Agricultural and Forest Meteorology, 33 (1984) 67--80 67 Elsevier Science Publishers B.V., Amsterdam -- Printed in The Netherlands

A M I C R O P R O C E S S O R S YS TEM F O R E D D Y . C O R R E L A T I O N

C.R. LLOYD, W.J. SHUTTLEWORTH, J.H.C. GASH and M. TURNER

Institute of Hydrology, Wallingford. Oxfordshire (Gt. Britain)

(Received February 4, 1984; accepted April 30, 1984)

ABSTRACT

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.

The application of a microprocessor-controlled data acquisition and processing system is described. The system, which is battery powered, takes data from six sensors at a frequency of 10 Hz and computes the fluxes of heat, water vapour and momentum in real time, using the eddy correlation method.

From results obtained at a field site, the microprocessor system is separately compared with a proven off-line eddy-correlation system and with measured net radiation. These tests indicate that, provided care is taken in interpreting the data in terms of the performance and exposure of the sensors, the system described is capable of adequately measuring energy fluxes at unattended sites.

INTRODUCTION

The eddy -co r r e l a t i on t echn ique is an a t t rac t ive m i c r o m e t e o r o l o g i c a l m e t h o d o f measur ing surface energy f luxes since it p rovides a d i rec t measure- m e n t wi th few theore t i ca l a s sumpt ions . In n o r m a l field cond i t ions the t e c h n i q u e requires da t a logging at a ra te equ iva len t to sampl ing at a b o u t 10 Hz. In the pas t this has been a c c o m p l i s h e d e i ther b y record ing the signals on a mu l t i - t r ack ana logue t ape recorder , or b y using a fast scanning digital v o l t m e t e r and t ape record ing digital data . B o t h these m e t h o d s are accura te , reliable, and a l low fo r a f lexible analysis p r o c e d u r e because the da ta process ing is car r ied ou t a f t e r the da ta acquis i t ion. However , because o f the large a m o u n t o f da ta r ecorded , these m e t h o d s are on ly sui table fo r m a k i n g m e a s u r e m e n t s over t ime per iods of a day or less. T h e long m e a s u r e m e n t pe r iods typ ica l o f agr icul tural and hydro log ica l research wou ld soon p r o d u c e p roh ib i t ive ly large da t a sets.

An a l te rna t ive a p p r o a c h , m o r e su i tab le fo r app l i ca t ions o f this t ype , is t ha t deve loped b y D y e r e t al. ( 1967 ) fo r the F luxa t ron . This i n s t rumen t , in e f fec t , uses an ana logue c o m p u t e r to m a k e the necessary cor re la t ions in real t ime , t h e r e b y reduc ing the da ta co l l ec ted to a single n u m b e r fo r each f lux, in each m e a s u r e m e n t per iod . The F l u x a t r o n has been used in m a n y research projects , bu t has d isadvantages because of the inf lexibi l i ty of ana logue c i rcu i t ry and the technica l p r o b l e m s involved in f i l ter ing low f r e q u e n c y eddies. The d e v e l o p m e n t o f cheap, low p o w e r c o n s u m p t i o n , digital micro- p rocessors has enab led these t w o a p p r o a c h e s to be c o m b i n e d in a field da t a

0168-1923/84/$03.00 © 1984 Elsevier Science Publishers B.V.

acquis i t ion system w~lci~ ofhw:~ both the advantage of digital comp~!.at~,, , and real t ime analysis. This paper describes such a sys tem which has b~.,~ designed as par t of an ins t rument capable of making rou t ine mea~.u~omc~v.'.~.. o f surface fluxes at unat tencted sites. The details desc.ribed relate to ~,r~m~t)'~,~ i n s t rumen ta t ion in us~, during the summer of 1983 at an exper iment sit~, c)~ Berner ' s Heath, near T h e t f o r d in East Anglia, U.K.

The i n s t rumen ta tkm, which is known as the Hydra , is shown in Vtg. 1 an(J comprises a vert ical sonic' a n e m o m e t e r o f the t y p e descr ibed by Shu t t t ewor th et al. (1982) , an IR h y g r o m e t e r (Moore, 1983) , similar to the type firsl descr ibed by Hyson and Hicks t 1975) , a fast response t h e r m o c o u p l e and two Gill p rope l lo r a n e m o m e t e r s m o u n t e d at r ight angles in the hor izonta l plant,. The ba t t e ry powered da ta acquisi t ion and processing system was designed to take signals f rom these sensors at a f r equen cy of 1 0 H z , anti to calculate average f luxes p ropor t iona l !,o those of water vapour , sensible heat and m o m e n t u m , toge the r with the means and variances of all p r imary variables. To allow in terchanging o f sensors, the cal ibrat ion coeff ic ients are applied in a

! ,

'!

Fig. 1. The comple te Hydra eddy-correlat ion sys tem. The data acquisi t ion and sensor electronics are housed in the a luminium case beside the instrument mast. The sensor head is 3.5 m above the ground.

69

subsequent off-line analysis. The data recording interval is easily altered in the software, but hourly average values are the realistic compromise generally used.

T H E O R E T I C A L C O N S I D E R A T I O N S

T h e e d d y cor re la t ion m e t h o d

The total flux, F, of any atmospheric entity, s, passing through unit horizontal area at a vertical velocity, w, is given by

m

F = ws (1)

o r

F = (~ + w')(g+ s') (2)

w__here a p r i m e denotes a deviation from the mean. Expanding eq. 2 with w' and s' by definition zero, gives

F = w s + w s (3)

In this expression fvg represents the flux transported by the mean flow (Dyer, 1963) and w's ' that flux, Fs, which emanates from the surface and is transported by the turbulent eddies. Combining eqs. 1 and 3 gives

Fs = w s - - w s (4)

In this way the equations for calculating the eddy correlation fluxes of evaporation, E, sensible heat, H, and surface stress, u2., are

E = W p v - - ~ p v (5)

H / p c , = w T - - ~ T (6)

u2. = w-u-- w u (7)

where Pv is absolute humidity, p is air density, cp is the specific heat of air at constant pressure, T is temperature and u the wind velocity in the direction of the mean wind.

Webb et al. (1980) have shown that eqs. 5 and 6 require corrections to account for the mean vertical velocity induced by correlated fluctuations of w and p. In practice these corrections are usually small (0.5%) and can be added during the off-line analysis.

T h e m o v i n g average

In steady-state conditions the averages in eq. 4 could be calculated as simple linear means over a specified time interval; however, in practice, steady-state conditions rarely occur and it is necessary to remove background trends in the variables to be averaged. In a real time computat ion this can be

done using a moving average. The calculation of this moving average shoui(i at any given time, weight the values near to that time more than thpse val~w~ more distant in time, and may be thought of as a smoothing filter. It ~; analogous to a low-pa.ss elect:rical filter and in its digital form i()r.nes m:(t Enochson, 19721 can be expressed as

( S ) i ::= Cg ( S ) i_ 1 @ ( 1 .... ,~ Isi ( ~s

where si is the present input variable, (s)i- t the previous moving average and (s)i the resultant present value of the moving average. The weighting function~ ~, is given by

0; = e - A t l r

where At is the time interval between inputs and r is the time constant. Equations 5--7 can therefore be rewritten in a form compatible with eq. 8

a s

E = ( W p v ) - - (w) (Pv) (9)

H / p c , = ( w T ) - - (w) (T) { 10}

u~ = ( w u ) - - (w) (u) (11~

The variance of any fluctuating variable may also be expresed in terms of a function of weighted moving averages as

0 2 = (s 2 ) - (s) 2 (12)

I n f r a r e d h y g r o m e t r y

The system described here has been specifically designed to operate with a 2.7-#m IR absorption hygrometer of the type first described by Hyson and Hicks (1975). This instrument utilises the exponential dependence of signal ou tpu t voltage on absolute humidi ty to reduce the effects of slow variations in optical and electronic performance. Previous versions of this instrument have achieved this by using an analogue voltage divider to give the ratio of the fluctuating signal to the mean component; in this instrument this division is performed digitally using the microprocessor. Further details of the development and calibration of this sensor are given by Moore (1983) and only the background theory used in the on-line calculations is described here.

Raupach (1978) described the absorption of IR for hygrometers operating in the 2.7 pm water vapour band. He related the rectified DC output voltage, V0, to the absolute humidi ty by an expression of the form

Vo = K e apv (13)

o r

Pv = l - ln ( V o / K ) (14) a

71

where K is an instrumental gain factor, and a is a calibration constant. The moving average value of the absolute humidi ty of the air can be

approximated by

<Pv> = l l n (<Vo>/K) (15) a

Subtracting eq. 15 from eq. 14 produces an expression for the instantaneous fluctuation in the value of the absolute humidi ty of the air

(16)

Equation 16 can be expanded as a convergent series, and since typically

V° -- 1 ~ 0.01 the error in approximating the expansion of the loga- <Vo>

r i t h m a s l n ((V~) V° - - <~00> 1 is close to 0.5%. Within this approximation

eq. 16 can be rewritten as

P v = a

Substituting eq. 17 into eq. 9 and treating <Pv> as a constant, gives the real time equation for calculating the evaporation flux as

In practice the calibration constant, a, and the calibration of the vertical wind sensor, are applied in off-line analysis. The variance of the function,

F = ((v-V~-I) can be calculated in a similar way using eq. 12.

Thermocouple thermometry

Chromel--constantan thermocouples of 50pm diameter together with circuitry in the sensor head produce a signal directly proportional to tem- perature and a flux proportional to the heat flux can be calculated using eq. 10, with the variance of the temperature fluctuations calculated from eq. 12. Again real time analysis proceeds in terms of measured voltage, with calibration constants introduced in the off-line analysis.

The horizontal wind velocit3

To obtain the friction velocity, u . it is first necessary to resolve the signa]s VA and VB from the two horizontal anemometers to obtain the instanlaneou~, wind velocity in the direction of t;he mean wind and, c, onsequenlly, thr direction of the metal wind itself. The procedure adopted is firsL to resolve V A and VB to give two orthogonal wind velocities V~ and Vy, such that ~q. bisects the angle between the anemometers (see Fig. 1). It can be shc~wn thai,

V~ - and V~ 2 cos (0/2) 2 sin (0/2)

where 0 is the angle separating the two horizontal anemometers. The instantaneous values of V~ and Vy then pass through digital filters

(eq. 8) to give moving average values, (V~) and (V,). In principle these are then used to determine the direction of the mean wind, ¢P, given by

cos 0v = V,:/t(G> 2 + ;V,.> 2 J~ 2

and the instantaneous wind vector then expressed as instantaneous com- ponents; u, in the direction of the mean wind and v, normal to the mean wind. In practice it is not necessary to pass through this intermediate stage and u and v are calculated directly from the expressions

G<G) + v,,<G~ /2 - - ( ( G ? + (G)~) ~'2

Vx<G> + V~<Vx> 7fl ~

( (Vx)2 q- (Vy>2) 1~2

The value of u obtained in this way is used to calculate u, from eq. l l and incorporated into eqs. 8 and 12 to give the mean variances of these components.

It should be noted that an on-line analysis of this type requires either that the horizontal anemometers are specific to a particular program, or that the instruments have identical, though not necessarily specified, calibrations.

THE DATA ACQUISITION SYSTEM

Electronic details

The data acquisition system is based on the RCA 1802 microprocessor, which is an assembler programmable device using CMOS logic. This com- bination has the advantage of efficient program operation with low power consumption, high noise immunity, and insensitivity to climatic and voltage variations.

The electronic hardware is mounted on four boards shown as a block diagram in Fig. 2. Two RCA production boards are used: the RCA COSMAC

73

,M-z

I CDP 18S601

M IC ROBOARD COMPUTER

~ J S

OAIA BUS

~H(2) BOARD

D a I A IN

, N , ' , n O L T ~ , , T

I CDP18S643 A/D Converter ] IH(1) 8OARO

Fig. 2. Block diagram of the RCA 1802-based data acquisition system.

Microboard Computer (CDP18S601) and the analogue-to-digital converter (ADC) (CDP 18S643). The software controlling the system is contained in a 4 Kbyte read-only memory (ROM) on the compute r board, which also has 4 Kbytes of random-access memory (RAM) available for program use.

The ADC is set up to perform 12 bit resolution conversions on eight differential mult iplexed inputs over the range + 5 V. This gives a voltage resolution of 2.44 mV per bit, with a conversion time for a single channel of 275 ps. The (standard) 2 MHz crystal clock is used, allowing a sampling rate of 10Hz.

Two purpose built boards are also used. One was constructed to perform the following operations:

(i) to provide a 100 ms (10Hz) interrupt pulse; (ii) to link together four 8-bit mult iply/divide units (RCA CDP1855) into

a cascaded 4 byte multiply/divide unit; (iii) to control the interface between the central processor and the data

module.

The second board provides a regulated voltage source for the ADC and also gives the opera tor a visual indication of whether or not the central processor is running. A circuit monitors the changing logic level on the micro- processors ou tpu t flip-flop, and, if the level on the line is not changed at least once every 70 ms, a light emitting diode is activated to indicate a fault.

Power for the instruments and data acquisition system was provided by a 1 0 0 A h lead--acid bat tery which gave sufficient power for five days operat ion of the complete Hydra system.

The data logger and o f f line processing

At the end of each hourly measurement period, up to eighteen ~mmbers representing the fluxes, and the means and variances of the measured variables, are transferred from the RAM to a solid-state data module (GK Instruments, Milton Keynes, U.K.) consisting of a self-powered 16 Kbyte CMOS memory bank. Although the turbulence variables are evaluated -all the time, the number of variables stored can be altered in the program. Th(, running time allowed by the store is dependent on the output format used; the format used for data presented here "allowed sufficient storage for tw() weeks operation. After removal from the field the data axe printed and transferred to a floppy disk using a GK data module reader coupled to a Commodore PET computer system. Sensor calibrations and other physical constants are incorporated at this stage.

Software

The online software consists of three parts. (i) A short "initialisation" section which occurs in the first millisecond

of operation. This clears the data stacks and attaches numerical values to fixed constants used in subsequent calculations.

(ii) The main sectiofi of the program is the " in te r rupt" routine, which is initiated every 100 ms. This routine controls the operation of the ADC and carries out all the computations necessary to provide running sums of instantaneous values of the fluxes, variances and means.

(iii) An " o u t p u t " section, which takes over from the disabled interrupt routine at the end of each averaging period, provides the average f luxes , variances and means which are then output to the solid-state data module. The data stack locations storing those variables are then cleared and the interrupt re-enabled.

A flowchart of the program is shown in Fig. 3. Service routines performing a sensor scan (SCAN), multiplication (MULT), divisioa {DIVIDE), a square root (SQRT), and the moving average calculation (RMA) are used at various points in the program as indicated in Fig. 3. The interrupt routine takes a maximum of 76 ms, including 4 ms to scan the input voltages.

Instrument performance monitoring

The sonic anemometer can fail with water on the transducers and the hygrometer may also fail if there is liquid water in the optical path between the source and detector. Failure by either instrument provides individual logic voltage levels. A single analogue status voltage is then created from these levels which is read each cycle. The program interprets this status voltage in terms of error conditions in the sensors and computes a running sum of the number of times this has occurred for each sensor. At the end of

75

N T;ALL%~ I XLD CCNSIANTS

DATA SlACkS

t t

NL) YES

PERIUD MEANS FOR <~ <~,<~> ,<u>,<v)

VARIA N(" S, FLUXES, & THE 2 SPARE SE NS()~ CHANNELS

OUlpUl SIATUb & m ,,I,3U ',~EANb

v

1

1 TO ~ ~ Vy d J

<v~> I" I

< o ~ . _ . j -

<w. >,<T '>,<~ > 4J >,<v.~

i

<w J>

I c O~¢PUTE l~L

i

6 ~ PERIOD SUMS ~OR

VARIANCES, ~LUXEb t AND THE 2 ~PARL SE NS©q CHANNELb

Fig. 3. A flowchart of the program. Service routines are shown for sensor scan (SCAN), multiplication (MULT), division (DIVIDE), square root (SQRT), moving average (RMA), flux and variance calculations (FLUVAR) and updated summations (SUM6).

an h o u r l y p e r i o d a c o d e n u m b e r is w r i t t e n to t h e data m o d u l e , w h i c h i n d i c a t e s t h e f r a c t i o n o f t i m e each s e n s o r r e p o r t e d an error.

FIELD T R I A L S

Tests

The field trials reported here were carried out above a stand of Corsican Pine (Pinus nigra var. maritirna (Ait.) Melv.) adjacent to Berner's Heath ~ea~ Thet ford in East Anglia. The trees had a mean height of about 10 m and a density of 4400 stems per hectare. The fetch was at least 320 m of uniform flat vegetation in al] directions. The instrument was mounted on a mas~ at ~ height of 15.3 m.

For the first test the signals from a Hydra were logged simultaneously by the microprocessor system under test and the independent data acquisition system used previously by Shut t lewor th et al. (1982) and Molion and Moore (1983). This comprised a fast scanning digital vol tmeter controlled by a Hewlett-Packard (H-P) mini-computer, which also wrote the data onto magnetic tape for later analysis on a larger computer . The H-P system sampled at a f requency of 20Hz, rather than the 16Hz which was tile f requency used in the Hydra system at the t ime of the test. Both systems were run in parallel for 58 20-min periods and the results of the comparison for the case of sensible heat flux are given in Fig. 4. The off-line analysis used an identical .moving average technique to that used in the microprocessor real t ime analysis. Similar results were obtained for the other variables, with differences of a few per cent or less observed. Such errors are consistent with differences in the ADCs used in the two systems.

In the second test the sum of the evaporation and sensible heat flux as measured by the eddy correlation system is compared with the available net radiant energy as measured by a radiometer which was part of an automatic

300]

i E

200"~

i I T !

~oo~ ~"

/ " ,oo

o l~ ~"

/ / "

- w i

200 300 H (H-P) Wm -z

Fig. 4. T h e sensible hea t f lux f rom a H y d r a head ca lcu la ted off - l ine using a H e w l e t t - Packard (H-P) mini -computer , wi th later analys is o n a larger computer , versus t h a t ca lcu la ted in real- t ime by the microprocessor sys tem. The data are 20-rain averages.

77

weather station (Didcot Instruments, Abingdon, U.K.). This test is also a test of the Hydra sensors and of the eddy correlation method itself. The instru- mentation was run unattended for a period of ten days and Fig. 5 shows the results of the comparison for four consecutive dry days. In calculating the fluxes we have fol lowed the off-line analysis procedure described in Shuttleworth et al. (1984) and used a calibration for the sonic anemometer derived from field comparisons with a Kaijo Denki DAT311 anemometer.

Shuttlework et al. (1984) also discussed the effects of using different time constants in the moving average digital filter. In this test a time constant

20~ 20

15

10-

5

7, o

uJ x ~ m -

.,4 15-

10-

5 O-

(a)

/ / / x "' . . . . . . "- "-

/

/ /

06~00 12100 18!00

(c)

, / /

06!00 12!00 18~00 21

TIME

10

5

0

0

(b) / / " ~

06:00 12:00 18:00 24:00

20 ~

15-

10~

5 0

)0

(d)

~ . . ° _ ~ . . ° _ j, 06~00 12~00 18"00 24

(GMT) 30

Fig. 5. Cumulat ive f lux of sensible plus latent heat as measured by the Hydra ( - - - - - - ) , compared wi th cumulat ive net radiation ( ), for 28- -31 July 1983.

78

T, of 18.75min was used. The use of a shorter time constant ( r /3 ) reduces the fluxes, and of a longer time constant (5r/3) increases the I luxes b~ generally a few per cent in both cases, although the differences may t:~:. greater in rapidly changing conditions.

Discuss ion

The results in Fig. 5 show the fluxes measured by the eddy correlation system and the comparable measurement of net radiation plotted cumula- tively to emphasise systematic errors. Soil heat flux is not included: previous measurements at this site indicate it is typically about 2% of the net radiation equivalent to a net daily input of about 0.4 MJ m --2 during a dry summer day. No account is taken of the radiant energy into storage, although this should be small over a 24-h cycle. However, the diurnal change in storage wilt cause the net radiation to overestimate available energy during the morning and early afternoon, and underestimate during the late afternoon and night. The measurement of net radiation is known only to an accuracy of the order of 5%.

The major errors in the eddy correlation measurement can be identified as follows:

(i) calibration errors, probably the largest of which is about -+ 5% in the vertical windspeed. This includes uncertainty in its effective calibration due to such effects as cosine errors and self-sheltering of the transducers;

(ii) high frequency loss resulting from the inadequate time response of the sensors (the sensors are designed to have time constants of the order 0.1 s in normal conditions);

(iii) low frequency loss due to inadequate sampling of the long period eddies, i.e., an inappropriate t ime constant in the filter used to derive the moving average;

(iv) under-estimation of the fluxes resulting from the physical separation of the sensors, and sheltering of the sensors when the instrument is badly exposed, i.e., the wind is blowing along the instrument rather than through it.

Neglecting the latter effect and assuming that the instrument is well exposed we estimate that the eddy correlation fluxes are likely to be measured to an accuracy of within 10%. As most of the errors act to reduce the measured flux the error is more likely to be negative than positive.

Figure 5 provides general support for this assessment. On 29 and 30 July (Fig. 5b, c) the Hydra was well exposed with the wind blowing perpendicular to the sensor mounting frame, and there is good agreement between the two measurements. On 28 July (Fig. 5a) exposure was bad with the wind blowing along the line of the sensors in a direction away from the major supporting frame; this could well be responsible for the divergence of the two measure- ments, with a total shortfall of 16% in the eddy correlation measurement over the 24-h period. On 31 July (Fig. 5d), when there was a 13% shortfall, the wind was again blowing along the line of the instrument but towards the

79

suppo r t i ng s t ruc ture . The re is also some ind ica t ion f r o m the h y g r o m e t e r s ta tus m o n i t o r i n g t h a t dew f o r m e d on the w i n d o w o f the h y g r o m e t e r in the ear ly m o r n i n g which m a y also have a f f ec t ed the m e a s u r e m e n t on this par t i cu la r day .

Concluding remarks

These resul ts indica te t ha t the m i c r o p r o c e s s o r s y s t e m descr ibed in this p a p e r is f unc t i on ing cor rec t ly , and t h a t it m o n i t o r s the i n s t r u m e n t a t i o n , and calcula tes and s tores the f luxes as in tended . The sys tem, by also p rov id ing s tored i n f o r m a t i o n on sensor p e r f o r m a n c e , al lows cri t ical eva lua t ion of the data . Provid ing care is t a k e n in in t e rp re t ing the da ta in t e r m s of the pe r fo r - m a n c e and e x p o s u r e o f the sensors, such a sy s t em is capab le o f measur ing ene rgy f luxes by the eddy co r re l a t ion m e t h o d at u n a t t e n d e d sites.

ACKNOWLEDGEMENTS

We are gra teful to our Di rec tor , J .S .G. McCul loch, fo r his c o n t i n u i n g s u p p o r t o f this p ro jec t and also t h a n k all those o f our col leagues w h o have c o n t r i b u t e d to the d e v e l o p m e n t and tes t ing of this sy s t em and the instru- m e n t a t i o n which it services. In par t icular , this p a p e r wou ld n o t have been possible w i t h o u t a grea t deal o f p rev ious w o r k by C.J. Moore , D.D. McNeil , H .R. Oliver, S.A. Oliver, N.F . Cowell and D.J. Harris , n o r w i t h o u t the cons iderab le technica l skills o f P .D.R. Andrews , R.M. F ros t and J. Cross.

We are also gra tefu l to the Conse rva to r s o f the Fo re s t ry C o m m i s s i o n fo r pe rmiss ion to w o r k in the Kings F o re s t and to the Earl o f Iveagh fo r pe rmiss ion to w o r k on the Elveden Es ta te ; t h anks are also due to W.M. Sloan fo r his co -ope ra t i on .

REFERENCES

Dyer, A.J., 1963. Discussion on the paper "Measurements of evaporation and heat transfer in the lower atmosphere by an automatic eddy-correlation technique". Q.J.R. Meteorol. Soc., 89: 556--557.

Dyer, A.J., Hicks, B.B. and King, K.M., 1967. The fluxatron -- a revised approach to the measurement of eddy fluxes in the lower atmosphere. J. Appl. Meteorol., 6: 408--413.

Hyson, P. and Hicks, B.B., 1975. A single beam infrared hygrometer for evaporation measurement. J. Appl. Meteorol., 14: 301--307.

Molion, L.C.B. and Moore, C.J., 1983. Estimating the zero-plane displacement for tall vegetation using a mass conservation method. Boundary-Layer Meteorol., 26: 115-- 125.

Moore, C.J., 1983. On the calibration and temperature behaviour of single-beam infrared hygrometers. Boundary-Layer Meteorol., 25: 245--269.

Otnes, R.K. and Enochson, L., 1972. Digital Time Series Analysis. Wiley, New York. Raupach, M.R., 1978. Infrared fluctuation hygrometry in the atmospheric surface layer.

Q.J.R. Meteorol. Soc., 104: 309--322.

~(~

Shuttleworth, W.J., McNeil, D.D. and Moore, C.J., 19~2. A switched continuous waw sonic anemometer for measuring surface fluxes. Boundary-Layer Meteoro l 2;:I: 12:) 448.

Shuttleworth, W.J., Gash, J.lt.C., Lloyd, C.R., Moore, C.J., Roberts, J.M., Marqu~::~. A. deO., Fisch, G., de Paula Silva, V., Ribeiro, M.N.G., Motion, L.C.B., der Sa, L.I).A . Nobre, C.A., Cabral, O.M.R., Patel, S.R. and de Moraes, J.C., 1984. Eddy-co~'retatio~ measurements of energy partition for Amazonian forest. Q.J.R. Metoorol. So~., in press.

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. So('., i 0 6 85--100.