Use of a mixed-layer model to estimate dimethylsulfide flux and application to other trace gas fluxes

. We discuss two techniques based on mixed-layer scaling for estimating trace gas surface emission fluxes from aircraft using instruments that do not have sufficient frequency response for direct eddy correlation measurements. The first is the mixed-layer gradient technique, which requires accurate measurements of mean concentrations at several heights in the clear convective planetary boundary layer (CBL) to resolve gradients from even strong surface sources of short-lived trace gases. The flux-gradient relationship is obtained from large-eddy numerical simulations of the CBLo We show that this technique is limited to trace gases with lifetimes of about a day or less. An example is dimethylsulfide (DMS), which is emitted from the ocean and has a lifetime of about a day. Surface DMS from data from the NASA aircraft during the Pacific Exploratory Mission-Tropics (PEM-Tropics) flight 7 (August 24, 1996), when the aircraft flew a sequence of constant altitude circles about 50 km in diameter at different heights in and above the boundary layer, following the boundary layer air trajectory. The flight took place between 0530 and 1330 local solar time, providing a good opportunity to observe diurnal changes within a Lagrangian framework under nearly clear-sky conditions. The resulting DMS of 2.5 q- 0.8 The second technique is the mixed-layer variance technique, which uses measurements of the variance at several heights in the CBL to estimate the surface flux. A major problem with the variance technique is accounting for the contribution of mesoscale variability to the measured variance. Several sources of mesoscale variability were identified: clusters of small cumulus clouds rising through the top of the boundary layer, mesoscale variations in the horizontal wind leading to inaccurate tracking of the air mass and, to a lesser extent, the presence of horizontal roll vortices in some areas of the boundary layer. We show that the variance technique should be applicable to estimating surface fluxes of short-lived trace gases in cumulus-free boundary layers that are horizontally uniform, if sample-collection times of about 10 s or less are used. We also show that it may be possible to utilize mesoscale variance measurements to estimate surface fluxes and lifetimes of species which have lifetimes of perhaps a week or more.


merical simulations (LES) of the CBL. The first applications of this to flux measurements as well as limitations and conditions under which the TD-BU technique
can be used were reported by Davis [1992] and Davis et al. [1994]. They obtained flux measurements of nonmethane hydrocarbons from tethered balloon profiles in the Amazon and southeastern United States and also applied the technique to aircraft measurements to show that the LES-derived gradient functions were consistent with observations. The TD-BU technique is based on two hypotheses. The first is the concept of mixed-layer similarity• The mixed layer is that part of the CBL lying above the surface layer (typically the first few tens of meters above the surface where the fluxes can be considered constant) and below the turbulent entrainment layer that caps the CBL. The hypothesis argues that by scaling the mixed layer with zi, the convective velocity scale, w,-•Fozi ,

Ts --[(1/S)Ds] -1,
is much slower than the characteristic turbulent mixing time , Here D8 is the diurnally averaged chemical rate of production or destruction of S (roughly 1/3 the midday growth/decay rate for photochemically reactive species). For flight 7, zi = 570 m, w. = 0.58 m s -1, and thus rt = 17 min. This is far shorter than the growth and decay times of the trace gases considered here, whose lifetimes are given in Table 1.

2.2, Mixed=Layer Variance Technique
Employing the TD-BU formulation, Moeng and Wyngaard [1984,1989]  The variance technique could be useful for evaluating fluxes for trace species whose gradients are too weak to be measured accurately and if the sampling time or sensor time constant is too long for a direct eddycorrelation approach• but short enough to resolve a significant fraction of the variance at the long-wavelength end of the power spectrum• The partial variance may then be related to the total variance by a scaling factor. If we can assume spectral similarity, then this scaling factor could be obtained from a reference scalar for which high-rate data are available. Using this approach, the variance technique could be applied to flask samples, if the sample collection time is short enough, and a sufficient number of samples is collected.
At first glance, it may seem that the variance technique is inherently more accurate than the gradient technique since variances can often be measured more accurately than mean differences and, disregarding other sources of error, the accuracy in the flux estimate is approximately equal to the accuracy in the variance estimate. However, a major problem is the difficulty in estimating the impact of mesoscale processes, as well as heterogeneity in the surface and CBL top on the production of variance.

Measurements
The data analyzed here were collected from the NASA P-3B research aircraft during P EM-Tropics flight 7.

Davis et al. [this issue] and Considine et al. [this issue]
give more details on the general conditions for this flight. On this day the aircraft flew constant altitude circles about 50 km in diameter (30 min duration) at different heights in the CBL in the vicinity of Christmas Island (2øN, 157o5øE). The sequence of circles approximately follows the air mass trajectory in the CBL, which traveled to the WNW. The portion of the flight track within the CBL is plotted in Figure 2.
In addition to the standard meteorological measurements (air and dew point temperatures, static pressure, etc.) recorded at 1 s intervals (or 100 m spacing for a typical P-3B airspeed of 100 rn s -1, the Turbulent Air

Diurnal Variations
On flight 7 the CBL data were collected between 0530 and 1330 local solar time, during which the concentrations of DMS, SO2, CHBr3, and CHsI underwent gradual changes, as shown in Figures 3 and 4. The squares, crosses, and asterisks mark data from circles in the boundary layer where z, = 0.11,0.27, and 0.53, respectively. The low DMS and SO• concentrations represent data collected above the CBL. The DMS destruction and the SO• production rates nearly balance each other, producing little change in the total DMS + SO• concentration. The estimated net rates, represented by the slopes of the lines in Figures 3 and 4, are listed in Table 2. During the flight the sky was mostly clear, with some small scattered clouds above the CBL (see Figure 10).
To obtain changes in concentration as a function of z,, all CBL data were normalized to the early morning valuesø Vertical gradients in DMS, SO•, CHBr•, CHsI, CHsONO2, and C:H5ONO• are shown in Figure 5. The error bars represent the 90% confidence limit using the Student's t test. As can be seen, the expected errors tend to be large. They arise from horizontal variability coupled with limited sampling intervals.
We shall limit surface flux calculations to D MS because only D MS shows a significant gradient near the surface that is well outside the range of the error bars.

Flux From Mixed-Layer Gradients
In this section we carry out the evaluation of DMS emission from the oceanø To do this, we first need to evaluate the convective velocity w,. Since we were not able to estimate the surface buoyancy flux directly, we estimate w, by the following two techniques: (1) using the relation for the vertical velocity variance in the mixed layer [Lenschow et alo, 1980   Here to is the starting time for the estimates.

Applications and Limitations of the Mixed-Layer Gradient Approach
The mixed-layer gradient approach works well for species with a lifetime of order I day such as DMS. However, as we show here• it is not applicable to species with lifetimes much greater than a day. To demonstrate this, we start with the budget equation for a reactive trace species in a horizontally homogeneous CBL: where the mean vertical air velocity is related to the mean atmospheric subsidence sub(z) by the relation We average a photochemically reactive species across the diurnal cycle and assume the diurnally averaged concentration is in steady state. Then integrating (8) across the CBL where OS/Oz is small, and introducing (4) gives Equation (14) can also be used to estimate the surface flux for a steady state species (averaged over the diurnal cycle) whose sole source is at the surface and whose destruction rate is proportional to the mean concentration without assuming negligible transport across the CBL top. The ratio of the second (mean motion) term to the first term in the integral term of (14)

Variance Technique
In this section we discuss the mixed-layer variance technique for variance generated by surface and entrainment fluxes that scale with zi, as has been studied by LES. The observations show, however, that variance exists at horizontal scales longer than zi.

Scale-Dependent Contributions to Moisture Flux •nd Variance
During P EM-Tropics a number of trace species were averaged over a 1 min (6 km) sampling period, which for the present CBL correspond to a horizontal distance of 10zi. The variance technique, on the other hand, depends on variance functions obtained via an LES model covering a 5zi by 5zi area [Moeng and Wynguard, 1984]. Thus the current variance formulation applies only to fluxes and variances up to 5zi wavelengths.
One approach we considered was to extend the variance technique to longer wavelengths by using a surrogate scalar with a large surface flux for which smaller-scale measurements were available. Here humidity was used, since it was sampled at about 18 s -• by the TAMMS.
We can then try to calculate a scale factor that relates contributions to the humidity variance for wavelengths > 10zi to contributions for wavelengths <5zi. Figure 6 shows the power spectra of humidity and vertical velocity fluctuations, and their cospectra for a 50 km (88zi) diameter circle at z, -0.11. Here the longer wavelengths (i.e., >5 km) make significant contributions to the humidity variance (area under the power spectrum) but contribute very little to the vertical velocity variance and, consequently, little to the total humidity flux Fq (area under the cospectrum).
Here, and in other data not shown, the contribution from wavelengths >10zi to the total humidity flux is quite variable, so that no well-defined relationship can be established between humidity variance contributions for wavelengths >10zi and wavelengths <5zi.  We conclude therefore that the I min (10zi) averaging time for trace gas species is clearly too long to obtain a reliable scaling factor from the present high-rate humidity data to estimate surface flux from variance generated by eddies that scale with zi. However, if the sampling time were reduced to 10 s, which is probably the shortest feasible sampling time for flask samples, then the samples would average over wavelengths up to 1 km, which here corresponds to 1.8zi. This cutoff would allow measurement of variance at scales that include contributions by eddies that scale with the convective eddies driven by the surface buoyancy flux, so that there would be a much better chance for obtaining a reliable scaling factor relating the variance scaling with zi to the flux.

The measured variances include not only contributions from actual atmospheric fluctuations of trace gas concentrations, but also contributions from errors in measurement.
We can estimate the variance contribution from measurement errors by considering the measured variance for inert gases emitted into the atmosphere far from the measurement area and over an extended period of time. In that case, the variance is due solely to measurement errors. One of the trace gas species measured over I min intervals [Blake et al., 1996] was an inert species, CFC-12, for which as/•SI --0.0086.
Using the same approach that we used for the estimate of (S1 -S2)/(S) from the gradient technique (

CH3ONO2, and C2H5ONO2, and 4 days for CHzI (Table 1)• In other words, the variances measured for these
species on the mesoscale are much larger than the ziscaled variance predicted by mixed-layer similarity. The reason is that the mesoscale contributions to the variance involve processes that occur at much longer temporal and spatial scales than the variance due to emission from a horizontally homogeneous surface. Variability at these scales is generated by, for example, transport of CBL air into the BuL by sporadic event• such as cumulus convection or Kelvin-Helmholtz instabilities across the CBL top. This is followed by differential horizontal advection and intermittent localized turbulence diffusion in the BuL, which has a much longer time scale than mixed-layer turbulence. That is, the redistribution process in the BuL is much slower than in the CBL, so that both horizontal and vertical variations can persist for much longer times than in the CBL. Concentrations of these photochemically reactive trace species in the BuL decrease with time after they are injected into the BuL, and are not replenished as rapidly as in the CBL where the ocean-emitted gases are efficiently mixed throughout on a timescale of a few tens of minutes. Thus the concentration difference between the CBL and the BuL increases at a rate proportional to the reaction timescale. Finally, intermittent horizontally heterogeneous entrainment events (likely, for the most part, to be the same events that transport CBL air into the BuL) transport BuL air back into the CBL. As a result, variance is generated on the scale of these mesoscale events that is proportional to the difference in concentration between the CBL and the BuL.

Relationships Among Mesoscale Variance, Entrainment and Surface Flux
Here we consider a simple model to show how variance •n the CBL is generated by mesoscale processes, which for reactive species emitted at the surface, can be related to surface flux: We consider a simple CBL of mean concentration IS) capped by a BuL of thickness h and mean concentration $Bu. We assume both are in steady state, and define entrainment velocities we, entraining BuL air into the CBL and Weo entraining CBL air into the BuL. For this analysis we assume diurnal averaging, so that the relevant chemical reaction rate is denoted by Tso Integrating the scalar budget equation (

Equation (22) can be solved for the jump across the CBL top AS = S• -(S), ' ( I )(23) A$---($) l + rsWeb/h ' This relation between the jump and the species lifetime provides a basis for the concentration differences assumed in obtaining (23).
We assume that the variance measured by the grab samples, which is obtained from an average over a 6 km collection distance, is generated solely by mesoscale variability; that is, that fluctuations in species concentration that are generated by surface emission are transported throughout the CBL by eddies that scale with zi, and thus do not contribute significantly to variance at scales >> zi. In the case of entrainment, we consider two sources of fluctuations. One is fluctuations generated by turbulent eddies in the CBL resulting from shear and buoyancy flux. These eddies again scale with zi and penetrate far enough into the capping inversion that they bring down air from the BuL into the CBL. This part of the entrainment flux still scales with zi [e.g., Moeng and Wyngaard 1989]. The other part is generation of fluctuations by mesoscale processes such as cloud-related entrainment and horizontal variations in stability within the BuL and between the BuL and the CBL. The variance generated by these processes is at distinctly longer horizontal scales than that generated by turbulence that scales with the CBL depth. Furthermore, in contrast to the turbulent eddies generated by buoyancy and shear, these events can also transport CBL air into the BuL. However, we argue that the variance generated by these longer-scale processes should still obey the same scaling behavior as the zi-

scaled processes considered in (6), although likely with a different (larger-valued) variance function. The basis
for this is that they generate concentration differences in the CBL in the same way as smaller-scale turbulence, but since the variance is at longer horizontal scales it will persist for longer time periods (and thus be mixed more thoroughly throughout the CBL before being dissipated) than at CBL scales. Thus, from (6) Table 1 were obtained from variances averaged over all circles. The results indicate that there is little variation in standard deviation from one species to another despite the estimated factor of six difference in species lifetimes indicated in Table 1. This could be due to either all the species lifetimes << h/we•, or that the actual species lifetimes are similar (i.eo, the actual lifetimes differ from the theoretical estimates). The measured standard deviation for CFC-12, which is essentially a conserved species, is about a factor of 5 smaller than for the reactive species, which indicates that the accuracy of the measured differences is su•cient to resolve real fluctuations in the reactive species listed in Table   1.

Sources of Mesoscale Variability
The large-scale variations in humidity can, in part, be attributed to drift in the Lyman-alpha humidity probe. However, similar large-scale variations can also be seen in the more steady, slow-rate (1 s) specific humidity data derived from dew point temperature. Figure 9 shows I s values of specific humidity, potential temperature, and sea surface temperature during the first and last circle at z. = 0.53. We see variations in humidity on scales 10zi to 100zi (1 tO 10 min). The humidity variations cannot be attributed to variations in sea surface temperature because it changes much more gradually. The variations in potential temperature and humidity tend to be inversely correlated.  , submitted manuscript, 1998). Furthermore• we note that over the 5.7 hour time between the two circles, both the potential temperature and the sea surface temperature have increased by about 0.7 øC• but the specific humidity remains nearly the same, which suggests a near balance between the humidity gained due to evaporation from the sea surface and lost due to entrainment.

Cumulus Convection
A few small clouds above the CBL were noted by observers on the aircraft, and they are evident as dips in the ultraviolet (UV) radiation recorded by the upward pointing radiometer while the aircraft was circling in the CBL (Figure 10). To see if these clouds were advected, inactive cloud patches or small cumulus clouds (Cu) rising from the CBL, we look at humidity fluxes during the various constant altitude circles and semicircles within and above the CBL (Figure 11). To avoid mesoscale variations, the fluxes here represent wavelength •5.3zi.
For circles at z, ( I the fluxes are measured over the entire circle; for z, ) I the airplane alternated between two levels, with 5 min at each level around the circle so that the total sampling period is less than half the 30 min period available for circles z, ( 1. The humidity fluxes for circles nearest the surface (z, -0.11) remain essentially constant during all three circles over a 6 hour period; at z, = 0.27 and 0.53 they increase somewhat over time, but there are no well-defined changes with altitude indicative of significant flux convergence/divergence within the CBL. This is consistent with the nearly constant humidity in the CBL observed during the experiment (Figure 9). In contrast, above the boundary layer top, at z, = 1.1, 1.33, and 1o6, the humidity fluxes are highly variable among runs at the same level, and the up and downward pointing UV radiometers indicate that the highest positive and negative fluxes are in regions with the most clouds. Figure 12 shows data from a flight segment passing through a cloud at z, = 1.1, where the upward pointing radiometer (UVZ) records a drop in UV radiation from above, while the downward pointing radiometer (UVN) shows an increase in UV radiation from below. Increases in radiation from below but with no changes in radiation from above, indicate that there are smaller clouds below the flight level. The expanded portion of the cloud penetration in Figure 12 shows that the high humidity regions associated with the cloud are, for the most part• in negatively buoyant downdrafts, which suggests that we are observing the dissipating stages of a small Cu. Figure 12 shows the potential temperature profile from a nearby aircraft sounding. Since this is a slantwise sounding, the small oscillations in poten-tial temperature are likely due to horizontal variations. While the CBL is well-mixed• it is not capped by an inversion. Instead, it is topped by a BuL [Russell et al., 1998] or cloud layer [e.g., LeMone• 1980], which here has a nearly wet-adiabatic lapse rate. Since there is no discernible temperature jump at the CBL top, large eddies carrying warmer, moister portions of the CBL air may easily rise into the BuL thus forming Cu clouds.

The last plot in
The UV radiometer data show that the small Cu are not randomly distributed, but appear in clusters with stretches of clear air in between (Figure 10). Over time, this type of nonuniform convection and the associated entrainment through the CBL top could produce mesoscale variations not only in the CBL humidity, but also in trace gases. Since the extent of these variations depends on the concentration differences across the CBL top, the resulting power spectrum for fluctuations in trace gas concentrations need not have the same shape as the power spectrum for humidity fluctuations.

Roll Organization
Horizontal roll vortices along the wind direction are often observed in CBLs [e.g., Etling and Brown, 1993].
To see if roll organization exists in this CBL, we examine cross-wind and along-wind portions of the constant altitude circles. Figure 13 shows the vertical velocity power spectra in nearly cross-wind and nearly along-wind portions of the circle, at z,= 0.53. The spectral peak is well defined in the cross-wind segments, whereas in the segments along the wind direction the peak spreads over a wide range of scales. The total variance is lower in the along-wind segments than in the cross-wind segments.
The time series of vertical velocity traces shown on the bottom of Figure 13 correspond to the power spectra directly above them. In the cross-wind segments the spacing between updrafts is somewhat variable, usually around 2zi or 3zi, which is compatible with roll organization (zi -570 m• and each 10 s subdivision corresponds to about 1 km)o The vertical velocities from the flight segment nearly along the wind direction suggest the presence of turbulent rolls intercepted at a wide angle.
Similar power spectra from cross-wind and alongwind portions of the flight are seen in data from other circles, but not consistently in every cross-or alongwind portion of the circle, which indicates that the roll organization is intermittent. While over a circular path the effects of roll organization tend to average out, intermittent roll organization could introduce some uncertainty in our scaling factor for relating the long and the short wavelength ends of the power spectrum.      The above illustrates the difficulties of following an air mass in the presence of variable and/or inaccurately measured horizontal wind. A +1 m s -1 error in the mean wind velocity will produce a +22 km error in position 6 hours later.

Strategies
In this section we outline the procedures necessary to optimize measurement strategies in order to estimate surface fluxes of trace species by both the mixed-layer gradient and the variance techniques.

Using the Gradient Technique
As pointed out earlier, the accuracy of flux measurement by the gradient technique improves considerably as the height of the lowest measurement decreases because the concentration gradient increases. Moeng andWyngaard [1984, 1989] found that the gradient changes approximately as z• -3/2 near the surface.) Thus, to optimize the accuracy of the flux measurement, the lowest flight level should be flown as low as possible.
An added advantage is the concomitant decrease in the integral scale of the turbulence as the height decreases , which means that the averaging length required for a specified measurement accuracy also decreases. On the other hand, LES does not necessarily accurately simulate flow in the lowest part of the CBL (the surface layer) because of the size of the grid used in the simulations, and deficiencies in the subgrid scale closure scheme. In fact, however, extrapolation of the LES results into the surface layer agrees well with measurements of both gradients and variances in the surface layer. Finally, since the gradient becomes small in the middle of the CBL, there is no need to obtain measurements at more than one level there. Davis [1992] has examined in detail various strategies for minimizing flux measurement errors using the gradient technique.
Another consideration for applying the gradient technique is the necessity for accurate measurements of height above the surface• especially close to the surface where the gradient becomes large. For example, a 20 m error in height translates roughly to a 20% error in the surface flux estimate for z. _• 0.1 and zi •-1000 mo This points to the necessity of accurate geometric altitude measurements by, for example, a radio altimeter, rather than by correcting pressure altitude measurements.
Finally, for gases which are destroyed by photochemical reactions, it would be preferable to measure before sunrise or after sunset to avoid corrections for diurnal changes. Scattered clouds may also reduce the measurement accuracy both by introducing horizontal variability into the photochemical destruction rate and into the entrainment rate at the top of the CBL.

Using the Variance Technique
Here we distinguish between variance that scales with zi, and mesoscale varianceø For the zi-scaled variance technique it is also important to select a horizontally uniform CBL, with minimal cloudiness, although the effects of mesoscale variability can, to some extent be mitigated by high-pass filtering. Again, as with the gradient technique• flying lower increases the measurement accuracy• but the rate of improvement is less than for the gradient technique• This also means that the variance technique is less sensitive to errors in altitude measurement• To estimate zi-scaled variance from grab samples, it is desirable to minimize the sampling time, so as to include as large a portion of the data from the shorterwavelength end of the variance spectrum as possible. If the sampling time were reduced to 10 s, which is probably the shortest feasible collection time for flask samples, then the sampled variance would include wavelengths as small as I km, which is well within the regime where variance is generated in a horizontally homogeneous CBL by the surface fluxes rather than by mesoscale processes. The larger the number of samples, the better the accuracyø Presently, practical considera-tions probably limit the number of samples to about 140 per flight. If the samples are independent, the measured variance samples follow a chi-squared distribution. Therefore, if 10 samples are collected, there is a 90% probability that the measured standard deviation (which is proportional to the flux) will lie between the limits 0.6a• • trs • 1.4a•, where tr• is the actual standard deviation• For 41 samples the limits are 0.8cr• • ors • 1.2cr•.
Fast-response measurements of a reference reactive scalar emitted from the surface would be very useful, in addition to humidity, for estimating a scaling factor to be applied to the grab-sampled variance estimates. DMS has ideal properties for this: a 1-2 day lifetime, a reasonably uniform surface source, and negligible solubility in cloud. A prototype chemiluminescence fastresponse D MS sensor has been demonstrated in the laboratory by Hills et al. [1998].
For estimating mesoscale variance from grab samples, collection times of I min or more are appropriate. Although this technique, applied to a single species, would be difficult to implement in order to give quantitative estimates of lifetimes or surface fluxes, it may be possible to estimate lifetimes or surface fluxes for a target species by taking ratios of standard deviations of the target species with a species whose lifetime or surface flux is known. The advantages of the mesoscale variance technique is that it can be used with measurements obtained over averaging times of a minute or more, and it can be applied to species emitted from the ocean with lifetimes of perhaps a week or more.

Summary and Conclusions
Flight 7 during PEM-Tropics provided a good opportunity to observe diurnal changes within a Lagrangian framework. We have estimated the daytime destruction (production) rates under nearly clear skies for DMS, SO2, CHBr3, and CH3I (Table 2) We show that the gradient technique requires high measurement accuracy even with fairly short-lived trace gases. To estimate fluxes of the more long-lived trace gases that did not show surface gradients outside the expected errors, we attempted to use the mixed-layer variance technique. This approach did not lead to useful results because of long sample collection distances (6 km) and mesoscale variability. We show that the mixedlayer variance technique could be applied to relatively short-lived trace gases in cumulus-free CBLs that are horizontally more uniform, if shorter sampling times were used (of the order of 10 s or less). For tropical 16,294 LENSCHOW ET AL•: DMS FLUX VIA A MIXED-LAYER MODEL marine CBLs it would be desirable to recompute the LES mixed-layer variance and gradient functions using soundings where the temperature jumps across the CBL top are weak to better simulate that regime. The presence of species emitted from the ocean that have a lifetime of a few days or less above the CBL indicates that transport of CBL air into the overlying BuL occurs. This transport arises, for example, from clusters of small cumulus clouds rising into the BuL, or episodic shear-induced turbulence. These processes induce horizontal variations in entrainment flux and concentration on the mesoscale in both the CBL and the BuL. The timescale for these processes is longer than for turbulent fluctuations directly generated by surface fluxes. We show how this process can be used to estimate surface fluxes and lifetimes for species with lifetimes that are too long to estimate fluxes by mixed-layer gradients or variance directly associated with surface fluxes.