their rates of exchange with the overlying atmosphere. There are many ways to measure fluxes in the PBL. However, the two most widely used platforms are: (l) tower measurements in the surface layer and (2) airplane measurements in the mixed layer. There are, of course, other platforms that are used. For example, in the marine surface layer, ship-mounted instruments are used and in the mixed layer tethered balloons and neutrally buoyant airships have been used. The most direct and fundamental flux measurement technique is the eddy correlation technique [Eq. (1)]. However, this requires fast-response high-resolution measurements of species concentration and vertical air velocity over a time period or distance long enough to obtain a sufficiently accurate average of the turbulent fluctuations. As a rule of thumb, to estimate the flux to about 10% accuracy, one should average over several times the maximum eddy size making significant contributions to the flux. Generally, measuring fluxes from a tower a few meters above the surface for moderate winds requires an averaging time of about 20 min, which is about the same as that required for measuring fluxes from an aircraft in the middle of the mixed layer flying at lOOm/s.
At the other end of the spectrum, the smallest scale eddies that need to be measured to estimate a flux in the surface layer are roughly about 0.5z. In the mixed layer, the smallest scales are roughly about 0. lz(. Therefore, for measurements from a tower at a height of 2 m, and a wind speed of 5 m/s, a frequency response of least 5Hz is required. In the mixed layer, for an aircraft flying at lOOm/s in the middle of a 1 -km-deep CBL, a frequency response of at least 1 Hz is required. If the aircraft is flying lower, say about 30 m, which is in the upper part of the surface layer, a frequency response of at least 7 Hz is required. [To achieve a frequency response of fc hertz using a sensor with a first-order time response, a sensor time constant of about 1/(6/1) s is required.]
In carrying out flux measurements by eddy correlation, both vertical velocity and species concentrations must be measured concurrently. Sonic anemometers are often used for the vertical velocity measurement from towers since they have good velocity resolution, adequate time response, and no moving parts. The air velocity component along the path between two sets of sonic transducers is obtained from the difference in the velocity of sound traveling along the same path in opposite directions. In addition, since the speed of sound is approximately proportional to the square root of virtual temperature, sonic anemometers are usually configured to also measure the virtual temperature, and thus the buoyancy flux can be obtained as well. Three-axis sonic anemometers are available commercially for measuring eddy correlation fluxes in the surface layer.
Measurement of air velocity components from aircraft requires measuring both the velocity of the air with respect to the aircraft and the velocity and angular orientation of the aircraft with respect to Earth. The former is often obtained from pressure measurements on the nose of the aircraft or from a probe mounted on a noseboom ahead of the aircraft. Pressure difference measurements are sensed from sets of ports. A forward-looking and a static pressure port are used to sense the airspeed, and sets of ports at different angles in both the horizontal and vertical plane of the aircraft are used to sense the flow angles of the air. The aircraft orientation and velocity are often obtained from an inertial navigation system (INS) which senses the attitude angles and acceleration of the aircraft. The acceleration components are then integrated to obtain the velocity, and integrated again to obtain the position of the airplane. Often, navigational information from the satellite-based Global Positioning System (GPS) is used to remove drift inherent in the INS due to integration of a bias in the accelerometers. The air velocity is obtained from the difference between the velocity of the air with respect to the airplane, which is rotated by means of the attitude angles to an Earth-based coordinate system, and the velocity of the airplane, which is also measured in an Earth-based coordinate system.
Several techniques have been used to measure species concentration with sufficient resolution and frequency response that direct eddy correlation fluxes can be obtained. Water vapor fluxes have been obtained from both infrared and ultraviolet absorption devices. Fluxes of several other trace gases can also be sensed by infrared absorption, including C02, CH4, and CO. Chemiluminescence is another inherently fast technique useful for ozone, isoprene, and possibly NO, N02, and dimethyl sulfide. In this technique, a reactive gas is mixed with the air, which reacts with the species being measured, with the resulting emission of photons detected by a photomultiplier tube. Finally, a tandem mass spectrometer, which ionizes, accelerates, and segregates the target species molecules has been used for measuring fluxes of acetone, ammonia, and formic acid in the surface layer.
Nearly all the techniques listed above (except for some open-path radiation absorption devices) require the air to be drawn into a sensing chamber of some sort. This requires careful consideration of the ducting system to ensure that the flow is fast enough and the ducting short enough that significant attenuation of concentration fluctuations does not occur in the frequency region with significant contributions to the flux. Generally this means that if the duct is longer than a couple of meters, the Reynolds number of the flow in the duct,
where d is the tube diameter, U, the flow velocity in the tube, and v is the kinematic molecular viscosity 0.15 x 10 4 m2/s for air at room temperature), must be greater than the critical value for turbulence to exist in the tube; i.e., Re > 2300.
In addition to direct eddy correlation, several other techniques have been used for flux measurement. Most of these alternatives are implemented to relax the high-frequency requirements of direct eddy correlation. Conceptually, perhaps the simplest approach is to make measurements of species concentration less frequently, but grab the sample quickly so as to still retain the required frequency response. By this disjunct sampling technique, a flux can be estimated even if the frequency response of the concentration measurement is reduced by nearly an order of magnitude below what is required for direct eddy correlation. Another approach, called eddy accumulation, is to collect the air sample at a rate proportional to the vertical velocity, with the upward-moving air going into one reservoir and downward-moving air into another. The flux is then proportional to the difference in concen-
tration between the two reservoirs. With this approach, there is no longer any requirement for fast-response species measurement. In effect, the requirement for fast response is shifted to the flow control. Disadvantages of this approach are the small concentration difference between the two reservoirs and the requirement for fast-response and accurate flow control.
There are many other techniques for estimating flux, mostly with the objective of reducing the high-frequency response requirement, but, in contrast to the above, these approaches utilize some empirical relationship between the flux and some other variables. One simplification of eddy accumulation, called relaxed eddy accumulation, is to collect the air at a constant rate, regardless of the magnitude of the vertical velocity, in either of the two reservoirs depending on the sign of the vertical velocity. The flux then depends, in addition to the concentration difference between the two reservoirs, on the standard deviation of the vertical velocity and a parameter that depends on the vertical velocity distribution.
Measuring the gradient of species concentration either in the surface layer or the mixed layer is also used to estimate the surface flux. In the surface layer, the flux can be estimated from the integral of Eq. (15); i.e., from a difference in concentration between two levels plus the friction velocity, and a measure of the stability L, which depends on and FM. Again, this does not require fast-response concentration measurements, but it does require measurement of small differences in concentration, as well as estimates of buoyancy and momentum fluxes.
In the mixed layer, Eq. (17) can similarly be integrated and solved for both the surface and the entrainment fluxes from mean concentration differences. However, since there are now two unknowns, mean concentration must be measured at a minimum of three levels to obtain two concentration differences unless one of the fluxes is estimated by another technique. Typical values of the normalized gradient functions have been estimated from large-eddy numerical simulations of the CBL to be, for g0(z/z,-) about 13 at z/z,- = 0.1 and about 1 at z/z,- = 0.5, and for g,,-(z/z,-) about 70 at z/z, =0.9 and about 3 at z/z, = 0.5. Since a typical value for wt is about 1 m/s, we see that by taking the ratio of (17) to (5) the mixed-layer gradient is roughly about 1% of the surface layer gradient. This is again a reflection of the relative efficiency of transport in the mixed layer compared to the surface layer. This relatively small mixed-layer gradient is offset to a considerable extent by the much larger height differences that can be used in the mixed layer. Nevertheless, the concentration differences obtained by integration of the surface layer gradient formulation (5) can be several times larger than the differences obtained from integration of the mixed-layer gradient formulation (17). Thus far, the mixed-layer gradient technique has been used to estimate surface fluxes of isoprene and dimethyl sulfide, both of which have sources only at the surface and lifetimes of less than a couple of days, which reduces their concentration above the CBL to near zero.
Both surface layer and mixed-layer similarity relationships have also been obtained for scalar variance profiles. These relationships are based on the hypothesis that CBL variance is generated solely by surface and entrainment fluxes. In practice, this may have advantages for measuring flux, particularly in the mixed layer if fast-response scalar measurements are practicable but concurrent vertical velocity measurements are not, since the mean concentration differences can be small. On the other hand, in practice mesoscale variability may contribute to the measured scalar variance and may be hard to estimate or remove from the measured variance.
Other less direct techniques exist for measuring constituent fluxes. One approach is to assume that the transport characteristics of a tracer species in the surface layer are the same as the species under consideration. Then if both eddy correlation fluxes and concentration differences are available for the tracer species, and only difference measurements are available for the species under consideration, the ratio of the unknown flux to the known flux is equal to the ratio of the tracer species difference to the unknown species difference.
Another approach is to use the budget equation of the species to solve for the surface (or entrainment) flux. The budget equation for the mean concentration of a species is given by aS , , BS 9F_
where Qs is the internal (e.g., chemical) source or sink of S, and we have assumed, for simplicity, that V = W = 0. This can be integrated, e.g., from the surface up to a height z and solved for the surface flux to obtain
where ( ) denotes an average over the layer from the surface to height z. This approach has been used by aircraft flying in a Lagrangian flight pattern—i.e., advecting the flight pattern with the PBL mean wind using constant-level balloons as tracers, so that the second term on the right side of (20) is zero—and carrying out a series of flights over a day or more. In this case, the surface flux is obtained from the residual of the time rate of change, the entrainment flux, and the chemical source/sink terms.
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