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Anomalies in Flux-Gradient Relationships Over Forest
Abstract
Simultaneous profile and eddy correlation flux data gathered over Thetford Forest, U.K., have been analysed to find values
of the vertical turbulent diffusivitiesK
M,K
H andK
E (for momentum, heat and water vapour transfer, respectively) at a reference heightz
R, nine roughness lengths above the zero-plane displacementd. The results show: (i), that values ofK
M over the forest are not significantly different from these predicted by semiempirical diabatic influence functions appropriate
to much smoother surfaces such as short grass; and (ii), thatK
H andK
E exceed their values predicted from the semiempirical functions by an average factor of 2 or more in unstable, near neutral
and slightly stable conditions. These conclusions are strongly dependent on the assumed behaviour ofd, here taken as 0.76 tree heights, independent of both property and stability. Consideration is given to an alternative analysis
procedure, in which values of the zero-plane displacementsd
H andd
E for heat and water vapour respectively, are obtained from the data by assumingK
H andK
E to be given by semiempirical diabatic influence functions; this procedure is shown to be unacceptable on both practical and
physical grounds. To account for the anomalies inK
H andK
E, a mechanism is proposed in which the horizontally inhomogeneous temperature structure of the canopy causes free convection
to be maintained by discrete; localized heat sources and/or sinks, effectively enhancing turbulent transport processes even
in nearneutral conditions.
... Since turbulence performs the majority of the vertical exchange of momentum, mass, energy, and trace gases (Gao et al. 1989 ), the dependence of turbulence parameterization on canopy seasonal changes should be included in weather and climate models (Fitzjarrald et al. 2001). To capture the vertical exchange of momentum, energy, and trace gases, it is crucial to determine how the flux–gradient relationships and turbulent kinetic energy are influenced by the leaf state and atmospheric stability (Thom et al. 1975; Raupach 1979; Denmead and Bradley 1985; Högström et al. 1989). Regarding the flux–gradient relationships, it has been recognized that the standard Monin–Obukhov similarity theory formulations (MOST; Monin and Obukhov 1954) are only valid at heights well above a rough vegetated surface (Högström 1996). ...
... The atmospheric layer in which the flux–gradient relationships are directly impacted by the canopy is called the roughness sublayer (RSL). It is in this layer that numerous studies over evergreen forests confirm that the heat exchange is more efficient than in the inertial surface layer above (Thom et al. 1975; Raupach 1979; Denmead and Bradley 1985; Högström et al. 1989). However, those studies failed to converge on a single relationship to describe momentum exchange above tall canopies, suggesting that additional physical processes must affect the exchange. ...
... where the vertical source/sink distribution of the quantities within the canopy S c is calculated as S c 5 ›w 0 c 0 /›z. In our analysis we a priori adopt the assumption made in Raupach (1979) that the displacement height for heat and moisture equals the displacement height for momentum (d m 5 d h 5 d q ). The reason for this assumption is further discussed in section 5b. ...
In this observational study, the role of tree phenology on the atmospheric turbulence parameterization over 10-m-tall and relatively sparse deciduous vegetation is quantified. Observations from the Canopy Horizontal Array Turbulence Study (CHATS) field experiment are analyzed to establish the dependence of the turbulent exchange of momentum, heat, and moisture, as well as kinetic energy on canopy phenological evolution through widely used parameterization models based on 1) dimensionless gradients or 2) turbulent kinetic energy (TKE) in the roughness sublayer. Observed vertical turbulent fluxes and gradients of mean wind, temperature, and humidity, as well as velocity variances, are used in combination with empirical dimensionless functions to calculate the turbulent exchange coefficient. The analysis shows that changes in canopy phenology influence the turbulent exchange of all quantities analyzed in this study. The turbulent exchange coefficients of those quantities are twice as large near the canopy top for a leafless canopy than for a full-leaf canopy under unstable and near-neutral conditions. This turbulent exchange coefficient difference is related to the differing penetration depths of the turbulent eddies organized at the canopy top, which increase for a canopy without leaves. The TKE and dissipation analysis under near-neutral atmospheric conditions additionally shows that TKE exchange increases for a leafless canopy because of reduced TKE dissipation efficiency relative to that when the canopy is in full-leaf stage. The study closes with discussion surrounding the implications of these findings for parameterizations used in large-scale models.
... eddy-covariance or energy balance measurements)." Raupach (1979) labelled this phenomenon 'aerodynamic discrepancy,' and it has been noted more generally to occur in the atmospheric surface layer (ASL) when terms such as turbulent transport become significant in the rate equations for momentum fluxes (e.g. Zeman 1981; Wyngaard 2004). ...
... Though uncertainty in the estimation of d was postulated to be one reason for such a 'discrepancy' (Thom et al. 1975;Hicks et al. 1979;Raupach 1979), this reasoning was rejected after a short debate (Hicks et al. 1979;Raupach 1979;Garratt 1979). With eddy-covariance measurements of stresses becoming common and the work of Thom (1971) connecting these measurements with definitions of displacement height, such arguments disappeared from the scientific literature. ...
... Though uncertainty in the estimation of d was postulated to be one reason for such a 'discrepancy' (Thom et al. 1975;Hicks et al. 1979;Raupach 1979), this reasoning was rejected after a short debate (Hicks et al. 1979;Raupach 1979;Garratt 1979). With eddy-covariance measurements of stresses becoming common and the work of Thom (1971) connecting these measurements with definitions of displacement height, such arguments disappeared from the scientific literature. ...
Displacement height (d) is an important parameter in the simple modelling of wind speed and vertical fluxes above vegetative canopies, such as forests. Here we show that, aside from implicit definition through a (displaced) logarithmic profile, accepted formulations for d do not consistently predict flow properties above a forest. Turbulent transport can affect the displacement height, and is an integral part of what is called the roughness sublayer. We develop a more general approach for estimation of d, through production of turbulent kinetic energy and turbulent transport, and show how previous stress-based formulations for displacement height can be seen as simplified cases of a more general definition including turbulent transport. Further, we also give a simplified and practical form for d that is in agreement with the general approach, exploiting the concept of vortex thickness scale from mixing-layer theory. We assess the new and previous displacement height formulations by using flow statistics derived from the atmospheric boundary-layer Reynolds-averaged Navier–Stokes model SCADIS as well as from wind-tunnel observations, for different vegetation types and flow regimes in neutral conditions. The new formulations tend to produce smaller d than stress-based forms, falling closer to the classic logarithmically-defined displacement height. The new, more generally defined, displacement height appears to be more compatible with profiles of components of the turbulent kinetic energy budget, accounting for the combined effects of turbulent transport and shear production. The Coriolis force also plays a role, introducing wind-speed dependence into the behaviour of the roughness sublayer; this affects the turbulent transport, shear production, stress, and wind speed, as well as the displacement height, depending on the character of the forest. We further show how our practical (‘mixing-layer’) form for d matches the new turbulence-based relation, as well as correspondence to previous (stress-based) formulations.
... Several experimental results (Thom et al., 1975;Garratt, 1978a,b and1980;Raupach, 1979) have shown, that conventional flux-profile relationships and the validity of the non-dimensional Monin-Obukhov functions for momentum and heat transfer must be questioned over horizontally uniform but very rough natural surfaces such as tall crops and forests. Results from field studies over these surfaces reinforce the idea that the surface layer over a very rough surface must be considered in two parts: usually referred to as the inertial sub-layer (Tennekes, 1973) and the roughness sub-layer (Raupach, 1979). ...
... Several experimental results (Thom et al., 1975;Garratt, 1978a,b and1980;Raupach, 1979) have shown, that conventional flux-profile relationships and the validity of the non-dimensional Monin-Obukhov functions for momentum and heat transfer must be questioned over horizontally uniform but very rough natural surfaces such as tall crops and forests. Results from field studies over these surfaces reinforce the idea that the surface layer over a very rough surface must be considered in two parts: usually referred to as the inertial sub-layer (Tennekes, 1973) and the roughness sub-layer (Raupach, 1979). In the former, under adiabatic conditions, height above the effective surface is the only length scale and the semi-logarithmic profile laws are obeyed. ...
... into local or meso-scale ones in the roughness layer (called the 'roughness sub-layer' by Raupach, 1979 and 'transition layer' by Garratt, 1980). The integrated effects of the urban 'surface' form the horizontally homogeneous turbulent surface layer and the mixed layer of the UBL. ...
... For the mean longitudinal velocity U, the RSL effects are traditionally accommodated using a so-called roughness sublayer correction function φ RSL so that the law-of-the wall 13,14 , presumed to be applicable in the ISL, is expressed as 11,[15][16][17][18][19][20][21][22] ...
... Thus far, studies (laboratory and field) suggest enhancement in momentum transport in the RSL when compared to ISL predictions [2][3][4]10,15,26,[33][34][35][36] thereby requiring that φ RSL ≤ 1 (though values close to unity have been reported in the RSL as well for near-neutral stratification 16,37 ). A common empirical form for φ RSL that satisfy these minimal constraints is 4,10,17,18,33,34,38 ...
Modification to the law-of-the wall represented by a dimensionless correction function $\phi_{RSL}(z/h)$ is derived using near-neutral atmospheric turbulence measurements collected at two sites in the Amazon in near-neutral stratification, where $z$ is the distance from the forest floor and $h$ is the mean canopy height. The sites are the Amazon Tall Tower Observatory (ATTO) for $z/h\in [1,2.3]$ and the Green Ocean Amazon (GoAmazon) site for $z/h\in[1,1.4]$. A link between the vertical velocity spectrum $E_{ww}(k)$ ($k$ is the longitudinal wavenumber) and $\phi_{RSL}$ is then established using a co-spectral budget (CSB) model interpreted by the moving-equilibrium hypothesis (MEH). The key finding is that $\phi_{RSL}$ is determined by the ratio of two turbulent viscosities and is given as $\nu_{t,BL}/\nu_{t,RSL}$, where $\nu_{t,RSL}=(1/A)\int_{0}^{\infty}\tau(k) E_{ww}(k)dk$, $\nu_{t,BL}=\kappa (z-d) u_*$, $\tau(k)$ is a scale-dependent decorrelation time scale between velocity components, $A=C_R/(1-C_I)=4.5$ is predicted from the Rotta constant $C_R=1.8$ and the isotropization of production constant $C_I=3/5$ given by Rapid Distortion Theory, $\kappa$ is the von K\'arm\'an constant, $u_*$ is the friction velocity at the canopy top, and $d$ is the zero-plane displacement. Because the transfer of energy across scales is conserved in $E_{ww}(k)$ and is determined by the turbulent kinetic energy dissipation rate ($\epsilon$), the CSB model also predicts that $\phi_{RSL}$ scales with $L_{BL}/L_d$, where $L_{BL}$ is the length scale of attached eddies to $z=d$, $L_d=u_*^3/\epsilon$ is a macro-scale dissipation length.
... Generally, the publication outputs supported by eddy covariance is on the rising trend ( Fig. 1 and mistakes were waiting to be made before more accurate measurements could be carried out (Dyer and Pruitt 1962, Dyer et al. 1967, Raupach 1979, Swinbank 1967. 15 Nevertheless, as performance of sensor improved, measurements of flux could be conducted for longer period at shorter intervals (Massman andLee 2002, Wofsy et al. 1993). ...
... It is, however, neither the first 50 nor the only method to do such measurement. First experiments that try to acquire CO2 exchange were based on flux-gradient method (Inoue et al. 1958, Lemon 1960, Monteith and Szeicz 1960, which proved to be problematic when applied in forest ecosystems (Raupach 1979, Simpson et al. 1998. Other optional methods include enclosure, cuvette and chamber, etc. ...
The history of eddy covariance (EC) measuring system could be dated back to 100 years ago, but it was not until the recent decades that EC gains popularity and being widely used in global change ecological studies, with explosion of related work published in papers from various journals. Investigating 8297 literature related with EC from 1981 to 2018, we make a comprehensive and critical review of scientific development of EC from a scientometric perspective. First, the paper outlines general bibliometric statistics, including publication number, country contribution, productive institutions, active authors, journal distribution, high cited articles and fund support, to provide an informative picture of EC studies. Second, research trends are revealed by network visualization and modeling based on keyword analysis, from where we could discover the knowledge structure of EC and detect the research focus and hotspots transitions at different periods. Third, collaboration in EC research community has been explored. FLUXNET is the largest global network uniting EC researchers, here we have quantified and evaluated its performance by using bibliometric indicators of cooperation and citation. Specific discussions have been given to the historical development of EC, including technical maturation and application promotion. Considering the current barrier for collaboration, the review closes by analyzing the reasons hindering data sharing and makes a prospect of new models for data-intensive collaboration in the future.
... The large roughness layer above a tall canopy also makes it difficult to apply many theories of wall flows as well as to apply and validate traditional similarity theory (Katul et al., 1995). As compared to, for example, a thin grass layer, the tall geometry and internal structure of the forest may allow large turbulent structures within the canopy layer, which will interact with the overlying atmospheric flow (Raupach, 1979). This turbulence may either be generated by wind shear from interaction with the canopy geometry or be generated and suppressed by local buoyancy effects (Baldocchi and Meyers, bient air (and is thus less dense), convection is generated. ...
... In the past some high density vertically distributed measurements have been performed in canopies, namely in a walnut orchard (Patton et al., 2011) and in a very open boreal forest (Launiainen et al., 2007). Several sonic anemometers were distributed along the height of the canopy. ...
Complex ecosystems such as forests make accurately measuring atmospheric energy and matter fluxes difficult.
One of the issues that can arise is that parts of the canopy and overlying atmosphere can be turbulently decoupled from each other, meaning that the vertical exchange of energy and matter is reduced or hampered.
This complicates flux measurements performed above the canopy.
Wind above the canopy will induce vertical exchange. However, stable thermal stratification, when lower parts of the canopy are colder, will hamper vertical exchange.
To study the effect of thermal stratification on decoupling, we analyze high-resolution (0.3 m) vertical temperature profiles measured in a Douglas fir stand in the Netherlands using distributed temperature sensing (DTS).
The forest has an open understory (0–20 m) and a dense overstory (20–34 m). The understory was often colder than the atmosphere above (80 % of the time during the night, >99 % during the day). Based on the aerodynamic Richardson number the canopy was regularly decoupled from the atmosphere (50 % of the time at night).
In particular, decoupling could occur when both u*<0.4 m s−1 and the canopy was able to cool down through radiative cooling.
With these conditions the understory could become strongly stably stratified at night. At higher values of the friction velocity the canopy was always well mixed.
While the understory was nearly always stably stratified, convection just above the forest floor was common. However, this convection was limited in its vertical extent, not rising higher than 5 m at night and 15 m during the day.
This points towards the understory layer acting as a kind of mechanical “blocking layer” between the forest floor and overstory.
With the DTS temperature profiles we were able to study decoupling and stratification of the canopy in more detail and study processes which otherwise might be missed. These types of measurements can aid in describing the canopy–atmosphere interaction at forest sites and help detect and understand the general drivers of decoupling in forests.
... where z is the wind speed observation height, d is the zero-plane displacement, z0_m is the roughness length for momentum (all in metres), U z is the wind speed (m s −1 ) at z and κ is the dimensionless von Karman Enhancement of momentum exchange has been observed both for tall canopies and in complex terrain owing to breakdown of theoretical vertical logarithmic wind profiles (Cellier & Brunet, 1992;Raupach, 1979;Simpson, Thurtell, Neumann, Den Hartog, & Edwards, 1998 It is often assumed that r a _s is equal to r a _m, but this assumption can to lead to considerable error (Brutsaert, 1982, p. 62) owing to so-called excess resistance for scalars. Excess resistance occurs because pressure forces associated with form drag increase momentum exchange, but not scalar exchange and because of differences in source and sink distributions for these entities (Brutsaert, 1982;Moors, 2012;Simpson et al., 1998;Stewart & Thom, 1973). ...
... The ratio of z0_s/z0_m used in previous studies varies over approximately an order of magnitude as it is influenced by canopy roughness, canopy density, atmospheric stability and wind speed (Bosveld, 1999;Brutsaert, 1982, p. 114;Lalic, Mihailovic, Rajkovic, Arsenic, & Radlovic, 2003;Raupach, 1979;Thom, Stewart, Oliver, & Gash, 1975). The sensitivity of r a _s and E PM to the ratio z0_s/z0_m is explored here using three scenarios: ...
There is increased interest in the potential of tree planting to help mitigate flooding using nature‐based solutions or natural flood management. However, many publications based upon catchment studies conclude that, as flood magnitude increases, benefit from forest cover declines and is insignificant for extreme flood events. These conclusions conflict with estimates of evaporation loss from forest plot observations of gross rainfall, throughfall and stem flow. This study explores data from existing studies to assess the magnitudes of evaporation and attempts to identify the meteorological conditions under which they would be supported. This is achieved using rainfall event data collated from publications and data archives from studies undertaken in temperate environments around the world. The meteorological conditions required to drive the observed evaporation losses are explored theoretically using the Penman‐Monteith equation. The results of this theoretical analysis are compared with the prevailing meteorological conditions during large and extreme rainfall events in mountainous regions of the UK to assess the likely significance of wet canopy evaporation loss.
The collated dataset showed that event Ewc losses between approximately 2 and 38% of gross rainfall (1.5 to 39.4 mm d‐1) have been observed during large rainfall events (up to 118 mm d‐1) and that there are few data for extreme events (> 150 mm d‐1). Event data greater than 150 mm (reported separately) included similarly high percentage evaporation losses. Theoretical estimates of wet‐canopy evaporation indicated that, to reproduce the losses towards the high end of these observations, relative humidity and the aerodynamic resistance for vapour transport needed to be lower than approximately 97.5% and 0.5 to 2 s m‐1 respectively. Surface meteorological data during large and extreme rainfall events in the UK suggest that conditions favourable for high wet‐canopy evaporation are not uncommon and indicate that significant evaporation losses during large and extreme events are possible but not for all events and not at all locations. Thus the disparity with the results from catchment studies remains.
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... Researchers soon found that forests did not operate like tall crops. A series of measurements at Thetford forest in England (Stewart and Thom 1973;Raupach 1979;Raupach and Legg 1984) drew attention to the fact that the application of flux-gradient theory would prove troublesome over tall forests. Hicks et al. (1975) concluded that to attain the same flux resolution using gradients as was achieved in their 1972 covariance study of a pine forest would require resolution of temperature differences to better than 0.01 ºC and humidity differences to better than 0.005 hPa. ...
... Measurements over forests also impose logistical difficulties, which arise from the need to deploy delicate instrumentation tens of metres above the ground. Evidence was growing that Monin-Obukhov scale theory-a theory that was successfully predicting gradient behaviour over short vegetation-breaks down within the roughness sublayer immediately above tall forests (Garratt 1978;Raupach 1979). ...
In the first half of the twentieth century the measurement of rates of exchange of momentum, heat, and especially water between the terrestrial surface and the atmosphere was an elusive challenge. A wide variety of methods evolved, ranging from reliance on drag plates, evaporation pans, and weighed lysimeters to a variety of methods based on measurement of vertical gradients in the air. None of these provided great confidence in the results. The promise of direct measurement by eddy covariance was held at bay by the lack of suitable fast-response instrumentation and the analytical requirement to average the products of pairs of these fast-response signals. Developments starting in the 1950s have now largely solved the problems that previously limited eddy covariance. Here, the history of flux measurement is summarized, and the path to now-standard capabilities is explored. The currently active major international programs making use of the modern instrumentation are addressed (with the focus on CO2 and CH4, as befitting global concerns regarding climate change), with particular attention to the emerging need to revisit the fetch and footprint constraints that confronted early workers. Finally, some areas of continuing uncertainty are mentioned, with an implicit request for increased experimental attention.
... In the late 20th century these scientists contributed to a growing understanding of two major environmental problems: the effects of large-scale air pollution that had spread across Europe and North America and the interactions of fossil-fuel-driven increases in atmospheric CO 2 and the ecosystem-atmosphere exchanges of carbon, water, and heat. However, not until the near collapse of what was then called flux-gradient techniques (Raupach, 1979) and major advancements made in anemometer, gas sensor, and computer technologies could eddy fluxes of energy, water, and carbon be measured. Year-round measurements of ecosystem-atmosphere exchange were first made in the early 1990s (Wofsy et al., 1993), and by 2000, over 100 flux sites were measuring energy and mass exchanges of ecosystems throughout the world. ...
... Given that the extent of forest and meadow vegetation at these elevations is affected by wildfires and climate, this bioturbation of the soil geomorphology ebbs and flows through time. In spite of some remarkably well-documented studies (e.g., Platt et al., 2016), bioturbation of the upper regolith is a tremendously understudied field of inquiry that could be much more comprehensively studied in all of the environmental research networks. ...
Long-term environmental research networks are one approach to
advancing local, regional, and global environmental science and education. A
remarkable number and wide variety of environmental research networks operate
around the world today. These are diverse in funding, infrastructure,
motivating questions, scientific strengths, and the sciences that birthed and
maintain the networks. Some networks have individual sites that were
selected because they had produced invaluable long-term data, while other
networks have new sites selected to span ecological gradients. However, all
long-term environmental networks share two challenges. Networks must keep
pace with scientific advances and interact with both the scientific community
and society at large. If networks fall short of successfully addressing these
challenges, they risk becoming irrelevant. The objective of this paper is to
assert that the biogeosciences offer environmental research networks a number
of opportunities to expand scientific impact and public engagement. We
explore some of these opportunities with four networks: the International
Long-Term Ecological Research Network programs (ILTERs), critical zone
observatories (CZOs), Earth and ecological observatory networks (EONs),
and the FLUXNET program of eddy flux sites. While these networks were founded
and expanded by interdisciplinary scientists, the preponderance of expertise and
funding has gravitated activities of ILTERs and EONs toward ecology and
biology, CZOs toward the Earth sciences and geology, and FLUXNET toward
ecophysiology and micrometeorology. Our point is not to homogenize networks,
nor to diminish disciplinary science. Rather, we argue that by more fully
incorporating the integration of biology and geology in long-term
environmental research networks, scientists can better leverage network
assets, keep pace with the ever-changing science of the environment, and
engage with larger scientific and public audiences.
... Beginning in the 1970s, high-order closure turbulence models and Lagrangian diffusion models (WILSON and SHAW, 1977;SHAW and PEREIRA, 1982;PAW U, 1986, 1987;RAUPACH, 1987;KATUL and ALBERTSON, 1998;MASSMAN and WEIL, 1999;LEUNING, 2000) have made it possible to study not only mean wind velocity speed within and above tall plant canopies but also the statistical characteristics of canopy turbulence. In the late 1970s, experi-mental studies showed that there are distinct anomalies in flux-gradient relationships above tall plant canopies (GARRATT, 1978;RAUPACH, 1979;DENMEAD and BRADLEY, 1985;CELLIER and BRUNET, 1992) and that turbulent air mass exchange within the upper part and just above tall plant canopies is dominated by large organised turbulent motions (BALDOCCHI and MEYERS, 1988a;BERGSTRÖM and HÖGSTRÖM, 1989;GAO et al., 1989;MAITANI and SHAW, 1990;BLACK, 1993a, 1993b;KRUIJT et al., 2000;VILLANI et al., 2003). ...
... This leads to an enhancement of K m , K h , and K q in the RSL. The increase in K m , K h , and K q can be quantified by the nondimensional factor β (RAUPACH, 1979;CELLIER and BRUNET, 1992): ...
... g c may strongly depend on canopy architecture (leaf area density, branching habits, and canopy height) in combination with leaf traits. For the tall forest, it has been shown that transfer coefficients of different layers may differ quite significantly during the daytime (Raupach 1979;Viswanadham and Sa 1987). Below the canopy, the flow is likely to be influenced by thermal effects directly attributable to the surface (Raupach 1979). ...
... For the tall forest, it has been shown that transfer coefficients of different layers may differ quite significantly during the daytime (Raupach 1979;Viswanadham and Sa 1987). Below the canopy, the flow is likely to be influenced by thermal effects directly attributable to the surface (Raupach 1979). Therefore, the different layers of tall forests should be considered in future studies. ...
Canopy temperature is a result of the canopy energy balance and is driven by climate conditions, plant architecture, and plant-controlled transpiration. Here, we evaluated canopy temperature in a rubber plantation (RP) and tropical rainforest (TR) in Xishuangbanna, southwestern China. An infrared temperature sensor was installed at each site to measure canopy temperature. In the dry season, the maximum differences (Tc − Ta) between canopy temperature (Tc) and air temperature (Ta) in the RP and TR were 2.6 and 0.1 K, respectively. In the rainy season, the maximum (Tc − Ta) values in the RP and TR were 1.0 and −1.1 K, respectively. There were consistent differences between the two forests, with the RP having higher (Tc − Ta) than the TR throughout the entire year. Infrared measurements of Tc can be used to calculate canopy stomatal conductance in both forests. The difference in (Tc − Ta) at three gc levels with increasing direct radiation in the RP was larger than in the TR, indicating that change in (Tc − Ta) in the RP was relatively sensitive to the degree of stomatal closure.
... However, it is well known that the validity of MOST is, strictly speaking, restricted to the inertial sublayer (ISL) of the atmosphere, failing in the roughness sublayer (RSL) (Raupach, 1979;Garratt, 1980;Raupach and Thom, 1981;Raupach and Legg, 1984;Cellier, 1986;Cellier and Brunet, 1992;Simpson et al., 1998;Finnigan, 2000). As a direct consequence, experiments carried out above forests suffer from some limitations, as the roughness sublayer height (z * ) can reach three times the mean canopy height (h) ( and Brunet, 1992), making it more difficult to apply flux-gradient methods over tall forests than over short vegetation. ...
... Typical values for the correction factor S have been found to vary between 1.3 and 3.4 (Simpson et al., 1998) for scalars. For the nondimensional gradient of wind speed ( ), values measured close to tree top yield a correction factor that can vary from values of 1.1 or 1.7 (Raupach, 1979;Garratt, 1980;Mölder et al., 1999) all the way up to 2.5 (Högström et al., 1989). Regardless of the absolute value of the 's, the majority of studies over forests find that appears to be less affected by the roughness elements than its scalar counterparts (see for example Table 1 of Cellier andBrunet, 1992 andFigs. 2-4 of Mölder et al., 1999). ...
The failure of the Monin–Obukhov Similarity Theory (MOST) in the roughness sublayer is a major problem for the estimation of fluxes over tall forests, whenever indirect methods that rely on MOST, such as flux-gradient or the variance method, are involved. While much research focuses on micrometeorological measurements over temperate-climate forests, very few studies deal with such measurements over tropical forests. In this paper, we show evidence that some similarity functions over the Amazon forest are somewhat different from temperate forests. Comparison of the nondimensional scalar gradients canonical values for the inertial sublayer with our measurements in the roughness sublayer showed smaller deviations than what is usually reported for temperate forests. Although the fluxes of water vapor and CO2 derived from mean profiles show considerable scatter when compared with the eddy covariance measurements, using calibrated dimensionless gradients it is possible to estimate their mean daily cycle during the period of measurement (36 days in May and June, transition between rainy and dry season). Moreover, since mean ozone profiles were available, although without the corresponding eddy covariance measurements, mean daily ozone fluxes were calculated with the flux-gradient method, yielding a nighttime value of −0.05 and a daily peak of −0.45 μg m⁻² s⁻¹ (−1.04 and −9.37 nmol m⁻² s⁻¹, respectively). These values are comparable to previously measured fluxes in the literature for the Amazon forest.
... (129)-(133) the experimental data of Danberg [68], Squire [69] and Mabey et al. [70] were used. The velocity profiles are plotted with the transformation defined by Eq. (82). The enthalpy behavior is tested with the following transformation ...
... While a clear distinction is made in the literature regarding the behavior of the roughness lengths for the velocity and temperature fields (see, e.g., the works of Malhi [80]) and Sun [81]), the position of the error in origin (ε) for both fields is normally considered identical or even not considered in the investigations. In fact, Raupach [82] argues that the error in origin is normally considered property independent for the pragmatic reason that independent assessments of ε and ε T are not available. ...
The present work studies the prevalence of logarithmic solutions in the near wall region of turbulent boundary layers. Local solutions for flows subject to such diverse effects as compressibility, wall transpiration, heat transfer, roughness, separation, shock waves, unsteadiness, non-Newtonian fluids or a combination of these factors are discussed. The work also analyzes eleven different propositions by several authors for the near wall description of the mean velocity profile for the incompressible zero-pressure-gradient turbulent boundary layer. The asymptotic structure of the flow is discussed from the point of view of double limit processes. Cases of interest include attached and separated flows for the velocity and temperature fields.
... Thus, any disturbances to the variance function caused by storage or transport (or horizontal advection over other surfaces) also affect the FG (and vice-versa). Indeed, we found high correlation between the variance transport and flux transport (w′w′s′, not shown here), which is aligned with earlier work documenting the role of the flux transport term in the breakdown of MOST (Raupach, 1979;Simpson et al., 1998). ...
Plain Language Summary
The Monin‐Obukhov Similarity Theory (MOST) is a cornerstone of Earth observations and models. It defines a set of functions that are commonly used to estimate the exchange of heat, water vapor, and other trace gases between the surface and the atmosphere. MOST was originally formulated for “ideal” conditions that rarely prevail in the real world (e.g., fair steady weather and large flat surfaces with little spatial variation in surface cover or moisture conditions). Here, we show that the theory may be equally inaccurate under supposedly ideal conditions where its assumptions are met. We investigate the performance of MOST above a large lake, identifying additional constraints on its performance related to the behavior of turbulence in the atmosphere. One consequential finding is that the theory misrepresents the exchange of small fluxes, which are prevalent over lakes and oceans. In our analyses, it predicted high CO2 fluxes from the lake when in reality the fluxes were very small, a problem that can hinder the understanding of the global carbon cycle. We show that the relaxed eddy accumulation method, an alternative to MOST, not only outperforms, but is also more robust to deviations from ideal conditions, representing small fluxes more accurately.
... In more realistic setups, where fluxes from the surface are calculated by a LSM, MO is providing momentum flux and u * and couples the LSM to the atmospheric part (Talbot, Bou-Zeid, and Smith, 2012). According to Raupach (1979) it should also not be used over forest canopies because their structure enhances turbulence compared to a flat surface. Sullivan, McWilliams, and Moeng (1994) find better agreements in their simulated wind profiles with MO under strongly convective conditions than during strong shear. ...
A Large-Eddy Simulation (LES) using the Weather Research and Forecasting (WRF) model is set up in a computationally efficient way, directly driving the single domain with reanalysis data as boundary conditions. The simulation represents two real episodes over a well-known and real area. It is shown that the model successfully produces turbulent structures as they are known from idealized LES in literature and that the inertial subrange of the turbulence spectrum is appropriately resolved. The simulated wind field is evaluated with measurements taken during the ScaleX-campaigns by a triple Doppler Lidar setup that can measure all three wind components with a high temporal and vertical resolution throughout the atmospheric boundary layer. Model results sufficiently recreate the measured wind speed and direction as well as the development of daytime and nocturnal boundary layers. The coarse spatial and temporal resolution of the boundary conditions limits the accuracy of the model, shown by the representation of low-level jets. A katabatic flow reveals that the model successfully produces local weather phenomena that are not present in the boundary conditions and proves that the model output can be considered as a four-dimensional representation of the flow structures for a known area. This is not achievable with measurements. The implementation of realistic soil information (moisture and temperature) allows for a simulation of the sensible and latent heat fluxes. The advantage of the model over measurements here lies in the possibility to evaluate the turbulent fluxes at every location and height and the chance to evaluate the dependence of the fluxes on the soil properties below. The presented setup can be used to gather in-depth knowledge of the small-scale flow structures in a known area or to generalize soil-atmosphere interactions for large-area climate models.
... Further, the validity of MOST is restricted to the areas sufficiently distant from the roughness elements. The classic concept of the structure of the urban boundary layer (e.g., Arnfield, 2003;Piringer et al., 2002) assumes a subdivision of the urban surface layer into a roughness sublayer (RSL; Raupach, 1979), with its thickness being few times the roof height, and an inertial (dynamic) sublayer (Roth, 2000) aloft. The air masses flow in RSL is dominated by individual roughness elements and consists of numerous wakes and plumes of heat, moisture, and pollutants. ...
This study explores the possibility of estimation of the sensible surface heat flux using satellite-derived surface temperature and road pavement temperature together with in-situ wind and air temperature measurements by the profile method. A 10-year series of data from the roadside weather observation network was used. This dataset contained wind (measured at 5.8–9.5 m above ground) and air temperature (measured at 2.6–4.8 m) together with road surface temperature. Another dataset consisted of 254 simultaneous MODIS observations. A high correlation (0.94) of the surface temperature measured by both methods was noted despite coarse pixel size. We considered satellite-derived surface temperature to determine the sensible heat flux by the profile method; these results were compared to the values obtained using road temperature measured by pavement-mounted sensors. While the overall correlation is relatively strong (0.70) and considerable systematic differences exist, the values of heat flux calculated at different locations show a high spatial coherence - either when using the in situ pavement temperature (correlation ranging from 0.84 to 0.94 for daytime and 0.63–0.84 for nighttime) or the satellite-derived temperature (correlation coefficient 0.72). In most cases, differences between the two flux estimates can be linked to local factors such as the land use structure.
... Το 2004 ( (Oliver 1971, Thom et al. 1975, Thompson and Pinker 1975, Raupach 1979, Gardiner 1994, Zoumakis 1995, Raupach et al. 1996, Mölder et al. 1999, Lalic et al. 2003, Aubrun and Leitl 2004, Stangroom 2004, Krzikalla 2005, Wang and Cionco 2007 ανάπτυξης, για τα έτη 1999, 2000, 2002, 2004, 2005 και 2006. Συγκεκριμένα η απουσία φύλλων το χειμώνα οδηγεί σε υποβιβασμό της θέσης του επιπέδου όπου απορροφάται η ορμή, ενώ σε πλήρες φύλλωμα το επίπεδο αυτό ανυψώνεται. ...
This study is a contribution to understanding the ways and mechanisms with which tree-stands interact with the environment, forming the micrometeorological regime of the soil-plant-atmosphere system, along with expanding knowledge on the mass and energy exchanges between vegetation and the atmosphere, under the Mediterranean climate conditions. The thesis is focused on the investigation of the micrometeorology of a natural deciduous ecosystem, compared to the weather conditions above, the specification of the interactions between the micrometeorological parameters on a diurnal, seasonal and annual basis (combined with the phenological phases of the vegetation), the differentiation of the micrometeorological regime following a forest fire or logging, the study of the weather effects on the vegetation water requirements and the relationship between water consumption and production, the evaluation of defense and adaptation mechanisms of Mediterranean ecosystems against extreme weather and climate conditions, the evaluation of the forest contribution on CO2 absorption, the study of radiation quantity, quality and distribution in and use by the canopy and finally the study of the ecosystem-environment energy exchanges.
Research was accomplished in a selected natural deciduous oak forest within the region of Corinth, S. Greece, where a well equipped micrometeorological station was placed. The data covers the period 1999-2006 with some missing gaps.
The results of the study show that the main portion of the global solar radiation, Rs and specifically the photosynthetically active radiation, PAR, is captured by the tree-tissues even when there is no foliage. Due to selective absorption of PAR, the light that finally reaches the forest floor is extremely reduced. Logging increases the radiation transmission and reduces reflection and absorption by the canopy, although radiation distributes more uniformly in the foliage. Crawling-fire effect on the optical properties of the ecosystem is rather periodic, because of changes in the properties of the ground only. The seasonal optical properties variation can be used for the accurate identification of the phenological stages of the trees. The exponential radiation model for the radiant energy distribution in the canopy gives satisfactory results, although the deciduous canopy architecture is non uniform.
The temperature and relative humidity profiles inside and over the canopy show an almost mirror effect to each other. During the day, maximum temperature and minimum relative humidity are observed at the top of the forest. Vapor pressure deficit profile is almost identical to that of temperature and vapor pressure, being maximum at the canopy top, reduces with height especially in summer. At night, the temperature and vapor pressure deficit profiles are positive, whereas those of relative humidity and vapor pressure are negative (in all seasons except in winter). Vapor pressure values increase with height in the forest and stabilize above canopy top. The daily temperature range over the ecosystem is relatively small, becoming maximum near the ground, especially at full foliage. The layer of dead leaves covering the forest floor protects roots from frost damage in winter and high temperature and evaporation loss in summer. The period favoring vegetation growth is quite long, but a significant part of it, is characterized by thermal stress.
Logging reduces drought conditions in foliage - by allowing better air mixture - and daily relative humidity range. In extremely low soil moisture conditions (mainly in August) oak trees inhibit their growth. Trees have been adapted to reduced water availability during summer, by developing an extended root system, which allows the exploitation of water in deeper layers. Development over a clay soil layer and formation of a relatively small leaf area increase their ability to survive under the intensive drought Mediterranean conditions. The soil-covering quite thick layer of slowly decomposing dead leaves reduces water losses through evaporation and strengthens vegetation to cope with dry periods.
The wind velocity profile over the canopy follows the typical logarithmic form, day and night. The wind speed values inside the forest (at and below the top) are very small. The canopy roughness parameters, d and zo, take the values 9.6±1.3 m and 1.2±0.9 m, respectively, at full leaf development and 11.2 m and 1.2 m at senescence. Forest surface seems to be very rough, absorbing momentum effectively. Limited tree logging has a negligible effect on wind profile, as vegetation gaps created seem to encourage vertical rather than horizontal air flow.
Net radiation fluxes, Rn, are almost 75% of Rs. Solar radiation is used more effectively during summer than in winter and at midday than at noon or morning. The thermal stress reduces the effective use of radiation but logging seems to increase effectiveness. On a 24 h basis, during the fully leafed period, Rn is composed by 53-56% latent heat, LE, and by 27-30% sensible heat, H. In August, the percentages become 16% and 31%, respectively, under rather extreme dry atmospheric conditions and reduced soil water availability.
The energy absorbed by the canopy (Rn-G) is “consumed” by 81% for H and LE (in June and July), whereas the rest is stored in plant tissues as heat, ΔΗ. ΔH becomes even greater in August, due to water shortage not allowing the productive use of the absorbed solar radiation.
Windspeeds greater than 0.6 m/s favor faster air mixing, reducing LE and H fluxes. However, a speed increase up to 0.6 m/s linearly increases heat fluxes. When trees are fully leafed and during daytime, the Bowen ratio, b, takes values between 0.70-1.67 and most of the time is greater than unit (with smaller values at midday). About 37-67% of the sum (LE+H) is devoted to LE (with lower percentages at midday). Soil heat flux, G, is quite small and gets positive values only a few hours during midday. The evapotranspiration efficiency of PAR absorbed by the ecosystem (ε=LE/PARabs) during the fully leafed period is about 0.69, a relatively small value (compared to similar ecosystems in northern Europe), due to reduced water availability in summer.
The annual water requirements of the ecosystem are about 440 mm, when the annual precipitation in the region is much greater. However, because of its imbalanced time distribution, the trees face water stress in summer, which becomes more intensive in August. The daily mean evapotranspiration rate is maximum in June and July (3.5 mm d-1), with an even greater value at midday (0.43 mm h-1). Under reduced soil water availability (as in August), stomatal resistance increases and water loss reduces rapidly. Stomatal closure is, thus, a defense mechanism that the vegetation calls up under strong drying atmospheric forces. Then, even at midday, the mean evapotranspiration rate is smaller than 0.16 mm h-1.
CO2 absorbance is maximum when the canopy has leaves. In other seasons, the ecosystem is functioning as a source rather than as a sink of carbon. The rates of CO2 absorption are increasing with absorbed radiation fluxes, becoming almost zero when PARabs is lower than 220 W m-2. The annual net carbon uptake by the ecosystem is 6.37 t C ha-1 y-1, when the greater monthly CO2 absorbance is achieved during June and July (mean value 752 g CO2 m-2 month-1) and especially at midday (0.82 g C m-2 h-1). On an annual basis, about 13,500 t CO2 are absorbed by the whole ecosystem (580 ha). Every tree absorbs about 7.3 kg CO2 per year. In August, CO2 absorbance reduces rapidly because of low photosynthetic rates and becomes about half of the maximum (July) values. Water use efficiency (WUE) is about 0.20 mmol H2O/μmol CO2 (water loss of 1 kg produces 3.3 g C). Maximum productive rates are achieved when soil moisture is about 0.35. At lower values CO2 and H2O fluxes reduce almost linearly. Mean daily values of VPD greater than 2 kPa lead to about 50% reduction in productivity.
Although the deciduous ecosystem develops under rather adverse (xerothermic) climatic conditions seems to be quite productive. It has relatively short water needs and developed adaptation (survival) mechanisms, such as the use of morning dew as an additional water source in summer, the root system development for deeper soil water use, the biomass development over a water holding clay soil layer, the evaptoranspiration and photosynthesis reduction under extremely dry conditions via stomatal closure, the development of a relatively small leaf area, the relatively inefficient use of the absorbed by leaves radiation and finally the existence of a thick layer of dead leaves covering the forest floor and protecting the root system against thermal and water stresses.
... The latter flux estimates were substantially smaller than the former. This anomaly in the flux-profile relationships was confirmed by Garratt (1978Garratt ( , 1980 at rough sites with scattered trees and shrubs, by Raupach (1979) in pine forests, and by Raupach et al. (1980) over rough surfaces in a wind tunnel. They all found that the non-dimensional vertical gradients of scalars, and of wind velocity in some cases, which had been shown to be universal functions of z/L in the ISL, become significantly smaller than expected when approaching the canopy from above. ...
Studying the microclimate of plant canopies has long motivated scientists in various
research felds such as agronomy, ecology or silviculture, and almost a century has passed
since the frst measurements of wind speed in a forest stand were published in the scientifc
literature. The behaviour of wind in canopies is an essential component of their microclimate, which largely conditions the rate of exchange of heat, water vapour, and other gases
and particles of interest with the atmosphere. This review examines the evolution of our
understanding of turbulent fow in plant canopies, focussing on the period that covers the
last ffty years (1970–2020). We frst describe how our knowledge and ideas have evolved
since canopy fow became a topic of interest, and show how the 1970s was a pivotal decade
in this feld. Until then, canopy turbulence was considered to result from the superposition of standard surface-layer turbulence and small-scale turbulence generated in the wakes
of plant elements. However, it was progressively found that the fow in plant canopies is
dominated by large coherent structures, giving canopy turbulence unique characteristics.
We thus describe the particular nature and structure of canopy fows, based on experimental observations accumulated over several decades. We show how canopy turbulence was
reconsidered on the basis of a now widely-accepted analogy with a plane mixing layer, and
we examine the signifcance of a key parameter, the “canopy-shear length scale”. Investigating the efects of canopy density and atmospheric stability, we then discuss the extent of
the mixing-layer analogy and the limits of our current understanding of canopy turbulence.
Finally, we review the modelling tools used in this feld and show how their development
has evolved to date to meet our needs. In conclusion, we present a historical summary of
the evolution of this research feld and suggest future directions.
[readable at https://rdcu.be/b7Jbt]
... The breakdown of the neutral logarithmic wind law, and in flux-profile relations generally, above tall crops and forests became apparent from 1975 onwards (e.g., Thom et al. 1975;Garratt 1978;Raupach 1979). The term "roughness sublayer" was almost certainly first used by Raupach et al. (1980) as part of a major wind-tunnel study on the breakdown of the log law close to a rough surface. ...
... The large roughness layer above a tall canopy also makes it difficult to apply many theories of wall flows as well as to apply and validate traditional 25 similarity theory (Katul et al., 1995). As compared to, for example, a thin grass layer, the tall geometry and internal structure of the forest may allow large turbulent structures within the canopy layer, which will interact with the overlying atmospheric flow (Raupach, 1979). This turbulence may either be generated by wind shear from interaction with the canopy geometry, or be generated and suppressed by local buoyancy effects (Baldocchi and Meyers, 1988). ...
Complex ecosystems such as forests make accurately measuring atmospheric energy and matter fluxes difficult. One of the issues that can arise is that parts of the canopy and overlying atmosphere can be turbulently decoupled from each other, meaning that the vertical exchange of energy and matter is reduced or hampered. This complicates flux measurements performed above the canopy. Wind above the canopy will induce vertical exchange. However, stable thermal stratification, when lower parts of the canopy are colder, will hamper vertical exchange. To study the effect of thermal stratification on decoupling, we analyze high resolution (0.3 m) vertical temperature profiles measured in a Douglas fir stand in the Netherlands using Distributed Temperature Sensing (DTS). The forest has an open understory (0–20 m) and a dense overstory (20–34 m). The understory was often colder than the atmosphere above (80 % of the time during the night, > 99 % during the day), and was regularly decoupled from the atmosphere (50 % of the time at night). The relationship between the temperature gradients and the friction velocity (u*) showed a clear threshold between coupling regimes. In particular, decoupling occurred when u*
... The eddy diffusivity for sensible heat can be calculated by employing Monin-Obukhov Similarity Theory (MOST) (Businger et al., 1971;Högström, 1988). However, MOST does not hold in the roughness sublayer above vegetation (Raupach, 1979), which can extend higher than double the vegetation height (e.g., Cellier & Brunet, 1992;Harman & Finnigan, 2007;Thom, 1975). Most observed gradients are located below this height. ...
Dry deposition of ozone is an important sink of ozone in near‐surface air. When dry deposition occurs through plant stomata, ozone can injure the plant, altering water and carbon cycling and reducing crop yields. Quantifying both stomatal and nonstomatal uptake accurately is relevant for understanding ozone's impact on human health as an air pollutant and on climate as a potent short‐lived greenhouse gas and primary control on the removal of several reactive greenhouse gases and air pollutants. Robust ozone dry deposition estimates require knowledge of the relative importance of individual deposition pathways, but spatiotemporal variability in nonstomatal deposition is poorly understood. Here we integrate understanding of ozone deposition processes by synthesizing research from fields such as atmospheric chemistry, ecology, and meteorology. We critically review methods for measurements and modeling, highlighting the empiricism that underpins modeling and thus the interpretation of observations. Our unprecedented synthesis of knowledge on deposition pathways, particularly soil and leaf cuticles, reveals process understanding not yet included in widely used models. If coordinated with short‐term field intensives, laboratory studies, and mechanistic modeling, measurements from a few long‐term sites would bridge the molecular to ecosystem scales necessary to establish the relative importance of individual deposition pathways and the extent to which they vary in space and time. Our recommended approaches seek to close knowledge gaps that currently limit quantifying the impact of ozone dry deposition on air quality, ecosystems, and climate.
... It should be noted here that our two approaches for estimating s w are not a result of Monin-Obukhov theory. Numerous authors [60][61][62][63][64] have shown that Monin-Obukhov theory does not adequately represent canopy turbulence. Instead, we use fits to observed s w profiles and the relationship 24 K ¼ s 2 w T L to infer the shape of the profile, which is then normalized to allow a smooth transition to resolved model layer K values above the canopy. ...
The chemistry of the Earth's atmosphere close to the surface is known to be strongly influenced by vegetation. However, two critical aspects of the forest environment have been neglected in the description of the large-scale influence of forests on air pollution: the reduction of photolysis reaction rates and the modification of vertical transport due to the presence of foliage. Here we show that foliage shading and foliage-modified vertical diffusion have a profound influence on atmospheric chemistry, both at the Earth's surface and extending throughout the atmospheric boundary layer. The absence of these processes in three-dimensional models may account for 59–72% of the positive bias in North American surface ozone forecasts, and up to 97% of the bias in forested regions within the continent. These processes are shown to have similar or greater influence on surface ozone levels as climate change and current emissions policy scenario simulations.
... Research on this issue has been carried out, for example, by Garratt (1978Garratt ( , 1980Garratt ( , 1983Garratt ( ,1992, Raupach (1979), Raupach et al. (1980), Cellier and Brunet (1992), Physick and Garratt (1995), Mölder et al. (1999), Harman and Finnigan (2007), Nakai et al. (2008aNakai et al. ( , 2008b and more recently by De Ridder (2010). The experimental work on the RSL effect has been conducted over various natural land surfaces ranging from tall agricultural crops to savannah forests. ...
... 90 Air temperature and enthalpy change versus radiation at departure station for Tablada -San Pablo analysis. R 2 (DT ) = 0.0191, R 2 (Dh) = 0.0261. ...
The purpose of this project is the development and testing of a new geographical surface heat exchange
measurement technique. The proposed approach is based on the indirect evaluation of advective moist
air heat fluxes and employs the most simple instrumentation available at the moment, consisting on a network
of automatic meteorological stations.
Urban surfaces will play a key role on this project, as it is focused on the evaluation of mean urban heat
exchanges. Consequently, this research connects with previous works about urban climatology and, more
specifically, its more noted manifestation, the Urban Heat Island (UHI). The Spanish city of Seville will be
used to test the model.
URI: http://hdl.handle.net/11441/44411
... For very rough surfaces (forest, urban areas. . . ), the influence of the surface can be significant at distances that are not negligible (up to several 15 canopy heights, e.g., Thom et al., 1975;Raupach, 1979) This layer is usually known as the roughness sublayer (RSL). Then, the introduction of a zero-plane displacement height, d , is a commonly used approximation. ...
Atmospheric dry deposition is typically modelled using an average
roughness length, which depends on land use. This classical
roughness-length approach cannot account for the spatial variability
of dry deposition in complex settings such as urban areas. Urban
canopy models have been developed to parametrise momentum and heat
transfer. We extend this approach here to mass transfer and a new
dry deposition model based on the urban canyon concept is
presented. It uses a local mixing length parametrisation of
turbulence within the canopy, and a description of the urban canopy
via key parameters to provide spatially-distributed dry deposition
fluxes. Three different flow regimes are distinguished in the urban
canyon depending on the height-to-width ratio of built areas:
isolated roughness flow, wake interference flow and skimming
flow. Differences between the classical roughness-length model and
the model developed here are investigated. Sensitivity to key
parameters are discussed. This approach provides
spatially-distributed dry deposition fluxes that depend on surfaces
(streets, walls, roofs) and flow regimes (recirculation and
ventilation) within the urban area.
... While in some studies of flux-gradient similarity within the forest RSL, m was found to be less than unity in the near-neutral range (e.g. Högström et al., 1989;Mölder et al., 1999;Raupach, 1979;Thom et al., 1975), other studies indicate that m is close to unity (e.g. Bosveld, 1997;Simpson et al., 1998;Dellwik and Jensen, 2005;Nakamura and Mahrt, 2001). ...
The local scaling approach was examined based on the multi-level measurements of atmospheric turbulence in the wintertime (December 2008–February 2009) stable atmospheric boundary layer (SBL) established over a heterogeneous surface influenced by mixed agricultural, industrial and forest surfaces. The heterogeneity of the surface was characterized by spatial variability of both roughness and topography. Nieuwstadt’s local scaling approach was found to be suitable for the representation of all three wind velocity components. For neutral conditions, values of all three non-dimensional velocity variances were found to be smaller at the lowest measurement level and larger at higher levels in comparison to classical values found over flat terrain. Influence of surface heterogeneity was reflected in the ratio of observed dimensionless standard deviation of the vertical wind component and corresponding values of commonly used similarity formulas for flat and homogeneous terrain showing considerable variation with wind direction. The roughness sublayer influenced wind variances, and consequently the turbulent kinetic energy and correlation coefficients at the lowest measurement level, but not the wind shear profile. The observations support the classical linear expressions for the dimensionless wind shear (ϕm) even over inhomogeneous terrain after removing data points associated with the flux Richardson number (Rf ) greater than 0.25. Leveling-off of ϕm at higher stabilities was found to be a result of the large number of data characterized by small-scale turbulence (Rf > 0.25). Deviations from linear expressions were shown to be mainly due to this small-scale turbulence rather than due to the surface heterogeneities, supporting the universality of this relationship. Additionally, the flux-gradient dependence on stability did not show different behavior for different wind regimes, indicating that the stability parameter is sufficient predictor for flux-gradient relationship. Data followed local z -less scaling for ϕm when the prerequisite Rf ≤ 0.25 was imposed.
... Above woody stands, the EC and the Bowen ratio methods are commonly used; aerodynamic methods or derivations are difficult or impossible to apply (Thom et al., 1975;Raupach, 1979), namely because of the very small gradients observed above these stands and the difficulty in finding appropriate functions to account for stability conditions. The Bowen ratio method should be applied with much caution whenever a large part of the radiation reaches the soil, as in many orchards, because the method supposes the same level for sensible and latent heat exchanges. ...
Irrigation management requires information on evapotranspiration (ET). The ET of a well irrigated crop (ETc) is usually approached through an empirical equation using reference ET (ETo) and crop coefficients (Kc): ETc = ETo × Kc. Discrepancies have been observedbetween Kc measured in several row crops and Kc values recommended in currently used manuals. Therefore, a need arises to address this problem via further field measurements of ET. Some limitations to the application of micrometeorological and hydrological methods tomeasure ET in small fields or in woody crops are briefly described and sap flow methods (SF) are presented as an alternative to quantify transpiration (T), the major component of ET. Aclear underestimation of T with SF data was observed in several conditions, when compared to data from eddy covariance (EC) micrometeorological method. By combining robust, low cost SF methods with reliable EC measurements, an EC-SF relationship can be developed to correct SF measurements. Using this combination, ET and Kc data series can be extrapolated in time (e.g., for a whole season) or space (when micrometeorological methods are not suitable, as in small areas). Some case studies show the combination of complementary ECSF methods to follow the seasonal variation of ET and Kc (vineyards, kiwi and peach orchards) proving its usefulness in long term studies. A second aspect discussed is the fact that calculating crop ET as ETo × Kc implicitly assumes continuous adequate available soil water for optimum plant growth. However, even for irrigated crops, ET is often below ETc andcalled actual ET (ETa). Besides, due to growing water scarcity, deficit irrigation strategies are increasingly being explored. Under water stress, the reduction of ET due to stomatal closure is higher for rough canopies and/or woody crops than for low crops and cannot be neglected. Therefore, for practical purposes, ETa can be estimated as ETo × Kc × Ks where Ks is a stress coefficient (Ks = ETa/ETc). The relationship between Ks and soil water depletion (SET since last irrigation) can be used to estimate how much water to apply and when to irrigate. This relationship varies with soil type, ET rate, and root distribution. Hence, it must be adjusted, which can be done empirically as a function of observations of plant water status. The use of relationships between water stress indicators improves the identification of threshold values for practical purposes.
... As suggested by other authors (Lee et al., 2004;McNaughton and Laubach, 1998), the sensible heat flux might be generated from other sources in addition to horizontal heat advection. The temperature differences between shaded and non-shaded parts of the canopy can generate convective cells (Raupach, 1979), those vertical movements could result in the injection of sensible heat into the canopy (Berliner, 1998;Figuerola and Berliner, 2006). From Fig. 5a, a maximum upward H in the sunlit (g sun ) and inter-row (g irow ) areas occurred at midday in November (spring) and three hours after a maximum downward H at the soil surface of the shaded (g sh ) area occurred. ...
A primary sink of air pollutants and their precursors is dry deposition. Dry deposition estimates differ across chemical transport models, yet an understanding of the model spread is incomplete. Here, we introduce Activity 2 of the Air Quality Model Evaluation International Initiative Phase 4 (AQMEII4). We examine 18 dry deposition schemes from regional and global chemical transport models as well as standalone models used for impact assessments or process understanding. We configure the schemes as single-point models at eight Northern Hemisphere locations with observed ozone fluxes. Single-point models are driven by a common set of site-specific meteorological and environmental conditions. Five of eight sites have at least 3 years and up to 12 years of ozone fluxes. The interquartile range across models in multiyear mean ozone deposition velocities ranges from a factor of 1.2 to 1.9 annually across sites and tends to be highest during winter compared with summer. No model is within 50 % of observed multiyear averages across all sites and seasons, but some models perform well for some sites and seasons. For the first time, we demonstrate how contributions from depositional pathways vary across models. Models can disagree with respect to relative contributions from the pathways, even when they predict similar deposition velocities, or agree with respect to the relative contributions but predict different deposition velocities. Both stomatal and nonstomatal uptake contribute to the large model spread across sites. Our findings are the beginning of results from AQMEII4 Activity 2, which brings scientists who model air quality and dry deposition together with scientists who measure ozone fluxes to evaluate and improve dry deposition schemes in the chemical transport models used for research, planning, and regulatory purposes.
Organised motion of air in the roughness sublayer of the atmosphere was investigated using novel temperature sensing and data science methods. Despite accuracy drawbacks, current fibre-optic distributed temperature sensing (DTS) and thermal imaging (TIR) instruments offer frequent, moderately precise and highly localised observations of thermal signal in a domain geometry suitable for micrometeorological applications near the surface. The goal of this study was to combine DTS and TIR for the investigation of temperature and wind field statistics. Horizontal and vertical cross-sections allowed a tomographic investigation of the spanwise and streamwise evolution of organised motion, opening avenues for analysis without assumptions on scale relationships. Events in the temperature signal on the order of seconds to minutes could be identified, localised, and classified using signal decomposition and machine learning techniques. However, small-scale turbulence patterns at the surface appeared difficult to resolve due to the heterogeneity of the thermal properties of the vegetation canopy, which are not immediately evident visually. The results highlight a need for physics-aware data science techniques that treat scale and shape of temperature structures in combination, rather than as separate features.
Dry deposition is an important sink of tropospheric ozone and influences background and episodic ozone air pollution. Plant canopies remove ozone through uptake by plant stomata, leaf cuticles, and soil. Stomatal uptake of ozone injures vegetation, thereby altering local‐to‐global water and carbon cycling. Observed ozone fluxes are used to inform dry deposition parameterizations in chemical transport models but represent the net influence of several poorly constrained processes. Advancing understanding of the processes controlling dry deposition is key for building predictive ability of the terrestrial ozone sink and plant damage. Here, we constrain the influence of spatial structure in turbulence on ozone dry deposition with large eddy simulation coupled to a multilayer canopy model. We investigate whether organized turbulence separates areas of efficient leaf uptake from areas of high or low ozone mixing ratios. We simulate summertime midday conditions at three homogenous deciduous forests with varying leaf area, soil moisture, and ambient humidity. Sensitivity simulations perturb atmospheric stability, parameters related to ozone dry deposition, how quickly stomata respond to local atmospheric variations, and entrainment of ozone from atmospheric boundary layer growth. Overall, we find a low covariance between ozone and leaf uptake, in part due to counteracting influences from micrometeorological variations on ozone and leaf uptake individually versus the influence of leaf uptake on ozone. The low covariance between ozone and leaf uptake suggests that dry deposition parameterizations and interpretations of ozone flux observations can ignore the influence of organized turbulence on dry deposition.
Climate Change and Terrestrial Ecosystem Modeling - by Gordon Bonan February 2019
This chapter is going to introduce the basic laws for the shape of the vertical profiles of wind speed and turbulence in a flat, horizontally homogeneous atmospheric boundary layer (ABL) over land because this is the simplest surface type.
Ammonia is a very important air pollutant, playing an widespread role in acid pollution chemistry. The knowledge of the deposition processes (wet and dry) is of extreme importance for both long-range transport modelling and evaluation of critical loads for specific ecosystems.
By characterizing the dynamics of a convective boundary layer above a relatively sparse and uniform orchard canopy, we investigated the impact of the roughness-sublayer (RSL) representation on the predicted diurnal variability of surface fluxes and state variables. Our approach combined numerical experiments, using an atmospheric mixed-layer model including a land-surface-vegetation representation, and measurements from the Canopy Horizontal Array Turbulence Study (CHATS) field experiment near Dixon, California. The RSL is parameterized using an additional factor in the standard Monin–Obukhov similarity theory flux-profile relationships that takes into account the canopy influence on the atmospheric flow. We selected a representative case characterized by southerly wind conditions to ensure well-developed RSL over the orchard canopy. We then investigated the sensitivity of the diurnal variability of the boundary-layer dynamics to the changes in the RSL key scales, the canopy adjustment length scale, Lc, and the β = u*/|U| ratio at the top of the canopy due to their stability and dependence on canopy structure. We found that the inclusion of the RSL parameterization resulted in improved prediction of the diurnal evolution of the near-surface mean quantities (e.g. up to 50 % for the wind velocity) and transfer (drag) coefficients. We found relatively insignificant effects on the modelled surface fluxes (e.g. up to 5 % for the friction velocity, while 3 % for the sensible and latent heat), which is due to the compensating effect between the mean gradients and the drag coefficients, both of which are largely affected by the RSL parameterization. When varying Lc (from 10 to 20 m) and β (from 0.25 to 0.4 m), based on observational evidence, the predicted friction velocity is found to vary by up to 25 % and the modelled surface-energy fluxes (sensible heat, SH, and latent heat of evaporation, LE) vary up to 2 and 9 %. Consequently, the boundary-layer height varies up to 6 %. Furthermore, our analysis indicated that to interpret the CHATS measurements above the canopy, the contributions of non-local effects such as entrainment, subsidence and the advection of heat and moisture over the CHATS site need to be taken into account.
For approximately the last 20 years the incentive for developing advanced parameterizations of land-surface processes has been provided by the great issues of climate modeling: Are we able to monitor the short-term global water budget of the planet and its long-term global change? However, mesoscale modelers have long been aware of the importance of correctly specifying the surface energy budget that forms the lower boundary condition of their models, since the thermal circulations that are induced by the spatial variability of the heat and moisture fluxes into the atmosphere are an integral part of mesoscale meteorology.
Using the flux gradient approach dry deposition of SO2, NOx and O3 to a 28 m tall spruce stand in the catchment “Grosse Ohe” in the National Park “Bayerischer Wald” is being studied. This catchment has a size of 19.1 km2 and is situated about 200 km northeast of Munich. The elevation reaches from 770 m to 1452 m above sea level. The catchment was established in 1978 as a forest hydrological reference basin now serving as an experimental watershed for water quality studies too.
Before the main deposition began in July 1986, a pre-experiment was performed in the “Ebersberger Forst” near Munich to test the performance of the instrumentation. For a day of this period the turbulent diffusivities are calculated showing considerable discrepances between aerodynamic and energy balance approach. At the new site, for which first concentration profiles of SO2 and NOx are reported, a taller measuring tower than at the test site is operated providing meteorological and chemical measurements up to 51 m height.
Recent experimental evidence over forests indicates that, due to surface effects, turbulent transfer coefficients for momentum and sensible heat exchange differ in a manner which is not predicted by the familiar diabatic influence functions. The question arises as to whether surface influences can also cause differences between the sensible and latent heat exchange coefficients, thus invalidating the Bowen ratio approach to water loss estimation over forests. The matter was examined by evaluating the Bowen ratio at three positions above the canopy of a forested wetland to see if systematic differences might be found between values obtained at different levels. Differences were found which appeared to be consistent with a radiatively controlled variation in zero-plane displacement or source location for sensible heat. However, the relationship does not appear to be particularly strong, nor do Bowen ratios obtained at different heights above the ground disagree sufficiently to justify modification or abandonment of the procedure in its present form.
Evapotranspiration was estimated from a mature pine forest at Jädraås, central Sweden, from May 27 to September 2, 1977. Estimates by the energy balance Bowen ratio method were achieved from direct mast measurements and separate interpolation of evaporation and transpiration measurements by an energy exchange model. Statistical errors and systematic sensor errors were given for the direct measurements but no evaluations of fetch and stability conditions were made. Estimates by the water balance method were based on indirect estimates of percolation by a soil water model. For the period considered the energy balance and water balance estimates of evapotranspiration were 350 and 150 mm, respectively. In spite of evaluation deficiencies, the discrepancy was so significant that theoretical explanations must be sought. It is proposed that one such explanation could be that the similarity principle is not valid over rough forest surfaces.
This chapter is going to introduce the basic laws for the shape of the vertical profiles of wind speed and turbulence in a flat, horizontally homogeneous atmospheric boundary layer (ABL) over land. The logarithmic wind profile and the power law profile are introduced and compared. The impact of thermal stratification of the air on the profiles is discussed. Extension of profile laws into the Ekman layer are presented. Internal boundary layers and low-level jets are addressed. Finally, specific features of wind and turbulence profiles over cities and forests are presented, too.
The Scientific Plan for GEWEX draws together and enhances a range of climate research activities which have the specific scientific objectives:
to determine the hydrological cycle and energy fluxes by means of global measurements of observable atmospheric and surface properties;
to model the global hydrological cycle and its effects on the atmosphere and oceans; and
to develop the ability to predict the variations of global and regional hydrological processes and water resources, and their response to environmental change.
INTRODUCTIONDRY DEPOSITION OF GASESBULK RESISTANCE (“BIG LEAF”) MODELDRY DEPOSITION OF PARTICLESMEASURING DRY DEPOSITIONWET DEPOSITION
This paper argues that the active turbulence and coherent motions near the top of a vegetation canopy are patterned on a plane mixing layer, because of instabilities associated with the characteristic strong inflection in the mean velocity profile. Mixing-layer turbulence, formed around the inflectional mean velocity profile which develops between two coflowing streams of different velocities, differs in several ways from turbulence in a surface layer. Through these differences, the mixing-layer analogy provides an explanation for many of the observed distinctive features of canopy turbulence. These include: (a) ratios between components of the Reynolds stress tensor; (b) the ratio K
H
/K
M
of the eddy diffusivities for heat and momentum; (c) the relative roles of ejections and sweeps; (d) the behaviour of the turbulent energy balance, particularly the major role of turbulent transport; and (e) the behaviour of the turbulent length scales of the active coherent motions (the dominant eddies responsible for vertical transfer near the top of the canopy). It is predicted that these length scales are controlled by the shear length scale L
s
= U(h)/U′(h) (where h is canopy height, U(z) is mean velocity as a function of height z, and U′ = dU/dz). In particular, the streamwise spacing of the dominant canopy eddies Λx
= mL
s
, with m = 8.1. These predictions are tested against many sets of field and wind-tunnel data. We propose a picture of canopy turbulence in which eddies associated with inflectional instabilities are modulated by larger-scale, inactive turbulence, which is quasi-horizontal on the scale of the canopy.
The interaction between air flow and exchange processes in the canopy is currently being re-examined. This has been prompted by a general disillusionment with the classical technique for evaluating heat and mass transfer from micrometeorological profiles (the one-dimensional flux-gradient approach). Not only is the technique inapplicable to non-homogeneous vegetation and uneven terrains, but complete failure to yield correct results has been demonstrated for forests (where heat seems to flow against the temperature gradient) and in model stands in a wind tunnel. More recently, instruments with a very rapid response time enable heat and mass transfer to be measured using eddy-correlation, and furnish turbulence statistics of the u, v, and w components of wind at different places in the canopy. Many problems involving wind in the canopy are more amenable to analysis by a theory, which rests on the dispersal of materials in parcels of air rather than quasi-diffusion in one dimension. The behavior of propagules in air, the mechanical excitation of tall plants, and the optimal design of shelter are all examples of such problems.
The legitimacy of using bulk aerodynamic and canopy resistances in surface energy budget equations is examined in this paper. Specifically, the variation of the effective source heights for momentum, water vapor, and heat is analyzed by estimating zero plane displacements for a modeled soya bean canopy, when model leaf surface resistances are changed, causing varying stability conditions. Also, the changes in bulk canopy resistances are examined as a function of the leaf surface resistances. The model used is a linked soil-plant-atmosphere model based on higher-order closure principles. The model confirms previous reports of major soil contributions to evapotranspiration under certain conditions. The erratic behavior of the zero plane displacements for water vapor and heat as a function of leaf surface resistance demonstrates that the concept of a single effective source-sink height is not easily applied to plant canopies. The zero plane displacement for momentum was found to be consistent with previous results, independent of leaf surface resistance. Canopy resistance changes qualitatively match leaf surface resistance changes, but quantitative differences can be large. The canopy resistance changes less quickly than the leaf surface resistance even when soil evaporation is not a factor.
In the 1970s, scientists met with difficulties in estimating fluxes over tall vegetation, like forests, using flux-gradient relationship (Raupach 1979). The roughness of the exchanging surface drive to efficient turbulent mixing reducing the concentration gradient and invalidating Monin-Obukhov similarity theory (Lenschow 1995). In the 1990s, the eddy covariance (EC) method was developed and turned out to be very promising for CO2, latent, and sensible heat exchange quantification over these tall ecosystems. When the first networks of EC measurements were implemented (EuroFlux, Valentini et al. 2000; Ameriflux, Running et al. 1999), they included then a majority of forest sites. The other reasons for this historical forest leading position were their large terrestrial cover (FAO 2005 report) and their potentiality to store carbon over long periods (Valentini 2003).
The report contains the authors lecture notes to courses in micro scale meteorology and atmospheric turbulence. The course has aimed to touch upon both the basic theories and the special formulations aiming at applications. The structure of the course can be seen from the “Content”. It has a chapter on concepts and statistics, two chapters on the basic fluid dynamics and turbulence closure. Three chapters on various atmospheric scaling laws, Ekman layer, surface layer and total boundary layer. It includes one chapter on the roughness and the surface–atmosphere exchange, one chapter on heterogeneous boundary layers, and one on atmospheric diffusion and turbulence. It has two chapters on boundary layer climatology involving radiation, temperature and wind issues, and finally a chapter discussing measurement and instrumental problems. The report has been loosely edited compared to the original notes.
Two-dimensional spectral analysis provides a comprehensive description of both the structure and scales of pattern in a spatial data set. It assumes no structural characteristics in the data prior to analysis. The authors demonstrate the advantage of this in an ecological situation where pattern may exist over a range of scales, be anisotropic and non-stationary. All these may be important features relating to the underlying biological and environmental pattern generating mechanisms and should be explained prior to model building. They discuss general problems of estimation, discrimination and interpretation of spectra and illustrate them through the analysis of a forest canopy data set.
During the summer of 1974, simultaneous heat flux measurements were made over a pine forest in three ways:
(a)
Using the Bowen ratio - Energy Budget technique, with the Bowen ratio estimated from temperature and humidity profiles measured with two pairs of wet-and dry-bulb thermometers at six levels.
(b)
Using the Bowen ratio - Energy Budget technique, with the Bowen ratio estimated from temperature and humidity measurements using pairs of wet-and dry-bulb thermometers mechanically interchanged every ten minutes.
(c)
Using the Eddy Correlation - Energy Budget technique, with a direct measurement of the sensible heat flux made by a simple eddy correlation apparatus.
Methods (b) and (c) are shown to give similar results apart from a systematic difference of about 25% in the measured sensible heat flux. This corresponds to an underestimate of the sensible heat flux by the eddy correlation apparatus.Although sometimes consistent with the other two methods, on occasions method (a) gave results which were significantly different from both (b) and (c). When differences occurred, they tended to be systematic and persistent over individual days; but they could change magnitude and sign if the particular sensors used at each level in the profile were rearranged. The experimental program used to collect these and previous data involved the rearrangement of sensors on a regular (two day) time scale. It is shown that, when averaged over several such rearrangements, method (a) produces median values of surface resistance which are more in keeping with those produced by the other methods. This is taken to imply that data previously gathered in this way can be used to produce physically reasonable results providing they are averaged over several days.On the basis of the results presented, recommendations are made on future experimental work in forest micrometeorology.
Extensive micrometeorological measurements have been made over and within a Scots pine canopy. The structure of the canopy and its surface are described by measurements made on individual trees and by constructing a two-dimensional power spectrum of canopy surface height. This latter technique reveals important structural features which are not apparent when measurements on individual trees are considered alone.A comparison is made between the two-dimensional spectrum of this surface and that of surfaces with very different values of kB−1 and the relationship between surface structure and wind flow pattern is discussed.
An extensive set of measurements of turbulent fluxes of sensible heat, water vapour and momentum together with mean profiles of temperature, water vapour and wind speed at a ‘non‐ideal’ agricultural site in southern Sweden have been analysed in terms of the Monin‐Obukhov similarity theory. The fluxes of sensible heat, H , and water vapour, E , have been determined with the eddy correlation method, the accuracy of H + EL v being c . Φ 12% according to comparison with net radiation minus ground heat flux. The momentum flux has been determined from low level wind measurements, with a stability dependent ‘skin friction method’.
During stationary conditions with winds from ‘undisturbed’ directions (extensive forest areas more than 3 km distant) and unstable stratification, the data for dimensionless wind and temperature gradients, Φ m and ϕ h , respectively, are well described by the expressions put forward by Businger et al. (1971), with von Kàrmàn's constant, k = 0.35. The corresponding dimensionless water vapour gradient, Φ e , is shown also to follow similarity during these conditions (although exhibiting larger scatter than the two other plots), coinciding with Φ h for strong instability but approaching Φ m = 1.35 Φ h , at neutrality.
For stable stratification the dimensionless profiles do not follow similarity in this study, nor do cases with winds from a 700 m distant forest nor non‐stationary cases, as might be expected.
A combined energy balance and gradient approach is shown to give good results not only for the ‘ideal’, unstable case but also for non‐stationary conditions and for conditions with winds from the ‘disturbed’ direction. With temperature and humidity differences measured between 0.5 and 1.14 m above ground and with Φ e /Φ h = 1.35 there is no systematic difference between measured and calculated fluxes, the accuracy in an individual calculated flux being better than 20%. For the stable case it is shown that the flux of sensible heat can be determined with good accuracy with the flux‐gradient method, using data from the 0.5 ‐ 1.14 m layer. The water vapour flux is obtained with good accuracy as a residual term from the energy balance equation.
CONTENTS: MATHEMATICAL DESCRIPTION OF TURBULENCE.SPECTRAL FUNCTIONS; SPECTRAL REPRESENTATIONS OF STATIONARY PROCESSES AND HOMOGENEOUS FIELDS, ISOTROPIC RAMDOM FIELDS, LOCALLY HOMOGENEOUS AND LOCALLY ISOTROPIC RAMDOM FIELDS, ISOTROPIC TURBULENCE; EQUATIONS FOR THE CORRELATION AND SPECTRAL FUNCTIONS OF ISOTROPIC TURBULENCE, THE SIMPLEST CONSEQUENCES OF THE CORRELATION AND SPECTRAL EQUATIONS, SELF-PRESERVATION HYPOTHESES, SPECTRAL ENERGY-TRANSFER HYPOTHESES, THE MILLIONSHCHIKOV ZERO-FOUR-CUMULANT HYPOTHESIS AND ITS APPLICATION TO THE INVESTIGATION OF PRESSURE AND ACCELERATION FLUCTUATIONS, DYNAMIC EQUATIONS FOR THE HIGHER-ORDER MOMENTS AND THE CLOSURE PROBLEM, TURBULENCE IN COMPRESSIBLE FLUIDS.LOCALLY ISOTROPIC TURBULENCE; GENERAL DESCRIPTION OF THE SMALL-SCALE STRUCTURE OF TURBULENCE AT LARGE REYNOLDS NUMBERS, DYNAMIC THEORY OF THE LOCAL STRUCTURE OF DEVELOPED TURBULENCE, EXPERIMENTAL DATA ON THE FINE SCALE STRUCTURE OF DEVELOPED TURBULENCE, DIFFUSION IN AN ISOTROPIC TURBULENCE, REFINED TREATMENT OF THE LOCAL STRUCTURE OF TURBULENCE TAKING INTO ACCOUNT FLUCTUATIONS IN DISSIPATION RATE.WAVE PROPAGATION THROUGH TURBULENCE; PROPAGATION OF ELECTROMAGNETIC AND SOUND WAVES IN A TURBULENT MEDIUM, STELLAR SCINTILLATION.FUNCTIONAL FORMULATION OF THE TURBULENCE PROBLEM; EQUATIONS FOR THE CHARACTERISTIC FUNCTIONAL, METHODS OF SOLVING THE EQUATIONS FOR THE CHARACTERISTIC FUNCTIONAL.
Analytical expressions which specify non-dimensionalized wind speed and
potential temperature gradients as functions of stability are
integrated. The integrated equations are tested against Swinhank's wind
and temperature profiles measured at Kerang, Australia. It is found that
a representation suggested independently by Businger and by Dyer gives
the best fit to temperature profiles and describes the wind profiles
equally as well as a relation suggested by Panofsky et al.
Wind and temperature profiles for a wide range of stability conditions
have been analyzed in the context of Monin-Obukhov similarity theory.
Direct measurements of heat and momentum fluxes enabled determination of
the Obukhov length L, a key independent variable in the steady-state,
horizontally homogeneous, atmospheric surface layer. The free constants
in several interpolation formulas can be adjusted to give excellent fits
to the wind and temperature gradient data. The behavior of the gradients
under neutral conditions is unusual, however, and indicates that von
Kármán's constant is 0.35, rather than 0.40 as usually
assumed, and that the ratio of eddy diffusivities for heat and momentum
at neutrality is 1.35, compared to the often-suggested value of 1.0. The
gradient Richardson number, computed from the profiles, and the Obukhov
stability parameter z/L, computed from the measured fluxes, are found to
be related approximately linearly under unstable conditions. For stable
conditions the Richard on number approaches a limit of 0.21 as stability
increases. A comparison between profile-derived and measured fluxes
shows good agreement over the entire stability range of the
observations.
From over 1000 half‐hour observations of near‐surface wind profiles at Hay, NSW, more than 500 high quality sets of data are selected. In unstable conditions, these closely confirm previous analyses and suggest near equality between z/L and Ri . The data are well described by either the KEYPS relationship (Panofsky) or that of Businger: ϕ M = (1–16 z/L ) −1/4 . In stable conditions, a log‐linear formulation (ϕ M = 1+ az/L ) is found to give an adequate description of the wind profile up to z/L ≃ 0.5, with some evidence for a slight variation in α between the values 4.0 at neutral and about 6 when z/L ≃ 0.2. The average value of α between these limits is found to be 5.0±0.2.
In conditions of very high stablity, a linear profile ( du/dz = cu * /( kL )) is suggested above the height z ≃ 10 L . In the transition region between the log‐linear and linear profile regimes, the log‐linear formulation appears to tend towards a purely logarithmic law as stability increases. There is no evidence for any sudden change in behaviour, nor is there any suggestion that a purely logarithmic relationship is ever attained as an average situation. The value of c in the purely linear relationship is found to be between 0.4 and 0.9. The data also indicate that in extremely stable conditions ( L ≃ 50cm) the dimensionless gradients of heat and of momentum may differ by about a factor of two, with ϕ H being the larger.
The roughness length of the site used is found to be 1.2±0.1 mm, considerably less than the values appropriate to earlier experiments performed in the same general area. There is some evidence for an increase in z 0 with decreasing wind speed (reaching about 3 mm when the wind at 1 m is about 1 ms ⁻¹ ), in accord with Deacon's hypothesis concerning the form drag of roughness elements. From the point of view of applying a low‐level drag coefficient in order to estimate friction velocities, the errors arising from the change in roughness length are sometimes comparable to those resulting from stability effects.
Not surprisingly, the data show that in slightly stable conditions dewfall was low, whereas in extremely stable situations dewfall accounted for most of the heat loss from the air.
The data used here form part of a much larger body of information obtained during 1967 and known as the ‘Wangara’ experiment.
Data for three summers (1955-1957) are presented, obtained from continuous recorders responding to temperature, humidity and wind in and above the wheat crop at levels up to about 2 m. Section 1 gives a brief account of the instruments (see Long, Q.J.83, p. 202 for details). § 2 a description of the site, 70 × 70 m, which may have been too small for full development of profiles. § 3 (from 1955) shows that planting density affects the daily cycles of temperature and humidity in the crop, a thin crop having a lower average relative humidity and a shorter period of saturation on a dew night. Such a night is characterized by a humidity lapse between ground and canopy, and a humidity inversion above the canopy. On the exceptional occasion illustrated, both the up flux and the down flux may have reached a maximum rate of about 3 mg ground cm−2 hr−1. An adventitious air-temperature ripple during a calm night is exploited to derive rough estimates of transport constant in a dense crop : near the ground it approached the molecular thermal diffusivity for air. § 4 (from 1956) displays anomalies in temperature and humidity profiles that can arise from interpolating readings within the 400 sec cycle of the recorders. It also gives soil temperature records from which estimates of soil thermal diffusivity, and soil heat flux, are made, indicating that on the first sunny June day after rain there may be a net heat flux into the ground of about 30 cal cm−2 : the equivalent of 0·5 mm of evaporation. From an energy balance further rough estimates of heat transport constant within the crop are found to be of order 2 to 20 cm2 sec−1 depending on height and external wind speed. The anomalies in profiles are attributed partly to periodicities in the air parameters almost identical with that of the recording instruments, and partly (§ 5, from 1957) to long-persisting differences in temperature and humidity at constant level across the site. Within the crop an average temperature difference of 0·8°C may persist for four hours at positions 8 m apart (and a vapour-pressure difference of 1·0 mb), and these ‘hot’ and ‘damp’ spots - not always coincident - move slowly during the day. The differences are smaller above the crop where mixing is more thorough. These differences swamp any that might be due to advective effects, and raise doubts about the meaning of ‘a profile’ over a tall crop.
§ 6, introduces an analytical Part II which uses the data from a period of eight days (12–19 June 1957). of fine weather after rain, discusses the generalized profile equation
(reducing to the standard logarithmic profile when α = 0) : measurements of temperature and humidity are not accurate enough to determine α for their profiles, and the swaying of the crop necessitates use of long-period averages of wind speed before α can be determined for wind profiles. Working on 4-hr periods (00-04, 04-08 and so on) it is found (§ 7) that profiles above the crop can be fitted either with α = 0, or a value of α chosen from the Deacon curve of 1 – α against Richardson number. Values for a crop height of about 60 cm, with heat transfer (Qs) and evaporation rates (E) from later sections, are:
The discrepancy in u*/k during the first period corresponds to a 12-fold estimated shearing stress.
Wind profiles in the crop have a completely different shape in calm and windy weather, in the sense that near the ground the absolute wind speed tends to be constant: the crop behaves as though self-sealing.
Experimental data on the Monin and Obukhov functions, ΦM(ζ) and ΦH(ζ), obtained above an aerodynamically very rough surface (trees and shrubs, with zo, the aerodynamic roughness length, =0.4 m) in unstable conditions suggest they depend upon a nondimensional height ξ = z/z0.
At the lowest height (ξ = 20), in neutral conditions, the inferred values of ΦM and ΦH(0) are 0.58 and 0.61 respectively, generally increasing as ξ increases to values not significantly different from unity at the greatest height (ξ = 85). Such values compare with the value unity found over ‘smooth’ surfaces at much greater values of ξ. This indicates that the depth of the transition layer for momentum transfer above this surface (=Zmin, the minimum height of validity of the neutral logarithmic law) is given by Zmins ≈ 4.5h, where h is the height of the main roughness elements; and for heat transfer Zmin ≈3h.
The results suggest that eddy diffusivities are considerably greater just above tall vegetation than at corresponding heights above ‘smooth’ surfaces.
Results are presented from six micrometeorological studies conducted over a grass turf at Davis, California, in 1966 and 1967. Highly reliable surface drag and evaporation data from very sensitive lysimeters of 6·1 m diameter afforded excellent opportunity to evaluate several parameters important to aerodynamic-prediction equations.
For the six studies the mean von Kármán constant, k, ranged from 0·40 to 0·44, strongly supporting continued acceptance of k at around 0·42.
The Monin-Obukhov (1954) universal ϕM function was found to vary as ∣Ri∣−1/3 under near-free convection, indicating significantly greater diabatic profile effects than suggested in the form of the KEYPS profile as given by Sellers (1965).
Empirical relationships providing excellent fit to experimental data for the range −3·5 < Ri < 0·3, were ϕM = (1–16 Ri)−1/3 and ϕM = (1 + 16Ri)1/3 respectively for unstable and stable conditions. For ϕw corresponding expressions were ϕw = ·885 (1–22 Ri)−.40 and ϕw = ·885 (1+34 Ri).40.
The ratio KW/KM showed a systematic drop from 1·13 at neutral to a value around 0·75 under strongly stable conditions, which conflicts with recent reports of no change of KH/KM within a wide range of stable conditions (Laykhtman and Panomareva 1969; Webb 1970; Oke 1970). The UCD results are in general agreement with the literature in that KW/KM systematically increased with increasing instability. In the range 0 > Ri > −2·0, KW/KM increased from 1·13 to 1·6.
No expressions relating ϕM and ϕW or KW/KM to z/L are presented due to uncertainties in Davis z/L data. However, use of Davis Ri data in several published z/L (Ri) relationships, allowed a limited comparison with results of previous studies.
An analysis is made of the Monin-Obukhov function ΦM in the familiar wind profile equation, using data from two recent expeditions to Gurley (New South Wales) and Hay (New South Wales). In one, the friction velocity u* is determined directly by the eddy correlation method, and in the other, conducted during mid-winter when small heat-fluxes were experienced, by the use of a friction coefficient applied to a low-level wind.
By collating with a similar earlier analysis for heat and water vapour transfer, the variations of ΦM, ΦH and ΦW with stability are presented in tabular form in the z/L range − 0.01 to − 1.0. Within this range the empirical relationships ΦM = (1 − 16 z/L)−1/4 and ΦH, W = (1 − 16 z/L)−1/2, and the implied equality between Ri and z/L, are found to approximate the data to within a few per cent.
Values of the total vertical flux of sensible and latent heat over a level forested region, obtained from aerodynamic (profile‐gradient) formulae appropriate to airflow over relatively smooth surfaces, are found to fall consistently short of independent energy‐balance estimates by a factor of 2 to 3 in unstable and near‐neutral conditions (Richardson number, Ri , in the range −0·4 to +0·01), whereas for Ri > + 0·02 no similar discrepancy is detected. These results, based on tangents drawn to (semi‐logarithmic) profiles at a height of about nine aerodynamic roughness parameters ( z 0 ) above the zero plane displacement level ( d ) of the forest, rely on the basic assumption that the value of d established in very nearly neutral conditions (| Ri | < 0·003), namely 0·76 mean tree heights, holds under all conditions of thermal stability.
Wake diffusion and thermal seeding effects are discussed as possible additional transfer mechanisms acting to reduce profile gradients immediately over aerodynamically rough surfaces. In terms of the former mechanism (assumed to operate below d + 25 z 0 , or so), approximate empirical formulae are derived which attempt to quantify the observed discrepancy in terms of Ri and the proximity of the surface.
It is concluded that aerodynamic equations ought not to be used to give independent flux estimates close to aerodynamically rough surfaces.
The diabatic mean profile forms in the surface layer are studied, by applying analysis methods having high resolving power to data from O'Neill, U.S.A. (heights up to 6.4 m) and from Kerang and Hay, Australia (heights mostly up to 16 m).
It is found, concordantly from the O'Neill and Australian data, that the log‐linear law is valid for z/L values between — 0.03 and + 1, which includes a small range of unstable and a surprisingly wide range of stable conditions. For all quantities studied (wind, potential temperature, and specific humidity), it is concluded that the Monin‐Obukhov coefficient α is near 4.5 in unstable and 5.2 in stable conditions, within a standard error of about 10 per cent. The ratios K H /K M and K W /K M evidently remain constant, equal to unity, over the whole of the log‐linear range (and somewhat beyond).
In stable conditions, the log‐linear law implies that Ri approaches a critical value α ⁻¹ , approximately 0.2, as z/L → ∞. However, at z/L a second régime sets in, in which the profiles are only quasi‐determinate, approximating, on the average, a simple logarithmic form (gradients proportional to z ⁻¹ ); this régime covers the range approximately 1 < z/L < (α + 1), i.e. (α + 1) ⁻¹ < Ri < 1. A third range of extreme stability, Ri > 1, is practically unrepresented in the data examined.
The major part of the unstable range, for z/L < − 0.03, will be discussed in a later paper.
During the 1971 growing season continuous measurements were made (with some breaks in the record due to instrumental faults) of the evaporation from barley using five methods: Bowen ratio method;
aerodynamic method;
use of the energy balance equation and the aerodynamic heat flux to obtain evaporation as the residue (for convenience called the energy balance method);
a weighing lysimeter; and
a neutron moisture meter.
In this paper some estimates are made of the error expected from each method and the results of the measurements are presented. It is shown that the energy balance method is almost as good as the Bowen ratio method and has the advantage of not requiring humidity measurements.
Hourly energy budgets measured in Thetford Forest, Norfolk, are analysed for seven fine days in months from May to September.
Values found for the Bowen ratio β ranging from near 1 to 4 or more, are used to show that the bulk physiological resistance rST of the forest exhibits a consistent diurnal trend, from near 1·2 s cm−1 in the forenoon (once the trees are dry) to as much as 4 s cm−1 by late afternoon - consistent with independent biological measurements (Robins, personal communication). In contrast, the forest's bulk aerodynamic resistance r generally lies between 0·05 and 0·10 s cm−1. The ratio rST/r alone, of order 20:1, is shown to imply that transpiration from the forest must occur at rates much less dependent, primarily, on net radiation, Rn, than on ambient vapour pressure deficit (v.p.d.), (provided that the latter is not too small, i.e. ≮ 1 mb per 100 W m−2 of Rn, say); and also that the evaporation of intercepted rainfall from the trees must occur at about 5 times the corresponding transpiration rate under the same meteorological conditions. In addition, because lighter winds during fine weather tend to favour larger v.p.d's the observed decrease in transpiration rate with increasing wind speed is much larger than that expected from the accompanying decrease in r alone.
Other conclusions are (i) that the storage associated with a 1° C change in air temperature per hour, within the canopy, is 18 W m−2, which is not always negligible, as it is for short vegetation; and (ii) that values derived for the dimensionless excess resistance parameter, B−1, although remarkably small, 2 to 3 for u* ∼ 0·75 m s−1, are commensurate with other bulk aerodynamic resistances in the system: accordingly, the easily-derived surface resistance parameter, rs, (Monteith 1965; Thom 1972) provides an estimate of rST for the forest within 10 per cent for all β > 0.
Measurements were made in a wind-tunnel of the drag on elements of a simply-structured artificial crop, and of the wind profiles above and within the crop. Analysis demonstrates
The relation z0 = 0.36 (h – d) is suggested for the roughness parameter of vegetation of height h.
Calculated values of the drag force, f, on unit column of a real stand of beans in the field, using individual-element drag coefficients (Cd) and measured wind speeds, give f = 3.5 τ0 where τ0 is the downward momentum flux derived from the shape of the wind profile above. On the evidence of conclusion (i) and the dense and complex nature of the bean canopy, the factor 3.5 is attributed to mutual sheltering of neighbouring canopy elements rather than as evidence that the Cd – values are modified by turbulent shear flow.
For the artificial crop, and for the real crop, recognition of the wind-speed dependence of the individual-element drag coefficients gives values of eddy viscosity, KM, almost constant in the height range h/3 < z ⩽ h and significantly larger than those found when constant drag coefficients are assumed. Constant KM within a crop canopy is consistent with the wind profile u(z)/u(h) = {1 + α(1 – z/h)}−2: an explicit expression is given for the parameter α.
Turbulent fluctuations of wind, temperature and humidity at heights up to a few hundred metres have been measured over the open sea by instruments supported by a tethered balloon. Wave-induced motion of the ship from which the balloon was flown produced unwanted contributions to the measured turbulence, but in light or moderate winds it has been possible to make allowances for these effects and to obtain useful estimates for vertical fluxes of heat and moisture: the calculated momentum fluxes in contrast appear less reliable and to obtain satisfactory values will require stabilization of the tethering point of the balloon cable. Some observations made in generally unstable conditions near OWS ‘J’ yield a value of (1.8 ± 0.7) × 10−3 for CE in the bulk aerodynamic formulation for evaporation (E = ρCE (q0 − q10)(U10 − U0)) and suggest that compared to the vertical moisture flux the heat flux may often have an insignificant rǒle in determining the buoyancy flux and hence the turbulence structure in the bulk of the boundary layer.
Eddy fluxes of momentum, sensible and latent heat, and turbulence spectra measured over the Thetford Forest during 10 days in the Spring of 1973 are described. The measured total heat flux (H + E) for 122 20-min periods agreed closely on average with independent estimates from an energy balance method. There was evidence that the energy balance data gave small systematic overestimates of available energy during the hours before noon, compensated by slight underestimates for the remainder of the day. A comparison of measured wind speeds and friction velocities in neutral stability confirmed the validity of the aerodynamic method for estimating momentum fluxes at heights of a few roughness lengths above the canopy. In stable conditions the log-linear wind profileU = (u
*/k)(ln ((z -d)/z
o) + (z -d -z
o)/L) with = 3.4 0.4 provided a good fit to the data. Spectra in unstable conditions were generally more sharply peaked than those measured by other workers over smoother terrain: differences were less marked in the case of vertical velocity in stable conditions. Temperature spectra in these stable conditions showed high energy at relatively low wavenumbers, andwT cospectra showed a cospectral gap; both of these results were associated with an intermittent sawtooth structure in the temperature fluctuations.
A one-dimensional, steady-state plant-atmosphere model using different formulae for the thermal stability function is applied to data for corn crops. There are two general types of formulae available. Those proposed by W. C. Swinbank, A. J. Dyer and B. B. Hicks, and E. K. Webb were derived from measurements taken hundreds or thousands of roughness lengths above grass fields. Formulae recently proposed by A. S. Thom, J. B. Stewart, H. R. Oliver and J. H. C. Gash were derived from measurements taken nine roughness lengths above a pine forest. Use of the latter formulae yields better agreement between predicted and measured values of thermal eddy diffusivity at canopy height in the corn crops. These improved diffusivity values result in improved temperature-profile predictions in the top metre of the canopy.
Quartz crystal thermometers with ceramic tubes for the wet bulbs were used to measure vertical profiles of temperature and humidity above a pine forest. The effect of the supporting structures on the measurements and an objective method of calculating the Bowen ratio are described. The surface resistance was computed from the Bowen-ratio results. The diurnal variations in the average surface resistance of the forest for groups of dry days in Spring, Summer and Autumn are presented.
Surveys of existing flux-profile relationships for wind velocity and temperature have been published recently by Dyer (1974) and Yamamoto (1975). However, both these surveys do not include some widely used forms of these relationships and they present the material in the form of graphs which are not fully satisfactory. Moreover both Dyer and Yamamoto do not indicate that the existing experimental data are apparently insufficient for the reliable determination of the universal functions entering flux-profile relationships. The present paper gives a more detailed and updated review of flux-profile relationships, based on a modified definition of these relationships. Included is a discussion of the deficiencies in the experimental data.
Three aerodynamic formulae were used to compute evapotranspiration from a cornfield, and results compared with estimates from the energy budget and with measurements from a floating lysimeter. The aerodynamic methods yielded results which were close to the lysimeter measurements when the corn was short at the beginning of the season, but fell to only 40% of the measured values at the end of the season. These results may indicate that the conditions for the validity of the formulae are not likely to be realized in an ordinary cornfield. In addition to the bias toward underestimation, many large random errors occurred in the calculated evapotranspiration. These are attributed to the inability of present instrumentation to measure the meteorological parameters with sufficient precision to meet the requirements of the aerodynamic formulae.
It is concluded that aerodynamic methods, when applied to calculating evapotranspiration from tall crops, cannot be expected to yield useful results, and it is recommended that the energy budget method, which was found to estimate evapotranspiration within 11% of measured values, be used instead.
Flux-profile relationships in the constant flux layer are reviewed. The preferred relationships are found to be those of Dyer and Hicks (1970), namely,
H
=
W
=(1–16(z/L))–1/2,
M
=(1–16(z/L))–1/4 for the unstable region, and
H
=
W
=
M
= 1+5(z/L) for the stable region.The carefully determined results of Businger et al. (1971) remain a difficulty which calls for considerable clarification.
Details regarding equipment used in obtaining field data on crop environment temp. published earlier [see FCA 30, 5292] are reported. Pt resistance mounting and error analysis, calibration of these resistances and data logger requirements and modifications are dealt with. Equipment details regarding the actual collection of accurately scanned field temp. are discussed. (Abstract retrieved from CAB Abstracts by CABI’s permission)
After extensive field experiments, we developed SPAM, a comprehensive mathematical model that simulates energy and material exchange in the plantair layer at the earth's interface. The model is based upon the conservation of energy, where the sun is the driving force. Our understanding and deficiencies were gauged initially by testing model predictions against actual experience with a relatively simple system-a cornfield. Climatic predictions are physically and biologically good enough for many applications, but they reveal inadequacies in our understanding of the fluid dynamics of airflow within the plant stand. Our present inability to measure or predict the degree of wetness of the soil surface hampers correct prediction of evaporation. Probably the most difficult problem to resolve is that of predicting how stomates open and close under drought stress, thus affecting both evaporation and photosynthesis in leaves. Along with resolution of these problems, the basic framework of the model can be adapted to more complex systems in nature, where variability is much greater than in an agricultural crop. The model in its present form can be used, with caution, as a powerful tool to help man order his priorities of plant community traits for whatever outcome he desires, be it food production, nature and water conservation, climate modification, or esthetic enjoyment.
Coniferous Forest’, Chapter 7 inVegetation and the Atmosphere
- P G Jarvis
- G B James
- J J Landsberg
Turbulence Measurements above a Pine Forest', Boundary-Layer Meteorol
- E I Mukammal
- K M King
- H F R Cork
- N Thompson
Mukammal, E. I., King, K. M., and Cork, H. F.: 1966, `Comparison of Aerodynamic and Energy Budget M. R. RAUPACH Thompson, N.: 1979, `Turbulence Measurements above a Pine Forest', Boundary-Layer Meteorol. 16, 293-310.
Measurements of Evaporation from Forest (Representative Basin Velen): Report on the work during 1972
- R Berggren
- M Aronsson
- B Bringfelt
- P-O Harsmar
- S Ljungqvist
- E Nilsen
- W Sandgren
- G Wiklund
Similarity Laws and Scale Relations in Planetary Boundary Layers
- H Tennekes
Measurements of Evaporation from Forest
- R Berggren
- M Aronsson
- B Bringfelt
- P-O Harsmar
- S Ljungqvist
- E Nilsen
- W Sandgren
- G Wiklund
- R. Berggren