A soil moisture flux transducer was built and tested in the
laboratory under steady-state conditions in a column of Portneuf
silt loam soil. Initial data indicate that the instrument may
be developed into a useful field research tool. Its principal
advantage is that measurements of moisture flow may be made
without any prior information concerning the unsaturated
hydraulic conductivity of the soil. Rather, one needs to know
only a soil moisture convergence factor which is dependent on
the state of the soil and the design of the transducer. While
this convergence factor is dependent upon the soil moisture
content, the dependence appears to be nearly an order of magnitude
less than the dependence of hydraulic conductivity on
soil moisture content. It may prove possible to develop the
unit for installation in the field to provide continuous measurements
of the unsaturated soil moisture flow in the tensiometer
range with errors no greater than those arising from the natural
heterogeneity of the soil

Cary, J.W.

USDA - ARS - NWISRL

Cylinder wallsFig. 1—Cross-sectional view of the first model of transducer ina soil column with a possible configuration of moisture flowlines.Reprinted from the Soil Science Society of America ProceedingsVol. 32, no. 1, January-February 1968 	 Furskzlid677 South Segoe Road, Madison, Wisconsin 53711 USADIVISION S-I SOIL PHYSICSAn Instrument for in Situ Measurements of Soil Moisture Flow and Suction'. W. GARY'ABSTRACTA soil moisture flux transducer was built and tested in thelaboratory under steady-state conditions in a column of Port-neuf silt loam soil. Initial data indicate that the instrument maybe developed into a useful field research tool. Its principaladvantage is that measurements of moisture flow may be madewithout any prior information concerning the unsaturatedhydraulic conductivity of the soil. Rather, one needs to knowonly a soil moisture convergence factor which is dependent onthe state of the soil and the design of the transducer. Whilethis convergence factor is dependent upon the soil moisturecontent, the dependence appears to be nearly an order of mag-nitude less than the dependence of hydraulic conductivity onsoil moisture content. It may prove possible to develop theunit for installation in the field to provide continuous measure-ments of the unsaturated soil moisture flow in the tensiometerrange with errors no greater than those arising from the naturalheterogeneity of the soil.Additional Key Words for Indexing: flow transducer, waterflow in soil.HEAT FLUX transducers have been used for a number ofyears to detect heat flow in soil. These units measurethe temperature gradient across a thin disc of some materialwith a known and constant thermal conductivity. The heatflux across the disc is then calculated; and since the unit isburied in the ground, the soil heat flux may be inferred.Several soil scientists have suggested that it might be pos-sible to develop a similar transducer to measure moistureflow in soil, see in particular the paper by Richard et al.(1938). 3 Because of the numerous practical applications ofsuch an instrument, a study was initiated along these lines.The unsaturated soil moisture flow has, in general, beencalculated through some application of the so-called Darcyequation—K q 	 [1]where J,, is the flow of water in mm per day, K is theunsaturated soil's hydraulic conductivity in mm per day,and q 4) is the potential gradient in cm of H2O per cm,including both matrix and gravitational components. Usingtensiometers to measure q (13, it is possible to calculate1 Contribution from the Northwest Branch, Soil and WaterConservation Research Division, ARS, USDA; Idaho Agr. Exp.Sta. cooperating. Received May 29, 1967. Approved Oct. 11,1967.2 Research Soil Scientist, Snake River Conservation ResearchCenter, Kimberly, Idaho.3 Richards, L. A., M. B. Russell, and 0. R. Neal. 1938. Fur-ther developments on apparatus for field moisture studies. SoilSci. Soc. Amer. Proc. (1937) 2:55-64.Jw provided one knows the value of K. Because K decreasessharply as the moisture content drops, it is difficult toapply equation [1] to field problems with any confidencein the accuracy unless a great deal of calibration work hasbeen done so that one knows the relationship between Kand soil moisture suction, r. Even with this knowledge,significant uncertainties may arise as a result of hysteresisand sample changes.An obvious advantage of a transducer-type instrumentis that K need not be known to measure unsaturated soilmoisture flow. The principal problem associated with usingsuch a transducer is the uncertainty of convergence of flowlines from the surrounding soil into the transducer. This isdiagrammed in Fig. 1. In this case, the transducer is asystem of 3 porous plates, cemented into a incite matrixsuch that water reservoir is formed on either side of themiddle plate. Thus, if the difference in potential across thecenter plate is measured, the amount of moisture flowingthrough the transducer is known because the water con-ductivity of the plate is a given constant. In order toproject this information to the rate of moisture flow throughthe soil surrounding the transducer, the amount of con-vergence must be known. One may express these relations asJ.L; = —kA4)	 [21and1w = --kA4, = —K q 4)	[3]where J.,' is the water flux through the transducer, A 4 isthe potential drop across the center plate, k is the conduc-tivity of the plate, / is the ratio of mean flux through themeter to the mean flux through the soil, and the othersymbols are as defined in equation [1].34	 SOIL SCI. SOC. AMER. PROC., VOL. 32, 1968Heat flux transducers are also subject to the convergenceproblem. They have been mathematically analyzed by sev-eral persons, Philip (1961), 4 for example, arrived at theequation(e - 1)H	 [4]where f is defined in 131, f is the ratio of meter conductivityto medium conductivity, and H is a constant dependingupon the geometry of the meter. In designing a flow meter,it is desirable to have H -* 0, which occurs as the trans-ducer becomes thinner. The amount of convergence of flowfrom the soil into the meter will approach a limit when themeter conductivity is greater than the conductivity ofthe surrounding medium; on the other hand, if the conduc-tivity differences are reversed, the value of f would be lessthan one and the measurement error could approachinfinity. Obviously the flow meter should be designed tohave a hydraulic conductivity greater than the surroundingsoil. Philip presented some sample calculations showingthat the meter conductivity could differ from the mediumconductivity by a factor of 20 times and still predict theheat flux through the medium with errors not greater than25%. This was sufficiently encouraging to warrant an at-tempt at calibrating	 a transducer for measurement ofunsaturated soil moisture flow. While equation [4] is notstrictly applicable to unsaturated flow because of thefunctional relations between K and 7, it appears that themoisture system may favor the use of a transducer due toits "buffering" effect on convergent flow paths.PROCEDUREOne obvious way to study the behavior of the transducer isto place it in a column of soil in which the moisture tensionat each end is controlled. Steady-state moisture flux throughthe column could then develop and be accurately measured.The moisture flow might then be compared with that predictedby the meter in the center of the column. To make a meaning-ful calibration with such a system, it is first necessary to findout what size soil column is required so that its boundaries willhave a negligible effect upon the convergence of flow into thetransducer.A preliminary investigation was made with an electricalanalog study of the problem. This was done in a tray of agargel approximately 1 m square. A cross-sectional agar modelof the meter was placed in the center of the tray. The conduc-tivity of this section was varied by changing the concentrationof salt in the water held in the gel. A line source, and a linesink potential were applied across the tray of agar and theequipotential contours were mapped with a voltmeter. Whilethis was only a two-dimensional study and therefore not anexact analog of the system of interest, preliminary results didsuggest that the equipotential lines were not noticeably dis-turbed by the transducer at distances greater than twice thediameter of the transducer.Concurrently, another preliminary experiment was set up assketched in Fig. 2. This equipment was held in a controlledtemperature box at 25 IC. Steady-state moisture flow throughthe soil column was established by setting different suctions inthe two vacuum jars. When the inflow rate became equal to4 Philip, J. R. Theory of heat flux meters. I. Geophys. Res.66:571. 1961.Flow	 Air bubbleFig. 2-Cross-sectional diagram of the apparatus used to cali-brate the transducer.the outflow rate, it was assumed that steady-state had occurred.This took from 1 to 4 weeks to achieve, depending upon thesoil moisture suction range. As diagrammed in Fig. 2, an oil-water manometer was used to measure the difference in hy-draulic head across the center plate in the meter. The oil waskerosene with a small amount of detergent added at the oil-water interface to stop clinging to the sides of the tube. Thisdevice has a sensitivity approximately 5 times greater than awater-air manometer system and automatically accounts forthe body force of gravity on flow. Nylon tubes were used toconnect the water chambers in the transducer to the externalpressure manometer and mercury manometer. The system wasalso arranged such that the lines could be flushed of air whennecessary. When the inflow and outflow rates became equal,the potential difference across the center plate, the soil moisturesuction in the meter, and the flow rate through the column wererecorded (see Table 1). These data were collected from a soilcolumn 19.6 cm in diameter and 21.0 cm long with 3.2-cmradius plates in the transducer. The two outside plates werefritted glass with an effective pore radius of I to 2 microns.The center plate was a 6.3 mm piece of 2-bar ceramic.Although the first model meter produced encouraging results,it did give some problems from occasional leaks in the systemunder high soil moisture suctions. Therefore, a second instru-ment was designed and built as diagrammed in Fig. 3. Thisproved to be much more reliable as far as leaks were con-cerned and had the additional advantage of making it possibleto easily change plates to regulate the conductivity. This unitwas fitted with plates 3.9 cm in radius. but otherwise similarto the plates as used in the first model.To evaluate the effect of column boundaries on flow lineconvergence, the second type of unit was installed in two sys-tems, each similar to that diagrammed in Fig. 2. The ratioof the cross-sectional area of the soil column to the area ofthe transducer was 4.2:1 in the smaller column and 9:1 in thelarger. The data recorded from these two experiments are pre-Table 1-Observations made with the first model of transducer;these data were collected in a horizontal column with a cross-sectional area of soil column to transducer ratio of 8.5:1cm HgManometerdisplacement, •cmmm/dayobservedk	 pmin/day dimensicedeas3.8 2. 5 0. 3 0.24 0.94.9 15. 7 1.0 1.59 1.87. 9 9.0 0.4 0.80 2.213. 7 3.8 0.25 0.38 1,418. 5 7.8 0.45 0.74 1.617.0 8.0 0, 45 0,78 1.725.8 3.0 0. 20 0.29 1.541. 4 3.7 0.15 0.95 2,5• The displacement In cal of the water-oil interfaces as diagrammed in Fig. 2.Table 2-Observations made with the second model transducer.The hydraulic conductivities are mean values averagedover 21 cm of soilcm HgManometer	 3,displacement, • mm/daycm	 observedha mmm/daydimen-sionless mm/day	 man/day4. 271 Area Ratio Desorption Cycle - Horizontal Column Tygon tubeLucite ring0 ringBoltTygon tulleNylon tubesLucite ring74mmBrass ringCARY: MEASUREMENT OF SOIL MOISTURE FLOW AND SUCTION	 545.2	 9.6	 11.5	 1. 2	 0, 2116.5	 2.0	 4.6	 2. 3	 0. 1112,1	 1. 0	 3. 0	 5.0	 0. 08313,0	 0, 9	 3.3	 1 7	 0.0669. 2	 0. 7	 2. 3	 3, 3	 0.0767.6	 0. 65	 1.9	 2, 9	 0.0864, 2:1 Area Ratio - Absorption Cycle - Horizontal Column15, 0	 1. 05 	3.7	 3.6	 0,0716.5	 0.55	 1.6	 2.9	 0. 08613.8	 2.05	 3. 5	 1, 7	 0, 159:1 Area Ratio - Desorption Cycle - Vertical Column0.08	 Fig. 3-Cross-section of second model transducer used to col-t). 23	 lect data in Table 2. The porous plates have a radius of1.0 3.9 cm and the unit has a thickness of about 5 cm.1. 10,530. 150. 170. 090.063.614.825. 025. 531.651.227.113, 23.63.35. 68. 410. 019, 825.710.8	 1. 55	 2, 7 	 1.78.5	 0, 7	 2, 1	 3. 0S. 0	 0.6	 1. 2	 2. 010.2	 0.9	 2.6	 2. 95.7	 0. 4	 1.4	 3. 52.6	 0, 2	 0.65	 3.2• The die placement in cm of the water-oil interfaces as diagrammed in Fig. 2.sented in Table 2. In addition to vertical and horizontal testsand the wetting and drying cycles which are specified in thistable, tests were also made with the suction gradient acting bothwith and against the gravity force in the case of the vericalcolumns and in both from left to right and right to left in thecase of the horizontal columns. Since the direction of flow madeno difference in the results, it is not specified in Tables 1 and 2.RESULTS AND DISCUSSIONBecause the f values shown in Table 2 are nearly thesame for the two soil column area ratios, it appears thatboundary effects were not important in the convergence ofmoisture flow into the instrument for any of the datareported. The most important result is the relation betweenthe effective conductivity, k1 f, of the transducer and theaverage hydraulic conductivity of the soil as shown in thefirst section of Table 2. As the soil moisture suction rosefrom 3.6 to 51.2 cm of mercury, the hydraulic conductivitydecreased almost 20-fold. However, the effective conduc-tivity of the transducer changed by a factor of only about2.5. Moreover, as a result of hysteresis and aging of thesoil column, the relationship between conductivity andmoisture suction changed by a factor of 2 on the wettingcycle, but values kIf showed little change from the resultsof the desorption cycle.The f values for the first design of transducer, Fig. I,were less than the f values for the second type, Fig. 3. Thiswas caused by the surface area taken up by the brass and0-ring seals in the second type instrument. Only about halfof this transducer's total cross-sectional area was availablefor flow, thus the amount of convergence was increased.It would be desirable to develop a unit with a maximumcross-sectional area available for moisture conduction asdiagrammed in Fig. 1, but with the rugged, leak-proofcharacteristics incorporated in the design of the unit dia-grammed in Fig. 3.As a matter of interest, it may be noted that the instru-ment described in Fig. 3 was buried in the soil and con-nected to a pressure transducer and recorder. It was thuspossible to continuously measure the unsaturated moistureflow through the soil profile. This setup operated well andgave what appeared to be reasonable responses to irrigationand subsequent drying of the soil surface.CONCLUSIONS AND SUGGESTIONSThe preliminary studies reported here indicate that theinstrument may be developed into a useful research tool.Its greatest merits are: (i) the soil's hydraulic conductivityneed not be known in order to measure unsaturated mois-ture flow in the field; and (ii) soil moisture convergence isrelatively independent of soil moisture content. Problemsarising from aging, soil moisture hysteresis, and changes insalt concentration may be largely eliminated. If these pre-liminary results also are applicable to soils of differenttextures and composition, it may be possible to develop aunit that can be placed in any soil at any depth to measureunsaturated flow within accuracy limits of possibly ± 30%.This measurement may require only some information onthe soil's texture and density rather than the accurate valuesof the hydraulic conductivity presently needed. Errors in-volved in this measurement may not be much greater thanthose arising from the natural heterogeneity of soil infield plots.There are several problems to be overcome. The unit willonly operate at moisture suctions of < I bar. However,this is the range in which the bulk of moisture flow occurs.Since the potential differences across the center plate inthe meter are small, serious errors can arise if air bubblesdevelop in the lines leading to the pressure-sensing deviceon the surface. This hazard can be overcome to an extentby using deaerated water and nylon tubing. However, thesystem must be flushed occasionally. Perhaps it will bepossible to develop a pressure sensor in the transducer itselfso that only an electrical signal need be transmitted to thesurface. Another disadvantage of the unit is calibrationtime. Under steady-state conditions as reported in thispaper, the calibration is time-consuming and tedious. How-ever, because the /Of function appears to be relativelyindependent of suction, it may be possible to develop atechnique for making calibrations under transient soil mois-ture conditions. This would reduce the time required tofully evaluate the usefulness of the unit in soils of othertextures and densities.ACKNOWLEDGMENTSThe author would like to acknowledge the valuable assistanceof Herbert D. Fisher and Richard Allen in various aspects ofthe experimental work reported in this communication.

An Instrument for in situ Measurements of Soil Moisture Flow and Suction

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An Instrument for in situ Measurements of Soil Moisture Flow and Suction

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