Journal of

Hydrology ELSEVIER

Journal of Hydrology 188-189 (1997) 589-611

A system to measure surface fluxes of momentum, sensible heat, water vapour and carbon dioxide J.B. Moncrieff a'*, J.M. Massheder a, H. de Bruin b, J. Elbers c, T. Friborg d, B.

590

J.B. Moncrieff et al./Journal of Hydrology 188-189 (1997) 589-611

1. Introduction

There is a need for eddy covariance equipment which has the following specifications: (1) the ability to perform continuous measurements of fluxes; (2) a design that minimises flow disturbances; (3) low power consumption, thus permitting the use of solar panels and removing the need for a power system such as a fossil-fuelled generator which would generate its own CO2; (4) the ability to store raw data to obtain additional information concerning the turbulent fluxes, e.g. second, third, fourth moments, spectra, etc.; (5) the standardisation of data processing procedures. The micrometeorological groups at the University of Edinburgh, Winand Staring Centre at Wageningen, the Agricultural University at Wageningen and the University of Copenhagen have been developing such a system over the last 3 years. It is the objective of this paper to describe the system which we have developed and which was used extensively in HAPEX-Sahel. The system is based on a commercially available sonic anemometer and IR gas analyser, the two pieces of hardware being controlled by software written at the University of Edinburgh. Individuals within our groups have developed post-processing routines which have been shown to be consistent between groups, having been based on a continuing dialogue between the groups involved. The eddy covariance technique should be viewed as a 'system' of measurement, i.e. one which includes not only the hardware but also the method of analysis, whether in real-time or off-line, and the algorithms used to filter or detrend the raw data and to apply calibrations and corrections. An example of the detail and considerations which are necessary in a typical eddy covariance system is revealed in the series of papers describing the development of the 'Hydra' by the UK Institute of Hydrology. This series of papers describes not only the instrumentation used, including sensors and microcomputer control, but also the corrections required for real-time analysis (Shuttleworth et al., 1982, Shuttleworth et al., 1988 Moore, 1983, Moore, 1986; Lloyd et al., 1984; Shuttleworth, 1988). Another set of papers by McMillen and co-workers (e.g. McMillen, 1983, McMillen, 1986, McMillen, 1988; Hicks and McMillen, 1988) give algorithms which allow the eddy covariance technique to be extended to areas of non-simple terrain and/or relax the sensor-levelling requirements. Our system develops and extends some of the aspects of these systems by making use of advances in commercially available sensors suitable for making flux measurements by eddy covariance. Up to five additional analogue inputs can be sampled with the three components of the turbulent wind. The ability of our system to perform real-time flux calculation using a ducted (closed-path) approach to scalar measurement while performing full co-ordinate rotation results in a system which heralds the demise of 'fair weather micrometeorology' as this system is technologically mature and can deliver the promise of being relatively routine to apply.

2. Theory The eddy flux of any scalar can be written F c = WPc

(1)

J.B. Moncrieff et aL/Journal of Hydrology 188-189 (1997) 589-611

591

where Fc is the flux density of scalar c, w is the vertical wind speed and pc is the density (or concentration) of the scalar c. The overbar represents the mean of the product over the sampling interval, Records of wind speed, temperature and concentration exhibit turbulent or irregular form; it is convenient to regard these variables as the sum of a mean and a fluctuating part. This process is known as Reynolds decomposition (Arya, 1988), and for wind speed and concentration can be written w = ~ + w'

(2a)

P~ = P--~+ Pc'

(2b)

where the primes represent the fluctuation about the mean value. Rewriting Eq. (1) making use of Eq. (2a) and Eq. (2b), we obtain F c = ~ p--~+ w ' p c '

(3)

which shows that the total vertical flux of any scalar is the sum o f a mean vertical flux w Pc and an eddy flux w'pc'. It will be noted that in the full expansion of Eq. (1), some terms involving the mean o__fa fluctuating component have been omitted from Eq. (3) because, by definition, w' and Pc' equal zero; terms involving the mean of the product of two fluctuating components, e.g. w'pc', will rarely be zero. One assumption normally made is that over a suitable interval of time there is no mass movement of the air in the vertical, i.e. ~ -- 0. With this proviso, we obtain from Eq. (3) the practical working equation for eddy covariance, which is Fc = w ' p c ' + correction terms

(4)

The assumption that ~ = 0 will be discussed in Section 4.1. Eq. (4) shows that we must either have instrumentation which can sample vertical wind speed and scalar concentration and be able to perform real-time analysis, in which means are subtracted from raw data to yield the fluctuating components then cross-products formed, or we must have the facility to store all the raw data for later processing in the laboratory. Our system uses a recursive digital filter to approximate a running mean and by this method we can calculate the required fluctuations in measured components in real-time (Lloyd et al., 1984; McMillen, 1986). The time constant of the digital filter we use is typically 200 s, and, as shown elsewhere (e.g. Shuttleworth et al., 1984; McMillen, 1986), the calculated flux is relatively insensitive to the value chosen within the range from about 100 to 1000 s.

3. Description of instruments and set-up Fig. 1 is a schematic representation of the complete system and shows the three main components of the instrumentation--analogue signals from the IR gas analyser (IRGA) are passed to the three-axis sonic anemometer, which uses an on-board analogue-to-digital converter to digitise the signals (at 10 Hz). The u, v, w components of the wind and the speed of sound (from which the sonic virtual temperature is derived) are available at a rate of 21 Hz at the serial output of the anemometer. The digitised signals from the IRGA are

592

J.B. Moncrieffet al./Journal of Hydrology 188-189 (1997) 589-611

Solent Ultrasonic Anemomete~

An~/ogue/nput

from IRGA

Serial output from sonic

.....

Li-Cor 6262 I R G A

. .... iy

P C running EdiSol

Magnesium Perchlorate

Silica Gel

Soda

Vent tap

3 i ! Sample Inlet

...........i ! To Buffer Bottle

Fig. 1. A schematic representation of the major components of the EdiSol system, and the air circuit and plumbing arrangements for the LI-COR IRGA.

J.B. Moncrieff et al./J ournal of Hydrology 188-189 (1997) 589-611

593

combined with the wind speed information and sent to the serial port of a personal computer (PC). Up to five analogue channels may be input to the sonic anemometer and digitised and combined with the turbulence data. The basic system, which was common to all groups, sampled the analogue output from the IRGA of the CO2 and H20 channels, but some groups also installed a krypton hygrometer and/or fast response thermocouples for digitising and subsequent sampling by the software. 3.1. Sonic anemometer

The ultrasonic anemometer used in our system is a three-axis design, manufactured by Gill Instruments (Solent A1012R, Gill Instruments, Lymington, UK). The instrument is fully waterproof, consumes 700 mW of power and can operate at windspeeds up to 60 m s -1. The time-of-flight principle is employed to produce u, v, w and speed of sound (which is used to calculate virtual temperature). Sets of eight transmissions are made between each pair of transducers at a rate of 21 Hz, producing an accuracy of 2 cm s -1 in horizontal and vertical components. The virtual temperature is obtained from the transit time of the ultrasonic pulses (Kaimal and Businger, 1963; Kaimal and Gaynor, 1991) using the relation cs ~ 403Tair (1 + 0.32p)

(5)

where Cs is the speed of sound in air, Tair is absolute air temperature, e is the vapour pressure of water in air and p is the absolute atmospheric pressure. A sonic temperature (T) is defined as T = c-2--~= Zair 1 + 0.32 403

(6)

According to Stull (1988), the sonic temperature is close to the virtual or potential temperature

0 ~=Tair (1+ 0.38p)

(7)

Using the sonic virtual temperature for the calculation of sensible heat flux will be adequate under most conditions. At high wind speeds there are additional errors owing to wind speed and momentum stress, which need to be considered (Schotanus et al., 1983). Additionally, when vapour pressures are high, as they will be during the wet season in the Sahel, then the corrections should be applied. Full details of the procedure have been given by Lloyd et al. (1997). The sonic transducers are arranged 120° apart, with pairs of transducers being 15 cm apart. The transducers are fully waterproof, with drip points improving the run-off of raindrops from the transducer. The anemometer is available in two configurations--one in which the supporting struts are 120 ° apart, the other being an asymmetric design in which the unobstructed acceptance angle for the sonic transducers is 240 °. Onboard software can be selected to apply the corrections for strut interference automatically. The sonic anemometer can operate in conditions of rain, as the on-board processor will

594

J.B. Moncrieff et al./Journal of Hydrology 188-189 (1997) 589-611

eliminate spurious signals introduced by rainfall yet maintain a reasonable average value which is output 21 times per second. Recent wind tunnel tests on the Solent anemometer have been reported by Mortensen and Larsen (1994).

3.2. IR gas analyser The IRGA used is the LI-COR 6262 model (LI-COR, Lincoln, NE, USA), which measures CO2 and H20 in air with a quoted 'response time' of 0.1 s. That would be the time taken for the analyser to respond to 95% of a one-time step change in gas concentration. In the real world of fluctuating gas concentrations a more useful indicator of the analyser's response is the cut-off frequency, i.e. the frequency at which the indicated amplitude of a sinusoidal oscillation in gas concentration is 0.707 of the real amplitude. For the LI-COR 6262 this is 5 Hz. A dichroic beam splitter in the optical bench splits the IR beam to two lead selenide detectors, both of which are thermostatically cooled to -5°C to maintain sensitivity and to reduce signal noise. The volume of the optical bench is 11.9 cm 3. The CO2 detector uses an optical interference filter centred at 4.26 #m with a bandpass of 0.15 #m. A similar filter centred at 2.59 #m with a bandpass of 0.15 #m is used for the H20 channel. Software on the IRGA can be used to correct CO2 measurements for dilution or band-broadening effects. Changes in barometric pressure affect the analyser span, which in practice should be checked every 2 - 3 days; changes in instrument temperature affect zero drift. In use, we found this IRGA to be remarkably consistent with regard to span; its zero drift rarely exceeded 1 ppm when remeasured after 3 days. Maximum flowrates through the analyser should not exceed 10 1 min-l; typically, the gas is drawn through the analyser at flow rates of 6 1 min -1, although some groups operated at higher flow rate to ensure fully turbulent flow in the sampling line. Higher flow rates have some advantages in that they reduce the loss of signal at the higher end of the frequency spectrum, and will be discussed further in the section on transfer functions. Power consumption of the IRGA is 8-12 W, dependent on temperature. Calibration for CO2 was performed according to the preferences of each of the laboratories; scale gases can be traced to the relevant national standards. Zero points were established using dry N2 gas or chemical methods. Water vapour calibrations were performed using chemical methods or by using water vapour generators (LI-COR Portable Dew Point Generator Model LI-610). Calibration can be performed at the same flow rates as exist when the system is measuring surface fluxes, thus ensuring all pressure differences are maintained equal when operating in field- or calibration-mode. Software in the LI-COR IRGA can also be employed to correct for changes in flow rate between calibration and actual rates. In recent discussions with the manufacturer of the IRGA, we have discovered that the calibrated CO2 signal is refreshed at 5 Hz but the calibrated water vapour signal only at 3 Hz (it is possible to sample uncalibrated CO2 and H20 from the IRGA which refresh at the same rate) (D. McDermott, personal communication, 1994). Fig. 1 depicts the air circuit part of our system with air being drawn through the analyser by having a pump at the end of the sampling line. The buffer bottle acts to reduce fluctuations in the sample line. The material of the sample tube should not interact with carbon dioxide and water vapour, and we have successfully used Dekabon tubing (6 mm internal diameter, Dekabon Ltd., Glasgow, UK) and polyethylene with 3 mm internal

595

J.B. Moncrieff et aL/Journal of Hydrology 188-189 (1997) 589-611

diameter. The length of the tube is not critical and the system has been operated with tube lengths of 3-16 m in this experiment. Tube diameter affects flow rate, pressure drop and the energy required to draw air through the system. More importantly, the internal diameter of the tubing can be chosen to ensure either turbulent or laminar flow. The mass flow controller (Tylan FC2900B, Tylan General, Swindon, UK) maintains the flow rate in the tube within a small range and thus ensures that the time of travel for any air sample remains nearly constant. It is possible to change the position of the pump in the air circuit so that air is pushed through the optical bench rather than pulling it through as in Fig. 1. The advantage of pushing the air through the system is that the optical bench can be vented to the open atmosphere, thus minimising the pressure difference between the optical bench and air outside. A further advantage is that the signal-to-noise ratio will be increased by this method, as the pressure in the optical bench will be increased and thus so will the CO2 concentration. The disadvantage of the pump being on the upstream side is that an increase in pressure may lead to enhanced risk of condensation of water vapour in the sample tube,

0.40

--

0.35

0.40

0.35 \ \x

0.30

,

0.30

/

0.25

0.20 //

///111 /!

~\\\

0.20

~ \\ ~\\

-"

0.15

0.25

\\

CO2 ----- ~O

0.15

- -

0.10 14C

,

t

,

1,

160

,

,

,

I

,

180

,

,I

,

200

,

,

,1,

220

,

,ll

,i

240

ill

ill

260

i

I,

280

,

,

,

I,

300

,

,

i

0.10

320

Lag ( no. of samplesat 21 Hz) Fig. 2. Relationshipbetweencorrelationcoefficientbetweenfluctuationsin verticalwindspeedand CO2(rwc)and between verticalwindspeedand H20 (rwq)measuredwith a closed-pathgas analyserand a sonic anemometer.

596

J.B. Moncrieff et al./Journal of Hydrology 188-189 (1997) 589-611

an effect which could be minimised by maintaining the sample tube a few degrees warmer than ambient temperature. As mentioned above, the LI-COR IRGA can make automatically the corrections for pressure drop in the optical bench. We have measured pressure differences between the optical bench and outside air of about 7 kPa under conditions of laminar flow in a tube of 30 m length and a flow rate of 6 1 min -1. Under conditions of turbulent flow in the sample tube (e.g. when the flow rate is high and the sample tube is narrow) the pressure drop in the optical bench is about - 20 kPa. At pressure differences of about - 10 kPa, the automatic correction applied by the IRGA starts to fail and specific humidity is underestimated by about 10% at - 20 kPa. This has now been corrected in the new version of software installed in the LI-COR 6262, but was not corrected at the time of the HAPEX-Sahel experiment. Fig. 4 shows the relative water vapour concentration in the optical bench as calculated by the LI-COR software. The calculated value falls at pressures less than 90 kPa; during the experiment both the actual water vapour content and ambient pressure were kept constant. One way to minimise this pressure drop is to move the pump upstream of the analyser. In this configuration there is an over-pressure of about 5 kPa; this can improve the signal-to-noise ratio compared with the low pressure set-up (more molecules per unit volume), and this effect can be important if fluxes are small. The disadvantage of working with an overpressure is that condensation will occur more quickly in conditions of high relative humidity, an effect which was noted on a few occasions at sunrise when this change was effected by the group from the Wageningen Agricultural University. 3.3. Processing software

A computer program (EdiSol) calculates real-time fluxes of momentum, sensible and latent heat, and CO2 from the output of the sonic anemometer and IRGA and any of up to three other subsidiary instruments. The program is written in object-oriented PASCAL and operates on the serial output from the sonic anemometer via the RS232 port of an IBMcompatible PC. The software performs coordinate rotation on the raw windspeed data according to the routines first described by McMillen (1986) and has been corrected for a number of typographic errors contained within that report (R.T. McMillen, personal communication, 1990). Crucially, the software allows for the delay introduced into the CO2/H20 signal as a result of the time of travel down the sampling tube, by continuously computing the correlation coefficient between the vertical wind speed and a range of delayed CO2 or H20 signals around a value which has been obtained previously under the same conditions of tube length and flow rate. The delay is calculated on a time series of raw data. EdiSol is programmed to calculate, in real-time, the covariance between the instantaneous vertical wind speed and the delayed signal in a user-selected range, but typically 0.5 s around the previously determined value (or about 10 sample points at 21 Hz). Fig. 2 shows a typical graph of correlation coefficients for a range of lags. The shape of this curve is partly stability dependent and the initial lag is best obtained in unstable conditions. The delay time down the tube is greater for water vapour compared with carbon dioxide because of the electrical nature of the water vapour molecule. Because the eddy flux of any scalar can be written as the product of the correlation coefficient and the standard deviation of the vertical windspeed and scalar concentration (fc " rwcOwO~),

J.B. Moncrieff et al.Hournal of Hydrology 188-189 (1997) 589-611

Closed-path

- -

150

597

.........

Open-path :il

E

-6

:'!

100 .%

~ o

= o

o _=

50

i

0

-50 -100

I

I

1

I

0 200 400 600 800 1000 Open-Path Sample Number from time = 0 (at 18 Hz) E

I

I

1

I

I

1

0

200

400

600

800

1000

1200

Closed-Path Sample Number from time = 0 (at 18Hz) Fig. 3. Intercomparison of CO2 fluctuations measured by an open- and closed-path gas analyser measured at a height of 9 m above a field of millet at the Southern Supersite during HAPEX-Sahel.

the relatively broad peak of the correlation coefficient relationship explains why the calculated flux varies by less than about 5% as the lag varies by as much as 10 sample points. Variations in flow rate which might influence the lag time can be controlled by the mass flow controller; variations in atmospheric stability may change the lag by several sample points but as the software continuously calculates the maximum covariance, the maximum flux is always obtained. A check on the accuracy with which the delay has been obtained can be made by comparing fluctuations in scalar concentration obtained using a ducted system with fluctuations obtained by an open-path system (Advanced Systems E009A, Osaka, Japan). Fig. 3 shows an intercomparison of CO2 fluctuations measured by open- and closed-path IRGAs over a period of about 1 min. The inlet of the sample tube for the closed-path analyser was within 10 cm of the open-path analyser and measurements were made at a height of 9 m above a field of millet during HAPEX-Sahel. The closed-path signal has been delayed by 183 samples (at 18 Hz) and the close agreement in phase is obvious. The reduction in the magnitude of the closed-path CO~ fluctuations is the consequence of the smearing of the high-frequency fluctuations, as will be revealed in the section on cospectral analysis below. (Strictly, the instantaneous fluctuations shown here should be corrected for changes to air density caused by the simultaneous transfer of sensible and latent heat. The intercomparison should be between the fully corrected partial

598

J.B. Moncrieff et al./Journal of Hydrology 188-189 (1997) 589-611

14

O

E 13 O

0 Q. m

11 I I

I

I

I

I

60

70

80

90

100

Pressure (kPa)

Fig. 4. The relative water vapour concentration in the LI-COR optical bench as calculated by the LI-COR software. The actual H20 content and pressure were kept constant throughout. density of CO2 as defined by Leuning and King (1992), but the difference made to this diagram would be small.) 3.4. Tower and enclosure

The sonic anemometer is of lightweight aluminium and polycarbonate construction and weighs about 1 kg. The sampling tube can be attached to one of the struts on the anemometer and as a precautionary measure to avoid raindrops being sucked into the sampling tube, we have cut the end of the sampling tube into a shape resembling that of the nib of an ink pen so as to form an effective drip point. It is also possible to shield the end of the sampling tube with a small enclosure; an empty case for a 35 mm film reel proved ideal in the field. Most micrometeorologists will have experienced the problems of having many items of equipment in the field which have to be protected from the elements yet all have to be connected and easily accessible for calibration or removal. We have solved this problem by developing a waterproof box in which the IRGA, laptop PC, power supplies and DC-to-DC converters, scrubbing and desiccant tubes, mass flow controller and flowmeters are securely fixed and have been arranged so that everything is easily to hand. The sampling tube and other tubing associated with scale gas cylinders can be fed into the base of this steel enclosure. Mains and signal cables can be attached to waterproof connectors also on the base of the box. The box can be outfitted in the laboratory and the whole assembly can be shipped to its field destination. Set-up times in the field are reduced considerably by this method.

J.B. M oncrieff et aL/Journal o[ Hydrology 188-189 (1997) 589-611

599

4. Corrections required to trace gas flux measurements Although the eddy covariance technique is widely considered to carry with it the least amount of empirical baggage of any micrometeorological technique there are two sets of corrections which need to be applied. First, the concentration of a trace gas may require correction if its partial pressure is measured rather than mixing ratio, as changes to air density arise from the simultaneous transfer of sensible and latent heat. A second group of corrections apply to the whole system, and arise from the unavoidable fact that any measuring system has some influence on the measurement itself and no sampling system can be regarded as responding perfectly to all flux-carrying eddies. 4.1. Corrections for changes in air density A paper by Webb et al. (1980), hereafter WPL, brought to the attention of experimenters making trace gas flux measurements the need to consider corrections to the measured flux because of changes to air density. The simultaneous transfer of sensible and latent heat causes fluctuations in air density which can be erroneously attributed to fluctuations in carbon dioxide and latent heat in sensors which measure the partial density of CO2 or H20 in air. Details have been presented elsewhere (e.g. I_zuning et al. (1982) provided experimental proof of the WPL corrections, Leuning and Moncrieff (1990) developed the arguments for the closed-path system and Leuning and King (1992) applied the equations to both open- and closed-path systems) and we can simply state the working equations for our closed-path system. The relationship between the CO2 density in air (Pc) and that measured inside the optical bench of the IRGA is { pr,~ where the subscript i refers to conditions inside the optical bench. The final working equation for C02 measured by a closed-path analyser is

This equation assumes that both water vapour and CO2 are brought to a common temperature and pressure within the optical bench. This is true for the LI-COR 6262 used in our system, and the correction term in the WPL scheme associated with the transfer of sensible heat does not need to be applied. If the latent heat flux is measured by an openpath instrument, the latent heat flux has to be WPL corrected before it can be used in Eq. (8) (Leuning and Moncrieff, 1990). In a closed-path system, evaporation can be found from ,

\ ~ T ] (1 + lxa)w P~i

,

(9)

where E is water vapour flux, # = ma/mv is the ratio of the molecular masses of dry air to water vapour, a = p v/p a is the ratio of mean water vapour density to that of dry air, T is absolute temperature, the overbars indicate time averages, and the primes denote fluctuations.

600

J.B. Moncrieffet aL/Journalof Hydrology188-189 (1997)589-611

4.2. Corrections required to account for whole system response It is not possible to create an eddy covariance system which has no effect whatsoever on the fluxes it is designed to measure. Instruments do not have an infinitesimally small response time, nor can nearly co-located instruments sample exactly the same parcel of air simultaneously, for example. As for actually digitising and recording the signal, the sampling frequency and time constraints of analogue or digital filters also influence the magnitude of the loss of signal. In this section we describe the errors introduced into flux measurements by the components of our system. Moore (1986) proposed a scheme whereby a series of transfer functions could be defined for each of the correction terms required in an eddy covariance system. We can write the fractional error in measured flux (AFc/F¢) as AFc ~ 1 -

Fc

J~ Twpc(n)Cwo(n)dn

(10)

~o Cw°(n)dn

where Two(n) is the convolution of all the transfer functions applicable to the measurement and Cwp(n) is the cospectrum of the flux Ft. n is the natural frequency, fp, f s are normalised frequencies (defined in Appendix A) Twp(n) can be written in full for our system (subscript p could refer to H20 or CO2) as

Two(n) = Tr(n).Td(itga)(n).T d sonic(n).Tm(n).Tw(fp)Ts(fs).Tt(n)

(11)

Appendix A describes the transfer functions which define our system and demonstrates graphically the relative importance of the transfer functions by frequency, for: T,(n), the digital recursive running mean; Td(n), the dynamic frequency response of the sensor (sonic or IRGA); Tin(n), the sensor response mismatch; Tw(fp), the scalar path averaging; Ts(fs), the sensor separation loss; Tt(n), the frequency attenuation of the gas concentration down the sampling tube. Although EdiSol can be used to post-process the raw turbulence data there was some merit in developing a new set of routines in a non-object-oriented language such as FORTRAN to allow wider verification and development of the analysis routines. The groups at the Wageningen Agricultural University and the Winand Staring Centre took the lead in this, and the group at the University of Copenhagen also used this software. In tests in which the same dataset is processed off-line by EdiSol or the FORTRAN routines, the results are effectively identical. The FORTRAN routines perform coordinate rotation and calibration and apply the relevant corrections based on the discussion outlined above.

4.2.1. Verification of transfer functions Having obtained the correction terms we now have to obtain representative co-spectral models which can be applied in Eq. (10) to estimate the whole system losses. The most widely used cospectral models are those from Kaimal et al. (1972) and we use normalised versions in which the numerical integrals of the normalised co-spectra equal unity over an unspecified frequency range as described by Moore (1986). In the following equations, fk is the normalised frequency ( ~ n(z - d)/u), n is natural frequency, u is horizontal wind

J.B. Moncrieff et al./Journal of Hydrology 188-189 (1997) 589-611

601

speed and z - d is height above the zero-plane displacement, c~ is a subscript denoting a scalar, in this case either CO2 or H20. For stable atmospheric conditions nCw~(n) =

fk aw,~ +BwJ 21

(12)

where Aw,~= 0.284 [1 + 6.4 (~-~-~) ] °75

(13)

B,~,~= 2.34Aw~'1

(14)

and

(note that in Eq. (14), the exponent is - 1.1 rather than i which was a typographical error in Eq. (21b) of Moore (1986) (C.J. Moore, personal communication, 1990) For unstable atmospheric conditions nCw,~(n) =

12"92fk [1 + 26.7fk] 1375 fk < 0.54

(15)

nCw~(n)=

4"378fk [1 + 3.8fk]24 fk -----0.54

(16)

and for Reynolds stress nCuw(n)

20.78fk [1 + 31fk]1575 fk < 0.24

(17)

nCuw(n )

12"66fk [1 + 9.6fk]24 fk >- 0.24

(18)

Fig. 5 shows a measured cospectrum of carbon dioxide obtained by the EdiSol system. The two other cospectra are a theoretical cospectrum under unstable conditions using Eq. (15) and Eq. (16) (the Kaimal cospectrum) and the same cospectrum but multiplied by the total transfer functions (the corrected cospectrum). The operating conditions for this particular set of data ensured laminar flow in the sampling tube. The difference between the Kaimal and corrected cospectrum at the higher frequencies shows the total error of the EdiSol system; the measured cospectrum fits the corrected cospectrum well, indicating that the errors in the system are adequately prescribed by this method of analysis. Cospectral functions, such as those of Kaimal, are a function of height above zero-plane displacement (the greater the measurement height, the less important are the high-frequency eddies) and atmospheric stability (the more unstable the conditions, the more the model cospectra shift to lower frequencies). Fig. 6 shows how the error terms in the EdiSol system vary with height above ground and windspeed for typical conditions during HAPEX-Sahel and again when this particular EdiSol system was operated with laminar flow conditions in the sampling tube. The greatest errors occur with high windspeeds and when the instruments are near the ground, both conditions favouring high-frequency

J.B. Moncrieffet aL/Journal of Hydrology 188-189 (1997) 589--611

602

1.0000

0

0

0.1000 r~

~

0

\

-4/3

0.0100

e°

0

.

0

0 ,

0.0010

O0 0

,

--

Kaimal Fit (unstable case)

',o

....

KaimalFit * transferfunctions

o, 0

measured co-spectrum

0

o

o

'

o 0 0

'

O0 0

', 0.0001

i

0.0010

t

I

I Illll

0.0100

I

,

, , I,III

t

.......

0.1000

I

1.0000

~l

~

.....

10.0000

normalised frequency (n, I-Iz) Fig. 5. Theoretical, measured and fully corrected cospectra of CO2. The theoretical model cospectra is a Kaimal model for unstable conditions. On this day the windspeed was 3.5 m s-1 and (z - d) - 8.5 m.

eddies and it is these eddies which are preferentially absorbed by tube smearing (see, e.g. Fig. 10 (below)). Low windspeeds, which favour a relatively greater proportion of large eddies, produce flux underestimates in the system of the order of 10-20%. Once the relationships between height, windspeed and stability have been established for a particular site, it is straightforward to apply these corrections in the post-processing phase of data analysis. If the flow in the tube was made turbulent by increasing the flow rate or decreasing the diameter of the sample tube the errors would be reduced. The theoretical case for making sure that turbulent flow conditions hold in systems such as ours has been made by Lenschow and Raupach (1991). Field measurements by Suyker and Verma (1993) showed that a configuration with laminar flow produced fluxes which were smaller by about 30% when compared with a reference open-path system but only 16% smaller when turbulent flow was created in the sampling tube. They also suggested optimum configurations for closed-path systems. The penalty for higher flow rates is of course the need for a more powerful pump and hence higher power requirements. Whatever

J.B. Moncrieff et al./Journal of Hydrology 188-189 (1997) 589-611

603

45

40

35

30 o 25

20

15

10

----0--- z-d =

5 0

~,,I,,tiltlllll,~,l 1 2

.... 3

4

I~,,,t 5

.... 6

8m

llnntlllnL 7

8

9

wind speed (ms "l ) Fig. 6. Typical whole system flux losses for an EdiSol system at a range of windspceds and measuring heights above the zero-plane displacement. Calculations assume a flow rate of 61 rain-1 down a tube of 9 m length and 3 mm internal radius (laminar conditions prevail) and unstable atmospheric conditions. Actual cospectrum from measurements averaged over 11:00-15:00 h GMT, SSS millet, HAPEX-SahcI.

mode of flow is used, the system of applying the appropriate transfer functions permits the 'true' flux to be established.

5. Testing of EdiSol system

There are two different types of tests which can be performed on field data obtained by a system such as ours. Assuming that calibration procedures are adequate and the usual micrometeorological conditions of adequate fetch and sampling height have been met, it is possible to attempt to close the energy balance. Although that will be appropriate to test the fluxes of sensible and latent heat, such a procedure is not available to check fluxes of carbon dioxide. It is then necessary to resort to comparing some parameters of turbulence with theoretical descriptions.

604

3.B. Moncrieff et aL/Journal of Hydrology 188-189 (1997) 589-611

(a) 700 600 5OO

•"~

400

o

300

E

200

10o W"

0

-100 L.

i

i

i

i

[

i

I

3

6

9

12

15

18

21

24

Local Time (h) - - o - - Sensible Heat

---D--- Latent Heat -Net Radiation .......... Closure

(b) 600

,K~

500 400

•~

300

c-

200 X

--~ EL

100

o

w

-100 -200 0

t 3

t 6

9

t 12

I 15

t 18

I 21

24

Local Time (h) Fig. 7. Energy balance closure obtained with an EdiSol-type system, WCSb, millet, Days 256 and 277 (redrawn from data of Soegaard and Boegh (1995)).

Fig. 7 shows energy balance closure for a system of the type we have described in this paper. The diurnal variation in the energy balance components are shown for two contrasting periods during the HAPEX-Sahel Intensive Observation Period (lOP) at the millet field of the West Central Supersite. Results on Day 256 were obtained during the latter part of the Sahelian wet season, and the midday Bowen ratio was about 0.3. No rain had fallen for a fortnight when the measurements on Day 277 were made, and the Bowen ratio at midday was about 0.7. Even though there are fluctuations of up to 100 W m -2 in the closure term on a half-hourly basis, the energy balance does close to within a few watts per square metre when averaged over the day. Such agreement on a daily basis is reassuring; on an hourly basis the failure to close completely the energy balance may have more to do with the heterogeneous nature of the terrain from which the flux has come and the

J.B. Moncrieff et al./Journal of Hydrology 188-189 (1997) 589-611

605

100 i

°

~ C02/C" I

•

(~ W/U"

I

10 o

o o

o ~X

o o

x -

o

o

c aeo

o o

o

03

.

0.1

........

0.001

o .o

o

o,~ o ~ o ~ _ . ~ e'*_~ • t

.. ,

•

o

-

i

. . _ . . _ _ .

I 0.01

........

•

• •

"o _ o . : .

~

........

0.1

~ 1

•

........

.

L 10

~ 1 O0

-z/L Fig. 8. Relationship between the diagnostic turbulent parameters aw/u. and e,./c, and atmospheric stability. WCSWAU fallow savannah.

difficulties involved in scaling up linear and non-linear terms associated with distributed sources and sinks (Lloyd et al., 1997). There are a number of diagnostic test statistics which illustrate the correct functioning of individual components of an eddy covariance system. Two useful statistics are the ratio of the standard deviation of vertical windspeed (aw) to the friction velocity (u,) and the ratio of the standard deviation of scalar concentration (ac) to the relevant scaling parameter (c.). The scaling parameter for CO2 is defined by the relation Fc = u,c,. These ratios have a unique relationship with atmospheric stability as predicted by Monin-Obukhov similarity theory. In unstable conditions aw/U. should increase at a rate proportional to [(z - d)/L] t/3; under the same conditions, trdc, should decrease at a rate proportional to [(z - d)/L] -t/3 (Kaimal and Finnegan, 1994). Fig. 8 shows the ratios for the EdiSol system on the fallow savannah site at the West Central Supersite, operated by the group from the Wageningen Agricultural University. The scatter apparent in the ode, is usually an indication that fetch requirements are marginal under some wind directions but the agreement between measurements and theory confirms the correct functioning of the system. In the range 0.01 < - (z - d)/L < 0.1, ac/c. was almost constant at about 2.5, whereas with increasing instability ac/C. decreased at a rate proportional to [(z - d)lL] -v3. The data for awlu, fit the relationship 1

aw U,

1.25(1-3L)

3

(19)

This is in agreement with several other published studies, e.g. those by Panofsky and Dutton (1984) and De Bruin et al. (1993).

6. Typical results One of the objectives of the HAPEX-Sahel experiment was to obtain information on the long-term water and carbon balance of Sahelian vegetation. The system we have

606

J.B. Moncrieff et al./Journal of Hydrology 188-189 (1997) 589-611 (a)

4"

,L

0

t5

Ill

-5

-10 "O

~= -15 IJ.

BIIIB

230

I

I

I

~

I

I

240

250

260

270

280

290

Day of Year (b) 1600 E 1400 1200 1000 800 600 = 400 C o 200 0 L) -200

230

I

I

I

I

I

240

250

260

270

280

290

Day of Year

Fig. 9. (a) Long-termCO2 fluxmeasurementsat the WCS-WSCfallowsavannahsite and (b) the carbonuptakeat this site for the same period.

developed jointly has the capability of being left in the field for extended periods with minimal power and maintenance requirements. Fig. 9 shows a time series of the net ecosystem flux of carbon dioxide over fallow savannah for the whole of the lOP at the West Central site operated by the Winand Staring Centre. The record covers a period of about 53 days. There are occasional days when no fluxes were recorded owing to instrumentation problems, and the short gaps in the data are for periods of calibration. Further descriptions of results obtained from our system have been presented elsewhere (e.g. Verhoef et al., 1996; Levy et al., 1997; Kabat et al., 1997; Moncrieff et al., 1997).

J.B. Moncrieff et al./Journal of Hydrology 188-189 (1997) 589-611

607

7. Conclusions We have described a system for measuring the surface fluxes of momentum, sensible and latent heat, and carbon dioxide. The system was developed jointly by several European laboratories and has resulted in a system which is well suited to its task. The system uses commercially available sensors (there are no 'eddy correlation specials' here). Surface fluxes can be monitored in real-time and raw turbulence data can be stored on hard-disk for post-processing if required. The system has proved to be reliable, requiring minimal maintenance. Typical results obtained from the HAPEX-Sahel experiment have been presented and shown to be consistent with meteorological and biological expectation. Sahel

608

J.B, Moncrieff et al./Journal of Hydrology 188-189 (1997) 589-611

a)

1.0

0.8

e-

0.6 t

t

0.4

....

0.2

t 0.0 0.0010

|

i Lllll]

i

t

i iiiiii

0.0100

i

t

0.1000

i i llllJ

i

i

1.0000

- digital running mean sensor separation sonic path averaging

i L±II

10.0000

natural frequency (Hz)

b)

1.0 0.8 0

0.6

c:

tube loss (laminar flow)

o,

- LI-COR dynamic frequency response

\\

p.,

....

sensor response mismatch

-

solent dynamic frequency response

0.2 0.0 , , ,,,,,,I , , ,,,,,,I , , ,,,.,1~ ...... 0.0010 0.0100 0.1000 1.0000 10.0000

natural frequency (Hz)

e) 1.0

•~

0.8

f

I¢

0.6

0.4

combined transfer function

0.2 o 0.0

0.0010

•

, , ~,,,,I

I

0.0100

ill

i

0.1000

1.0000

,,,,L

10.0000

natural frequency (Hz) Fig. 10. The transfer functions which define our system are shown individually in (a) and (b). The combined transfer function shown in (c) shows the total response of our system under typical operating conditions (i.e. flow rate 6 ! rain-l, tube radius 3 mm, z - d - 8 m, 200 s digital running mean, cutoff frequency 5 Hz, sensor separation 5 cm, sonic path length 15 cm, sonic cutoff frequency 20.8 Hz).

J.B. Moncrieff et aL/Journal of Hydrology 188-189 (1997) 589-611

Appendix A. 1. Symbols used Dc

molecular diffusion coefficient of CO2 in air

fp

normalised frequency fp - npj/~

fs

normalised frequency defined by fs = n s / ~

n

natural frequency

ns

sample frequency

Pl

sonic path length

r

tube radius

Re

Reynoid's number

s

sensor separation distance

tr

response time of an instrument

tr~ and tr2

response times of particular instruments

tt

time taken for an air parcel to travel through the tube, tt = X / U mean wind speed

U

discharge velocity in the tube

X

tube length

l?

time constant of the filter

At

time interval between the samples

~/

a constant given by 7/= e x p ( - A t / r )

rr

effective time constant, rr - ~[(n~(1 - ~/)]-i

Tr(n) is the recursive digital running mean Tr(n ) =

2rnrr

~/1 + (2rnrr)2 /rl To(n) is the sensor dynamic frequency response Td(n ) =

1

X/(1 + (2rntr) 2

Tin(n) is the sensor response mismatch Tm(n ) =

1 + (2rn)2trltr2 X/[1 + (27rntrl)2][1 + (21rnta) 2]

609

610

J.B. Moncrieff et aL/Journal of Hydrology 188-189 (1997) 589-611

T,,,(n)is the sonic anemometer path averaging Tw(fp)= ~p2 {1+ exp( -2XfP)2 3[1- exp( ~ 4 _- ~2~rfp)] fp J

rs(,0 is the sensor separation loss Ts(fs) = exp( - 9.9fs1'5) rt(n) accounts for the frequency attenuation of the gas concentration down the sampling tube, assuming laminar flow, Tt(n) sexp (

- ~2r2rl2tt~

~c

]

Lenschow and Raupach (1991) provided the equivalent transfer function for turbulent flow in the sampling tube: Tt(n) ~ exp (

\

160(Re)rnEX~ u2

J

References Axya, P., 1988. An Introduction to Micrometeorology. Academic Press, New York, 307 pp. De Bruin, H.A.R., Kohsiek, W. and van der H u r l B.J.J.M., 1993. A verification of some methods to determine the fluxes of momentum, sensible heat and water vapour using standard deviation and structure parameter of meteorological quantities. Bouodary-Layer Meteorol., 63: 231-257. Grace, J., Lloyd, J., McIntyre, J., Miranda, A., Meir, P., Miranda, H., Moncrieff, J.B., Massheder, J.M., Wright, I. and Gash, J., 1995. Fluxes of carbon dioxide and water vapour over an undisturbed tropical forest in southwest Amazonia. Global Change Biol., 1: 1-12. Hicks, B.B. and McMillen, R.T., 1988. The measurement of dry deposition using imperfect sensors and in nonideal terrain. Boundary-Layer Meteorol., 42: 79-94. Kabat, P., EIbers, J. and Dolman, A.J., 1997. Dynamics of surface fluxes above two typical land cover types in HAPEX-SaheI: a comparison. L Hydrol., this issue. Kaimal, J.C. and Businger, J.A., 1963. A continuous wave sonic anemometer-thermometer. J. Appl. Meteorol., 2: 156-164. Kaimal, J.C. and Finnegan, LJ., 1994. Atmospheric Boundary Layer Flows: their Structure and Measurement. Oxford University Press, Oxford, 289 pp. Kaimal, J.C. and Gaynor, J.E., 1991. Another look at sonic anemometry. Boundary-Layer Meteorol., 56: 401410. Kaimal, J.C., Wyngaard, J.C., lzumi, Y. and Cote, O.R., 1972. Spectral characteristics of surface-layer turbulence. Q. J. R. Meteorol. Soc., 98: 563-589. Lenschow, D.H. and Raupach, M.R., 1991. The attenuation in fluctuations in scalar concentrations through sampling tubes. J. Geophys. Res., 96: 15259-15268. Leuning, R. and King, K.M., 1992. Comparison of eddy-covariance measurements of CO2 fluxes by open- and closed-path CO2 analysers. Boundary-Layer Meteorol., 59: 297-311. Leuning, R. and Moncrieff, J.B., 1990. Eddy-covariance CO2 flux measurements using open- and closed-path CO2 analysers: corrections for analyser water vapour sensitivity and damping of fluctuations in air sampling tubes. Boundary-Layer Meteorol., 53: 63-76. Leuning, R., Denmead, O.T., Lung, A.R.G. and Ohtaki, E., 1982. Effects of heat and water vapour transport on eddy covariance measurement of CO2 fluxes. Boundary-Layer Meteorol., 23: 209-222.

J.B. Moncrieff et al./Journal of Hydrology 188-189 (1997) 589-611

611

Levy, P., Moncrieff, J.B., Massheder, J.M., Jarvis, P.G., Scott, S. and Brouwer, J., 1997. CO2 fluxes at leaf and canopy scale in millet, fallow bush and tiger bush vegetation at the HAPEX-Sahel Southern Supersite. J. Hydrol., this issue. Lloyd, C.R., Shuttleworth, W.J., Gash, J.H.C. and Turner, M., 1984. A microprocessor system for eddy-correlation. Agric. For. Meteorol., 33: 67-80. Lloyd, C.R., Bessemoulin, P., Cropley, F.D., Culf, A.D., Dolman, A.J., Elbers, J., Heusinkveld, B., Moncrieff, J.B., Monteny, B. and Verhoef, A., 1997. An intercomparison of surface flux measurements during HAPEXSahel. J. Hydroi., this issue. McMiUen, R.T., 1983. Eddy correlation calculations done in real-time. In: 7th Conf. Fire and Forest Meteorology, Ft. Collins, CO, 25-28 April 1983. McMillen, R.T., 1986. A BASIC program for eddy correlation in non-simple terrain. NOAA Tech. Memo. ERL ARL-147. NOAA, Air Resources Lab., Oak Ridge, MD. McMillen, R.T., 1988. An eddy correlation technique with extended applicability to non-simple terrain. Boundary-Layer Meteorol., 43: 231-245. Moncrieff, J.B., Monteny, B., Verhoef, A., Friborg, Th., Elbers, J., Kabat, P., de Bruin, H., Soegaard, H., Jarvis, P.G. and Taupin, J.D., 1997. Spatial and temporal variations in net carbon flux during HAPEX-Sahel. J. Hydrol., this issue. Moore, C.J., 1983. On the calibration and temperature behaviour of single-beam infrared hygrometers. BoundaryLayer Meteorol., 25: 245-269. Moore, C.J., 1986. Frequency response corrections for eddy correlation systems. Boundary-Layer Meteorol., 37: 17-35. Mortensen, N.G. and Larsen, S.E., 1994. Flow response characteristics and temperature sensitivity of the Solent Sonic anemometer. Ann. Geophys., 12(Suppl. If): C539. Panofsky, H.A. and Dutton, J.A., 1984. Atmospheric Turbulence and Methods for Engineering Applications. Wiley, New York. Schotanus, P., Nieuwstadt, F.T.M. and de Bruin, H.A.R., 1983. Temperature measurement with a sonic anemometer and its application to heat and moisture fluxes. Boundary-Layer Meteorol., 26: 81-93. Sellers, P., Hall, F.G., Baldocchi, D.D., Cihlar, J., Crili, P., den Hartog, J., Goodison, B., Kelly, R.D., Lettenmeier, D., Margolis, H., Ranson, J. and Ryan, M., 1994. BOREAS Experiment Plan. NASA Goddard, Greenbelt, MD. Shuttleworth, W.J., 1988. Corrections for the effect of background concentrations change and sensor drift in realtime eddy correlation systems. Boundary-Layer Meteorol., 42: 167-180. Shuttleworth, W.J., McNeil, D.D. and Moore, C.J., 1982. A switched continuous-wave sonic anemometer for measuring surface heat fluxes. Boundary-Layer Meteorol., 23: 425-448. Shuttleworth, W.J., Gash, J.H.C., Lloyd, C.R., Moore, C.J., Roberts, J.M., Marques, A. de O., Fisch, G., de Paula Silva, V., Ribeiro, M.N.G., Molion, L.C.B., de Sa, L.D.A., Nobre, C.A., Cabral, O.M.R., Patel, S.R. and de Moraes, J.C., 1984. Eddy-correlation measurements of energy partition for Amazonian forest. Q. J. R. Meteoroi. Soc., 110: 1143-1162. Shuttleworth, W.J., Gash, J.H.C., Lloyd, C.R., McNeil, D.D., Moore, C.J. and Wallace, J.S., 1988. An integrated micrometeoroiogical system for evaporation measurement. Agric. For. Meteorol., 43: 295-317. Soegaard, H. and Boegh, E., 1995. Estimation of evapotranspiration from a millet crop in the Sahel combining sap flow, leaf area index and eddy correlation technique. J. Hydroi., 166: 265-282. Stull, R.B., 1988. An Introduction to Boundary Layer Meteorology. Kluwer Academic, Dordrecht, 666 pp. Suyker, A.E. and Verma, S.B., 1993. Eddy correlation measurements of CO2 flux using a closed-path sensor: theory and field tests against an open-path sensor. Boundary-Layer Meteorol., 64: 391-407. Verhoef, A., Allen, S.J., de Bruin, H.A.R., Jacobs, C.M.J. and Heusinkveld, B.G., 1996. Fluxes of CO2 and water vapour from a Sahelian savannah. Agric. For. Meteorol., 80: 231-248. Webb, E.K., Pearman, G.I. and Leuning, R., 1980. Correction of flux measurements for density effects due to heat and water vapour transfer. Q. J. R. Meteorol. Soc., 106: 85-100.