Turbulence Statistics Inside and Over Forest: Influence on Footprint Prediction

Observations of wind statistics within and above a Scots pine forest are comparedwith those predicted from an analytical second-order closure model. The roughnesssublayer (RSL) effects, and the influence of stability on similarity functions, arestudied using observations. The commonly accepted forms of similarity functionsdescribe the influence of diabatic effects above the RSL well. According to earlierstudies they are expected also to apply within the RSL. As an exception, the averagewind speed normalised with friction velocity was found to be invariant with stabilityclose to the canopy top under unstable conditions. Lagrangian stochastic trajectorysimulations were used to evaluate the influence of canopy turbulence profiles onfootprint prediction. The main uncertainty was found to arise from parameterisationof the random forcing term in the Lagrangian velocity equation. The influence ofdiabatic conditions was studied, and it was found that thermal stability affectssignificantly the footprint function above the forest canopy, but significantuncertainty exists because of uncertainties in the formulation of stability functions.     

Micrometeorological Observations of a Microburst in Southern Finland

On the afternoon of 3 July 2004 in Hyytiälä (Juupajoki, Finland), convective cells produced a strong downburst causing forest damage. The SMEAR II field station, situated near the damage site, enabled a unique micrometeorological analysis of a microburst with differences above and inside the canopy. At the time of the event, a squall line associated with a cold front was crossing Hyytiälä with a reflectivity maximum in the middle of the squall line. A bow echo, rear-inflow notch, and probable mesovortex were observed in radar data. The bow echo moved west-north-west, and its apex travelled just north of Hyytiälä. The turbulence data were analysed at two locations above the forest canopy and at one location at sub-canopy. At 1412 EET (Eastern European Time, UTC+2), the horizontal and vertical wind speed increased and the wind veered, reflecting the arrival of a gust front. At the same time, the carbon dioxide concentration increased due to turbulent mixing, the temperature decreased due to cold air flow from aloft and aerosol particle concentration decreased due to rain scavenging. An increase in the number concentration of ultra-fine particles (< 10 nm) was detected, supporting the new particle formation either from cloud outflow or due to rain. Five minutes after the gust front (1417 EET), strong horizontal and downward vertical wind speed gusts occurred with maxima of 22 and 15 m s^?1, respectively, reflecting the microburst. The turbulence spectra before, during and after the event were consistent with traditional turbulence spectral theory.     

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.     

Intra-City Variation in Urban Morphology and Turbulence Structure in Helsinki, Finland

Most atmospheric boundary-layer theories are developed over vegetative surfaces and their applicability at urban sites is questionable. Here, we study the intra-city variation of turbulence characteristics and the applicability of boundary-layer theory using building-morphology data across Helsinki, and eddy-covariance data from three sites: two in central Helsinki (400 m apart) and one 4 km away from the city centre. The multi-site measurements enable the analysis of the horizontal scales at which quantities that characterize turbulent transport vary: (i) Roughness characteristics vary at a 10-m scale, and morphometric estimation of surface-roughness characteristics is shown to perform better than the often used rule-of-thumb estimates (average departures from the logarithmic wind profile are 14 and 44 %, respectively). (ii) The drag coefficient varies at a 100-m scale, and we provide an updated parametrization of the drag coefficient as a function of z/z _H (the ratio of the measurement height to the mean building height). (iii) The transport efficiency of heat, water vapour and CO₂ is shown to be weaker the more heterogeneous the site is, in terms of sources and sinks, and strong scalar dissimilarity is observed at all sites. (iv) Atmospheric stability varies markedly even within 4 km across the city: the median difference in nocturnal sensible heat fluxes between the three sites was over 50W m^?2. Furthermore, (v) normalized power spectra and cospectra do not vary between sites, and they follow roughly the canonical theory as developed over vegetated terrain.     

Autoregressive filtering versus linear detrending in estimation of fluxes by the eddy covariance method

The application of autoregressive running mean filtering (RMF) and linear detrending (LDT) in the estimation of turbulent fluxes by the eddy covariance method is analysed. The systematic, as well as the random, errors of the fluxes arising from filtering and/or limited observation time effects are described. To observe negligible systematic errors in fluxes, the RMF has to be applied with moderately long time constants. However, the obtained flux values are subject to increased random errors during periods of non-stationarity and the method leads to systematic overestimation of variances. These shortcomings are not inherent in the LDT approach, which is recommended for use. But the systematic errors of fluxes due to LDT are not negligible under certain experimental conditions and have to be accounted for. The corrections are important because the relatively small errors in short-period fluxes can translate to significant errors in long-period averages. The corrections depend on the turbulence time scales, which should be preferably estimated as ensemble mean variables for a particular site.     

Numerical analysis of flux footprints for different landscapes

Summary A model for the canopy – planetary boundary layer flow and scalar transport based on E- closure was applied to estimate footprint for CO₂ fluxes over different inhomogeneous landscapes. Hypothetical heterogeneous vegetation patterns – forest with clear-cuts as well as hypothetical heterogeneous relief – a bell-shaped valley and a ridge covered by forest were considered. The distortions of airflow caused by these heterogeneities are shown – the upwind deceleration of the flow at the ridge foot and above valley, acceleration at the crest and the flow separation with the reversed flow pattern at lee slopes of ridge and valley. The disturbances induce changes in scalar flux fields within the atmospheric surface layer comparing to fluxes for homogeneous conditions: at a fixed height the fluxes vary as a function of distance to disturbance. Correspondingly, the flux footprint estimated from model data depends on the location of the point of interest (flux measurement point) and may significantly deviate from that for a flat terrain. It is shown that proposed method could be used for the choice of optimal sensor position for flux measurements over complex terrain as well as for the interpretation of data for existing measurement sites. To illustrate the latter the method was applied for experimental site in Solling, Germany, taking into account the complex topography and vegetation heterogeneities. Results show that in certain situations (summer, neutral stratification, south or north wind) and for a certain sensor location the assumptions of idealized air flow structure could be used for measurement interpretation at this site, though in general, extreme caution should be applied when analytical footprint models are used in the interpretation of flux measurements over complex sites.     

An Analytical Model for the Two-Scalar Covariance Budget Inside a Uniform Dense Canopy

The two-scalar covariance budget is significant within the canopy sublayer (CSL) given its role in modelling scalar flux budgets using higher-order closure principles and in estimating the segregation ratio for chemically reactive species. Despite its importance, an explicit expression describing how the two-scalar covariance is modified by inhomogeneity in the flow statistics and in the vertical variation in scalar emission or uptake rates within the canopy volume remains elusive even for passive scalars. To progress on a narrower version of this problem, an analytical solution to the two-scalar covariance budget in the CSL is proposed for the most idealized flow conditions: a stationary and planar homogeneous flow inside a uniform and dense canopy with a constant leaf area density distribution. The foliage emission (or uptake) source strengths are assumed to vary exponentially with depth while the forest floor emission is represented as a scalar flux. The analytical solution is a superposition of a homogeneous part that describes how the two-scalar covariance at the canopy top is transported and dissipated within the canopy volume, and an inhomogeneous part governed by local production mechanisms of the two-scalar covariance. The homogeneous part is primarily described by the canopy adjustment length scale, and the attenuation coefficients of the turbulent kinetic energy and the mean velocity. Conditions for which the vertical variation of the two-scalar covariance is controlled by the rapid attenuation in the mean velocity and turbulent kinetic energy profiles, vis-à-vis the vertical variation of the scalar source strength, are explicitly established. This model also demonstrates how dissimilarity in the emissions from the ground, even for the extreme binary case with one scalar turned ‘on’ and the other scalar turned ‘off’, modifies the vertical variation of the two-scalar covariance within the CSL. To assess its applicability to field conditions, the analytical model predictions were compared with observations made at two different forest types—a sparse pine forest at the Hyytiälä SMEAR II-station (in Finland) and a dense alpine hardwood forest at Lavarone (in Italy). While the model assumptions do not represent the precise canopy morphology, attenuation properties of the turbulent kinetic energy and the mean velocity, observed mixing length, and scalar source attenuation properties for these two forest types, good agreement was found between measured and modelled two scalar covariances for multiple scalars and for the triple moments at the Hyytiälä site.     

Direct Numerical Simulation of a Turbulent Channel Flow with Forchheimer Drag

Boundary-Layer Meteorology - We characterize the turbulent flow, using direct numerical simulations (DNS), within a closed channel between two parallel walls with a canopy of constant areal density...     

Footprints and Fetches for Fluxes over Forest Canopies with Varying Structure and Density

A stochastic trajectory model was used to estimate scalar fluxfootprints in neutral stabilityfor canopies of varying leaf area distributions andleaf area indices. An analytical second-order closure model wasused to predict mean wind speed, second moments and the dissipationrate of turbulent kinetic energy within a forest canopy.The influence of source vertical profile on the flux footprint wasexamined. The fetch is longer for surface sourcesthan for sources at higher levels in the canopy. In order tomeasure all the flux components, and thus the total flux, with adesired accuracy, sources were located at the forest floor in thefootprint function estimation. The footprint functions werecalculated for five observation levels above the canopy top. Itwas found that at low observation heights both canopy density andcanopy structure affect the fetch. The higher abovethe canopy top the flux is measured, the more pronounced is the effectof the canopy structure. The forest fetch for flux measurements isstrongly dependent on the required accuracy: The 90% flux fetchis greater by a factor of two or more compared to the 75% fetch. Theupwind distance contributing 75% of flux is as large as 45 timesthe difference between canopy height and the observation heightabove the canopy top, being even larger for low observationlevels.