lOS Note 7

LABORATORY DETERMINATION OF THERESPONSES OF THERMOMETER AND CONDUCTIVITY

CELL OF THE GUIDELINE 8101A(with some a;rrplications to sampling water profiles)

r'.

by

E.R. Walker

_ INSTITUTE OF OCEAN SCIENCES, PATRICIA BAYSidney, B.C.

IDS Note 7

LABORATORY DETERMINATION OF THERESPONSES OF THERMOMETER AND CONDUCTIV ITY

CELL OF THE GUILDLINE 8l01A(with some ~plications to sampling water profiles)

~

by

E.R. Walker

Institute o€ Ocean Sciences, Patricia Bay

Sidney, B.C.

1978

This is a manuscript which has received only

limited circulation. On citing this report

in a bibliography, the title should be followed

by the world "UNPUBLISHED MANUSCRIPT" which is

in accordance with accepted bibliographic custom.

LABORATORY DETERMINATION OF THE

RESPONSES OF THERMOMETER AND CONDUCTIVITY

CELL OF THE GUILDLINE BIOlA

(with some applications to sampling water profiles) .

ABSTRACT

An experiment is described in which time constants (0-63% response)of thermometer and conductivity cell of the Guildline BIOlA in situ salino­meter were determined in the laboratory. Use of these response times toestimate the fidelity of recording of water column structures is brieflydiscussed in the context of operations of the Frozen Sea Research Group,Institute of Ocean Sciences, Patricia Bay, B. C.

Introduction

Use of moving in situ instrumentation to measure parameters of a watercolumn necessitates knowing the time responses of the system, in fact, whatmay be called "dynamic" calibration is needed. This term is used to contrastwith "static" calibration in which comparison is made with appropriate"standards" under realistic conditions in which motion or change need notoccur.

These subjects, of course, are basic to measurements made in manydisciplines but only aspects of oceanographic interest will be noted here.Static calibrations have been reported by users and presumably many proceduressimilar to those noted below are in use. The temperature sensor may be cali­brated in the laboratory and also in situ in zones of minimum vertical gradi­ent of temperature, being compared to secondary standard thermistors (Lewisand Sudar 1972) or reversing thermometers (Prokhorov et al 1973, F~fonoff

et all 1974). The conductivity cell may be standardized in the laboratorybaths of known salinity and temperature. For in situ calibrations, readingsof the instrument, converted to salinity, are compared to salinity of samplescollected at as nearly the same time and place as possible (Lewis and Sudar1972), (Prokhorov et al 1973) and (Fofonoff et al 1974). Fofonoff et al(1974) also discusses the relationship between the usual salinity comparisonand the conductivity error or correction that is frequently more useful.Hydrostatic tests on pressure sensors in the laboratory are reported byFofonoff et al (1974). In situ checks on readings of the pressure sensor bycomparison with length of line paid out are reported by Lewis and Sudar (1972)and Prokhorov et al (1973), while checks against pressure readings from pro­tected and unprotected reversing thermometers are reported by Fofonoff et al

2

(1974). The effects of changes in temperature and pressure upon the conduct­ivity cell are considered by Fofonoff et al (1974). Presumably, pressure andtemperature effects upon the system performance must have been measured orestimated by many users and all manufacturers although little is reported inthe major oceanographic literature. To some extent these effects are takeninto account with an adequate in situ standardization. Fofonoff et al (1974)also report in situ checking of temperature and salinity recordings againsthistorical temperature-salinity relationships.

Dynamic calibrations are designed to measure the response of a singlesensor, or ideally, the whole system in situ. Measurements of thermometerresponse in the laboratory have been reported, for a step function, by Gouletand Culverhouse (1972), and by passage through a heated plume by Fabula (1968).By comparing features of salinity and temperature profiles measured in situ,at different lowering rates, Dantzler (1974) estimated time constants ofconductivity cell and thermometer. By comparing, on an S-T diagram, profilesmeasured during lowering and raising an in situ instruments, Federov andProkhorov (1972) estimated their system time constants. Several similarschemes for estimating system responses by optimizing, in one way or another,measured profiles are reported by Pingree (1971), Scarlet (1975) and others.I feel that these methods are desirable in that they measure the response ofthe whole system in situ, but there is always an element of uncertainty orsubjectivity about the profile optimization. The response of the pressuresensor has not been remarked upon. It is less critical in computation ofsalinity or density than are responses in temperature and conductivity.

Roden and Irish (1975) discuss errors introduced by data loggingtechniques which sample sensor outputs sequentially so that readings of thedifferent sensors are made at different times and places. They suggestmethods of correcting such procedures and optimization techniques. Much thesame result can perhaps be attained by proper positioning of the sensors inthe vertical to allow for asynchronous sampling. Another item of importancewhen outputs of two or more sensors are to be combined is to ensure that allsensors have the same time and character of response. The system noiseintroducted by digitization or quantization has been discussed briefly byFofonoff et a1 (1974).

Laboratory determination of the response times of the Guildline 8l0lA

thermometer and conductivity cell

The Frozen Sea Research Group uses an electrode cell instrument, aGuildline 8l0lA in waters of the Canadian Arctic. Sensors in this instrumentwere enclosed in a shroud 0.11 m in diameter for protection during operationthrough a 0.23 m hole drilled through sea ice cover. Water flow throughthis shroud seemed likely to be complicated so in 1972 we decided to determinethe time constants of the whole system experimentally in the laboratory.While instruments using induction-type conductivity cells are difficult tocalibrate in the laboroatory because of wall effects, the same effects areless pronounced on systems using electrode-type conductivity cells.

As shown in Figure 1 the Guildline 8l0lA 'fish' is a long cylinder,diameter 0.12 m, overall length 1.10 m. A 0.7 m long pressure case contains

3

the electronics and the lower 0.4 m has the sensors mounted in line. Thetemperature sensor is composed of 8 strands of #40 AWG copper wire in an oil­filled O.Olm O.D. stainless steel tube bent into a helix 0.037m in diameterand 0.05m long, and mounted with the axis horizontal. The conductivity cellis a 0.2m long Pyrex tube of 0.01 m bore with 4 platinum electrodes along thewall, spaced about 0.05m apart, about the midpoint of the length of the tube.The pressure is measured by a Viatran PTB 207Cl diaphragm strain gauge. Therange ·of sensors is given by the manufacturer as -2° to 30°C, 28 to 40 ppt,and 0-1000 db. The manufacturer advertises the resolutions as ±0.003°C.'±O.005 ppt, and ±O.05% FS, and overall accuracies as ±0.02°C, ±0.04 ppt:±0.2% FS. The time constant of each sensor is stated to be 0.2 seconds.

The Experiment

In planning the experiment we decided to test the time constants onlyof the conductivity cell and thermometer. The effect of pressure errors insalinity calculations is less critical than errors in temperature or salinity.We gave some thought to subjecting the system to periodic flow by rotationthrough side-by-side currents of different characteristics. However, wedecided on a vertical drop through a sharp interface. The scale of the ex­periment had to be sizeable, to allow measurements of response over severaltime constants. In the event, we obtained a steel culvert pipe, 6.1Om long,0.61m inside diameter. The pipe was closed at one end and put upright, thenfilled with water. A replaceable diaphragm of aluminum foil was placed half­way down the cylinder. The sensor was lowered at a uniform controlled ratefrom a pulley at top. Temperature was used to distinguish the step functionwith only enough salt (about I kg) in the water to allow the conductivitycell to record. The routine was to stir the whole water column, top tobottom, with compressed air. Then a diaphragm was installed. After additionof an appropriate amount (about 40 1itres) of hot water to the top layer, thistop was stirred with compressed air. The instrument was then lowered fromjust below the water surface through the diaphragm to just above the bottomof the lower water layer. Sufficient time elapsed between stirring andexperimental drop for visible air bubbles to clear from the water column inorder that they not interfere with sensor responses. Because the upper layerwas less dense and mixing at the interface not pronounced during one passageof the instrument, second and third drops downward were recorded withoutfurther stirring or diaphragm replacement. The output of the conductivitycell, thermometer, and a small thermistor (T = 0.25 sec. 0-63%) were recordedon two Brush 220 analog recorders and also on our Vidar data logger.-

From the analog traces, and also from a plot recording by the Vidardata logger, estimates were made of the response 0-95%. This response wasconsidered equal to 3 time constants. In general the analog traces were morehelpful because only points at 0.4 sec. intervals were available from theVidar plots. From the analog traces an estimate of time was also obtainedfor 0-63% response.

As these response times include a component due to passage through atemperature interface of finite thickness, a crude attempt to remove thiscomponent was made in the following way. From previous records of the thermi­stor response to a temperature step function (hopefully of zero thickness)the 0-95% response time was estimated at 0.8 sec. It was assumed that in our

4

experiment the thermistor suffered no hydrodynamic effects but would alwayshave a 0-95% response time to a perfect step function of 0.8 sec. In any ofour trials, therefore, the difference between recorded 0-95% response timefor the thermistor and 0.8 sec. was regarded as due to finite thickness ofthe interface. This time difference when subtracted from response times ofconductivity cell and thermometer should give their effective response timeto a perfect step function. Because of experimental error the response timeof the thermistor was, in a few trials, less than 0.8 sec. In these casesthe interface thickness was considered to be zero, and the conductivity celland thermometer response times as measured. As a corollary the interfacethickness was calculated by multiplying the instrument velocity by thedifference between recorded thermistor 0-95% response time and 0.8 sec.

A very crude error analysis was attempted, in order to get a feelingof the errors in the results. As not enough trials were carried out to obtaina firm statistical basis for error analysis, an attempt was made to estimatethe maximum error likely in the different measurements. This likely maximumerror was then considered equal to 3 standard deviations. When these maximumerrors in simple measurements were used in compound quantities, the differencebetween maximum positive, and maximum negative values was considered equalto 6 standard deviations.

The maximum likely errors were: a) positioning of sensors ±0.5 em.,b) time of drop ±1.0 sec., c) distance of drop ±30 em., d) reading of 0-95%response from analog trace ±20%, e) reading of 0-95% response from datalogger trace ±40% for short times, 20% for longer times, f) time of firstresponse ±0.5 sec. and g) response of thermistor (0-95%) ±O.2 sec.

When these values are used the estimates of standard errors of thetime constants were about ±O.05 sec.

Review of our experimental procedures indicated that the mechanicalarrangements were good. The air stirring was effective and seemed not tointerfere with sensor response. The data logger plots indicate a temperaturevariation in the stirred water columns of less (usually much less) than±O.loC while the interface temperature; difference was 1.5° to 3.0°C. A muchfaster thermistor (or other device) would have been desirable to allowdelineation of the interface thickness more precisely. The method ofmeasuring conductivity was adequate. The amount of salt to enable thismethod to work properly is fairly critical and should always be pre-calculated.The fast analog record is very necessary although the data logger recordswere useful in a few cases where the analog record was unsatisfactory.Obviously from the size of the errors estimated just above, our experiments,and similar ones, are useful only for checking time constants which aresome appreciable fraction of a second.

Results

A total of 71 lowerings was made. Of these 16 had failures of somesort leaving 55 useful trials. Nineteen trials were made with the diaphragmintact, the others after one or two passes of the instrument through thetemperature interface. The speeds of lowerings were either about 20 em sec- I

or about 75 em sec-I. Seven different configurations of the instrument were

5

used. These are sketched in Figure 2. Configuration #2 was the Gui1d1ineModel 8101A, having a solid metal shroud over the sensors with openings atthe top and bottom. The thermometer was attached directly to the metalshroud, allowing thermal leakage. Configuration #1 was the same shroud withmany holes 0.7 - 1.2 em. in diameter drilled 1.0 - 2.0 em. apart in it. Thethermometer was thermally insulated from the shroud. Configurations #3 to#7 used a very open wire cage around the sensors. In Configuration #4 theconductivity cell had end pieces attached in an attempt to improve the flowthrough the sensor. In Configuation #6 the top of the conductivity cell wasonly 3.6 em. below the bottom of the electronics case. In Configurations #3,#5, and #7 the positions of the Gui1dline sensors differed but time constantsshould not be affected. In every configuration the thermistor was well ex­posed, outside the shroud where necessary.

Details of the time constant estimates from all useful experimentsare given in Appendix I. Best estimates of time constant (0-63%) for alltrials in which an intact diaphragm were pierced are given in Table 1. Fortrial 59 the analog traces are reproduced in Figure 3. A plot of the datalogger points for the same trial is given in Figure 4. For the very fewpoints in Table 1 the mean and standard errors of the cell time constant were

-1 -10.65 ± 0.07 sec? W- = OsZm sec ,0.25 ± 0.07 sec f or w"> 0.7m sec • TheGuild1ine thermometer constant was 0.60 + 0.05 sec forw = 0.2m sec-I, 0.25iO.03 sec for W = O.7m sec-1.

Examination of the estimates in Table 1 and Appendix I reveals thattime constants with the wire cage configurations were smaller than thosewith either the solid or holed shroud. On the analog traces a much cleanerresponse was present with wire cage configurations. The time constants werelarger at lower speeds, and the conductivity cell was then slower to respondthan the thermometer. In the results using the wire cage at speeds of75 em sec- 1 the time constants of both conductivity cell and thermometerapproached the manufacturer's specifications of 0.2 sec. Typical shapes ofthe response curves are shown in Figures 3 and 4. Responses of both thermis­tor and thermometer are fairly well representedras shown,by theexponential response of a first order sensor although sensitive experimentshave revealed small apertures from this ideal. The response of the conducti­vity cell is more complicated with a longer lag at the beginning and a longertail off at the end of the trace of the interface penetration. Indeed,examination of records from our field experiments (R. Perkin, private com­munication) indicate a small residual effect in the conductivity cell timeconstant. Also, turbulent-laminar transitions of the flow regime withinthe cell complicate cell response so that it is rather less well representedby the exponential form than the thermometer. However, in what follows theapproximation to exponential response will be made.

From the very crude estimates from column 21 in Appendix I it appearsthat, even with the intact diaphragm, the interface between upper and lowerwater layers had thickness values of a few centimeters in many trials. Afterpassage of the instrument the interface thickness increased systematicallyafter each trial without diaphragm replacement and subsequent water columnstirring. The results indicated no appreciable improvement of conductivitytime constant when modified ends were fitted to the cell. In the optimumconfiguration, using the wire cage, there was a suggestion that the

6

conductivity cell was perhaps placed too high (towards the electronic case)in Configuration #6. It proved not possible to distinguish the shape ofthe time constant for the Guildline thermometer used uninsulated in the solidshroud (Configuration #2). There were small, long time components due toheat leakage through the thermometer fittings.

Attempts at reading the records to find the lag of one sensor overanother were unsuccessful largely because of the difficulty of determiningthe initial response to the rather small interval of time involved. Theaverage deviations of observed lag times from calculated lag times are shownin Table 2. These, which include trials with an already disturbed interface,probably give values rather larger than would be recorded on the first passthrough an undisturbed interface.

Discussion

The values for the time constant (0-63%) quoted above may be comparedwith values expected from component parts of the time constant quoted byT. M. Dauphinee (personal communication). On November 27,1969 Dauphineeadvised: (a) Thermometer time constant 0.12 sec. (0-63% response),(b) Conductivity time constant basic 0.05 sec. plus flushing time,(c) Thermometer coil 4 cm. in diameter with horizontal axis, and (d) Electr­odes - 5 cm. apart in cell 21 cm. long. Theoretical components of timeconstant of sensors, including dimensions, for various lowering rates (w)are given just below.

Thermometer Conductivity Cell

Total (Intrinsic) Total Immersion TotalImmersion +0.12 8 cm. 5 cm. 8 cm. Immersion Im.+0.05

m sec- 1 sec. sec. Bottom Electrodes Top Total Intrinsic

0.2 0.20 + 0.12 =0.32 0.40 0.25 0.40 LOS LIO

0.5 0.08 0.20 0.16 0.10 0.16 0.42 0.47

0.75 0.05 0.17 0.11 0.07 0.11 0.29 0.36

LOO 0.04 0.16 0.08 0.05 0.08 0.21 0.26

1.50 0.03 0.15 0.05 0.03 0.05 0.13 0.18

2.00 0.02 0.14 0.04 0.02 0.04 0.10 0.15

2.50 0.02 0.14 0.03 0.02 0.03 0.08 0.13

3.00 0.01 0.13 0.03 0.02 0.03 0.08 0.13

The actual time constant should consist of some function (or fraction)of the time of the immersion of the whole sensor, plus the intrinsic compon­ent. The time constant for the conductivity cell might be expected to becomplicated and velocity-dependent. Even apart from considerations of flowsof laminar or turbulent character, one might expect the response to indicatea slow rise in reading, becomdng much faster as water from a new environmententers the electrode area, then a slow die-away as the new water clears theupper end of the cylinder (postioned with the long axis vertical).

7

Examination of Table 1 and Figure 5 reveals the poor reproducibility-1of our results at a lowering rate of 0.2 m sec However, our experimental

results and the theoretical results shown in Figure 5 indicatethat reasonable values for our sensor time constants as configured after 1972(see Figure 2) would be about 0.65 sec for w = 0.2 m sec- I and about 0.25 secfor w = 0.75 m sec-I. For lowering rates of 0.3 to 0.4 m sec- I the criticalReynolds number is reached within the conductivity cell so that changes inthe flow regimes occur between lowering s~eeds of 0.2 m sec- I and 0.75 m sec-I.Fow lowering rates faster than 1.0 m sec- time constants Ie = ~T = 0.2 secmight be appropriate.

Data Logging and Operations

FSRG Data Logging

In operation the Guildline was lowered through a hole in the sea iceon seven conductor armoured cable, 0.31 cm in diameter. Analog voltageswere sent to the surface through this cable. The winch containing 1000 mof the cable was constructed in house and is driven by a small electricmotor. The lowering speeds have ranged up to about 0.75 m sec-I. There isa device on the winch which allows initiating the data logger channel scan­ning cycle at any depth interval being a multiple of 0.25 m or 1.0 m.Currents are very low in those areas of the archipelago in which we haveworked so wire length paid out is very closely equivalent to depth. Almostalways only the three channels of pressure, temperature and conductivitywere scanned so that if scan cycle is initiated by wire length interval fromthe winch then lowering rate must be recorded externally. On the other handif the scan cycle is initiated by clock then the wire length paid out is notknown but depth must be computed from the pressure reading.

In the past operational practice has varied. In 1969 the Gui1dlineBIOlA was used with sensors well exposed, as provided by the manufacturer.From 1970 to 1972 the version described above with excessive shrouding wasused. After 1972 the sensors were again well exposed. The usual scaninitiation was by wire length interval. The lowering rates were not alwaysadequately recorded and certainly do not appear in published data records.For example in the spring 6f 1973 in only 5 out of 25 profiles was thelowering rate unambiguously recorded. In the spring of 1974 the figureswere none of 15, in August 1974 3 of 7, in the spring of 1975 14 of 26 andin the spring of 1976 3 of 24.

The logging systems used by the FSRG with their Guildline BIOlA fishare the Vidar MOdel 5400's.The system usually used has an IDVM (IntegratingDigital Volt Meter) with a sampling time of 0.017 sec. The resolution ofthe system is governed by the data logger range, which for the systemusually used, is 4 decimal digits plus 50% over range for 15,000 divisions.When used with the ranges given for the Guildline the resolution is then0.002°C, 0.003 ppt and 0.07 db.

Sensor outputs are sampled sequentially by the ID\~ at a rate governedby data logger output, a small line printer rated at 5 lines per second anda paper tape punch also rated at 5 outputs per second but whose actual punchis closer to 4 per second. So each channel is sampled for 0.017 sec. about

8

once per second and the time separation between different channels is, atbest, about 0.25 seconds. If, of course, the sampling cycle is initiated atline intervals of 1.0 m with a lowering rate of 0.25 m sec-1 the intervalbetween sampling of the same sensor will be 4 seconds although the samplinginterval between different sensors will be governed by maximum punch speedas noted above. For a lowering rate of 0.75 m sec-1 the sampling intervalbetween sampling of an individual sensor will be 1.3 seconds.

Sampling Considerations

When the equivalence between vertical distance' Sc' time increment, &t' and instrument lowering speed 'w , is considered then sampled watercolumn profiles can be considered as time series, analysis of which is anintegral part of instrumentation theory. The fidelity of recording anyfeature of intrinsic frequency' fr " or vertical wavenumber, say 1)1:: f:r./wcan depend upon whether the total length of record taken is adequate, themethod of sampling, and the time response of the sensor used.

The total length of record must be long enough to delineate (severalcycles of) the largest feature of interest. The effect of limited recordlength (R) in reducing spectral density at different fractions of R is shownin Table 3 (after Pasquill 1974). In measuring parameters of water profilesrecord length is not of practical importance although it can be in timeseries at fixed water depths.

The sensor time constant acts as a low pass filter. In oceanographicinstruments with first order time constants we have, using temperature asan example, with 0-63% thermometer time constant -(j-, IS thermometer temperature(a function of time t), T the ambient temperature, the time change of thethermometer temperature is governed by

T-TsI,

After Sabinin (1967), the frequency characteristics of a sensor with thefirst order (or exponential) time constant is:

Transmission function

Amplitude characteristic /\ (w 7 ~

phase characteristic

'/fI+w~T":

,H-C TCl n (- w 'f" )

energy transmission function I iIi l i. w)IJ. :::

where IN: "n f is the circular frequency (rad sec-I).

To illustrate the application of simple sampling theory to ouroperations assume: (a) l' is sensor time response 0-63%, (b) "(' is ideally afirst order response. For the Guildline 8l0lA we have:

0.2

0.65

0.4

0.45

0.6

0.35

9

0.8

0.25

m sec-1

sec SE ± 0.07

0.13 0.18 0.21 0.20 m SE ± 0.04

where D is the distance traversed for response to 63%, (»::::-'('w-) , w is thelowering rate, IT = thermometer time constant, ~ = the conductivity celltime constant.

To put this in another way, the distance travelled to the givenpercentage response for a sharp edged change, using the time constants justabove is:

vr = 0.2 0.4 0.6 0.8 m sec-1

50% 0.09 0.13 0.15 0.14 m

80% 0.22 0.31 0.36 0.34 m

90% 0.30 0.41 0.48 0.46 m

95% 0.39 0.54 0.63 0.60 m

99% 0.60 0.83 0.97 0.92 m

The percentage response in amplitude of the Guildline at loweringrates indicated, time constants noted above, to sinusoidal variations inthe vertical with the wavelength '2 ' given is shown as:

0.2 0.4 0.6 0.8 -1m sec

0.5m 52 40 36 37 per cent

l.Om 80 67 52 62 per cent

1.5m 88 80 75 77 per cent

2.Om 92 88 85 86 per cent

The effect of the methods of sampling sensor output and optimizationthereof is complicated and will not be discussed at any length. However,Sabinin (1967) in an oceanographic context has discussed some aspects ofoptimization of sampling rates for a sensor with the exponential type timeconstant. Using frequency rather than the wavenumber vie"~oint Sabinindiscusses simple relationships between time constants of the sensor and theamount of "aliasing" or feed over of possible spectral energy at frequencieshigher than the Nyquist or 'folding' frequency 'fN ' where tN = I/~ A t and, ~ t, is the time interval between (instantaneous) sampling, into frequenciesof interest below the Nyquist frequency. Sabinin's paper (1967) should beconsulted for a" full discussion. To summarize, with respect to errors whichmight be caused in spectra of fluctuations in ambient conditions, takinginto account the largest terms in corrections for aliasing, and using~~~/At?

r"* -:: +.r:/f", where~tis the interval between (instantaneous) sampling,

10

~x is the frequency of interest in the spectra and -PN = Va.a.t is the Nyquistor folding frequency, Sabinin produced the diagram shown in Figure 6 relatingaliasing error (~?. (~~r-{ - F::: )+ ~"{)tNr +x )) to the spectral filtering causedby the inertia of the instrument q?).(PI).

For use of the diagram Saninin's (1967) paper should be consulted butto give one example, for our instrument, with a sensor time constant of 0.25seconds, a time interval between instantaneous sampling of 1.3 seconds, andat a lowering rate of 0.75 m sec- 1 features of vertical extent of 4 meterswould result in values of-r*=f"/...... t=o.tq andF)(=.fr/FIY= 6·S- • Entering thediagram in Figure 6 with these values we find if~({I)= 0.91, is the fractionalresponse due to instrument time constant and (<J?l( J..Prv-h) -r- ep~ (JrN'f-Fr ))::Jc. 0 .~;;...or 82 per cent of the energy of the two frequencies (,.f/ll-tr. \ and (J-PN+(::X)is a1iased o~to the frequency of interest.

From his analysis of the effect of sensor inertia and sampling atdiscrete intervals, Sabinin draws a number of general conclusions:

1) If the discrete sampling interval exceeds the timeconstant of the instrument by at least three times,then at least 40% of the high frequency energy isintroduced into the measured spectrum and, therefore,aliasing can be significant;

2) If the time constant of the instrument is equal to thediscrete interval, then the high frequency oscillationsare practically completely damped and the aliasinghardly occurs; however, the measured spectrum is simul­taneously strongly damped and only the lowest frequencypart of the spectrum ( .p <. 0./ PI')ts distorted by less than10%.

3) In order to decrease the first two correction terms ofthe aliasing at least by a factor of two and, at thesame time, not to dampen the low frequency half of thespectrum by the filtering due to the inertia by morethan 20%, the discrete interval should not exceed thetime constant by more than 3.5 times.

The values of f lf and 1"1t which can be reconnnended forpractical work, i.e. the ratio between the discreteinterval of measurements and the time constant shouldbe located in the range from 1 to 3.5 and the partsof the spectra used, in the range from 0.1 to 0.5 oftheir calculated width +N . The final choice of theratios indicated depends upon the problem formulationand upon that which is more undesirable and apparent ­the damping of the spectrum by the filtering due tothe measuring instrument's inertia or the aliasing.In particular, for the measurements of turbulentpulses obeying the "5/3 law", it is convenient toselect the ratio between the discrete interval ofmeasurements and the time constant equal to 3.5:1,

11

since, for this damping of the spectrum, the instru­ment's inertia and the aliasing almost completelycompensate one another in the wide frequency bandup to 0.8 tN.

With data logging systems presently available sampling rates and lowpass filter construction allow for more versatile schemes than Sabinindiscusses although his analysis applies to almost all our CTP operationsto date.

Recent measurements (Gregg and Cox 1972, Elliott and Oakey 1976) haveshown appreciable variabili!i at very high frequencies or small verticalwavenumbers (1-100 cycles m ). Any worthwhile treatment of aliasing, orcorrection of spectra for filtering caused gy instrument inertia~ requiressophisticated processing of the sort reported by these authors and by Luecket al (1977) amongst others.

Averaging

One form of low pass filtering which is sometimes useful is thefilter formed by averaging the sampling over some period say's'. The effectof averaging a time series over a period say's' is to apply a low passfilter which affects the higher frequencies very much as does the timeconstant of a sensor with the first order response. Of interest are thetransfer functions

amplitude characteristic

energy transmission function

The filter is rather sharper than that due to inertia of an instrument witha first order response. The relative shapes on the amplitude levels andspectra are shown in Figures 7 and 8 and have been noted, in part, inTable 3.

In Figures 7 and 8 usage is (,o.J -= .2 n4=', ?... Yf =).TTIw ,"W" "d';'t so ~ t::<.~'lw­6 t z: -iN- b t ,f-=w '1 where J'( is wavenumber, the absolute spectrum function-W )(fl;: ') ('i) , and the averaging interval's'. The material can be appliedto the case of immediate interest by using appropriate values of thedifferent parameters.

In 1975 an electronic integrating device was constructed in-housewhich accumulated the voltages for each sensor channel for a period ofabout one second, then meaned and digitized these voltages during thenext second while the following accumulation was being carried out. Thedevice therefore gave simultaneous mean readings over a one second periodfor the pressure, temperature and conductivity sensors, applying filterswhose characteristics may be estimated from Figure 7 and 8.

o

We have not routinely used our analog averaging device and indeedhave hardly tested it. Three meaningful field trials in which each of our

12

regular sampling technique was used followed as rapidly as possible by aprofile sampling using the integrating device, were carried out in 1975 inthe top 50 m of water in d'Iberville Fiord, Ellesmere Island. In one ofthese trials there were twelve density inversions in theunintegrated profile,none in the integrated profile. In the other two trials at other timesthere were no density inversions in either integrated or unintegratedprofiles.

Non-Simultaneous Sampling

Further to proper measurement of each individual parameter is thequestion of compatible measurements of the difference parameters of (in thiscase) temperature, conductivity and pressure, so that salinity can beproperly calculated as a function of pressure. This has been discussed byRoden and Irish (1975) who present methods to correct, to the first order,salinity calculated from temperature and conductivity sensors which,because of sequential sampling techniques, are not sampled at the sametime or place.

We have attempted to allow for non-synchronous sampling of our datalogger by positioning sensors on the Guildline 8lOlA at vertical intervalswhere, from considerations of the lowering rates used the sensors should besampling at the same depth and within 1/3 second of each other (for tempera­ture and conductivity). We have found this method be no means fool proof,due we suspect, to turbulence engendered by the instruments' descent. Forexample in temperature-salinity profiles from d'Iberville Fiord in 5 of 11profiles the value of salinity calculated just below the interface at thebase of the under-ice mixed layer was so unreasonable it had to be discarded.These differences of observed from expected times of sampling can also beseen in Table 2 of the section describing our time constant laboratoryequipment.

Desiderata (or Truismsl)

From this brief review it is plain that operators should know all(relevant) characteristics of their whole system and the implications ofmebhods of operation of it. Characteristics and operation should be matchedto measurements desired.

As for the Frozen Sea Research Group, we have recently acquired aHewlett Packard 9825A desk calculator and have mated our present system toit, cutting out the slow printer and paper tape punch, going to magnetictape cassette storage at a rate of about 15 samples per second. Thisshould allow more flexibility in optimizing sampling with our instrument.

Acknowledgements

Most of the Frozen Sea Reseach Group enthusiastically took part inthe response time experiment.

13

REFERENCES

Dantzler, H. L. 1974 Dynamic salinity calibrations of continuous salinity/temperature/depth data.Deep~SeaRes. 21, 675-682

Elliott, J. A. and N. S. Oakey 1976 Spectrum of small-scale oceanictemperature gradients. J. Fish. Res. Board Canada, 33, 10, 2296-2306

Fabula, A. G. 1968 The dynamic response of towed thermistors. J. FluidMech., 34,449-464

Federov, K. N. and V. I. Prokhorov 1972 True response lag in temperaturemeasurement and the reliability of ocean salinities determined withtemperature-salinity probes. Izv. Akad. Nauk. SSSR, Atmospheric andOceanic Physics, 8, 9, 998-1003

Fofonoff, N. P., S. P. Hayes and R. C. Millard, Jr. 1974 W.H.O.r./BrownCTD Microprofiler: methods of calibration and data handling. WHOI~74~89

Woods Hole Oceanographic Institution, Woods Hole, Mass., pp 66

Goulet, J. R. Jr., and B. J. Culverhouse Jr. 1972 STD thermometer timeconstant. J. Geophys. Res. 77, 24, 4588-4589

Gregg, M. C. and C. S. Cox 1972 The vertical microstructure of temperature'and salinity. Deep-Sea Res. 19, 355-376

Lewis, E. L. and R. B. Sudar 1972 Measurement of conductivity and tempera­tures in the sea for salinity determinatiort J. Geophys Res., 77, 33,6611-6617

Lueck, R. G., O. Hertzman and T. R. Osborn, 1977 The spectral response ofthermistors Deep-Sea Res. 24, 951-970

Pasquill, F. 1974 Atmosphere Diffusion Ellis Horwood, Chichester.England, 429

Pingree, R. D. 1971 Regularly spaced instrumental temperature and salinitystructures Deep~Sea Res. 18, 841-844

Prokhorov, V. I., K. N. Federovand A. G. Volachkov 1973 In situ calibra­tion of the "Aist" automatic STD probe Oceanology 13,3, 524-530 (Russian)434-439 (English)

Roden, G. r. and J. D. Irish 1975 Electronic digitization and sensorresponse effects on salinity computation from CTD field measurements.J. Physical Oceanography, 5, 195-199

Sabinin, K. D. 1967 Selection of the relation between the periodicity ofmeasurement and instrument inertia in sampling Izv. Akad. Nauk. SSSR,Atmospheric arid Oceanic Physics, 3, 5, 973-980

Scarlet, R. I. 1975 A data processing method for salinity, temperature,depth profiles Deep-Sea Res. 22, 509-515.

14

FIGURE CAPTIONS

"1) Actual shape of Gui1d1ine 8l0lA instrument. Measurements are those ofConfiguration #2 in Figure 2.

2) Schematic of the configurations of the Guildline 8l0lA used in timeresponse experiment. Not to scale although all measurements are given.Configuration #2 was the version used from 1970-1972 inclusive. Con­figuration #3 with vertical spacing of sensors appropriate for loweringrate was used after 1972.

3) Analog recording of sensor response in experiment 59.

4) Vidar data logger response of conductivity cell and Guildline thermometerin experiment 59.

5) Experimentally determined time constants (0-63%) and those calculatedto immersion as described in text. Conductivity cell time constantis -r~ and Guildline thermometer time constant is I'T .

6) Fractional aliasing of energy from frequencies ('- VN - Ft) and (,.~",+fJ:)on the vertical axis, and fractional response due to instrument timeconstant (-r) on the horizontal axis. Quantities are given as functionsof 1"'* =1"(aot where (At') is the interval between (instantaneous) sampling,and ff =f:t./PN where Fr: is the frequency of interest, and ff{ is theNyquist, or folding frequency (from Sabinin 1967).

7) Amplitude response and phase shift as a function of sensor time constantdivided by period of a sinusoidal oscillations, and amplitude responseas a function of data averaging time divided by the period of a sinus­soidal oscillation.

8) Spectral estimate response as a function of sensor time constant dividedby the period of a sinusoidal oscillation, and as a function of dataaveraging time divided by period of the sinusoidal oscillation.

15

TABLES

1. Time constants (0-64% response) for the conductivity cell Cft ) and thethermometer (iT) of the Guildline 8101A instrument, and the thermistor(1' ). All values from analog records from experiments with intactinterface diaphragms.

2. Mean difference in lags of the Guildline thermometer first responseto that of the conductivity cell, Ca) - (b) where (a) calculated fromsensor spacing and vertical velocity of instrument and (b) experimentalvalues observed from analog recordings.

3. Summary of separate filtering effects of sampling over record of length(R), averaging over time (S), and of instrument with exponential timeconstant ('1) (after Pasquill 1974).

16

TABLES

1. Time constants (0-63% response) for the conductivity cell eJlC) and thethermometer C~~) of the Gui1d1ine 8101A instrument t and the thermistor(-r ) . All values from analog records from experiments with intactinterface diaphragms.

Time Constant (sec.)-W Trial

Configuration ~ 1;- -1 em sec-1 No.

111 1.1 0.8 0.8 26 13

111 0.3 0.4 0.4 75 16

112 M 0.7 0.6 24 19

It2 0.9 1.0 0.3 26 22

112 1.7 1.2 0.6* . 21 24

112 M 0.4 0.3 75 27

112 M 0.4 0.4 58 28

It3 0.6 0.6 0.4 18 34

113 0.8 0.6 0.5 20 35

113 1.3* 0.5 0.6 20 37

113 0.2 0.2 0.2 71 40

114 0.4* 0.5 0.5 21 43

114 M 0.3 0.3 76 46

115 0.7 0.7 0.3 19 48

Its M 0.2 0.2 66 51

It6 0.7* 0.8 0.4 21 56

It6 0.5 0.5 0.3 20 62

116 M 0.3* 0.3* 71 53

116 0.3 0.3 0.3 76 59

*Unre1iab1e

MMissing

17

2. Mean differences in lags of the Guild1ine thermometer first response tothat of the conductivity cell, (a) - (b) where (a) calculated fromsensor spacing and vertical velocity of instrument and (b) experimentalvalues observed from analog recordings.

Approx.Velocity

Number of Mean of N samplesConfiguration em sec- 1 Trials (sec.)

111 25 3 -0.9

111 75 3 -0.4

1/2 25 9 -0.7

112 65 2 +1.0

113 20 6 -0.1

113 75 3 -0.2

114 22 2 -0.9

/14 75 2 +0.2

115 20 3 -0.8

115 65 0 M

116 22 6 -0.5

116 75 4 -0.2

117 20 2 -0.5

117 75 1 -0.2

18

3. Summary of separate filtering effects of sampling over record oflength (R), averaging over time (S), and of instrument with exponentialtime constant (;- ) (after Pasquill 1974).

Reduction of Frequency at which reduced spectral density appliesor as a result of:

Spectral DensityLimited Averaging Instrument InertiaSampling

Z 5" °(0 I...o.(?r;//Z ) O'ffl /5 '> 0·6,9 /f'

S-d 6~ o '1~/« 6,'+0 o· 1':1/1'

>qi) trio >o·8r!1<. <D·n.f/r <0·0,7/('

19

Guildline BIOlA

Electronics

Openings

Solid Shroud --u-Jf!IP

Open Wire Cage-z.--¥

1. Actual shape of Gui1d1ine 810lA instrument. Measurements are those ofConfiguration #2 in Figure 2.

20

1-12crn-'

1.70cm. Configuration 111

Shroud with holes.

-T T.Scm.J.

1-/2 cm.-t

. v'" 1~x 70cm.

",..0v~ra

Configuration tf2

Solid shroud.

T

y" i cm.

~ 42.cm.

T. }OiTGIfHHT Icm.IO.5cm.1

2. Schematic of the configurations of the Guildline 8l0lA used in timeresponse experiment. Not to scale although all measurements are given.Configuration #2 was the version used from 1970-1972 inclusive. Con­figuration #3 with,vertical spacing of sensors appropriate for loweringrate,was used after 1972.

21

r-12cm.

j

..T.Bern.oJ.

c

1-12em.--1

70cm.

I25em.

158em.

t 3cmj8cm....

70em.

Configuration 113

Wire cage around sensors

TT.8em ....

T23cm.

158em.

.• • • . • -T1.- " -. TT 9 II~ 1 1

Configuration #4

Wire cage, end pieces

on conductivity cell

(2 cm long).

2. Schematic of the configurations of the Guildline 8l01A used in timeresponse experiment. Not tb scale although all measurements are given.Configuration #2 was the version used from 1970-1972 inclusive. Con­figuration #3 with,vertica1 spacing of sensors appropriate for loweringrate,was used after 1972.

22

.-12cm.-t

1

::;3cm

1-12cm.-t

70cm.

TIO.2c.L

58em.

p.2[1!.6cm.

170cm.

58cm.

f3.227.2cm.

1

Configuration tl5

Wire cage

Configuration 116

Wire cage

2. Schematic of the configurations of the Guildline 8l0lA used in timeresponse experiment. Not to scale although all measurements are given.Configuration /12 was the version used from 1970-1972 inclusive. Con­figuration #3 with,vertica1 spacing of sensors appropriate for loweringrate1was used after 1972.

23

1-12em.-I

70em.

Configuration InWire cage.

T,L5.6em

58em.

,~em'l~em.

2. Schematic of the configurations of the Guildline 8I0lA used in timeresponse experiment. Not to scale although all measurements <lre given.Configuration 1/2 was the version used from 1970-1972 inclusive. Con­figuration #3 with,vertical spacing of sensors appropriate for loweringrate1was used after 1972.

24

---~~ -·-1·=1= -'-!-I'--~ :. -- - ........---._- .... -- .--- -- - - ._-

-~.~-- -~~ -~~ ._'. _.- =~. ~=~ -~=._-- (-.---,-... - -- - -.-

I iI •

---- - ._--. ..-=1-I-I--~'\~"-- .... _-- ............~_..._- ._-- - ~_.- -_.-- _. -- -- -- _.

ER...

-+i~:

;-1- --,- --_.. - _. -- _..--- f-- -- - - -,-,

E -- - - '--- - 1- -'- .•. :::':r- -';

.:

:.

l--I"~l-~.- -- - ·1·:.'- -'- -- _.• ._-f- ..

I.. .' : ...

I SEe0 N0 -+- , I .

I

~ -- _._- -' ...._.- --- .-....__ . -- _.

1-' ~=: -,:'-, .~. :::.' --~~ ..='-= ==~I __

._--'-" THERMOMET- ---- RESPONS-==---,_ .~- _"-J-~t--

. f- TIM E ~"I!e--~~, I

-- ---- .. --- ... .-_.- ...._- _._- -- -- -_.~-"-~- -' -_.. ... _- . - - .. .--- ._. _. - - ~ --- ---- -J-- --- _. ... .... .... ....... -- ._-

--~- -- ._-- -- ._- -.....r'.

.,-- _.-. .. .--.. . .. ..... _._- . ... ---- '" ..... _.. ... .. .. -._~ .. .-_0 _. ... -_. -- .- -... '-- ......- --.' ---1--_.. _.. ._-. ....._. -" -- .._- .-.. -_. - .._. -.-- '--. --- ._. --. ..- ..- _.. - .- .. - -~ - -- ---- .... - --'-" ..... _.- --- - -- .._.

~-'- f-- ..I._I-- eON DU CT IVITY CELL - f-- - _..-,- .1--- -.-'1--

.:-+ I_.... .. - .._-- .__.'- .. ..... RESPON SE -- - .. - ._. ... -- ....... .- _._-

._-~. ..--

1=~~LJ=l±±±±±1±..'- .__.

-' -' ...-- .._-- .-.....~.I I I 'II I

.,- ........... ~- ........... ..

"I i. 'I . ~

. I

. 3. Analog recording of senso~ response in experiment 59.

\15.87

II i II Ii !II' 1"1' I I ill' i 11;-j:I!I': i-r: j~:.'I I I I' JI 1 11'1 I""":_'.1 .l-;-g. ..U ._L! ..W-. .~ i ~

,II 'i" ~" ,'i.!' :'1'1' 1LJ+11 I'," ,.'I ! i II t" 'I I'j: 1 r '1

I': •• r ! I'" I , : " .. ,I I I! I I! . I !! ; i ! I!' I

l'j I I 1. 1 i 1 '1'; "II : j

1..1 i.!. LI !.! ..l .: .lir..UH 111 -

NlJ1

13.91

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I.: :':." ~.I· :.:. ~ I': ., :.:..:..:: .. .:.: ':.:":"':'~. _:..L0- ;,' I .JJ-~.lL~ i I '.':' I ." .. ;,:: I I,,: !!!;'1 ., .. : ,., .. , , .,." ,II' ~ 1,1,1 '1 1 " ,',.!TTi !":I ,; .. ' .•. 1 . I',,!., I .'" I '" ill .• ,.1 Jill 1'1 1,1 fl'l Ill. :1', I' '.. ,.... , ". .;:: I' III : i: 1,1 f r I:; i II I:.: . oj

I'-- _ -t () .. , . Q .. . . .., . .. " . :' i' I I , ; ; , I: i, '. I I : .1 I .

O. )(:. '~I : --.,c-;o. ~ . 0 :J( O ..J" 0 :""! ':.", I ii" I!'; "I! ! i I" 'I I I' I '1: ": . . ,.... '." . . .. : " :·I'·':'·.·()'!: I I, . 1 I I I ,. : 'I I ., I,· :, I .' : 1 : I i l ' Ij • • • .., ••••• "1' '" '!':' I I" I • I I I : I • ,I J It i I l.!_: I •• l I I II,.. · .. 1· .. · .. 1· .. · !!" I .. ".:,1.: ... 1 :'11 !." 'I" till III, "'1 I,I! ;,:1; I, I::: i!;' :'1'i . : ..":.;. ;-.-:.: .. ::: ,':':-:-';- :;";' -~-:- -;::-:.~'TG"'i'~i;-tITITt -:--:t. " '''- ..J-I._. ~•• - - : ..

, . :." .::::,:: ::: ;:1· :i:· ;:;: Ilii Iii; ii.;"II:; ill CONDUCTIVITY CELL RESPONSE U._ •. _' " ,. ... .. I .,., :,., ""'" I, 1""":";"0~ 0 0

., .: ;;;::" ~;;' I:;: '::: '~;! I!:; ~i: it:i "I' I . ,'-""...J ,: :'" I'"~ ·Ii, !' : j,[, ',I X THERMOMETER RES·PONSE : w

• • I I, ":'" I I I, ". It!' ! I , I I,. I I 1

...J .. .. : i :: ... : :::' :: I" .:": ;::: 'r!T~ ;: : I ;'1 I i'I' ; a:: 'W ",."" 'I' ,III 1;1' ,.1, ,I" I' I ,II,! , ..... 1

I " , • I' .!,., I" 1,_ I, i I I II 1 ) I I -J.U .:""! :', ". "': :1' .. :1 i!'1 II ' i!,,!. " EXPERIMENT 59 ~i

· .. :;;. :::: J:: :; I; ::!: ,:::;~ i' I: : i:! i!:: :! i i ::: <{ I

>- w .... , ,',' i.'" 1"1 i,:· " ..... , ,I" "[' .. " "I' ,.: a::,n . ,. I • I I I .!: II!; I, i II I ,;. I: iIi; Ii:;;' II I; I I'.... _ . . ...... .•. ;. ,.. :-'-T ..l-.~_ . _ ...... , ....._.. ~J. 1...i-l..,·I..;...I-+-l. -l-I-J--. :T"":' -_....:. . W

>« ' ":: I::; ':;i: i:!; '.':!: :i;1 •• 11:11 !:ii I..!ii il;; :11 1' '.::; :';! 111.'11: ' 1 1",'1 11'11 1111 11;1 11

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· ,,' , ' . , ., . : .. ,., "', I I : I : J '~' ; " !' r' ,:,. . I' I J !. I I t I I I; 'I 1 I :." I , I: ,.: Ii: ,: I .-'::> > .::: :.. ."" ~'... ,.. i : ...... ". I, . ".' ', ......' ''' ': ... :.': " :.. ; ._;., I-I .... ,.;.;. J·d·' .I.!,,!, 1"...1. ':·I··· ..H .,"'" :.1;., ·1·i·I··· ·I·~"·· IIo .;. 'ii· 1.::: :'1' :.::: ::1: i'" 11111[;: iii: 1:1.:'; I I I ;:Ii III' '11 i i"I' [III ill!! II!: !! '1:: I! :!!I I:'

Z.':' :.' .~ ,',' ;,,1 .,': II!I III' 'ii· I .. ' III: :[1: I: il'I" j i'lll I:I!II I!II I, " Ii' .Ii l I!I'

11' 1 ,, .. ": .. ,. :"!",,.~ ....~" . ", "".", ,," , I:' I,. I I . '. ~ j', I' ,I: I" .'1 .,. ;.11 '

o --.- -;-:-~ -.- '~j-.-: .. ,. --;-:-;--.: :' I - I " ,I I I I'! .. " ,,;, I' .' II II ::'! 'I' I '111 : i I I !I' Ii' II' I II' !' I' 1""1 i' 1 i .' "." I,... " .... ''''I ,,, I, .. "" 'I' '111 1' I, 'V" .,1 II, ' ,,'., II I ,]" I' 111'1 'I ',1'" I": II I I_ ... '.' I',. ," .. , .. ,,1 !'I 'I ,I, ". ;"" 01: !II' '11 ;,11 i I: I.: I'! "." II: I' I 111 'I" .11 '"~

I ,.' 1 I' " "'!" I' I t I '1 I I I I ,." ':, I' "II I : I I I. 11 .I!! I, I I J ,I. 1 ' " :, .,· "', .::. "'jlillJ'" .. , , :.j.! I" 'I'" "'llt'l '.":' ':." 1.1,--1~I_!, ..J I·r·, , .Il·~·: ··,_··I.'n·!·1 I~-r·' _..;",..1'''':'''1,:,1 ..1'1'"-1._",, .r -!-~I

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I-.' " . I· ,. I, ! I • '. , ,I . I, . I , ' I : , ': :",', '!', I;, ' " O,·j I 1'0 ,)( i ..: I I, : ; iv' 0 ". . 1'0 ". 0' I .".... ,of' I 0.._ .. -'-- _, ~_ ___. ~.r-----' --,-, .L.L.o.-__ ~ ..~....... 0 -f'or-;- ~1"":" .-l-){.-'- . -

: • I ',' "1," I. .".1'1':' 'I" ,,,' "" ".: .'.... :,:; "'1 ,.:, "~"~ "I" '1'11 . ", .... "'1 i;~: , :, I;.· I',i ., I. !" ., , I l I,., ' , I I I I: I I I I : ~ I I It: ~ ;, • I J, I' '! I. I I I 1 , : ' I' ~ I It' I; iI, I I I j [ I r I.' I l: : I' I '1 I... ." ....:',,'!.J . I , " !.! I !;:: :." 1 I :! ;!:. !,:, :: I: ,i II I ,II: .! I,; I . I . J !I I! ,. 1! I! ., I :, :;;, I!;, I'; I ',:

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I, ... ;, :"'1 .. 1... ;1' Ii" III!I ; I:i, Ii : "I. "I' II' "I'" .. II ,.,'. ·,·;;!I I" :!! :"1' !.:' "", .. .., .:, "; .. !' "" " 'I :' ,':' ., . ':. "!! I I II I I I. 1 II! I 'j . "', , I' .: i! I I'" : 1:1 ", I. '.' ,".'1" t ,., , ..•.. , .. , I I.· ,I. r I .• I· ',,:.! ·1· .. , , , I' I' .", ,

234

)127

4. Vidar data logger response of conductivity cell and Guildline thermometerin experiment 59.

26

; '-­;

i

t, Ii;·1 . " '

• 1

.-:-. :."

,"" . t

L •...J--'......_~.._. .' .

I , .:,

:~ilTI~tQt !twirei : H· ~: ;- ':1: 't'

.1 f'~ •. , ,Q .. , T':·1·, '

I--... ··t-~~ 'X-,.~,c

.1- -

5hie~d}

2

Rate

I

Lowering m sec-IExperimentally determined time constants (0-63%) and those calculatedto immersion as described in text. Conductivity cell time constantis~ and Guildline thermometer time constant is 17- •

5.

27

f*=O.1~--==*=====---b_......:::::::::::...-.l_--_..".!.L.~ t*= 1.0

0.2

1.0 ,..------r---o;;::-----,-------r---r--r---rJ-T1

0.8 l---~~----+--~-__hL-____:I--____:'F'=-~

-~f*=0.3+

z 0.6N-C\I.e+-~I 0z 0.4"+-

C\I-C\If*=0.2"9

0.90.80.6oC::::=====C:==-_h::====:=±====-_L---.-J0.5

6. Fractional aliasing of energy from frequencies (:ttN -Pr ) and (j.fwtff )on the vertical axis, and fractional response due to instrument timeconstant (~) on the horizontal axis. Quantities are given as functionsof -r f = "",4. t where (Lot) is the interval between (instantaneous) sampling,and f'* = r1/tN where f r is the frequency of interest, and fN is theNyquist· , or folding frequency (from Sabinin 1967).

90 0

80°

70° ."':I:»

60'0 en",

50° en::I:-

40° ~

-30° - NC 00

CO

20° -

10°

00°1.0'. 1.2 1.4 1.6'X.

" ·X-._ XX· - :x-.~.,.

0.8

l:z\

~\' 1'>0.

•';or--...

~i"~[.,

.... ,. - -{ ---(tr- - -~~--, _..li"\-- - r--

\ ',I....- , .-.0- -....~\. 1 -~ . '

I 'y"

'6 1,~ 1"""\.(,..I'.

.X: ' .....~'.,

~l ' \.II .

\.

l ~-,".

I .... \. \

(~ "

f~ -l~ '~k.', I ,~)-,

~~1~I

,k

I ..I \.

.( ",

0.8

LtJenz0 0.6a,U)I.LIa=:w 0.4Q::>....:JQ. 0.2~«

1.0

oo 0.2 0.4 0.6

1" TIME CONSTANT OF SENSORo =P = PERIOD OF FLUCTUATION

lag.0= PHASEAVERAGING PERIODPERIOD OF FLUCTUATION

s __X=p=7. Amplitude response and phase shift as a function of sensor time constant

divided by period of a sinusoidal oscillations, and amplitude responseas a function of data averaging time divided by the period of a sinusoidaloscillation.

Nvo

IIk.

-

. "!

~

i),...

,

(, .

-

-

-I"

f--.- \

'~,

Ko

..0

~ Pf L·J 0

~ ~ Ioc k .-

I~ t» .....

-~

,

Law(f)z0o,en 0.8wct:

w~ 0.6::2:t-soW

-l 0.4<l0.:t-UW0.. 0.2(f)

o _a 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

0- .!._.TIME CONSTANT OF SENSOR. _..§.._ AVERAGING PERIOD- P - . PERIOD OF FLUCTUATION X - P - PERIOD OF FLUCTUATION

8. Spectral estimate response as a function of sensor time constant dividedby the period of a sinusoidal oscillation, and as a function of dataaveraging time divided by period of the sinusoidal oscillation.

30

APPENDIX I

Outline of experimental results

ColumnFORM CONTENT

Content

Experiment Number

Configuration (from Figure 2)

Time of day

Date in October 1972

{

Conduct i v i t y Cell C

Time response 0-95% Analog trace Gui1dline thermometercs ec.)

Thermistor T

Ll (0-6]%) as 1/3 (0-95%) response - analog trace \~TG(sec) l

L2 (0-63%) read from analog trace {~TG(sec)

T, (0-63%) as 1/3 (0-95%) response time on data logger trace t:G

T, (0-63%) from 0-95% response time adjusted for T time constant[:G

Estimate of interface t hf.ckness (em.) Black square indicatesintact diaphragm

1

2

3

4

5

:}1~}11

~~}14

~:}17

~:}20

21

Speed of drop em sec- 1

* Uncertain

31

32

Q

o

1'2 (Q - 63 '1. )!CO'l -1 I 0-95'1. R=:S? 1'1(0-63"/.) 1'3(0-63':.) '1'4(0-63'1.) IINT.-NO. FIG. TIME DATE VEL. I I I I F "-CE

C TG T C TG T C TG T C T GTe TG T

5 6

33

9 10 \ 11

ICO N -I ._ I - INO. FIG. ITlk'IDA'E VEL.

0- 95 -t, RES?

c

-(1 CO-G3 '1. )

C T G I T

-(2{0-G3 '(.) -(3 CO-G3 '1.) I -(4{ 0-G3 ·t.) \I>IT.­

CiT GTe T G I Tel T G I T rtL'O

~_± 4 5 6 7 8 9 \ 10 \ 11 \ 12 \ 13 \ 1 4 1 5 \ 1 6 17 \ 1 8 19 \ 20 \ 2.1

ICO N -T 0-95'/. RES? -(lCO-G3'/.) -(2{0-G3·t.) -(3CO-G3"'.).\ -(4CO-G3'1.) INT.-

NO. FIG.\TIME DATE VEL. C TG T C ITG T C ~LLC ITG TiC TG IT FACE

(,") \ L IfOlq [(, \).?_ [(" ).. 0 [. I S \ '7 .4- .{/ lli~--!.~Jf-( • Lf .{; . \ '"3 7

~ _\ (. IOl(~ ~~, )..t\ ,.).. :J'G .q \ /.J ·7 /"/\ /./\ [.-/" (·IfbL .<) ·7 \., )~

~c; 7 /Ire> II. :Ie> ~'o \ ).).. (.). ·7 \'7 '4_L J·'7; "~;~l~ \. ". <; \ .r" \.) ~ i2

:;:F JIIA " 2'- I~ ~'IJ' :~,"-I'--.Lf.__.".~'__~-.~., \.7. ,,1 J'J 1\, llt,\L717 '''" Ie ,0 ,." '·7 ,.•., ,'') \., '7l·-,.I·, >-1 1'·~L .(. '7J~,- J'

~]~=- \---~---- -l[-l-~C--tl-~ ---t- \-- L~-~_I_J[ J-- ---- - --~ \ --~r ----I ~\ \ ~

\ I --~ 1 -'-If---- - .\- -- -" -- -- -1----- __1~1.__:__ -- __L- T_\~I------L I

F-- ---- L-- ------ -- --+----~ I " ~ I l '\ ~-Ir------r------;~._\ L _ __ ILL-- __L __ ~- ----------,---I--'-'-