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Archive Document Historic, Do assume not content reflects current scientific knowledge, policies, or practices. nr.% 7 MFOSoutfc iONTHLY alert CGPt MONTH ITEM # „ 9-1 United States Eddy Diffusivities for Sensible (i^j) Department of Agriculture Momentum Heat, Ozone, and Forest Service From Eddy and Correlation Rocky Mountain Forest and Range Gradient Measurements Experiment Station Fort Collins, Colorado 80526 K. F. Zeller Research Paper RM-313 Abstract The eddy-correlationmeasurementtechniquewas usedto obtain micrometeorologicalfieldmeasurements ofthefluxes ofmomentum, sensible heat, and ozone at 3 and 8 meters at the Pawnee site. A method to accurately measure mass (ozone) gradients from surface- layer-based meteorological towers was developed and used. Both flux and gradient measurements were used for the determination of eddy diffusivities. Ozone was used as the mass tracer to explore similar relationships between the eddy diffusivities of momentum K^, sensible heat K and mass K h, c. Eddy-diffusivity ratios were computed using dimensionless- gradientratios classified fromthe dataandregressionmodels. These ratios were classified by atmospheric stability determined at the geometric mean of the measurement heights. The assumption of similarity between the eddy diffusivities of ozone and sensible heat, K = K based on scalar turbulent transfer c h, theory, was verified for unstable atmospheric conditions. Eddy diffusivities of sensible heat are, however, 50% greater than diffusivities of ozone for stable atmospheric conditions. Chemical reac- tion of ozone, and/or the need for flux-measurement corrections, decrease the resulting values for ozone diffusivities during stable periods. Established eddy-diffusivity ratios for water vapor and momentum are valid for ozone and momentum under stable atmospheric conditions over smooth terrain, but not under unstable conditions for flow disturbed by irregular terrain. The relationships between the eddy diffusivities ofmomentum and ozone, as well as those between momentum and sensible heat, are controlled by free-convection conditions, < K and < K^; c these results are inconclusive for unstable-atmospheric, smooth- terrain conditions for the Pawnee site during easterly winds. For disturbed-flowconditions atthePawnee site duringwesterlywinds, theeddydiffusivities formomentumwereenhancedandbothK^/K^ and Kh/Km become approximately constant (0.35 and 0.5, respec- tively) for both stable and unstable conditions. Theoretical flux measurement corrections were applied to a subset of the data in an attempt to investigate the concept of a constantfluxlayerandtovalidatefluxcorrectiontheory. Theresults indicate that flux corrections are warranted. However, improve- ments to flux correction theory are needed, especially for stable atmospheric conditions, as demonstratedbythe significantincrease in datavariabilityas aresultofthese corrections. The "constantflux- layer" concept holds for momentum flux and sensible heat flux, but is questionable for ozone flux. Acknowledgments This study was sponsored by the USDA Forest Service, Rocky Mountain Forest and Range Experiment Station. Support was also provided by the Environmental Protection Agency under Inter- agency Agreement DW12933093-01-0. USDA Forest Service September, 1993 Research Paper RM-313 Eddy Diffusivities for Sensible Heat, Ozone, and Momentum From Eddy Correlation and Gradient Measurements K. F. Zeller, Meteorologist Rocky Mountain Forest and Range Experiment Station1 Headquarters is in FortCollins, COin cooperation with Colorado State University. Paperis basedon a thesis submittedto Colorado State University, inspring 1990. CONTENTS Page MANAGEMENT IMPLICATIONS 1 INTRODUCTION 1 Governing Equations 1 Eddy Diffusivities 2 Goals and Hypotheses 2 SUMMARY OF PREVIOUS INVESTIGATIONS 3 Eddy Diffusivities 3 Eddy Correlation Flux Measurements 4 Surface-Layer Considerations 5 EXPERIMENTAL DESIGN 7 Field Site 7 Meteorological Measurements 8 Ozone Measurements 9 Ozone Analyzers 9 CAAM Response 9 CAAMLag 9 Ozone Calibrations 10 TECO Response vs. Ambient Temperature 10 Ozone Depletion Due to NOx 11 RESULTS AND DISCUSSION 11 Gradients of Ozone, Temperature, and Horizontal Wind Speed 12 Variance of Ozone, Temperature, and Vertical Wind Speed 12 Surface Roughness 14 Fluxes of Ozone, Sensible Heat, and Momentum 14 Dimensionless Gradients of Ozone, Sensible Heat, and Momentum 17 Eddy Diffusivities of Ozone, Sensible Heat, and Momentum 19 CONCLUSIONS 24 Eddy Diffusivity Comparisons 24 Constant Flux Layer 25 Other Findings 25 Recommendations for Future Research 26 REFERENCES 26 APPENDIX A. DATA ACQUISITION AND HANDLING 30 Data Acquisition and Real-Time Computations 30 Data Editing 30 Ozone Gradient Determination 30 Flux Measurement Corrections 33 Effects of Heat and Water Vapor 33 Insufficient Averaging Time 34 Random Noise 34 Homogeneity and Stationarity 34 Sampling Height 35 Inadequate Fetch 35 Flow Distortion and Shadowing 35 Assumptions 35 Measurement Error 36 APPENDIX B. SPECTRA AND COSPECTRA 37 Temperature Spectra 37 Temperature Cospectra 37 Vertical Velocity Spectra 37 CAAM (Ozone) Spectra 38 CAAM (Ozone) Cospectra 39 APPENDIX C. DATA PLOTS 40 APPENDIX D. TABLE OF SYMBOLS 42 Eddy Diffusivities for Sensible Heat, Ozone, and Momentum From Eddy Correlation and Gradient Measurements K. F. Zeller MANAGEMENT IMPLICATIONS The physical origin ofthe deposition ofa pollutant, c, can be understood by visualizing its mass balance Fluxes of trace gases ("greenhouse gases") in the within any airshed as a simple control volume (McRea atmospheric boundary layer have attracted the con- and Russell 1984): cerned interest of the scientific community because of the major climate changes projected for the present and — the near future. Although concentrations ofthese trace * I cdv + fFr . nds - | Rdv = 0 [1] Jv Js Jv gases are known and have been monitored for years, it is information on sources, sinks, and transport ofthese where the first term accounts for emissions of c [gm m"3 gases that is necessary for predicting future concentra- or parts per billion (ppb) by volume] integrated within tions and the consequence ofclimate change. The mea- the control volume, V; the second term accounts for the surementandanalysis offluxes andverticalgradients of flux Fc [gmm"2 s"1], ofcintegratedacrosstheboundaries ozone, aswell astraditionalmicrometeorological fluxes of heat and momentum over long time periods, offer S ( n is the unit normal) ofthe surface; and R is the rate of chemical production or reduction integrated within comparisons and better understanding of measured the control volume. boundary layer eddy diffusivities of momentum, heat, Assuming that the airborne pollutant in question is and ozone. These measurements over dry grasslands nonreactive and that it eventually exits the atmosphere provideregion-specificfluxes, informationon thetrans- at the earth's surface, the correct evaluation of the port behavior of ozone, and the documentation of how to make such flux measurements. surface integral (second term) in [ll over the lower control volume boundary determines the ultimate cor- rectness of the modeled scenario. The flux of material INTRODUCTION for a specified pollutant species c passing through the lower surface is its deposition flux F Since the mid 1960's with the advent of modern- c. environmental legislation, the horizontal transport and dispersion characteristics of the wind in the atmo- Governing Equations spheric surface layer have been studied and modeled with the goals not just ofbasic research, but ofenviron- The expression for the concentration ofa pollutant mental management and protection. Modern environ- (scalar quantity) transported through a boundary layer mental decisions have been based on modeled and is (Businger 1986; Rohsenow and Choi 1961): measured pollutant concentrations within the ambient air (Cermak 1975; Kao 1984; Randerson 1984). Now, as a result of the "acid rain" issue, emphasis is being 9t axj 5x2 shifted to the amount of a pollutant delivered to and 1 "taken up" by various components of the earth's sur- where face: bare soil, water surfaces, biological canopy, or man-made ornatural material surfaces (NRC 1983). The c = c(t, Xj), the instantaneous concentration (in amount of a pollutant removed to a surface—mass per gm m"3 or ppb) (Einstein's summation con- — vention applies over repeated indices); unitareaperunittime isthepollutantdepositionflux. Knowledge of and predictions of pollutant deposition Uj = u(t, Xj), the instantaneous orthogonal compo- are required for acid rain related and other air pollutant nents of wind velocity; relatedimpactassessments.Depositionhasconsequently Dc = the molecular diffusivity of c; and become an important consideration in recent modeling S = a source or sink of c. developments (Hicks 1984; NCAR 1985; Venkatram et al. 1988; Walcek et al. 1986; Walcek and Chang 1987). When the instantaneous concentration and instan- Deposition can be either "wet" or "dry," depending taneous velocities are decomposed into their average, upon the delivery process. An air pollutant making its c and fluctuating or turbulent parts, c', (i.e., c = c + c' , way to a surface without the aid ofprecipitation would and Uj = u + u\), and then combined and averaged, [2] i be dry-deposited upon leaving the atmosphere. becomes: 1 — — dlu\c 2 where Km is the eddy (or turbulent) diffusion coeffi- 3c + d(ui*C) ~3x7 = D, a ^ + S [3] cient for momentum, Kc for ozone (mass), Kh for sen- at 3x' sible heat, and for water vapor; pis the density ofair; Assuming steady-state, horizontalhomogeneity, andno v is the average water vapor; and 6 is the average potentialtemperature. The conceptofaneddy diffusion local sources or sinks allows the first, second, and fifth coefficientformomentumisrootedinPrandtl's "mixing terms of [3] to be canceled leaving: length theory" (Haltner and Martin 1957). 3w'c' 3^c Two recent models have used the K approach. The 3z = DC 3z2 [4] Regional Acid Deposition Model, RADM (Chang et al. 1986; NCAR 1985), developed for EPA at NCAR, for where w' = u' and z = x the vertical wind velocity 3 3, instance, integrates [8b] as a starting point in the devel- fluctuation and vertical distance coordinate, respec- opment of a method to calculate pollutant fluxes. In tively. Integration of [4] betweenthe earth's surface and RADM, K is provided for through a similarity relation- height z yields a description of the vertical flux of c ship withcKm The AcidDeposition and OxidantModel, between those levels: ADOM . (Venkatrametal. 1988), aninternationallyspon- w 'acp 'acp sored model similar to RADM, uses the same approach. w'c c = D, D, [5] 3z 3z The recommended engineering approach to speci- 'o fying K for ozone or for any other airborne mass is to Since w' approaches zero at the surface, (w'c')o is assumectheprinciple ofsimilarity (Galbally 1971; Munn minimal and can be disregarded. Also (Wc')z, the verti- 1966; Oke 1978;RiderandRobinson 1951; Sellers 1965): cal turbulent transport at height z is many orders of magnitude greater than Dc(3c / 3z)z.the vertical molecular diffusion transport at height z; therefore, it can Kc = Kh = Kv = aKm [9] also be disregarded. This leaves the expression: where a is a constant (~ 1.35) for stable atmospheric -bJ— conditions and a function ofstability forunstable atmo- = [6] ) spheric conditions (Businger 1986). 3z A) to describethevertical transport, flux, or dry deposition of pollutant c (Businger 1986). Equation [6] is valid for Goals and Hypotheses any scalar (e.g., temperature, water vapor) given the same assumptions in the derivation. The surface mo- Thispaperinvestigatesexchangeprocessesbetween lecular transport, second term in [6], cannot be mea- the atmosphere's surface layer and the earth's surface. sured directly (Businger 1986); therefore, the first term, Pollutants are transported from the earth's air-surface wV, measured at height z, is the only opportunity to layer to an underlying surface. Measurements of sur- directly measure F the vertical flux of c. face-layer fluxes and vertical gradients ofsensible heat, c , ozone, and momentum were acquired over a relatively Fc = w'c' [7] flat-terrain, shortgrass steppe prairie (Zelleret al. 1989). The eddy correlation technique is used to measure the Diffusivities obtained directlyfromthesemeasurements right-hand side of [7] directly, although indirect mea- are compared to established empirical relationships, surement techniques exist. and the similarity assumptions, [9], are evaluated. Mass diffusivities, such as the diffusivity for ozone, are used by the scientific and engineering communities Eddy Diffusivities to describe the diffusion of mass through the atmosphere. The results presented in this paper can be used Specification of flux for momentum t, mass F to improve pollution impact assessments and to help sensible heat H, and water vapor XE have historicallcy, establishrelationshipsbetweenpollutantsandthedam- been based on the gradient (or profile) approach (Bache age they cause. More clearly understood and specifi- 1986; Munn 1966; Rosenberg 1974; Sellers 1965). The cally defined mass diffusivities, for example, will more assumptionisthatthe sametype ofequation formolecu- accurately account for actual mass deposition ofpollut- lar diffusion transfer applies to turbulent transfer: ants. This study had two main objectives: t= PKm (3u73z) [8a] 1. To investigate the validity of using eddy diffu- Fc = -Kc (3c/3z_) [8b] sivities ofsensibleheat ormomentumto specify H= -pCpKh O0/3z) [8c] the eddy diffusivity for ozone under various XE = -pLK (3v73z) [8d] atmospheric stabilities. v 2 ) 2. To investigate the assumption of a constant Given temperature and mass are both scalars, heat vertical flux layer for heat, momentum, and and mass transfer by the turbulent atmosphere should ozone within the lower atmospheric surface be similar, hence the expected ratio Kh/Kc is 1. Empiri- layer. cal data for various flows indicate thatthe ratio K /1^= h a should be in the range 0.5 and 1 (Bird et al. 1960); My aim was to investigate time-honored assump- however, based on atmospheric experiments, a de- tions that are commonly used, but as yet have not been pends onstabilityand, aspresentedabove, is sometimes completely verified by experimental methods. In fact, estimated as 1.35 for stable conditions. Businger et al. attempts to prove or disprove these assumptions have (1971) provide an empirical relationship for the ratio a met with mixed results (Businger 1986). The data col- as a function of atmospheric stability: lected at the Pawnee site were culled and edited to -9Q1/2 provide representative data records, which were then a = 1.35(1 f.or £r <0n ,(unstable)v used to calculate and analyze dimensionless gradient, (1-15QJ eddy diffusivity, and atmospheric stability quantities. [10] Objective 1 was evaluated by comparing measured re- a = (l + 4.7z) for z > 0 (stable sults and regression models of the measured results (0.74 + 4.7z) with accepted empirical theories for smooth terrain at where various atmospheric stabilities. Objective 2 was evalu- £ = z/L, an atmospheric stability parameter; ated by comparing pairs of observed corrected and z = height above ground; and uncorrected fluxes attwo levels with the expected ratio L = the Monin-Obukhov length, [13]. of 1:1. Based on [10], a is equal to 1.35 only when £—0, then it quickly drops to -1 for £>0. An earlier empirical 025 SUMMARY OF PREVIOUS INVESTIGATIONS result given by Swinbank (1968), a=2.7£ for £<0 , better describes the Pawnee site results. Eddy Diffusivities In an attempt to preview the behavior of Kc/Km, Y^/Km is used here to represent a "mass" diffusivity as Flux equations [8a-d] are the turbulent analogies to opposed to Kh/Km. Rosenberg (1974) provides an em- the basic physical law relating molecular viscosity to pirical relationship for the ratio ofKv/Km as a function molecular diffusion. The eddy diffusivity (also called ofatmospheric stability based on experiments by Pruitt eddyviscosity,eddyexchangecoefficient,andaustausch et al. (1971): coefficient) Km is theturbulentanalogyto Newton's law Ky/I^ = 1.13(l-60Ri)0 074 Ri<0.017 (unstable) for molecular viscosity. The eddy diffusivities Kc, Kh, [U] and are the eddy diffusivities analogous to Fourier's fc^/^ = 1.13(l+95Ri)-011 Ri<-0.011 (stable) and Fick's laws for the molecular diffusion coefficients where for mass, heat, and water vapor. The units of these coefficients are the same, cm2s_1 however, the eddy Ri = the gradient Richardson number, ; diffusivities are several orders of magnitude greater another stability parameter, [14]. than their molecular counterparts. Eddy diffusivities Note that an asymptotic overlap exists in [11] around are based on assumptions about the similarity between Ri=0. Panofsky and Dutton (1984) use the approxima- molecularandturbulenttransfer, not on soundphysical tions £=Ri for £<0 and £=Ri/(l-5Ri) for £>0. Equations lsaiwmspl(yArfyluaid19p8r8o)p.erTthieesy.aTrheerperofpoerret,iveasroifattihoensflionw,menao-t [10] and [11], the ratio Kh/Kv, [10] divided by [11], and a=2.75£ are plotted in figure 1 as functions of £. sured Kq's are expected as the atmospheric-surface- Figure 1 shows that the eddy-diffusivity similarity as- layer characteristics change. sumption, does not hold exactly based on data [9], Basedonscalingarguments, Lettau (1951) limitsthe reported intheliterature, astheempirically determined vthaaltueKomfKwilltovaarmyaxfriommu~m1ofto10-810cm2csm_1,sandbehtewpereenditchtse ratio K^/Ky, is not precisely 1. The ratio K^/K^ reaches a constant value of 1.2 for £>1 and is still increasing at earth's surface and 1-km height. Jacobi and Andre the value 1.8 for £<-5. The ratio K^/fC^ plotted in figure (1963) provide estimated height-dependent values 1 different fromunity, is agood preview estimatebased (cm2s"a) based on atmospheric stability: on, reported data available for K /K because both K h c c Height Stability and Ky are mass diffusivities different from and K h, Inversion Stable Neutral Unstable momentum and heat diffusivities. m 3 30 250 5,500 55,000 Eddy-diffusivity similarity, [9], is used throughout m 8 80 790 16,000 160,000 the technical literature (e.g., Businger 1986). A variety 3 ) 4 and H, then using [8b] with the similarity assumption. Kh/ (Swinbank1968) This approach has been used by many (Droppo 1985; 3.5 Woodruff 1986); however, concentration differences Kh/Km (Busingeretal. 1971) 3 - ^ measured over short vertical distances are difficult to Ky/K^, (Pruittetal. 1971) resolve because of limited instrument resolution. To o 2.5 CO Kh/Ky (Previewestimate) circumvent this limitation, one instrument is typically >> 2 usedwiththe sampling-intake height switched periodi- w callybetween the chosen 8z levels over the data averag- 1.5 H ing period (Businger 1986). Woodruff(1986) quantified 1 errors up to 32% using this approach to the gradient 0.5 technique. Table 1, a review of experimental results from cur- -5 -3 rent literature, shows a paucity ofdc/dz data are avail- z/L able fromwhich to estimate K This paper includes the c. Figure 1—Empirically derived eddy diffusivities vs. stability development of a better technique to measure dc/dz parameter (z/L). specifically for ozone that will be applicable to other oftechniques canbe used to estimate K For instance, trace gases. c. by specifying Kh = K^, H and X.E can be determined All ofthe methods that employ [8b] for determining through [8c] and [8d] using the Bowen ratio method Kc and Fc use the similarity assumption [9]. All of the (Rosenberg 1974), which involves measuring the sur- acid deposition models developed to date use the simi- face energy-balance components using well-proven, larity assumption, although proof of this assumption reliable instruments. Once XE or H are known, either through experiment has not been thoroughly explored. [8c] or [8d] with either calculated K or calculated h can be used to specify K by [9] (Sellers 1965). In c another approach, X.E and H are determined by Eddy Correlation Flux Measurements calculating t using the logarithmic wind profile and assuming the similarity relationship with aKm and the The direct measurement of the flux w'c', [7], is other eddy diffusivities, [9]. called the eddy correlation technique. It has long been Themass eddy diffusivity K and fluxF can alsobe considered the most reliable (Arya 1988) and most c c estimated by applying a modified Bowen ratio, a gradi- fundamental approach to flux measurements as mass, ent technique that involves measuring dc/dz, dd/dz, heat, and momentum are primarily transported by tur- — Table 1. Ozone flux experiments. Sample Sample Measured range height freq. EC: GR: V Reference Method* location Instruments (Hz) (ppb m s1) (ppb rrr1) (cmds:"1) Delany et al. EC 4 & 8 m Chemiluminescence, 10 0 to -0.7 (1986) sonic anemometer Droppo (1985) EC 9.1 m Chemiluminescence, ? 0 to -0.55 uvw Gill anemometer GR 0.75 & 5.5 m -0.55 to 3.38 Lenschow (1982) EC/V Aircraft Chemiluminescence ? -0.05; 1.0 d Meyers EC/V ? Summary report ? 0 to -0.04 d & Yuan (1987) (daily average) Wesely et al. EC/V 5.2 m Chemiluminescence, 20 -0.05 to -0.3 d (1982) assume: uvw Gill Wesely et al. EC 5 to 8 m Chemiluminescence, ? -0.01 to -0.13 (1981) (winter) uvw Gill Wesely et al. EC 4 & 5 m Chemiluminescence, ? -0.2 to -0.55 (1978) uvw Gill Zeller et al. EC 6 m Chemiluminescence, 14 0 to -0.5 0 to -0.7 (1989) uvw Gill Zeller& Hazlett EC 6 m Chemiluminescence, 14 0 to -0.3 0 to -0.35 (1989) sonic anemometer GR: gradient ECA/d: eddy correlation with only deposition velocity reported (Vd=Fc/C EC: eddy correlation flux not specified in report. 4