Concentration prediction for meandering plumes based on probability theory

A procedure is proposed for the calculation of the probability function of the concentration of gas in a pollutant plume that is meandering. As input, the velocity field must be known as well as the plume behaviour in the presence of turbulence but without meandering. It is assumed that the high-frequency turbulence and the low-frequency fluctuations that cause meandering are independent and can be superposed. Small-scale experiments are described which simulate meandering, in which these assumptions are verified. The concentration measurements in these experiments are also compared with the predictions using this calculation method. The agreement of the calculation with experiments shows the usefulness of this type of calculation.     

Fumigation of pollutants in and above the entrainment zone into a growing convective boundary layer: a large-eddy simulation

Fumigation of a passive plume located in or above the entrainment zone (EZ) into a growing convective boundary layer (CBL) has been simulated by large-eddy simulation (LES). Three non-dimensional parameters, α(=w_e0/w_*0), z₀/z_i0, and σ_z0/z_i0, are used to classify different cases, where w_*0 is the convective velocity scale, w_e0 the initial entrainment velocity, z_i0 the initial CBL height, z₀ the initial plume height, and σ_z0 is the initial plume half-depth. Forty cases have been run and analysed. The crosswind-integrated concentrations have been compared with existing laboratory data from a saline convection tank. The results show that LES is a promising tool to reproduce fumigation processes. With a relatively coarse grid mesh near the EZ, LES derives reliable results that are in a good agreement with the laboratory data. The first parameter, α, containing the effects due to inversion strength, plays an important role in determining C₀(T), the ground-level concentration (GLC) as a function of dimensionless time, T. For large α (say >0.03, corresponding to fast entrainment), variation of α gives significant change in C₀(T); whereas for a wide range of α between 0.01 and 0.02 (corresponding to slow entrainment), C₀(T) is almost independent of α. The starting time of fumigation does not vary significantly with the second parameter, z₀/z_i0 (relative height of plume), although C₀(T) is, in general, smaller for a higher plume. This confirms laboratory findings that the traditional notion of zero fumigation for a high plume (say above 1.10z_i) is not correct. The effect of the third parameter, σ_z0/z_i0, is on the magnitude of C₀(T); thinner initial plumes have higher GLCs.     

Unsteady characteristics of the dispersion process in the vicinity of a pig barn. Wind tunnel experiments and comparison with field data

Two complementary methods, field experiments and physical modelling in a wind tunnel, have been used to investigate the dispersion of tracer-gas released from the ventilation system of a pig barn, under near-neutral stability conditions. In both cases, concentration fluctuations were measured and the deduced statistical results were compared. The choice of data processing applied to the time series of concentration was motivated by special issues in the assessment of odour annoyances: “where, how often, how long and how strong does it smell?” These features were described by the mean concentration distribution, the intermittency factor, the persistence and the 90-percentile. The good agreement between field and wind tunnel data confirmed the ability to replicate in wind tunnel the unsteady properties of a dispersion process, if the unsteady turbulent behaviour of the atmospheric boundary layer was properly modelled.A parametrical study of the influence on the dispersion process of the ratio between the exhaust velocity from the stack and the wind speed was then performed in wind tunnel. The fundamental outcome was that the near-field dispersion process under neutral stability conditions, despite the strong influence of the building wake, was for the most part driven by the meandering behaviour of the plume and not so much by the diffusion process.This study was also focused on the influence of the averaging time on the statistical results. The scatter generated by using dimensionless averaging times 200<T_a^*<400 (used during field experiments) instead of T_a^*→∞ (averaging time to ensure reproducible statistic results) was quantified in the wind tunnel. A degree of representativity of the results obtained from short-term samples, compared to fully converged statistical results was therefore assessed.     

A wind tunnel study of dense gas dispersion in a neutral boundary layer over a rough surface

Measurements of the vertical entrainment velocity into two-dimensional dense gas plumes over fully rough surfaces were carried out as part of a co-operative research programme with wind tunnel facilities in the USA. This paper presents results obtained for neutral boundary layer conditions in the EnFlo wind tunnel at the University of Surrey; a companion paper treats the stable boundary layer case. Entrainment velocities, W_E, were deduced from the streamwise development of the concentration field, non-dimensionalised with respect to the friction velocity in the undisturbed flow, u^*, and correlated with the plume Richardson number, Ri^*. Results for Richardson numbers in the range Ri^*<15 were found to be well fitted by the empirical expression: W_E/u^*=0.65/(1+0.2Ri^*). Flow visualisation studies showed layered plume structures with a sharp upper interface at higher Richardson numbers and in this regime turbulent motion below the interface became progressively more intermittent as Ri^* increased. Measured turbulence levels collapsed within such high Richardson number plumes and flow and dispersion were significantly affected by molecular processes. Up-welling above the source was observed when the emission speed exceeded the approach flow friction velocity, though there was no clear evidence that this affected plume behaviour away from the immediate vicinity of the source.     

A wind tunnel study of dense gas dispersion in a stable boundary layer over a rough surface

Measurements of the vertical entrainment velocity into two-dimensional dense gas plumes over fully rough surfaces were carried out as part of a co-operative research programme with wind tunnel facilities in the USA. This paper presents results obtained for stable boundary layer conditions in the EnFlo wind tunnel at the University of Surrey; a companion paper treats the neutral boundary layer case. Mean velocity and temperature, turbulent normal and shear tresses, temperature fluctuations and heat fluxes were measured and used to demonstrate that a moderately stable atmospheric boundary layer had been successfully simulated in the tunnel. Entrainment velocities, W_E, were then deduced from the streamwise development of the concentration field, non-dimensionalised with respect to the friction velocity in the undisturbed flow, u^*, and correlated with the plume Richardson number, Ri^*. Higher non-dimensional entrainment speeds, W_E/u^*, were observed for Ri^*>5 in the stable boundary layer than in the neutral boundary layer, the difference growing with increasing Richardson number. Emission velocity ratios, W₀/u^*, were however larger in the stable experiments, and exceeded one at about Ri^*=18. Entrainment in the stable boundary layer appeared therefore to be more sensitive to emission velocity ratio than in the neutral case. Entrainment behaviour for Ri^*⩽5 followed that found in the neutral boundary layer. In this regime, use of the neutral boundary layer entrainment speed correlation is unlikely to lead to the over-prediction of plume dilution rates in moderately stable boundary layers.     

Comparison of PDFs, closure schemes and turbulence parameterisations in Lagrangian stochastic models

Six one-dimensional models, based on the Ito-type stochastic equation, are presented and compared. Four of these take into account up to the fourth order moment of vertical velocity fluctuations, and two up to the third order moment. Four models make use of a bi-Gaussian probability density function (PDF) and the other two are based on a Gram-Charlier series expansion truncated to the third or fourth order. All the models were run with a parameterisation of input turbulence (i.e. w², w³, and τ profiles). Concerning the fourth order moment w⁴, two different parameterisations were considered. Comparisons are made between ground-level concentrations, plume height and plume width observed in the Willis and Deardorff water tank experiments and those predicted by the different models here considered. The goal of this study was to find the models that give greater confidence in their applicability in dispersion studies and to verify the importance of considering the fourth order moment. The main conclusions are: simulation results largely depend on the turbulence parameterisation chosen; the Gram-Charlier PDF gives the best agreement with observations; some combinations of models and turbulence parameterisations perform well in simulating the shape of the ground-level concentration (g.1.c.) trend but fail in correctly simulating the form of the plume (plume height and vertical width); in the case of the Gram-Charlier PDF, the fourth order model reproduced the vertical plume width better than the third order one, whereas the two schemes yielded similar g.1.c. distributions.     

Plume behaviors observed using lidar and SF6 tracer at a flat and hilly site

Two field experiments, one at Kincaid, IL, in flat terrain, the other at Bull Run, TN, in rolling terrain, were conducted under the auspices of the Electric Power Research Institute's (EPRI) Plume Model Validation and Development program. Simultaneous observations were made of ground-level SF₆ concentrations; plume cross-sections using light detection and ranging (lidar); turbulence; and routine meteorology at the surface and aloft. Due to terrain influences, surface wind-speeds at the Bull Run site were significantly lower than those at the Kincaid site, whereas thermal winds at Kincaid were generally larger than at Bull Run. At both sites, a reduction in turbulent intensity and an increase in atmospheric stability with height correlate with a substantial decrease in the rate of vertical plume dispersion. SF₆ ground-level concentration (GLC) patterns over distances of 1–50 km from the source were categorized by shape. The GLC patterns at Bull Run were frequently ‘blobby’, when significant GLCs occurred over an azimuth angle exceeding 90°, whereas patterns at Kincaid were generally coherent and nearly elliptical. Plume behavior was examined for 154 h during which both GLCs of SF₆ tracer and lidar cross-sections of the plume were of good quality. Results show that plume looping was rare at Kincaid, but occurred substantially more often at Bull Run (3%: 14%), with the reverse true for meandering (11%: 14%). Inversions that trapped plume material occurred much more often at Kincaid that at Bull Run (11%: <1%). Correlation of cross-wind concentration distributions of the plume aloft with those cross-wind SF₆ concentrations distributions at the ground were poor at both sites.     

Monte Carlo simulation of nitrogen oxides dispersion from a vehicular exhaust plume and its sensitivity studies

The pollutant dispersion behavior from the vehicular exhaust plume has a direct impact on human health, particularly to the drivers, bicyclists, motorcyclists, pedestrians, people working nearby and vehicle passengers. A two-dimensional pollutant dispersion numerical model was developed based on the joint-scalar probability density function (PDF) approach coupled with a k–ε turbulence model to simulate the initial dispersion process of nitrogen oxides, temperature and flow velocity distributions from a vehicular exhaust plume. A Monte Carlo algorithm was used to solve the PDF transport equations in order to obtain the dispersion distribution of nitrogen oxides concentration. The model was then validated by a series of sensitivity experimental studies in order to assess the effects of vehicular exhaust tailpipe velocities, wind speeds and chemistry on the initial dispersion of NO and NO₂ mass concentrations from the vehicular exhaust plume. The results show that the mass concentrations of nitrogen oxides decrease along the centerline of the vehicular exhaust plume in the downstream distance. The dispersion process can be enhanced when the vehicular exhaust tailpipe velocity is much larger than the wind speed. The oxidation reaction of NO plays an important role when the wind speed is large and the vehicular exhaust exit velocity is small, which leads to chemical reduction of NO, and the formation and accumulation of NO₂ in the exhaust plume. It is also found that the effect of vehicular exhaust-induced turbulence in the vicinity of the exhaust tailpipe exit is more dominant than the effect of wind turbulence, while the wind turbulence gradually shows a significant role for the dispersion of nitrogen oxides along with the development of exhaust plume. The range of dispersion of nitrogen oxides in the radial direction is increased along with the development of vehicular exhaust plume.     

A simple and fast model to compute concentration moments in a convective boundary layer

Recently, a modified meandering plume model for concentration fluctuations in a convective boundary layer has been formulated (Atmos. Environ. 34 (2000) 3599). This model is based on a hybrid Eulerian–Lagrangian approach and it accounts for the skewed and inhomogeneous turbulence characteristics of the convective flow. Using the same hypotheses, but eliminating the need for Lagrangian particle model, we propose a generalised approach, that only requires the knowledge of mean concentration field. The proposed model is independent from the method used to obtain the mean concentration field. The evaluation of the concentration fluctuation field needs a computational time of only few seconds on a standard PC. Therefore, the model is suitable for practical applications.     

Reactive plume model: Effect of stack exit conditions on gas phase precursors and sulfate formation

A simple form of a carbon-bond smog mechanism has been introduced into a complete set of plume conservation equations. The conservation expressions for mass, momentum, energy and component species have been solved numerically for typical source and neutral or adiabatic ambient conditions to simulate the homogeneous gas phase chemistry for approximately two hours of travel time downwind from the stack exit. The influence of stack exit conditions including the ratios of momentum-to-buoyancy length l_m/l_b, source-to-ambient velocity R and mixing-to-reaction time τ are demonstrated.It was found that homogeneous processes in the plume near-field do not significantly contribute to the overall conversion of SO₂ to SO²⁻₄. In the far-field maximum sulfate formation rates of 2.3% h⁻¹ were predicted for clear summer noon hours, consistent with plume measurements. Variation of stack exit conditions were found to have little effect on the maximum SO₂ conversion rate or the peak OH radical concentration where local HC/NO_x ratios between 16 and 22 were predicted. Parameter changes resulting in greater ambient entrainment rates, however, were found to shift the development of the radical pool closer to the source and to significantly increase the total molar flux of plume sulfate.     

Applied dispersion modelling based on meteorological scaling parameters

A method for calculating the dispersion of plumes in the atmospheric boundary layer is presented. The method is easy to use on a routine basis. The inputs to the method are fundamental meteorological parameters, which act as distinct scaling parameters for the turbulence. The atmospheric boundary layer is divided into a number of regimes. For each scaling regime we suggest models for the dispersion in the vertical direction. The models directly give the crosswind-integrated concentrations at the ground, x_y, for nonbuoyant releases from a continuous point source. Generally the vertical concentration profile is proposed to be other than Gaussian. The lateral concentration profile is always assumed to be Gaussian, and models for determining the lateral spread σ_y are proposed. The method is limited to horizontally homogeneous conditions and travel distances less than 10km. The method is evaluated against independent tracer experiments over land. The overall agreement between measurements and predictions is very good and better than that found with the traditional Gaussian plume model.     

Kinetics of the oxidation of hydrogen sulfite by hydrogen peroxide in aqueous solution:: ionic strength effects and temperature dependence

Conductometry was used to study the kinetics of the oxidation of hydrogen sulfite, HSO⁻₃, by hydrogen peroxide in aqueous non-buffered solution at the low concentration level of 10⁻⁵–10⁻⁶ M, typically found in cloud water. The kinetic data confirm that the rate law reported for the pH range 3–6 at higher concentration levels, rate=k_H·[H⁺]·[HSO⁻₃]·[H₂O₂], is valid at the low concentration level and at low ionic strength I_c. At 298 K and I_c=1.5×10⁻⁴ M, third-order rate constant k_H was found to be k_H=(9.1±0.5)×10⁷ M⁻² s⁻¹. The temperature dependence of k_H led to an activation energy of E_a=29.7±0.9 kJ mol⁻¹. The effect of the ionic strength (adjusted with NaCl) on rate constant k_H was studied in the range I_c=2×10⁻⁴–5.0 M at pH=4.5–5.2 by conductometry and stopped-flow spectrophotometry. The dependence of k_H on I_c can be described with a semi-empirical relationship, which is useful for the purpose of comparison and extrapolation. The kinetic data obtained are critically compared with those reported earlier.     

Influence of short-time imidacloprid and acetamiprid application on soil microbial metabolic activity and enzymatic activity

The influence of two neonicotinoids, i.e., imidacloprid (IMI) and acetamiprid (ACE), on soil microbial activities was investigated in a short period of time using a combination of the microcalorimetric approach and enzyme tests. Thermodynamic parameters such as Q _T (J g^?1 soil), ?H _met (kJ mol^?1), J _Q/S (J g^?1 h^?1), k (h^?1), and soil enzymatic activities, dehydrogenase, phosphomonoesterase, arginine deaminase, and urease, were used to evaluate whole metabolic activity changes and acute toxicity following IMI and ACE treatment. Various profiles of thermogenic curves reflect different soil microbial activities. The microbial growth rate constant k, total heat evolution Q _T (expect for IMI), and inhibitory ratio I show linear relationship with the doses of IMI and ACE. Q _T for IMI increases at 0.0–20 μg g^?1 and then decreases at 20–80 μg g^?1, possibly attributing to the presence of tolerant microorganisms. The 50 % inhibitory ratios (IC₅₀) of IMI and ACE are 95.7 and 77.2 μg g^?1, respectively. ACE displays slightly higher toxicity than IMI. Plots of k and Q _T against microbial biomass-C indicate that the k and Q _T are growth yield-dependent. IMI and ACE show 29.6; 40.4 and 23.0; and 23.3, 21.7, and 30.5 % inhibition of dehydrogenase, phosphomonoesterase, and urease activity, respectively. By contrast, the arginine deaminase activity is enhanced by 15.2 and 13.2 % with IMI and ACE, respectively. The parametric indices selected give a quantitative dose-response relationship of both insecticides and indicate that ACE is more toxic than IMI due to their difference in molecular structures.     

Monoterpene and sesquiterpene emissions of three Mediterranean species through calcareous and siliceous soils in natural conditions

Little is known about terpene emissions released by plants in response to abiotic factors, except for climate-related factors. Standard emissions (E_S) of monoterpenes (E_SM) and sesquiterpenes (E_SS) of Rosmarinus officinalis, Pinus halepensis and Cistus albidus in siliceous and calcareous sites were examined. Their dependency on some nutrients in these soils was also analyzed. The study was carried out in the south of France at the end of March, when C. albidus exhibited a leaf growth state, while the other two species exhibited a pre-budbreak state. The results revealed that E_S of all major monoterpenes released by R. officinalis and E_S of α-pinene and α-humulene of P. halepensis were higher in plants growing in calcareous soils. In contrast, for C. albidus, E_SM and E_S of β-bourbonene and α-humulene were higher in siliceous soils. E_SM of all species was mainly correlated with nitrogen (N) and available phosphorous (P_A), while dependency on Ca²⁺ or K⁺ was variable. None of these nutrients was significantly correlated with E_SS, suggesting that sesquiterpene synthesis pathway requires different nutrient supplies. While higher soil nutrient content stimulated E_SM of R. officinalis and P. halepensis, it had a negative effect on E_SM of C. albidus, probably because C. albidus exhibited a different phenological state. Considering the soil nature, and particularly N and P_A as inputs in plant terpene inventories could hence contribute to obtain more accurate terpene estimates.     

On plume meandering in unstable stratification

Vertical plume meandering of gaseous pollutant is commonly experienced in the daytime atmospheric boundary layer (also know as convective boundary layer, CBL) that arose from the complicated interaction between buoyancy-generated turbulence and gravitational force. It leads to rapid pollutant mixing that cannot be accurately modeled by conventional Gaussian plume model. In the light of explaining the mechanism of plume rises and descents in CBLs, this study employs a direct numerical simulation (DNS) technique to compute the plume behaviors for pollutant emitted from line sources placed parallel to the spanwise direction in an unstably stratified turbulent open channel flow. The DNS results show that the plume meandering is due to the domination of uni-directional mean vertical pollutant fluxes above and below the mean plume height.     

A fluctuating plume model for concentration fluctuations in a plant canopy

A one-particle Lagrangian model for continuous releases in the non-Gaussian inhomogeneous turbulence of a canopy layer is derived based on the fluctuating plume model of Franzese [2003. Lagrangian stochastic modeling of a fluctuating plume in the convective boundary layer. Atmos. Environ. 37, 1691–1701.]. The model equations are filtered by a time-dependent low-pass filter applied to the turbulent kinetic energy in order to obtain a fluctuating plume model able to simulate the vertical meandering of the cloud centroid through non-stationary Lagrangian equations. The model satisfies the well-mixed condition. The relative dispersion of particles and the concentration fluctuation statistics of a passive tracer inside a modeled vegetal canopy are studied. The probability density function of the concentration relative to the plume centroid is parameterized and the mean and variance fields of concentration are simulated and compared with wind-tunnel data and numerical simulations. A skewed, reflected probability density function for the vertical position of the plume centroid is considered.     

Evaluation of the reactive and optics model of emissions (ROME)

The reactive and optics model of emissions (ROME) is a reactive plume visibility model that simulates the potential atmospheric impacts of stack emissions. We present here an evaluation of the ability of ROME to simulate several plume physical and chemical variables, using an experimental data base that consists of a total of 40 case studies from four field programs. The evaluation variables include plume height, horizontal width, NO_x and SO₂ maximum concentrations, NO₂/NO_x concentration ratio at the plume centerline, and plume-to-sky radiance ratios. Three algorithms used to simulate plume dispersion in ROME were compared: (1) the empirical Pasquill–Gifford–Turner (PGT) scheme, (2) a first-order closure (FOC) algorithm and (3) a second-order closure (SOC) algorithm that simulates the instantaneous plume dimensions.The plume height results show a correlation of 0.82 between simulated and measured values and a gross error that is 13% of the mean measured value. For plume horizontal dispersion, the second-order closure algorithm produces a moderate correlation (0.54) and a small bias (5% of the mean measured value) in comparison with the field data. Although the PGT scheme also demonstrates moderate correlation with the measurements, it produces a negative bias by significantly underestimating plume horizontal dispersion. The first-order closure algorithm overestimates plume width and shows the least correlation (with the measurements) of the three dispersion algorithms.For the NYSEG data set where coordinated measurements of stack emissions, meteorology at plume height and plume characteristics were available, the SOC algorithm provides better correlations for NO_x concentrations, NO₂/NO_x ratios and plume visibility than the FOC and PGT algorithms. For plume visibility, the SOC algorithm shows a correlation of 0.96 at 405 nm, the wavelength where the plume was visible, and it simulates no visible plume at the other wavelengths (550 and 700 nm).A comparison of ROME simulations with those of the plume visibility model PLUVUE II shows that ROME, with the SOC algorithm, performs better for all variables.     

Wind-tunnel study of entrainment in two-dimensional dense-gas plumes at the EPA's fluid modeling facility

This wind-tunnel study has been conducted as part of a collaborative effort to investigate the effect of large surface roughness on the entrainment of air from a neutrally stable simulated atmospheric boundary layer into a continuous dense-gas plume. The present study examined the entrainment rates of dense-gas plumes as they were transported over two surfaces with similar geometry but significantly different roughness lengths (factor of 6). Extensive measurements of the flow and plume structures over a wide range of source Richardson numbers (Ri*) are reported. Carbon dioxide was released from a two-dimensional source in order to obtain a plume with virtually constant Ri*. Over the small roughness, the plume depths were generally large compared with the element heights, whereas over the large roughness, plume depths were comparable with the element heights. Retardation of mean velocities in the lower levels of the dense plumes (with compensating increases in the upper levels) was observed, as well as strong suppression of turbulence over quite large fractions of the boundary-layer depth. These effects increased as Ri* increased. Propagation of dense gas was observed upstream of the source due to gravity spreading. The flow within the plumes was observed to become laminar at the larger Ri*. The primary measurements comprised longitudinal surface concentration profiles. Where the plumes were fully turbulent, the plots of inverse concentration versus downwind distance formed reasonably straight lines. The sought-after entrainment velocities are proportional to the slopes of these lines and were found to diminish quite rapidly with Ri*. More in-depth analyses and intercomparisons with the results of the other laboratories are contained in a companion paper in this same volume (Briggs et al., 2001, Atmospheric Environment 35, 2265–2284).     

Neural network approach for modelling ammonia emission after manure application on the field

This paper presents a neural network approach, which enables one to simulate ammonia emission after manure application on the field. Based on the data from 227 experiments out of previously published research, it can be illustrated that the time course of accumulated ammonia emission follows a non-linear Michaelis–Menten-like function. This function is determined by the two parameters E_max and K_M, which are dependent on manure-specific driving forces, application parameters and climate. 102 data sets of the 227 experiments showed sufficient data for training and validating neural networks for estimating E_max and K_M. The neural networks could be trained to R² values of 0.926 and 0.832 for the training set and the validation set of E_max, and to R² values of 0.988 for the training set and 0.527 for the validation set of the K_M-value, respectively.     

On dispersion above a forest—Measurements and methods

Data collected over a mixed conifer/deciduous forest at the U.S. Department of Energy’s Savannah River Site in South Carolina using sonic anemometry reveal that on-site and real-time measurements of the velocity component standard deviations, σ_v and σ_w, are preferred for dispersion modeling. Such data are now easily accessible, from the outputs of cost-effective and rugged sonic anemometers. The data streams from these devices allow improvements to conventional methodologies for dispersion modeling. In particular, extrapolation of basic input data from a nearby location to the site of the actual release can be facilitated. In this regard reliance on the velocity statistics σ_v and σ_w appears to be preferred to the conventional σ_θ and σ_?. In the forest situations addressed here, the uncertainties introduced by extrapolating initializing properties (u, θ, σ_θ, and σ_?, or alternatively, σ_v and σ_w) from some location of actual measurement to some nearby location where an actual release occurs are similar to those associated with the spread of the plume itself and must be considered in any prediction of the likelihood of downwind concentration (exposure) exceeding some critical value, i.e., a regulatory standard. Consideration of plume expansion factors related to meander will not necessarily cause predicted downwind maxima within a particular plume to be decreased; however, the probability of exposure to this maximum value at any particular location will be reduced. Three-component sonic anemometers are affordable and reliable, and are now becoming a standard for meteorological monitoring programs subject to regulatory oversight. The time has come for regulatory agencies and the applied dispersion community to replace the traditional discrete sets of dispersion coefficients based on Pasquill stability by the direct input of measured turbulence data.

Implications: The continued endorsement of legacy Pasquill-Gifford stability schemes is presently under discussion among professional groups and regulatory agencies. The present paper is an attempt to introduce some rationality, for the case of a forested environment.