Calibration of a Soil Moisture Sensor in Heterogeneous Terrain

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1 Calibation of a Soil Moistue Senso in Heteogeneous Teain Melin, O. 1, J.P. Walke 1, R. Panciea 1, R. Young 1, J.D. Kalma 2 and E.J. Kim 3 1 Depatment of Civil and Envionmental Engineeing, The Univesity of Melboune, Austalia 2 School of Engineeing, The Univesity of Newcastle, Austalia 3 NASA Goddad Space Flight Cente, Geenbelt, USA omelin@unimelb.edu.au Keywods: soil moistue senso, calibation, uncetainty assessment, spatial sampling EXTENDED ABSTRACT Reliable soil moistue measuements ove lage aeas ae much needed fo both hydologic modelling and emote sensing applications. Fo collecting such data, potable electonic sensos offe a pactical altenative to gavimetic measuements. The convesion of the measued electical output to soil moistue is nonetheless a non tivial task as it depends on soil type and tempeatue. In this study, diffeent calibation appoaches of the Stevens Hydapobe soil dielectic senso opeating at 50MHz ae tested with the National Aibone Field Expeiment (NAFE) data. The objective was to evaluate the impact of soil type and tempeatue on the senso esponse and test the applicability of a geneal calibation equation. Duing the NAFE, a spatially enabled platfom (Hydapobe Data Acquisition System, HDAS) was used to collect extensive measuements of nea-suface soil moistue. HDAS is a handheld system integating the soil dielectic senso and a PC pocket/gps eceive allowing fo diectly stoing the measuements onto GIS softwae. HDAS measuements ae composed of the dielectic constant (DC) of the soil/wate mixtue, soil tempeatue, soil moistue, salinity and conductivity. A diect compaison between the factoy calibation and gavimetic measuements indicate that the senso esponse diffes significantly with soil type. It was found that the pobe signal is linea in sand but satuates above 20% v/v in clay. On the othe hand, the eal component of the measued elative DC was found to behave similaly fo clay and sand, with a diffeent slope fo individual soils. Following these obsevations, two calibation appoaches diectly based on the measued DC ae tested. The fist is deived by aveaging the slope obtained with vaious soil types (geneal equation). The second uses the atio of the imaginay to eal component of DC (loss tangent) to descibe the diffeence in soil popeties (loss-coected equation). Results indicate that the calculated loss tangent is able to explain most of the vaiability among soil types. The oot mean squae eo (RMSE) of the pedicted soil moistue is deceased fom 4.0% v/v with the geneal equation to 3.3% v/v with the loss-coected equation. A thid-ode polynomial egession between the factoy equation and obsevations gave the best oveall accuacy with a RMSE of 2.7% v/v. The loss-coected equation is howeve moe obust as it does not satuate above 20% v/v and is moe stable than the polynomial egession with diffeent soil types. Pevious analyses have shown that the senso is sensitive to tempeatue. In this study, the tempeatue effect on the eal component of the measued DC was evaluated with sand and clay in diffeent moistue conditions. With sand, the tempeatue was found to have a negligible effect with the lagest effect on eal DC fo a 15 C tempeatue incease (elative to 25 C) of about - 0.6, coesponding to a soil moistue change of about -1% v/v. With clay, the obseved tempeatue effect of a 15 C incease is about at 30% v/v and 4 nea satuation, coesponding to a soil moistue change of about 3% v/v and 4% v/v espectively. It was also found that the manufactue-supplied tempeatue coection algoithm inceases the obseved tempeatue effect on the measued eal DC. A simple coection is then deived based on the loss tangent to account fo diffeent effects accoding to soil types. The loss-coected equation including the poposed coection fo tempeatue effect is finally applied to the NAFE data. Images of the calibated soil moistue at 250m esolution ove an aea of 27 km 2 ae pesented fo thee sampling days following a ainfall event. Such spatial data will be used fo calibation/validation of hydologic models, emote sensing of soil moistue and

2 undestanding contols on spatial pattens in soil moistue. 1. INTRODUCTION Rapid measuement techniques using electonic sensos such as time domain eflectometes, capacitance, impedance and dielectic sensos offe an altenative to destuctive and time consuming gavimetic sampling. They howeve equie a pope calibation to convet the senso esponse to soil moistue in diffeent soils and tempeatue conditions (Cosh et al. 2005). The National Aibone Field Expeiment (NAFE) is a seies of two soil moistue-dedicated expeiments undetaken in South-Easten Austalia (Walke et al. 2005, 2006). NAFE 05 was undetaken duing 4 weeks in the Goulbun ive catchment and NAFE 06 duing 3 weeks in the Muumbidgee catchment, New South Wales. Duing NAFE, top 5cm soil moistue was measued intensively fom paddock to egional scales using a spatially enabled platfom (Panciea et al. 2006) based on the Hydapobe (Vitel, 1994, Mention of manufactues implies no endosement on the pat of the authos). The Hydapobe, heeafte efeed to as the soil moistue senso, is a soil dielectic senso opeating at 50MHz with an embedded themisto in the pobe head. At each measuement point, a volumetic soil moistue value is infeed fom the eal component of the measued elative dielectic constant (DC). Because the eal component of DC ( ) may vay with tempeatue, a tempeatue coection is poposed by the manufactue that uses the measued soil tempeatue (assumed to be the tempeatue of the pobe head). The wate content is then calculated based on the tempeatue-coected eal DC via one of thee possible calibation equations fo sand, silt and clay. Independent evaluations of the pefomance of this senso wee notably made by Seyfied and Mudock (2002, 2004) and Seyfied et al. (2005). Seyfied and Mudock (2002) epoted that the thee calibation cuves povided by the manufactue do not effectively descibe obsevations, and that soil tempeatue effects may be significant. Seyfied et al. (2005) developed two multi-soil calibation equations; a geneal calibation equation and a calibation equation that incopoates the effects of soil popeties. The objective of the study is to evaluate the impact of soil type and tempeatue on the senso esponse and test the applicability of a geneal calibation equation to the NAFE data set. In paticula, the two calibation equations of Seyfied et al. (2005) ae tested and compaed to a 3 d ode polynomial egession in tems of accuacy and obustness. The analysis is based on fou distinct data sets, one collected in the field (NAFE 06) and thee in the laboatoy with both NAFE 05 and NAFE 06 samples including a wide ange of soil types fom sand to clay. 2. DATA Among the fou datasets used in this study, thee wee obtained in the laboatoy (Temp 05, Lab 05 and Lab 06) and one in the field (NAFE 06). These datasets wee all collected in the NAFE famewok with the aim of facilitating calibation of the soil moistue senso. Duing NAFE 06, gavimetic measuements wee collected at five pe-defined locations within six focus fams (denoted by Y1, Y2, Y7, Y9, Y10 and Y12). These locations wee chosen to cove a ange of soil type and moistue conditions. The five gavimetic points emained unchanged all along the field expeiment so as each gavimetic measuement was associated with a given soil but with time vaying moistue conditions. A HDAS eading was taken at each gavimetic point, and a soil sample was collected at the same location. In the case when the pobe was modifying the soil suface (e.g. soil stuck on the pins of the pobe), the soil sample was collected at the middle of a 10-20cm wide tiangle of thee successive HDAS measuements. Gavimetic sampling was undetaken as much as possible at the same time on evey sampling day, so as to meet simila tempeatue conditions. Soil samples wee pocessed using the standad themo gavimetic appoach. Lab 06 complements the field data of NAFE 06 with a set of thiteen soil samples. Soil samples wee collected in the same fams as fo NAFE 06. Locations wee in geneal diffeent fom the gavimetic points of the field expeiment. Lab 05 is a laboatoy expeiment undetaken with soil samples fom the NAFE 05 Goulbun ive catchment egion. Eight soil samples wee used, one in each of the eight focus fams. Note that this dataset does not include the output voltages. The infiltation-addition method was applied to all soils of Lab 05 and Lab 06 by pouing wate on the top of the containes, and allowing samples to satuate fo a minimum of 24 hous. A pobe was then inseted into the containe and samples wee oven died at 45 C.

3 Temp 05 is a laboatoy expeiment specifically designed to quantify the tempeatue effect on the soil moistue senso. The infiltation-addition method was applied to the soil samples of Lab 05 by pouing diffeent amounts of wate to get diffeent moistue conditions fom dy to satuated soil. Samples wee then put in the oven at diffeent tempeatues 20, 30, 40, 50 and 60 C. 3. TEMPERATURE EFFECT Seyfied and Mudock (2002) estimated that the tempeatue effect of a 40 C tempeatue change was about 4-6% v/v depending on soil type. In this section, the Temp 05 dataset is analysed and a coection fo tempeatue effect on the measued eal DC deived. Results of the Temp 05 expeiment ae pesented in Fig 1. Fo each soil sample analysed, the effect of a 15 C incease elative to 25 C on the measued DC is evaluated fom the DC constants measued at 20 C and 40 C. It is computed as the atio of the diffeence between the DC measued at 40 C and that estimated at 25 C, divided by the tempeatue change (15 C). The DC at 25 C is intepolated by assuming a linea tempeatue effect between 20 C and 40 C (Seyfied and Mudock, 2004). In Fig. 1, the tempeatue effect on the eal and imaginay DC is plotted as a function of soil moistue. Both the measued DC and the DC coected fo tempeatue effect by the manufactue s algoithm ae pesented fo compaison. Tempeatue has a diffeent effect on the eal and imaginay components of the measued DC. Concening the imaginay component, the tempeatue effect is always positive and geneally inceases with soil moistue (Seyfied and Mudock, 2004). It is howeve efficiently coected by the manufactue s algoithm, which educes the tempeatue effect on the imaginay DC down to 20% on aveage (see Fig. 1a). The tempeatue effect on the eal component of the measued DC diffes with soil type. With sand, the effect is slightly negative nea satuation (Seyfied and Mudock, 2004). This can be explained by the fact that soil wate in sand has dielectic popeties simila to those of pue wate. In that case, the tempeatue coection poposed by the manufactue is in good ageement with obsevations. With clay, the tempeatue effect is positive and inceases with soil moistue. The obseved change in eal DC ove the 15 C tempeatue incease is about 2 at 30% v/v and 4 at 40% v/v, coesponding to an estimated soil moistue change of about 3% v/v and 4% v/v espectively. It is found that the coection poposed by the manufactue is not satisfactoy with clay as the eo on the measued eal component of DC is inceased fo all soil samples (see Fig. 1b). A coection fo tempeatue effect on the measued eal DC is then poposed. The coection equation is based on the obsevations that (i) the tempeatue effect diffes lagely with soil types; (ii) the tempeatue effect is significant with clay and inceases with soil moistue. As the manufactue s tempeatue coection amounts to calculating the coect dielectic constants at 25 C, ou coection equation is also elative to 25 C, and can be witten as co [ 1 K( 25) ] = ε T ε, (1) with co the tempeatue-coected eal DC, T the senso tempeatue and K a constant. As the tempeatue effect diffes with soil types (negative with sand and positive with clay), paamete K was coelated to loss tangent to integate the effects of soil dielectic popeties. The loss tangent is defined as Figue 1. Tempeatue effect on the uncoected DC and the DC coected fo tempeatue effect by the manufactue s algoithm: a) the imaginay component of DC; b) the eal component of DC. With clay, the obseved tempeatue effect on eal DC is inceased by the manufactue s coection. In (c), the tempeatue effect (K) fo a 15 C incease is shown as a function of loss tangent.

4 ε δ = ε i tan, (2) This quantity is popotional to the enegy dissipation expeienced by the input voltage. Fig. 1c illustates the elationship existing between the estimated K and the loss tangent computed with the Temp 05 data set. A linea egession gives K = tan with a coelation coefficient of CALIBRATION APPROACHES Fig. 2 shows the vaiations of the senso esponse with datasets Lab 05 and Lab 06. The soil moistue simulated by the manufactue s algoithm (option silt) and the eal DC measued by the senso ae both plotted against gavimetic measuements. Note that the ecommendation of the manufactue fo when the soil type is unknown is to set the pogamming option fo silt. The eal DC could not be computed with data set Lab 05 as the input data of the algoithm (voltages) wee not stoed. Fig. 2a indicates that with sand the senso soil moistue is linealy coelated with obsevations, while with othe soils, the senso soil moistue satuates above 20-25% v/v. Howeve, as shown in Fig. 2b the measued DC keeps inceasing until satuation, and the elationship is simila with diffeent soil types. These esults ae consistent with Seyfied et al. (2005), who developed a calibation equation of the pobe diectly fom the dielectic constant. They use a linea elationship between and given by θ = A ε + B, (3) with A and B two soil-dependent paametes. In that study, a geneal equation was deived by aveaging the paametes obtained with measuements made on 20 diffeent soil types. This calibation equation (A=11.0; B=-18.0 % v/v) was found to be supeio to any of the thee equations povided by the manufactue. Seyfied et al. (2005) then coelated the diffeence between the measued and pedicted soil moistue with the loss tangent at satuation tan s. The loss tangent was used fo coecting the obseved diffeences between individual soil calibations. Since most of the vaiation in soil calibations was due to vaiations in A, the loss-coected A paamete value A lc is based on the egession between A and tan s. The new calibation equation was witten Figue 2. Senso esponse as function of soil moistue: a) soil moistue pedicted by the manufactue s calibation equation (option silt); b) eal DC measued by the senso. ( ε ε ( = 0) ) θ = θ A, (4) lc with A lc = tan s (% v/v) and = 2.7 at = 0. Note that B was eplaced by - A lc 2.7. A thid calibation appoach consists of fitting the senso soil moistue to obsevations using a polynomial egession 3 2 θ = aθ silt + bθ silt + cθ silt + d, (5) with silt the soil moistue pedicted by the manufactue s calibation equation (option silt) and a, b, c and d fou paametes. As an illustation of the thee calibation appoaches, the polynomial equation and the geneal equation ae plotted espectively in Fig 2a and 2b. It is appaent that the geneal equation is moe linea than the polynomial equation and fits elatively bette the senso esponse with the ange of soil types of NAFE. Note that the loss-coected equation cannot be plotted in the same figues as the pedicted soil moistue is also a function of the imaginay component of DC.

5 5. MULTI-SOIL CALIBRATION The geneal equation (3), the loss-coelation equation (4) and the polynomial egession (5) ae successively applied to the NAFE 06 datasets. The diffeent appoaches ae then assessed in tems of accuacy and obustness. To apply the loss-coelation equation to the oving measuements made duing NAFE 06, which uses the loss tangent measued at satuation, one needs to assume that loss tangent is constant (i.e. does not depend on soil moistue). Fig. 3 shows the vaiation of tan as a function of soil moistue at six pemanent sites in the NAFE 06 aea. At most sites, the value at satuation appeas to be eached at about 15% v/v, which means that the loss-coected equation can be applied fo soil moistue values above 15% v/v. Note that the diffeence between soil types is expected to be small below 15% v/v. One can theefoe assume that the diffeence due to the use of tan instead of tan s in the loss-coected equation is elatively small ove the full ange of soil moistue. A second assumption is about the tempeatue measued by the senso. To coect fo tempeatue effect in the field, one needs to make sue that the tempeatue measued by the senso, which is located in the head of the senso, is consistent with the top 5cm soil tempeatue. Fig. 4 plots the senso tempeatue measued in the field by the oving HDAS as function of the 0-5cm tempeatue measued continuously at the pemanent sites in the sampling aea. The standad deviation between oving and station-based measuements is about 2 C, which is smalle than the ange coveed by tempeatue values (15 to 35 C). In the less favouable case whee the diffeence in tempeatue is maximum (10 C), and with a high loss tangent (1.5), the pedicted maximum eo on the measued eal DC is about 10% of its value, coesponding to an eo in soil moistue of about 4% v/v at 30% v/v and 5% v/v at 40% v/v. In geneal, the tempeatue measued by the soil moistue senso is a good estimate of the 0-5cm soil tempeatue that can be used fo the tempeatue coection. The tempeatue coection of equation (1) is applied to the measued eal DC of the NAFE 06 dataset. Results obtained with the geneal and loss-coected equation of Seyfied et al. (2005) ae then compaed in Fig. 5a and 5b. The use of the loss tangent educes the oot mean squae eo of the pedicted soil moistue fom 4.0% to 3.3% v/v. This impovement confims the existing coelation between the loss tangent and the change in the measued eal DC among soil types Figue 3. Loss tangent (tan ) vesus soil moistue at six stations of the Muumbidgee netwok in Sping Cuves wee geneated fom best-fit polynomial equations fo each soil. Figue 4. Roving vesus station-based soil tempeatue measuements fo thee diffeent days duing NAFE 06: a typically cold (16 Nov), dy (9Nov) and wet (13 Nov) day. and entails the assumption that the loss tangent can be appoximated to the loss tangent at satuation fo the calibation. The loss-coelated paamete A lc is then fitted to the NAFE 06 data set. A linea egession between the measued A and tan gives A lc = -4.3 tan With the new slope, the oot mean squae eo of the loss-coected equation is slightly deceased to 3.1% v/v. A thid ode polynomial egession between the soil moistue computed by the manufactue s calibation equation and obsevations is deived ( )/100 and esults ae plotted in Fig. 5c. The oot mean squae eo of the pedicted soil moistue is 2.7% v/v, which epesents the best fit among the fou calibation equations poposed. Howeve, when suing the whole NAFE 06 data set to compae the polynomial and the loss-coected equations (see Fig 5c), one obseves that the soil moistue

6 pedicted by the polynomial egession stongly satuates at about 25% v/v. This finding is consistent with the esults obtained in the laboatoy, and pesented in Fig. 2. In fact, the best fit obtained with the polynomial fit is an atefact of the NAFE 06 soil and moistue conditions. The soil in the NAFE 06 study aea is elatively homogeneous (mainly clayey), and the ange of soil moistue values measued duing the expeiment was elatively low. It is expected that the polynomial equation (o any equation fit to the senso measued soil moistue) would induce systematic eos with soils that ae nonepesentative of whole aea (in paticula sand fo NAFE) and fo soil moistue values above 25% v/v. In this egads, the multi-soil calibation equation of Seyfied et al. (2005) with the tempeatue coection developed hee is a moe obust appoach fo an opeational application. 6. APPLICATION The calibation equation of Seyfied et al. (2005) including the coection fo tempeatue effect deived in this pape is applied to the NAFE data with the assumption of a constant loss tangent. As the calibation of the slope with the NAFE 06 data did not significantly impove the accuacy of the pedicted soil moistue (eo of 3.1% instead of 3.3%), the slope of Seyfied et al. (2005) is used instead of the calibated one. An illustation of the calibated data is povided in Fig. 6. The soil moistue maps obtained on 13, 14 and 16 Novembe 2006 at thee fams Y2, Y9 and Y12 ae pesented. A ainfall of about 15mm occued in the sampling aea on Novembe. The geneal dying of the study aea is clealy visible fom an aveage of about 25% v/v on 13 Novembe down to 15% v/v on 16 Novembe. Ove the dying peiod, the spatial vaiability within fams Y9 and Y12 is mainly due to iigated cops; Y2 is dy land pastue while Y9 and Y12 ae copping fams with some iigated cops (maize and wheat). Satuated soils ae appaent in the iigated aeas at the south-west cone of Y9 and the middle of Y12. To assess the impact of loss tangent on calibated data, loss tangent is computed on the wettest day of the field campaign (13 Novembe). Only the HDAS measuement points with a soil moistue value highe than 30% v/v ae used, giving an aveage of soil moistue of about 35% v/v fo Y2, Y9 and Y12. The computed loss tangent vaies fom 0.7 to 2.2 in Y12 (mean 1.2), fom 0.3 to 1.8 in Y9 mean (1.0) and fom 0.4 to 1.1 in Y2 (mean 0.9). The pedicted maximum diffeence in soil moistue between the minimum (0.3) and Figue 5. Diffeent calibation equations: in a) the geneal equation; in b) the loss-coected equation; in c) the polynomial equation. In d), the polynomial equation is plotted against the losscoected equation with the whole NAFE 06 data set. Figue 6. Example of nea-suface soil moistue maps using the calibation equations pesented in this pape. maximum (2.2) loss tangent is evaluated to be about 8% and 10% v/v at 30% at 40% v/v soil moistue espectively. 7. CONCLUSION The objective of this study was to evaluate the impact of soil type and tempeatue on the senso esponse and test the applicability of a geneal calibation equation to the NAFE data set. The analysis is based on fou distinct data sets, one

7 collected in the field (NAFE 06) and thee in the laboatoy with both NAFE 05 and NAFE 06 soil samples. The tempeatue effect on the soil wate senso esponse was evaluated with sand and clay in a ange of moistue conditions. With sand, the tempeatue appeas to have a negligible effect with the lagest tempeatue diffeence (15 C) estimated to have only about 1% v/v impact on the soil moistue value. With clay, the obseved tempeatue effect is moe significant with a soil moistue change up to 4% v/v. It is found that with ou data set the manufactue s algoithm inceases the obseved tempeatue effect on the measued eal DC. A simple coection was then deived based on the obseved elationship between the elative effect on the eal DC and loss tangent. The geneal and loss-coected calibation equations of Seyfied et al. (2005) wee applied to the tempeatue-coected dielectic constant, and compaed to obsevations. Results indicated that the computed loss tangent is able to explain most of the vaiability among soil types. The RMSE of the pedicted soil moistue is educed fom 4.0% to 3.3% v/v. A thid-ode polynomial egession between the manufactue-simulated and the obseved soil wate content gives the best oveall accuacy with a RMSE of 2.7%. The losscoected equation is howeve moe obust than the polynomial egession fo diffeent soil types, and soil moistue values above 25% v/v. The tempeatue coection and the loss-coected equation have been applied to the NAFE data set. As an illustation of the calibated data, a time seies of soil moistue maps at 250m esolution ae pesented. The tempoal and spatial vaiability is high with nea-suface soil moistue values coveing the full ange fom nea 0 to 40%. Such spatial data will povide the gound tuth that can be used fo calibation/validation of hydologic models and emote sensing techniques. 8. ACKNOWLEDGEMENT We wish to thank Daniele Biasioni and Hannah Meade fo thei lab wok, and all the NAFE paticipants fo field calibation and data collection. The National Aibone Field Expeiments have been made possible though ecent infastuctue (LE and LE ) and eseach (DP ) funding fom the Austalian Reseach Council, and the collaboation of a lage numbe of scientists fom thoughout Austalia, United States and Euope. Initial setup and maintenance of the study catchments was funded by eseach gants (DP , DP and DP ) fom the Austalian Reseach Council, the CRC fo Catchment Hydology, and NASA. 9. REFERENCES Cosh, M.H., Jackson, T.J., Bindlish, R., Famiglietti, J.S., and Ryu, D., Calibation of an impedance pobe fo estimation of suface soil wate content ove lage egions. Jounal of Hydology, 311: Panciea, R., Melin, O., Young, R., and Walke, J.P, The Hydapobe Data Acquisition System (HDAS): Use guide. Repot, Univesity of Melboune. Seyfied, M., and Mudock M., Measuement of soil wate content with a 50-MHz soil dielectic senso. Soil Sci. Soc. Am. J., 68: Seyfied, M.S., and Mudock, M.D., Effects of soil type and tempeatue on soil wate content measuements using a soil dielectic senso. P1-13. In I.C. Paltineanu (ed.) Fist intenational symposium on soil wate measuement using capacitance and impedance, Beltsville, MD. 6-8 Nov Seyfied, M.S., Gant, L.E., Du, E. and Kumes, K., Dielectic Loss and Calibation of the Hyda Pobe Soil Wate Senso Seyfied et al. Vadose Zone J., 4: Vitel, Inc Hyda soil moistue pobe use s manual. Vesion1.2. Vitel Inc., Chantilly, VA. Walke, J.P., Hacke, J.M., Kalma, J.D., Kim, E.J. and Panciea, R., National Aibone Field Expeiments fo Pediction in Ungauged Basins. In A. Zege and R. M. Agent (Eds), MODSIM 2005 Intenational Congess on Modelling and Simulation. Modelling and Simulation Society of Austalia and New Zealand, Decembe 2005, Walke, J.P., Melin, O., Panciea, R. and Kalma, J.D., National Aibone Field Expeiments fo Soil Moistue Remote Sensing, 30th Hydology and Wate Resouces Symposium [CD-ROM]. The Institute of Enginees Austalia, Launceston, Austalia, 4-8 Decembe, 2006.