperature sensors in an urban Pinus elliottii tree row to estimate \(E_\mathrm{C}\) and \(E_\mathrm{S}\) under the assumption that crown surfaces behave as “wet bulbs”. From December 2015 through July 2016, 33 saturated crown periods (195 h of 5-min observations) were isolated from storms for determination of 5-min evaporation rates ranging from negligible to 0.67 \(\hbox {mm h}^{-1}\). Mean \(E_\mathrm{S}\) (0.10 \(\hbox {mm h}^{-1}\)) was significantly lower (\(p < 0.01\)) than mean \(E_\mathrm{C}\) (0.16 \(\hbox {mm h}^{-1}\)). But, \(E_\mathrm{S}\) values often equalled \(E_\mathrm{C}\) and, when scaled to trunk area using terrestrial lidar, accounted for 8–13% (inter-quartile range) of total wet-crown evaporation (\(E_\mathrm{S}+E_\mathrm{C}\) scaled to surface area). \(E_\mathrm{S}\) contributions to total wet-crown evaporation maximized at 33%, showing a general underestimate (by 2–17 times) of this quantity in the literature. Moreover, results suggest wet-crown evaporation from urban tree rows can be adequately estimated by simply assuming saturated tree surfaces behave as wet bulbs, avoiding problematic assumptions associated with other physically-based methods.     

Understanding Diurnality and Inter-Seasonality of a Sub-tropical Urban Heat Island

We quantify the spatial and temporal aspects of the urban heat-island (UHI) effect for Kanpur, a major city in the humid sub-tropical monsoon climate of the Gangetic basin. Fixed station measurements are used to investigate the diurnality and inter-seasonality in the urban–rural differences in surface temperature (\({\Delta } T_\mathrm{s}\)) and air temperature (\({\Delta } T_\mathrm{c}\)) separately. The extent of the spatial variations of the nighttime \({\Delta } T_\mathrm{c}\) and \({\Delta } T_\mathrm{s}\) is investigated through mobile campaigns and satellite remote sensing respectively. Nighttime \({\Delta } T_\mathrm{c}\) values dominate during both the pre-monsoon (maximum of 3.6 \(^\circ \hbox {C}\)) and the monsoon (maximum of 2.0 \(^\circ \hbox {C}\)). However, the diurnality in \({\Delta } T_\mathrm{s}\) is different, with higher daytime values during the pre-monsoon, but very little diurnality during the monsoon. The nighttime \({\Delta } T_\mathrm{s}\) value is mainly associated with differences in the urban–rural incoming longwave radiative flux (\(r^{2}=0.33\) during the pre-monsoon; 0.65 during the monsoon), which, in turn, causes a difference in the outgoing longwave radiative flux. This difference may modulate the nighttime \({\Delta } T_\mathrm{c}\) value as suggested by significant correlations (\(r^{2}=0.68\) for the pre-monsoon; 0.50 for the monsoon). The magnitude of \({\Delta } T_\mathrm{c}\) may also be modulated by advection, as it is inversely related with the urban wind speed. A combination of in situ, remotely sensed, and model simulation data were used to show that the inter-seasonality in \({\Delta } T_\mathrm{s}\), and, to a lesser extent, in \({\Delta } T_\mathrm{c}\), may be related to the change in the land use of the rural site between the pre-monsoon and the monsoon periods. Results suggest that the degree of coupling of \({\Delta } T_\mathrm{s}\) and \({\Delta } T_\mathrm{c}\) may be a strong function of land use and land cover.     

The Effect of Breaking Waves on $$\hbox {CO}_2$$ Air–Sea Fluxes in the Coastal Zone

The influence of wave-associated parameters controlling turbulent \(\hbox {CO}_2\) fluxes through the air–sea interface is investigated in a coastal region. A full year of high-quality data of direct estimates of air–sea \(\hbox {CO}_2\) fluxes based on eddy-covariance measurements is presented. The study area located in Todos Santos Bay, Baja California, Mexico, is a net sink of \(\hbox {CO}_2\) with a mean flux of \(-1.3\, \upmu \hbox {mol m}^{-2}\hbox {s}^{-1}\) (\(-41.6\hbox { mol m}^{-2}\hbox {yr}^{-1}\)). The results of a quantile-regression analysis computed between the \(\hbox {CO}_2\) flux and, (1) wind speed, (2) significant wave height, (3) wave steepness, and (4) water temperature, suggest that the significant wave height is the most correlated parameter with the magnitude of the flux but the behaviour of the relation varies along the probability distribution function, with the slopes of the regression lines presenting both positive and negative values. These results imply that the presence of surface waves in coastal areas is the key factor that promotes the increase of the flux from and into the ocean. Further analysis suggests that the local characteristics of the aqueous and atmospheric layers might determine the direction of the flux.     

Spatially-Averaged Temperature Structure Parameter Over a Heterogeneous Surface Measured by an Unmanned Aerial Vehicle

The structure parameter of temperature, \({C_{T}^{2}}\) , in the lower convective boundary layer was measured using the unmanned mini aerial vehicle M²AV. The measurements were carried out on two hot summer days in July 2010 over a heterogeneous land surface around the boundary-layer field site of the Lindenberg Meteorological Observatory—Richard-Aßmann-Observatory of the German Meteorological Service. The spatial series of \({C_{T}^{2}}\) showed considerable variability along the flight path that was caused by both temporal variations and surface heterogeneity. Comparison of the aircraft data with \({C_{T}^{2}}\) values derived from tower-based in situ turbulence measurements showed good agreement with respect to the diurnal variability. The decrease of \({C_{T}^{2}}\) with height as predicted by free-convection scaling could be confirmed for the morning and afternoon flights while the flights around noon suggest a different behaviour.     

Turbulence in Continental Stratocumulus,Part I: External Forcings and Turbulence Structures

Comprehensive, ground-based observations from the US Department of Energy Atmospheric Radiation Measurements program Southern Great Plains site are used to study the variability of turbulence forcings and cloud-scale turbulence structures in a continental stratocumulus cloud. The turbulence observations are made from an upward facing cloud (35 GHz) Doppler radar. Cloud base and liquid water path are characterized using a lidar at the surface and a microwave radiometer. The turbulence characterizations are compared and contrasted with those observed in marine stratocumulus clouds. During the 16-h observation period used in this study the cloud-base and cloud-top heights evolve with time and changes in liquid water path observed by the radiometer are consistent with variations in cloud depth. Unlike marine stratocumulus clouds, a diurnal cycle of cloud thickness and liquid water path is not observed. The observed surface latent, sensible, and virtual sensible heat fluxes and the radiative fluxes exhibit a diurnal cycle with values increasing from sunrise to afternoon and decreasing afterwards. During the night, the sensible heat, virtual sensible heat and the net radiative fluxes at the surface are slightly negative. Solar radiative heating prevails in the cloud layer during the day and strong radiative cooling exists at cloud top even during the day. Unlike marine stratocumulus, surface heating described by the convective velocity scale \(W_\mathrm{s}^{*}\) and cloud-top cooling described by \(W_\mathrm{r}^{*}\) are both important in driving the in-cloud turbulence during the day, whereas cloud-top cooling is the exclusive contributor during the night. The combined \(W_\mathrm{s}^{*}\) and \(W_\mathrm{r}^{*}\) (the total velocity scale \(W_\mathrm{t}^{*})\) provides a useful way to track the evolution of the turbulence structure in the cloud. The variance of the radar-measured radial velocity, which is related to resolved turbulence, follows the diurnal cycle and is consistent with the total velocity scale \(W_\mathrm{t}^{*}\) variations. It is higher during the day and lower during the night, which is contrary to that in marine stratocumulus. The \(W_\mathrm{t}^{*}\) values are lowest around sunset when the radiative cooling is also small due to upper-level clouds observed above the low-level stratus. The vertical distribution of the variance results from the surface heating during the day and cloud-top cooling during the night. The squared spectrum width, which is related to turbulence structures within the radar sampling volume (unresolved turbulence) also follows the diurnal cycle. Its vertical distribution indicates that the unresolved turbulence more closely relates to the processes near cloud top. Turbulence in the cloud requires about an hour to respond to the external forcings of surface heating and cloud-top radiative cooling. Positive skewness prevails during the day and negative skewness prevails at night with a sharp transition around sunset. Resolved turbulence dominates near cloud base whereas unresolved turbulence dominates near cloud top. The turbulence characteristics and variability defined in this study can be used to evaluate the time evolution of turbulence structures in large eddy simulation forced by surface and cloud-top radiative forcings.     

Water-Channel Estimation of Eulerian and Lagrangian Time Scales of the Turbulence in Idealized Two-Dimensional Urban Canopies

Lagrangian and Eulerian statistics are obtained from a water-channel experiment of an idealized two-dimensional urban canopy flow in neutral conditions. The objective is to quantify the Eulerian \((T^{\mathrm{E}})\) and Lagrangian \((T^{\mathrm{L}})\) time scales of the turbulence above the canopy layer as well as to investigate their dependence on the aspect ratio of the canopy, AR, as the latter is the ratio of the width (W) to the height (H) of the canyon. Experiments are also conducted for the case of flat terrain, which can be thought of as equivalent to a classical one-directional shear flow. The values found for the Eulerian time scales on flat terrain are in agreement with previous numerical results found in the literature. It is found that both the streamwise and vertical components of the Lagrangian time scale, \(T_\mathrm{u}^\mathrm{L} \) and \(T_\mathrm{w}^\mathrm{L} \), follow Raupach’s linear law within the constant-flux layer. The same holds true for \(T_\mathrm{w}^\mathrm{L} \) in both the canopies analyzed \((AR= 1\) and \(AR= 2\)) and also for \(T_\mathrm{u}^\mathrm{L} \) when \(AR = 1\). In contrast, for \(AR = 2\), \(T_\mathrm{u}^\mathrm{L} \) follows Raupach’s law only above \(z=2H\). Below that level, \(T_\mathrm{u}^\mathrm{L} \) is nearly constant with height, showing at \(z=H\) a value approximately one order of magnitude greater than that found for \(AR = 1\). It is shown that the assumption usually adopted for flat terrain, that \(\beta =T^{\mathrm{L}}/T^{\mathrm{E}}\) is proportional to the inverse of the turbulence intensity, also holds true even for the canopy flow in the constant-flux layer. In particular, \(\gamma /i_\mathrm{u} \) fits well \(\beta _\mathrm{u} =T_\mathrm{u}^\mathrm{L} /T_\mathrm{u}^\mathrm{E} \) in both the configurations by choosing \(\gamma \) to be 0.35 (here, \(i_\mathrm{u} =\sigma _\mathrm{u} / \bar{u} \), where \(\bar{u} \) and \(\sigma _\mathrm{u} \) are the mean and the root-mean-square of the streamwise velocity component, respectively). On the other hand, \(\beta _\mathrm{w} =T_\mathrm{w}^\mathrm{L} /T_\mathrm{w}^\mathrm{E} \) follows approximately \(\gamma /i_\mathrm{w} =0.65/\left( {\sigma _\mathrm{w} /\bar{u} } \right) \) for \(z > 2H\), irrespective of the AR value. The second main objective is to estimate other parameters of interest in dispersion studies, such as the eddy diffusivity of momentum \((K_\mathrm{{T}})\) and the Kolmogorov constant \((C_0)\). It is found that \(C_0\) depends appreciably on the velocity component both for the flat terrain and canopy flow, even though for the latter case it is insensitive to AR values. In all the three experimental configurations analyzed here, \(K_\mathrm{{T}}\) shows an overall linear growth with height in agreement with the linear trend predicted by Prandtl’s theory.     

High-Resolution Vertical Profile Measurements for Carbon Dioxide and Water Vapour Concentrations Within and Above Crop Canopies

We present a portable elevator-based facility for measuring \(\hbox {CO}_{2}\), water vapour, temperature and wind-speed profiles between the soil surface and the atmospheric surface layer above crop canopies. The end of a tube connected to a closed-path gas analyzer is continuously moved up and down over the profile range (in our case, approximately 2 m) while concentrations are logged at a frequency of \(20 \hbox { s}^{-1}\). Using campaign measurements in winter wheat, winter barley and a catch crop mixture (spring 2015 to autumn 2016) during different stages of crop development and different times of the day, we demonstrate a simple approach to correct for time lags, and the resulting profiles of 30-min mean mole fractions of \(\hbox {CO}_{2}\) and \(\hbox {H}_{2}\hbox {O}\) over height increments of 0.025 m. The profiles clearly show the effects of soil respiration and photosynthetic carbon assimilation, varying both during the diurnal cycle and during the growing season. Profiles of temperature and wind speed are based on a ventilated finewire thermocouple and a hot-wire anemometer, respectively. Measurements over bare soil and a short plant canopy were analyzed in the framework of Monin–Obukhov similarity theory to check the validity of the measurements and raw-data-processing approach. Derived fluxes of \(\hbox {CO}_{2}\), latent and sensible heat and momentum show good agreement with eddy-covariance measurements.     

Evaluation of Density Corrections to Methane Fluxes Measured by Open-Path Eddy Covariance over Contrasting Landscapes

Corrections accounting for air density fluctuations due to heat and water vapour fluxes must be applied to the measurement of eddy-covariance fluxes when using open-path sensors. Experimental tests and ecosystem observations have demonstrated the important role density corrections play in accurately quantifying carbon dioxide \((\hbox {CO}_{2})\) fluxes, but less attention has been paid to evaluating these corrections for methane \((\hbox {CH}_{4})\) fluxes. We measured \(\hbox {CH}_{4}\) fluxes with open-path sensors over a suite of sites with contrasting \(\hbox {CH}_{4}\) emissions and energy partitioning, including a pavement airfield, two negligible-flux ecosystems (drained alfalfa and pasture), and two high-flux ecosystems (flooded wetland and rice). We found that density corrections successfully re-zeroed fluxes in negligible-flux sites; however, slight overcorrection was observed above pavement. The primary impact of density corrections varied over negligible- and high-flux ecosystems. For negligible-flux sites, corrections led to greater than 100% adjustment in daily budgets, while these adjustments were only 3–10% in high-flux ecosystems. The primary impact to high-flux ecosystems was a change in flux diel patterns, which may affect the evaluation of relationships between biophysical drivers and fluxes if correction bias exists. Additionally, accounting for density effects to high-frequency \(\hbox {CH}_{4}\) fluctuations led to large differences in observed \(\hbox {CH}_{4}\) flux cospectra above negligible-flux sites, demonstrating that similar adjustments should be made before interpreting \(\hbox {CH}_{4}\) cospectra for comparable ecosystems. These results give us confidence in \(\hbox {CH}_{4}\) fluxes measured by open-path sensors, and demonstrate that density corrections play an important role in adjusting flux budgets and diel patterns across a range of ecosystems.     

Quantifying the Influence of Random Errors in Turbulence Measurements on Scalar Similarity in the Atmospheric Surface Layer

The influence of random errors in turbulence measurements on scalar similarity for temperature, water vapour, \(\hbox {CO}_{2}\), and \(\hbox {NH}_{3}\) is investigated using two eddy-covariance datasets collected over a lake and a cattle feedlot. Three measures of scalar similarity, namely, the similarity constant in the flux–variance relationship, the correlation coefficient between two scalars and the relative transport efficiency, are examined. The uncertainty in the similarity constant \(C_{s}\) in the flux–variance relationship resulting from random errors in turbulence measurements is quantified based on error propagation analyses and a Monte-Carlo sampling method, which yields a distribution instead of a single value for \(C_{s}\). For different scalars, the distributions of \(C_{s}\) are found to significantly overlap, implying that scalars are transported similarly under strongly unstable conditions. The random errors in the correlation coefficients between scalars and the relative transport efficiencies are also quantified through error propagation analyses, and they increase as the atmosphere departs from neutral conditions. Furthermore, the correlation coefficients between three scalars (water vapour, \(\hbox {CO}_{2}\), and \(\hbox {NH}_{3}\)) are statistically different from unity while the relative transport efficiencies are not, which highlights the difference between these two measures of scalar similarity. The results suggest that uncertainties in these measures of scalar similarity need to be quantified when using them to diagnose the existence of dissimilarity among different scalars.     

Ejective and Sweeping Motions Above a Peatland and Their Role in Relaxed-Eddy-Accumulation Measurements and Turbulent Transport Modelling

The three turbulent velocity components, water vapour (\(\text {H}_2\text {O}\)), carbon dioxide (\(\text {CO}_{2}\)), and methane (\(\text {CH}_{4}\)) concentration fluctuations are measured above a boreal peatland and analyzed using conditional sampling and quadrant analysis. The overarching question to be addressed is to what degree lower-order cumulant expansion methods describe transport efficiency and the relative importance of ejections and sweeps to momentum, \(\text {CH}_{4}\), \(\text {CO}_{2}\) and \(\text {H}_2\text {O}\) fluxes across a range of atmospheric flow regimes. The patchy peatland surface creates distinctly different source and sink distributions for the three scalars in space and time thereby adding to the uniqueness of the set-up. The measured and modelled fractional contributions to the momentum flux show that sweep events dominate over ejections in agreement with prior studies conducted in the roughness sublayer. For scalar fluxes, ejections dominate the turbulent fluxes over sweeps. While ejective motions persist longer for momentum transport, sweeping events persist longer for all three scalars. Third-order cumulant expansions describe many of the results detailed above, and the results are surprising given the highly non-Gaussian distribution of \(\text {CH}_{4}\) turbulent fluctuations. Connections between the asymmetric contributions of sweeps and ejections and the flux-transport term arising in scalar turbulent-flux-budget closure are derived and shown to agree reasonably well with measurements. The proposed model derived here is much simpler than prior structural models used to describe laboratory experiments. Implications of such asymmetric contributions on, (i) the usage of the now proliferating relaxed-eddy-accumulation method in turbulent flux measurements, (ii) the constant-flux assumption, and (iii) gradient-diffusion closure models are presented.     

Test of Scintillometer Saturation Correction Methods Using Field Experimental Data

Saturation of large aperture scintillometer (LAS) signals can result in sensible heat flux measurements that are biased low. A field study with LASs of different aperture sizes and path lengths was performed to investigate the onset of, and corrections for, signal saturation. Saturation already occurs at \({C_n^2 \approx 0.074 D^{5/3} \lambda^{1/3} L^{-8/3}}\), where \({C_n^2}\) is the structure parameter of the refractive index, D is the aperture size, λ is the wavelength, L is the transect length, which is smaller than theoretically derived saturation limits. At a transect length of 1 km, a height of 2.5 m, and aperture ≈0.15 m the correction factor exceeds 5% already at \({C_n^2=2\times 10^{-12}{\rm m}^{-2/3}}\), which will affect many practical applications of scintillometry. The Clifford correction method, which only depends on \({C_n^2}\) and the transect geometry, provides good saturation corrections over the range of conditions observed in our study. The saturation correction proposed by Ochs and Hill results in correction factors that are too small in large saturation regimes. An inner length scale dependence of the saturation correction factor was not observed. Thus for practical applications the Clifford correction method should be applied.     

Partitioning Eddy-Covariance Methane Fluxes from a Shallow Lake into Diffusive and Ebullitive Fluxes

Methane (\(\mathrm {CH}_{4}\)) is known to be emitted from lakes to the atmosphere via processes such as diffusion and ebullition (i.e., bubble emission). We developed a practical method for partitioning eddy-covariance \(\mathrm {CH}_{4}\) fluxes from a shallow lake into diffusive and ebullitive fluxes using a wavelet analysis based on local scalar similarity between the \(\mathrm {CH}_{4}\) concentration and other reference scalars, such as the air temperature or water vapour concentration, in the wavelet time-scale domain, with the hypothesis that similar and dissimilar fluctuation components are related to diffusive and ebullitive \(\mathrm {CH}_{4}\) fluxes, respectively. Our method is applied to approximately two weeks of data obtained at a shallow mid-latitude lake. The partitioned diffusive flux has a physically sound relationship with wind speed, supporting the validity of the method. The ratio of the diffusive flux to the total flux is typically 0.11 with flow from an area of steady bubble emission, but otherwise 0.36. Further validation is required using a larger dataset and data from other lakes. The proposed method can be easily applied to historical data because it requires only 10-Hz data of \(\mathrm {CH}_{4}\) concentration and other reference scalars, along with an empirical parameter.     

Observations of Lake-Breeze Events During the Toronto 2015 Pan-American Games

Enhanced meteorological observations were made during the 2015 Pan and Parapan American Games in Toronto in order to measure the vertical and horizontal structure of lake-breeze events. Two scanning Doppler lidars (one fixed and one mobile), a C-band radar, and a network including 53 surface meteorological stations (mesonet) provided pressure, temperature, humidity, and wind speed and direction measurements over Lake Ontario and urban areas. These observations captured the full evolution (prior, during, and after) of 27 lake-breeze events (73% of observation days) in order to characterize the convective and dynamic processes driving lake breezes at the local scale and mesoscale. The dominant signal of a passing lake-breeze front (LBF) was an increase in dew-point temperature of \(2.3 \pm 0.3 \,^{\circ }\hbox {C}\), coinciding with a \(180^{\circ }\) shift in wind direction and a decrease in air temperature of \(2.1 \pm 0.2 \,^{\circ }\hbox {C}\). Doppler lidar observations over the lake detected lake breezes 1 hour (on average) before detection by radar and mesonet. On days with the synoptic flow in the offshore direction, the lidars observed wedge-shaped LBFs with shallow depths, which inhibited the radar’s ability to detect the lake breeze. The LBF’s ground speed and inland penetration distance were found to be well-correlated (\(r = 0.78\)), with larger inland penetration distances occurring on days with non-opposing (non-offshore) synoptic flow. The observed enhanced vertical motion \(({>} 1\hbox { m s}^{-1})\) at the LBF, observed by the lidar on 54% of lake-breeze days, was greater (at times \({>} 2.5\hbox { m s}^{-1}\)) than that observed in previous studies and longer-lasting over the lake than over land. The weaker and less pronounced lake-breeze structure over land is illustrated in two case studies highlighting the lifetime of the lake-breeze circulation and the impact of propagation distance on lake-breeze intensity.     

A Hybrid Wind-Farm Parametrization for Mesoscale and Climate Models

We investigate the area-averaged sensible heat flux (\(Q_{H}\)) obtained with a scintillometer along a 3.1-km path length over the city centre of ?ód?, Central Poland. The annual cycle of \(Q_{H}\) peaks in June but is lower by the middle of summer. In winter, due to a large amount of anthropogenic heat input, \(Q_{H}\) remains positive all day long, with positive night-time fluxes also found during months with frequent cold advection, e.g., June 2010. In the diurnal cycle of this flux, several features specific to urban areas are seen: the peak shifts 1–2 h after noon, the heat flux turns from positive to negative 1–2 h after sunset. In ?ód? \(Q_{H}\) was observed during inflow from the north and north-west, i.e. from the city centre. As this area is mostly covered with impervious materials, most of the heat exchanged between the ground and the overlying air is in the form of sensible heat flux. Under the conditions of inflow from the east and south-east, the maximum heat flux is approximately \(100\,\hbox {W}\,\hbox {m}^{-2}\) lower than during the inflow from the city centre, since more vegetation exists to the east and south-east of the scintillometer path. Cold and warm advection are found to be a vital factor in the observed heat-flux variability in the centre of ?ód?.