Environ. Sci. Technol. 2004, 38, 2693-2700
Experimental and Numerical Test of the Micrometeorological Mass Difference Technique for the Measurement of Trace Gas Emissions from Small Plots VINCENZO MAGLIULO,† G I O V A N N I A L T E R I O , * ,† A N D ALESSANDRO PERESSOTTI‡ CNR-ISAFOM, Consiglio Nazionale delle Ricerche, Istituto per i Sistemi Agricoli e Forestali del Mediterraneo, Via Patacca 85, 80056, Ercolano (Napoli), Italy, and DPVTA, Universita` di Udine, Via delle Scienze 208, 33100 Udine, Italy
Micrometeorological methods for measuring fluxes of gases between the land surface and the atmosphere are noninvasive: in fact, they do not interfere with natural processes of gas exchange. The Micrometeorological Mass Difference (MMD) approach can be used for many environmental monitoring purposes, such as to measure methane and carbon dioxide emission from landfills, methane production by grazing animals, trace gas emission from waste products and from agricultural soils, photosynthesis, and transpiration of plant canopies. The purpose of this study is to adapt the MMD technique, originally developed in Australia, to monitor CO2 and trace gases exchange rate at the plot level. Comparison of different treatments in replicated experiments requires plots of few rather than tens of meters. The tests reported here were performed on a square area (4 m × 4 m) in the meteorological field of the experimental farm of CNR-ISAFOM located in Vitulazio, province of Caserta, Italy (40°07′ N, 14°50′ E, 25 m above sea level) and consisted of the release of pure CO2 at different rates (1.7, 1.3, 0.6 L min-1) from a single source on the ground in the center of the experimental area and the consequent measurement of the environmental variables (wind speed and direction, CO2 concentration) at different times at four heights (up to 1.2 m) in order to compute the mass balance according to MMD technique. Measured flow rates well accounted for the mass of CO2 released. A flow underestimation occurred when wind speed dropped below 1.5 m s-1, in accord with the previous findings obtained in Australia: this happened because anemometers can stall at low speeds, and their measurements are unreliable and because of significant loss of mass from the top of the apparatus. The experimental results were compared with outputs of Computational Fluid Dynamic (CFD) simulations. The commercial CFD package Fluent was used to evaluate performances and sources of errors. According to the experimental and numerical results, the MMD apparatus in our present configuration is suitable to be used for the monitoring of trace gas emissions * Corresponding author e-mail:
[email protected]; phone: +390815746606; fax: +390817718045. † Istituto per i Sistemi Agricoli e Forestali del Mediterraneo. ‡ Universita ` di Udine. 10.1021/es0341790 CCC: $27.50 Published on Web 04/02/2004
2004 American Chemical Society
of experimental plots. Advantages and limits of the present approach are discussed.
Introduction Waste products can be valuable resources as fertilizers and suitable to be applied to crops and pastures. However, when concentrated over a small geographical area or applied in excessive amounts, they can have detrimental environmental effects. Excess application can result in enhanced CO2, CH4, and N2O emissions to the atmosphere influencing global warming and destruction of the ozone layer (1, 2). These gases have long atmospheric lifetimes and are consequently fairly well-mixed and therefore of global as well as local or regional importance. They may represent the most serious threat to global climate in terms of greenhouse effects. Ammonia gas molecule (NH3) emitted following waste applications can be transported in remote areas and contribute to acidification processes. To improve understanding of trace gas emissions as a function of agronomic techniques, it is necessary to apply suitable methodologies to measure emissions at the plot level. Chamber methods are widely utilized to measure gas emissions from soils because they are relatively easy to use and relatively inexpensive (3). There are, however, drawbacks to using chambers since emissions from soils are spatially variable and large numbers of replicates are required to obtain accurate results. Chambers may also alter the microclimate, especially turbulence, significantly affecting the emissions. Microclimatic techniques do not alter the microenvironment, average out spatial variability, and in most cases, allow for unattended continuous monitoring. Traditional micrometeorological approaches however have stringent fetch requirements so that large homogeneous fields are necessary and different treatments cannot be compared in real time. The proposed alternative approach is the mass balance micrometeorological method, which provides no disturbance to gas production and emission processes. It is suitable for use in small plots and under conditions of heterogeneous surfaces and/or point sources in factorial experiments. The experimental setup we tested consists of a downscaled version (4 × 4 × 1.5 m) of the Micrometeorological Mass Difference (MMD) system originally proposed by Denmead et al. (4, 5), which instead enclosed a much larger area (22 × 22 × 3.5 m). The conceptual approach does not differ from the above cited studies, but it is applied at much a smaller scale (16 m2 compared with 484): smaller dimensions might increase the experimental error due to several causes (reduced air mixing, insufficient sensor resolution for wind and scalar profiles, increased border effects) and even violate some of the assumptions (negligible vertical transport, fetch/height requirements, etc.). We evaluated its performance through mass recovery tests and comparison with numerical results obtained running Computational Fluid Dynamic (CFD) simulations.
Mass Balance and the MMD Technique In the classical fluid dynamics, for an incompressible fluid, if we consider a finite volume V, the control volume, fixed in space with the fluid moving through it and enclosed by a surface S, the control surface, the equation of continuity can be written as
∫∫∫ ∂F∂t dV ) -∫∫ n‚FV dS V
(1)
S
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FIGURE 1. Outline of the different parts and components of the MMD apparatus. where F is the gas density, t is the time, V is the wind velocity, n is the unit vector normal to the surface S, which positively points out of the surface. In eq 1, since n always points in a direction out of the control volume when V also points out of the control volume, then the positive product n‚FV denotes an outflow; otherwise if V points inward, the negative product n‚FV denotes an inflow. The dimensions of both sides of eq 1 are a mass flow (kg s-1). In our test, the finite volume is a parallelepiped, whose bottom square base side is X and the height is Z. We also introduce a Galilean, Cartesian frame of reference (Ω, x, y, z) relative to which the motion is analyzed (Figure 1). The y axis points toward the north, and the x axis points toward the east. Let us suppose the following: (i) The intensity and direction of fluid moving through the control volume are steady state. (ii) The vertical component along the z axis of the wind is negligible. (iii) The Archimedean convective motions of the air driven by the thermal gradients are negligible. (iv) The velocity field V is
V(z) ) u(z) + v(z)
(2)
where u and v, which are the wind speed components along x and y axes, are a function only of the height z. The wind direction is specified by angle Θ measured clockwise from the north. From eq 2, we derive that, in the planes parallel to the ground, the wind components are constant everywhere if no obstacles (e.g., animals or plants) exist in the surroundings and within the fenced volume that could perturb the velocity field. The enclosed volume in our case has six plane faces: faces 1 and 2 are upwind, faces 3 and 4 are downwind, face 5 is the plane parallel to the ground, and face 6 is the ground. At the right-hand side of eq 1, the scalar product n‚FV is null on surface 6 (the ground) and is negligible on surface 5. Introducing F1, F2, F3, and F4 as the gas density respectively on the 1-4 sides of the control volume, we can write:
∫∫ n‚FV dS ) ∫∫ [u(F s
s
4
- F2) + v(F3 - F1)] dS (3)
where the product of the wind speed components u and v, which are perpendicular to the boundaries, times gas density (Fgas), gives the horizontal convective density flux at a point 2694
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in the atmosphere. In eq 3, let us define F as the result of this surface integral, measured as kilograms per second. F will be positive for gas emission within the test space regardless of wind direction and negative for gas absorption. Furthermore, the variables F, u, v, and F are time averages, and we can denote them by an overbar:
F h)
∫∫ {uj (z)[Fj (x, z) - Fj (x, z)] + vj(z)[Fj (x, z) 4
s
2
3
Fj1(x, z)]} dS (4)
Since the bottom square base side of the control volume is X, we synthetically can write:
F h)
∫∫ X
0
Z
0
{u j (z)[Fj4(x, z) - Fj2(x, z)] + vj (z)[Fj3(x, z) Fj1(x, z)]}dx dz (5)
Equation 5 is essentially the same as eq 1 of ref 4. According to the micrometeorological theories, if a gas is released within a defined space (e.g., a square field of side X), the flux released can be calculated from the difference between the total gas fluxes across the upwind and downwind boundaries of the space. The mean emission rate of released gas F h is given by eq 5.
Materials and Methods A square test plot (Figure 1) was setup over grass in the meteorological field of the CNR-ISAFOM experimental farm, located in Vitulazio, province of Caserta, Italy (40°07′ N, 14°50′ E, 25 m above sea level). Tests consisted of releasing pure CO2 from a gas cylinder at several emissions rates (1.7, 1.3, and 0.6 L min-1) from a single point source (i ) 4 mm) positioned on the ground, in the center of the experimental plot, and measuring the environmental variables (wind speed and direction, temperature, and CO2 concentration profiles) at different times necessary to compute the mass balance according to eq 5. At each boundary of our version of the MMD apparatus there are four horizontal gas sampling lines that provide a continuous measurement of gas concentrations over its total length: each gas sampling line is provided with precisioncalibrated orifices every 0.2 m to allow for homogeneous air intake throughout the entire length. A single central outlet is fed into Bev-A-Line tubing to connect with the gas switching
FIGURE 2. Measurements during the CO2 metered release of 1.7 L min-1: wind velocity profiles (a); difference of CO2 mean concentration between the north and south boundaries (b) and between the east and west boundaries (c); difference of horizontal CO2 flux density (cm3 m-2 s-1) between the north and south boundaries (d) and between the east and west boundaries (e); comparison of CO2 volumetric flow released and measured by mass balance by the MMD apparatus (f). apparatus. Measurement heights of the gas sampling lines in our study were 0.15, 0.3, 0.6, and 1.2 m. Equation 5 shows that the wind profiles and gas concentrations should be measured on each surface of the control volume: the selection of four sampling heights was a compromise between the accurateness required in assessing the gas concentration profile and the time required to make a measurement on each air sample. More sampling heights would enhance the precision of the flux measurement, but conditions may depart from stationarity in the meantime. For each gas sampling line, we provided integrating cylinders, where sampled air is completely mixed, to damp out rapid changes in gas concentration: these cylinders (10 L each) provide a system time constant of about 10 min when sampling air at the rate of 1 L min-1 by means of 8 double-body AC-powered piston pumps. Mean wind velocity is measured at the same heights of gas concentrations sampling lines by four rotor anemometers (Vector, Rhyl, North Wales, U.K.). A conventional wind vane is used to measure wind direction. The data acquisition and control system is comprised of a 21X datalogger (Campbell Scientific, Shepshed, U.K.) to log data from the wind and gas concentration sensors and control the switching of the gas channels by actuating 14 four-way solenoid valves (Numatics Italia, Brescia, Italia) via an SDM 416 relay driver (Campbell Scientific, Shepshed, U.K.); a LICOR 6262 CO2 and H2O infrared gas analyzer (IRGA) (Licor, Lincoln, NE); two dew point hygrometers (General Eastern, Woburn, MA) to assess water vapor exchange rates out of the soil and plant canopies; and two mass-flow meters
(Omega Engineering, Broughton Astley, U.K.) to monitor gas flow to the channels of the IRGA. All sensors were scanned every 3 s, and mean values are stored every 45 s. Real-time graphic display of the state variables and final storage data were output to a notebook PC using the PC208W datalogger communication software (Campbell Scientific, Shepshed, U.K.). The LICOR 6262 was configured in differential mode to output the difference in concentration between the sample and the reference cell. Each individual sampling period was set to 45 s. During the first sampling period, starting from the bottom level of north and south boundaries, the air sampled from the upwind side goes in the reference cell of the IRGA, and the air sampled from the downwind side goes in the sample cell. For the first 25 s, the sample was allowed to flush the common path of the sampling lines and then gas concentration was measured every 3 s, thus providing eight readings that were averaged out. In the second sampling period, a solenoid valve was actuated to invert air samples between IRGA cells, and the difference in concentration between the same two lines was again measured. The mean value between these two consecutive readings was taken as the north-south differential CO2 concentration, thus eliminating systematic errors due to possible offset and gain mismatches in analyzer calibration. The switching apparatus then routes east and west sample lines of level one to the measuring device and so forth. The IRGA automatically corrects for water vapor interference due to both dilution and band broadening effects. The effect of pressure in the VOL. 38, NO. 9, 2004 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 3. Measurements during the CO2 metered release of 1.3 L min-1: wind velocity profiles (a); difference of CO2 mean concentration between the north and south boundaries (b) and between the east and west boundaries (c); difference of horizontal CO2 flux density (cm3 m-2 s-1) between the north and south boundaries (d) and between the east and west boundaries (e); comparison of CO2 volumetric flow released and measured by mass balance by the MMD apparatus (f). sample cell is also corrected for by means of a built-in pressure device. Care was taken to avoid pressure fluctuations in the lines and pressure imbalance between the cells. T-pieces were inserted in each line downstream of the pump, and most of the flow was exhausted through an hydraulic closure by placing the dead end of the T-piece on the bottom of a water tank. At the other end of the T-piece, a needle valve was regulated to send a subsample of air to the IRGA. Values were precisely set at the beginning of the measuring cycles to deliver 200 ( 30 mL min-1 air of each of the sampling lines to the IRGA cells. For the purpose of flux calculation, the wind vector V was split in its components u and v perpendicular to west and south boundaries according to the method (Figure 1). The wind direction is specified by angle Θ measured clockwise from the north. With the experimental sampling system described above, eq 5 becomes
F h)X
∫
Z
0
{u j (z)[Fj4(z) - Fj2(z)] + vj (z)[Fj3(z) - Fj1(z)]} dz (6)
which can be evaluated numerically using the trapezoidal rule.
Experimental Results and Discussion Experiments were performed on three different days, and CO2 releases were maintained for several hours on each day. The measuring cycle of each sample test lasted 12 min. For each CO2 release trial, three consecutive runs with slightly different environmental conditions but with consistent wind 2696
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speed and direction were selected to compute statistics and for the purpose of the following discussion. CO2 Release of 1.7 L min-1. Figure 2a shows the mean wind velocity (2.01 ( 0.18 m s-1) during the tests. The mean wind direction Θ, measured clockwise from the north, and its standard deviation within the run was 68 ( 7° (1746 h run), 68 ( 5° (1758 h run), and 68 ( 6° (1810 h run). Measured wind profiles were nearly logarithmic throughout the experiment and when extrapolated attained a zero value in correspondence of the roughness height of the vegetation (6). Calculated roughness height was 0.038 ( 0.004 m. Mean air temperature was 25 °C. The differences between downwind and upwind concentrations (that is the north concentration minus the south concentration and the east concentration minus the west concentration, respectively) are reported in Figure 2b,c. During this test, the north and east sides were downwind with respect to the south and west sides, respectively, and the air sampled at the north and east boundaries is expected to be richer in CO2. At all sampling heights, the difference in carbon dioxide partial pressure (∆CO2) measured in parts per million (ppm) by volume between north and south and between east and west was in fact positive and decreasing in magnitude with height. The product of wind speed components times the corresponding difference in CO2 mean concentration yields the CO2 density flux, which goes in or out of the plot at each level. The input-output differences of CO2 density flux at each sampling height are given in Figure 2d,e. The highest CO2 flux density across north and south boundaries was
FIGURE 4. Measurements during the CO2 metered release of 0.6 L min-1: wind velocity profiles (a); difference of CO2 mean concentration between the north and south boundaries (b) and between the east and west boundaries (c); difference of horizontal CO2 flux density (cm3 m-2 s-1) between the north and south boundaries (d) and between the east and west boundaries (e); comparison of CO2 volumetric flow released and measured by mass balance by the MMD apparatus (f). detected at the lowest sampling height (Figure 2d), and the same thing happened between east and west boundaries (Figure 2e). In both cases, the difference at the highest sampling point was almost zero, confirming the hypothesis of the conditions of our test; vertical wind speed was negligible; and atmospheric buoyancy motions due to thermal gradients were unable to upraise gas mass above the top sampling heightsat least in the conditions of the present experiment. With hyper adiabatic thermal profiles and lower wind velocities, it could be necessary to move lines and anemometers upward to achieve a null differential in concentration at the top sampling height and therefore the closure of the mass balance. The CO2 gas emissions, evaluated numerically by the trapezoidal rule, are reported in Figure 2f in comparison with the CO2 released from the gas cylinder. The mean rate of mass flow was 1296 ( 59.5 cm3 min-1, accounting for 75% of the released mass, but dropped below 70% when wind speed at top level dropped below 1.7 m s-1 (1810 h run) in accord with previous findings (4, 7). The reason for this must be found in the uncertainties in the transport of mass at low levels of mechanical turbulence and in the sampling patterns, with part of the gas escaping out of the top the “box” or flowing perpendicular to the mean flow direction without being accounted for (no wind component contributing to the mass balance account). CO2 Release of 1.3 L min-1. The first selected run is at 1455 h, the second is at 1507 h, and the third is at 1519 h. Figure 3a shows the mean wind velocity (3.35 ( 0.5 m s-1) during the tests, which was higher but more variable with respect to the previous case. The wind profile again had a
near-logarithmic trend and attained a zero value at the roughness height (0.035 ( 0.003 m). The mean wind direction was 130 ( 12° (1455 h run), 130 ( 10° (1507 h run), and 130 ( 6° (1519 h run). Mean air temperature was 19.2 °C. The differences between downwind and upwind concentrations are reported in Figure 3b,c. In these runs, the south and east sides are downwind with respect to the north and west sides, respectively; the air sampled at south and east should be richer in CO2. At all sampling heights, the measured difference in carbon dioxide (∆CO2) between north and south was negative (Figure 3b) and that between east and west was positive (Figure 3c). The CO2 flux density at each sampling heights are given in Figure 3d,e. The highest difference in CO2 density flux between south and north was detected at the lowest sampling height (Figure 3d), and the same thing happened between east and west (Figure 3e). In both cases, the difference at the highest sampling point was almost zero. The mean calculated flux (Figure 3f) was 970 ( 18.7 cm3 min-1, which accounted for 74% of the mass of CO2 released. CO2 Release of 0.6 L min-1. The first run is at 1459 h, the second is at 1511 h, and the third is at 1523 h. Wind profiles are shown in Figure 4a (calculated roughness height is 0.010 ( 0.002 m). Mean wind speed was 3.73 ( 0.28 m s-1; air temperature is 16.2 °C. The mean direction Θ, measured clockwise from north, was 120 ( 12° (1459 h), 120 ( 11° (1511 h), and 120 ( 8° (1523 h). The differences between downwind and upwind concentrations are reported in Figure 4b,c. In these runs, the south and east sides are downwind and the north and west sides are upwind, so that differences in carbon dioxide VOL. 38, NO. 9, 2004 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 5. Relationship between recovery rate (ratio between mass of CO2 released and mass of CO2 calculated by the mass budget) vs CO2 release rate (left axis) and wind speed at the top sampling level (right axis). concentration between north and south were negative (Figure 4b) and those between east and west positive (Figure 4c). The highest difference in CO2 flux density was detected for both north-south and east-west boundaries at the lowest sampling height (Figure 4d,e). There was no measurable difference in CO2 flux density at the uppermost level. The calculated mass balances515 ( 10.5 cm3 min-1s accounted for a higher percentage of recovered mass (0.84 ( 0.033) than in the other cases. Calculated flow was also more repeatable between consecutive runs (Figure 4f). This can be attributed to both high wind speed but more likely to the constancy in wind direction. Denmead et al. (4) pointed out that this parameter is critical and care must be taken to discard data points collected across significant wind shifts. Some relationships among environmental conditions and recovery rates are reported in Figure 5. The fraction of recovered mass was positively correlated with mean wind speed. However, the correlation coefficient was low (0.55*), and the relationship appeared biased by a threshold effect, losing significance when data collected at wind speed lower than 3 m s-1 were discarded. More evident (r ) -0.73**) was the inverse relationship between the percent of recovery and the amount of released CO2. This is due to the fact that in small plots the plume deriving from diffusion of gases heavier than air out of the soil remains confined in the shallowest layers, where mean wind speed is likely to be underestimated and the measurement of concentration profiles with a constant linear sampling approach is uncertain. Chances exist that most of the released mass may “slide” below the lowest sampling height and not be accounted for in the calculation. 2698
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The main difficulties arising from adapting mass balance methodologies originally developed to monitor fluxes out of large fields (450 m2) derive from the necessity of a better sensor accuracy to detect smaller differences linked to the reduced size of the source. Since the plume originating from such a source is closer to the ground, sampling points need to be closely spaced, and again care must be exercised to assess smaller gradients in wind speed and scalar concentration along the vertical profile. Our study confirm these difficulties so that care must be exercised in doing measurements when the magnitude of the efflux is such that steep gradients are established at the lowest heights (that is high source strength, low wind speed, and low buoyancy). Uncertainties are also related to the magnitude of the counter gradient diffusion; border effects may play a major role when dealing with an object 1 order of magnitude smaller than the original optimized apparatus, as in our case. Therefore, it is important to choose the correct value of the semi-empirical coefficient to apply to correct for those uncertainties. According with Figure 5, wind speed lower than 3 m s-1 and emission rates in large excess of 600 mL min-1 in the case of CO2 may significantly reduce recovery rates. When discarding these data, the mean value of the recovery rate was found to be 0.844, a value very close to that suggested by Denmead et al. (4) and Harper et al. (7), who proposed a 15% value to take into account the counter gradient diffusion. According to reported results, the MMD apparatus in its present configuration is suitable to be used for the monitoring of trace gas (such as CO2, N2O, CH4, and NH3) exchange rate out of the soil-canopy system in experimental plots on order of magnitude smaller than those used in previous papers. Important biological processes such as ammonia volatilization, etc. could therefore be studied by applying this technique in replicated open field experiments, and autotrophic and eterotrophic respiration and photosynthesis can be monitored on a continuous basis. It is important to note however that, according to our assumptions, the terrain enclosed and surrounding the test plot should be homogeneous. Care must therefore be taken to ensure that the measured wind profile is representative of aerodynamic conditions at either the upwind and downwind side of the MMD plot (i.e., the size and distribution of vertical elements inside and outside of the plot should be the same). If this condition is not met, then four separate wind profiles must be established, further complicating the setup. Evapotranspiration fluxes may also be measured without further modifications, although problems may arise due to water vapor absorption or even dew formation on the surfaces of tubing and reservoir tanks, so that the reliability of such estimates remain to be assessed in subsequent trials with the appropriate choice of material for tubing and tanks and the use of heating tape to maintain all surfaces constantly above dew point temperature. For applications related to the quantification of emission/absorption of greenhouse and reactive gases, a suitable specific sensor should be connected downstream to the H2O/CO2 IRGA. Gas-specific tunable diode lasers (TDL) are the most accurate and reliable sensors, which have been fully tested for the continuous measurement of CH4, N2O, and NH3 concentrations in open air. Fourier transform infrared spectrometers (FTIR) and photoacustic multiple gas analyzers are alternative choices, with possible drawbacks deriving from slower sampling rate and lower resolution with respect to TDLs.
Error Analysis To quantify the uncertainty linked with emission measurements at the small plot level, systematic and random error analysis was carried out. The MMD measurement is based
on mass conservation of the source/sink included in the enclosed area. This translates in three basic assumptions: (i) The flux out of the top is negligible. This requires that the height of the downwind boundary must be such as to capture most of the concentration gradient. However, as discussed below, a tall boundary implies a large number of sampling layers or a reduced accuracy unless the top layer is placed exactly in correspondence of the null horizontal concentration gradient, which cannot be known a priori. (ii) The flux passes entirely through the downwind boundaries. This requires that the downwind sampling boundaries are wide enough to ensure that all the flow exits from not more than two surfaces. (iii) Trace gas transport occurs mainly by advection (i.e., turbulent and diffusive transport can be neglected). Turbulent transport is proportional to horizontal and vertical turbulence intensities and depends on source position. With a source centered in the middle of the MMD area, the effect of horizontal turbulent transport on the flux is maximum when mean wind direction points toward MMD cornerssand is almost negligible when points toward sides. In fact, in the last case, horizontal fluctuations are spatially averaged over the sampling line. Systematic errors associated with these assumptions can only be reduced by changing the setup and/or the algorithms for flux calculations. A discussion of the approach toward an improved flux calculation is outside the scope of the present paper. The aim of developing the MMD concept further and an improved algorithmsusing an advection-diffusion transport equation to interpolate vertical wind and concentration profilessmight be developed in subsequent work. This could lead to substantially enhance the accuracy of the measurements in both large- and small-scale plots and avoid some of empiric assumptions. Random errors can instead be analyzed according to the error propagation theory based on individual errors of each sensor (8). A single flux measurement relies on individual measurements of eight concentration gradients, four wind speeds, and one wind direction; thus, the total is a function of 13 individual measurement errors (ri). Assuming that individual measurements errors are small, normally distributed, and independent, absolute error can be calculated as
∆F )
x∑
13 1
( ) ∂F ∆r ∂ri i
2
(7)
where ∆F is the absolute flux root-mean-square error (cm3 min-1); ∆ri is the individual measurements errors, estimated from instrument accuracies; and ∂F/∂ri is the partial derivative of the flux (eq 6) with respect to each ri variable. ∆ri values associated with anemometers, gas analyzers, and wind vane were set to 0.1 m s-1, 0.1 cm3 m-3, and 10°, respectively. The calculated random errors for our experimental conditions were 155, 74, and 45 cm3 min-1, respectively, for the 1.7, 1.3, and 0.6 L min-1 release experiment corresponding to a relative error of 11, 7, and 9%. These errors are smaller if compared to previous results, also in relation to the improved accuracy of the concentration measurements. The associated sensitivity analysis showed that ∆F was most sensitive to wind speed measurements for the 0.6 L min-1 release experiment and most sensitive to concentration measurements for the other two experiments. Wind direction measurement accuracy resulted as less important and increased the final absolute flux error of only 3% in response to a 100% increase of the individual error.
Numerical Results and Discussion The experimental and theoretical results of the modified MMD technique were evaluated by running a CFD simula-
FIGURE 6. Comparison of numerical and experimental difference of horizontal CO2 flux density between the north and south boundaries during the 1.7 metered release tests (1758 h). tion: the commercial CFD package Fluent (Fluent Incorporated, Lebanon, NH; version 5.4 released to Universita` Federico II, Napoli, Italy) was used to evaluate performances and highlight sources of errors. The spatial domain we numerically analyzed is a cube having a side of 6 m. The MMD square test plot is located at the center of this spatial domain: in this way, the velocity field inside the MMD square test plot is fully developed. The spatial domain is discretized into a 3D mesh of linear cubical elements, having a side of 0.20 m. The equations to be solved are the Reynolds equations that in a Cartesian coordinate system can be written as
∂u j ∂p j ∂ ∂u j ∂ j + vj )j - F (u′2) + (u′v′) Fu + µ∇2u ∂x ∂y ∂x ∂x ∂y
[ ] [ ] ∂vj ∂p j ∂ ∂vj ∂ F[u j + vj ] ) + µ∇ vj - F[ (u′v′) + (v′ )] ∂x ∂y ∂y ∂x ∂y 2
(8)
2
These are the Navier-Stokes equations, with the mean values of the velocities u j and vj and viscous stresses replacing instantaneous values and the Reynolds stresses, which are independent of viscosity and depending on the velocities fluctuations u j ′ and vj ′. In eq 8, p is the pressure, µ is the gas dynamic viscosity, ∇2 is the Laplacian operator (∇2 ) ∂2/∂x2 + ∂2/∂y2). The boundary conditions imposed at the ground level were u ) v ) 0. On the other surfaces of the control volume, we imposed the wind profile experimentally measured in field during our tests. The approach adopted for the closure of the system is the well-known κ - model in which the solution of two separate transport equations allow the turbulence velocity and length scales to be independently determined. The standard model in Fluent falls within this class of turbulence model and has become the workhorse of practical engineering flow calculations since originally proposed by Launder and Spalding (9). VOL. 38, NO. 9, 2004 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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The field measurements taken in a significant range of environmental conditions and the simulation with a CFD package confirm the suitability of the MMD approach for the unattended and non-invasive assessment of trace gas fluxes at the small plot level. The wind speed threshold and the value of the empirical counter gradient coefficient did not differ from those determined in previous studies at largerscale plot. This implies that data records not reaching the desired threshold must be discarded. On the other hand, the sampling patterns and calculation algorithms of the MMD failed to account for all the released mass of gas at high release rates. The higher rates of CO2 emissions we used for our tests, however, are more than 1 order of magnitude larger than those found under natural field conditions for respiratory processes. The opposite constraint is most likely to occur (i.e., not having sufficient sensor resolution to assess small vertical gradient at low respiratory/photosynthetic activity or other trace gas emission/deposition). In this regard, attention must be given toward the recent development of high-resolution specific sensors such as quantum cascade TDLs.
Acknowledgments We thank Gianfranco Rana for helping in the analysis of error, Ferdinando di Matteo for assembling the experimental setup, Diego Paterna for running the CFD simulations, and Lowry Harper for his contribution in designing the system and the many useful suggestions. FIGURE 7. Comparison of numerical and experimental difference of horizontal CO2 flux density between the east and west boundaries during the 1.7 metered release tests (1758 h). For the purpose of the simulation and comparison, we selected the concentration profiles as measured during the release test of 1758 h, with a release rate of 1.7 L min -1 (Figure 2b,c). We defined a volumetric point source of CO2 in the center of the ground of MMD spatial domain. The CO2 profile concentrations were calculated over all the surfaces of our control volume. We also computed the difference of the volumetric CO2 flows between downwind and upwind sampling heights. The simulated and measured horizontal CO2 mass flows are reported in Figures 6 (north and south boundaries) and 7 (east and west boundaries). The highest discrepancy in flow between north and south was detected at the lowest sampling height, and the same thing happened between east and west. Overall the agreement was better for the east-west profile. The numerical results confirm that measured concentration profiles are those to be expected from theory under the conditions of our test. The mass flow calculated on the basis of the simulated concentration was equal to 1.23 L min-1 with respect to the MMD flow of 1.4 L min-1.
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Received for review February 27, 2003. Revised manuscript received February 6, 2004. Accepted February 12, 2004. ES0341790
