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Application of TDR to water level measurement
Journal of Hydrology 236 (2000) 252–258 www.elsevier.com/locate/jhydrol
Technical note
Application of TDR to water level measurement A. Thomsen*, B. Hansen, K. Schelde Danish Institute of Agricultural Sciences, Department of Crop Physiology and Soil Science, PO Box 50, DK-8830 Tjele, Denmark Received 2 March 2000; accepted 14 July 2000
Abstract A specialised time domain reflectometry (TDR) probe for measuring water level in tanks collecting surface runoff was developed, calibrated and field-tested. The water level probe — in the form of a slightly modified soil moisture probe — was developed as part of a TDR measuring system designed for continuous monitoring of soil water content and surface runoff in plot studies of water erosion and sediment transport. A computer algorithm for the analysis of TDR traces from the new probe was developed and incorporated into existing software for automated acquisition and analysis of TDR data. Laboratory calibration showed that water level could be measured with sufficient accuracy (standard deviation ⬍2 mm) for a range of applications in hydrology. Soil erosion is typically a short duration process closely linked to soil moisture content and rainfall intensity. A major benefit of integrating time critical measurements of surface runoff and soil moisture into a single system is the synchronisation of measurements. Measurements were made on a regular schedule except during rainfall events when the measuring rate depended on rainfall intensity. In a parallel calibration study it was shown that the performance of the TDR probe was comparable to a commercial ultrasonic liquid level sensor used for measuring runoff at an erosion site not instrumented for automated TDR measurements. 䉷 2000 Elsevier Science B.V. All rights reserved. Keywords: Time domain reflectometry; Water depth; Water level; Water erosion; Probe design
1. Introduction Time domain reflectometry (TDR) instrumentation is widely used in hydrology and soil science for accurate and flexible measurement of soil water content. Water content is measured using suitable measuring probes of varying design (Topp et al., 1984; Zegelin et al., 1989), with the ‘global’ Topp (Topp et al., 1980) or a locally derived calibration function (Roth et al., 1992; Jacobsen and Schjønning, 1993) relating TDR measured soil dielectric constant to volumetric water content. TDR measurements can be made manually or automatically using computer * Corresponding author. Fax: ⫹45-89-991-619. E-mail address: [email protected] (A. Thomsen).
software (Baker and Allmaras, 1990; Heimovaara and Bouten, 1990; Thomsen, 1994). Only automated TDR systems are practical for projects where short duration processes such as surface runoff and water erosion are investigated. The development of a new type of TDR probe for measuring water level was initiated in order to integrate time critical measurements of near surface water content and volume of surface runoff into a single automated system. The water level probe — in the form of a slightly modified two-wire soil moisture probe — was designed for measuring water level in square tanks placed below ground level at the downslope end of field plots. Plot layout, soil tillage, crops and selected results of the field erosion studies are discussed by Hansen et al. (1996).
0022-1694/00/$ - see front matter 䉷 2000 Elsevier Science B.V. All rights reserved. PII: S0022-169 4(00)00305-X
A. Thomsen et al. / Journal of Hydrology 236 (2000) 252–258
Water level was determined by measuring the distance between the probe head placed at a known distance above the bottom level and the water level in the tank. Because of impedance changes at the beginning of the probe and at the air–water interface, the length of probe above water level could be estimated from the recorded TDR trace using suitable software. Employing much longer transmission lines in the form of insulated cables or wires, Dowding and Huang (1994) were able to measure ground water pressure in piezometric tubes up to 15 m deep, using a similar approach to locate both the air–water interface and the end of the transmission line. An alternative approach would have been to design a probe for measuring water depth directly with reference level below the water surface. This approach would have been preferable because of the much lower propagation velocity of the TDR pulse in water than in air (1:9) and the limited time resolution of the Tektronix 1502 cable tester (Tektronix Inc., Beaverton, OR, USA) used as TDR instrument. Direct measurement of water depth is however not feasible when the medium is a mixture of water and sediments with unknown pulse propagation velocity instead of sediment-free water with known dielectric properties. Further, the pulse propagation velocity in water is temperature dependent requiring the temperature to be monitored and corrected for in the analysis. The accumulation of silt on the bottom of the tanks also complicated the use of other submerged sensors such as pressure transducers that were considered because of their simplicity and moderate costs.
253
significant negative slope whether water is present or not simplifying software development. The probe is connected to the cable tester or the multiplexer of a multiprobe system using 50 V coaxial cable (Belden no. 9907, Belden, Richmond, IN, USA). The coaxial cable and probe rods made from 3 mm stainless steel wire are connected using a 50/200 V (1:4) balun transformer made as described by Spaans and Baker (1993). The balun transformer is included in order to match the impedances of the coaxial cable and the probe and convert from unbalanced to balanced transmission lines. An approximate matching of the impedances is important for reducing signal losses. Spaans and Baker (1993) provide a detailed discussion of baluns in TDR probes. Probes of lengths up to 1.2 m have been tested, but longer probes are possible because of the small transmission losses in air. The probe head is made from polyoxymethylene (POM; generally available as Delrin), machined to hold the probe components in place during assembly. After soldering, the cavity is filled with a twocomponent adhesive to bond the probe together and waterproof it. In Fig. 2a the trace produced by the probe is shown together with the other graphical output produced by the acquisition and
2. Probe design and trace analysis The water level probe shown in Fig. 1a was designed much like a two-wire balanced soil moisture probe (Topp et al., 1984), the only difference being the probe rods forming a closed loop instead of an open fork that allows insertion into the soil. The closed loop probe was chosen because of mechanical stability (no spacers necessary for lengths up to 1.2 m) and the similarity of signals from the shorted end of the probe and an air–water interface. The end reflection has a
Fig. 1. (a) Isometric drawing of water level probe. Materials are Delrin plastic and 3 mm stainless steel wire. An impedance matching (50/200 V) pulse transformer is placed between the coaxial cable and probe wires in a cavity machined in the Delrin block. The cavity is filled with a two-component adhesive after parts have been soldered together. The placement of the probe in the collection tank and an idealised trace are shown in (b) and (c), respectively.
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analysis software used with the water level probe, as well as with soil moisture probes of several designs (Thomsen, 1994). The end of the probe section measuring in air is located at the intersection of two short regression lines fitted to trace segments bordering the signal from the air– water interface as discussed by Heimovaara and Bouten (1990). If the tank is empty, the end reflection is similar and the same procedure can be applied. The beginning of the probe is located at the intersection of a regression line and a horizontal line through the local trace maximum (not shown in
Fig. 2a). The beginning of the probe is located at the impedance discontinuity where cable, balun transformer and probe rods are soldered together rather than at the face of the Delrin block, necessitating probe calibration. Maximum and minimum points on the first derivative trace are used for locating the trace segments used for fitting the regression lines. After the beginning of probe and the air–water interface have been located, the length of probe above the water surface is calculated assuming a relative pulse velocity of 1 as for vacuum.
Fig. 2. (a) An example of a TDR trace recorded during laboratory calibration of the water level probe. The trace is shown together with other output from the software developed for general TDR acquisition and analysis (details provided in the main text). The beginning and end of the active trace are shown using vertical lines. The probe was attached to the cable tester using a short (1 m) coaxial cable. (b) The same data as shown in (a); the only difference is 15 m of coaxial extension cable added to the 1 m probe cable used in (a). The trace has been analysed using the same software parameters as used in (a). The heavily filtered look of the recorded trace is due to dispersion in the long cable of the step pulse generated by the TDR instrument.
A. Thomsen et al. / Journal of Hydrology 236 (2000) 252–258
3. Calibration of TDR probe and acoustic water level probe Erosion plots were located at two sites with contrasting soil types (Hansen et al., 1996). Only one of the sites could be instrumented with an automated TDR station due to the relatively high costs of TDR equipment. The other site was instrumented with ultrasonic liquid level probes connected to a conventional data logger for continuous recording of water levels. Soil water content was monitored periodically using manual TDR measurements (Thomsen, 1994). A calibration study was planned in order to calibrate and evaluate the two approaches to water level measurements. A prototype 1 m long TDR water level probe was placed in a 1.3 m tall, clear Plexiglas cylinder with an inside diameter of 25 cm. A steel measuring tape was placed inside the cylinder with the scale clearly readable through the Plexiglas wall. An ultrasonic liquid level probe, PL-396 (Milltronics, Peterborough, Ontario, Canada) was placed at the centre of the top of the same cylinder for calibration and comparison with TDR. The acoustic instrument outputs a 4–20 mA current proportional to measuring distance. No calibration function was available for the instrument. Transducer output was recorded as a voltage difference across a 100 V shunt resistor using a quality multimeter as readout instrument. Water was gradually added to the cylinder and water depth visually read to the nearest millimetre using the measuring tape and recorded together with the voltage output from the acoustic sensor and TDR measurements made with five replications. In Fig. 3a mean TDR measured water depth is shown together with the depth visually measured using the steel tape placed inside the cylinder. TDR measurements were converted from distance between probe head and water surface to water depth directly by subtracting individual measurements from an initial measurement made before any water was added. As water was added and the length of probe in air was reduced, the cable tester settings were gradually changed so the active trace occupied most of the screen (and the digitised trace acquired by the PC software). In Fig. 3a, a second-order polynomial has been least-
255
squares fitted to the data and plotted together with the residuals. Standard error was 1.6 mm with no apparent trend in the residuals. The fitting of a first-order polynomial resulted in a higher standard error (2.5 mm) and a trend in the residuals. This effect is likely due to the non-systematic changing of trace analysis parameters with changing trace resolution. In a later version of the software, an option will allow the parameters to be automatically scaled according to the settings of the cable tester. In Fig. 3b measurements made using the acoustic sensor have been analysed analogous to the TDR measurements. Standard error was 1.4 mm for a second-order polynomial comparable to TDR measurements. No systematic trend in the residuals was evident.
4. Effects of long sensor cables From experimentation with TDR probes for measuring soil water content, it was known that cable length strongly affects the waveform of a given probe due to degraded rise time of the reflected pulse from long cables (Tektronix, 1987). In Fig. 2a and b the waveforms of the TDR depth probe with 1 m of coaxial cable and 15 m of additional cable are shown together. It is seen how the longer rise time due to the longer cable resulted in traces with a smoothed appearance. Both traces shown in Fig. 2 were analysed using the computer algorithm previously discussed and identical parameters. From a limited experiment, it was concluded that the additional 15 m of sensor cable did not seriously degrade measurements if the parameters of the algorithm were optimised for the degraded trace. The length (vertical projection) of the regression lines shown in Fig. 2 was found to be especially critical and should be increased to compensate for the lower slope of degraded traces. For applications where cables longer than the 15 m used in this study are required, standard RG 58 coaxial cable should be replaced by more expensive low loss cable. Tests have shown that traces from a relatively short soil moisture probe connected to the TDR instrument using 50 m of RG 214 coaxial cable were well defined and could readily be analysed. The tanks to be monitored in the field erosion
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Fig. 3. (a) Depth measurements (closed symbols) made under laboratory conditions. TDR measurements are shown together with manual measurements of water depth made in a clear Plexiglas cylinder. A second-order polynomial has been least-squares fitted to the measurements. Standard error is 1.6 mm. There is no apparent trend in the residuals (open symbols). (b) Depth measurements (voltage output) made together with the measurements shown in (a), using a commercial ultrasonic liquid level probe (‘The Probe’, Milltronics PL-396). Standard error using a second-order polynomial is 1.4 mm. There is no apparent trend in the residuals (open symbols).
project had a spacing requiring up to 15 m long cables. To simplify trace analysis, the four TDR depth probes to be used in the experiment were all made with 15 m long sensor cables. After workshop assembly the four depth probes were calibrated in the laboratory as previously discussed for the prototype probe. Measurements were made using the multiplexed TDR system (Thomsen and Thomsen, 1994) and associated control software to be installed in the field after probe calibration. Initially the cable tester controls were adjusted manually so that the trace from
the probes placed together in the empty calibration cylinder extended across the entire display. During calibration the settings were left unchanged to resemble the field measuring situation. The major calibration results are given in Table 1. Both firstand second-order polynomials were fitted to the data resulting in negligible differences in standard deviations. No trend in the residuals was found. This result supports the discussion of the trend in residuals observed in the calibration of the prototype probe.
A. Thomsen et al. / Journal of Hydrology 236 (2000) 252–258 Table 1 Calibration of four identical water depth probes with 15 m of standard RG 58 coaxial sensor cables. Regression relationship: Water depth in cm a ⫹ b × TDR measured distance from probe head to water surface in cm. The b value is less than 1 for all probes. This can partly be explained by the relative velocity of the TDR pulse in atmospheric air being slightly less than unity as was assumed in the calculation of TDR distance. The standard error (Std) in cm is relatively high because of the long sensor cables Probe no.
a
b
Std
1 2 3 4
92.87 94.53 93.47 93.22
⫺0.991 ⫺0.993 ⫺0.984 ⫺0.988
0.29 0.24 0.34 0.25
Although the probes were carefully made to have identical dimensions, Table 1 shows that the total TDR measured length (a) of the probes differs by more than 1 cm. Most of this spread is due to length differences inside the probe head where the cable, the unwieldy balun transformer and the probe rods are connected. The standard deviations are larger than
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found in the initial calibration experiment because the cable tester was not adjusted here for maximum trace resolution and because of the long sensor cables and multiplexing used.
5. Field measurements Fig. 4 shows soil moisture and water level measurements during three days for one of the erosion field plots. The TDR system was connected to a tipping bucket-type rain gauge and the sampling interval was reduced from 2 h to 15 min during and for some time after — depending on the intensity — rainfall events. In Fig. 4 TDR and rainfall data are shown using a common 2 h resolution for direct comparison. During periods with sub-zero temperatures and the formation of significant ice cover in the collection tanks, the measurements were seriously degraded because of the much lower contrast in dielectric constant between air and ice than between air and free water.
Fig. 4. Three days of selected measurements made in a 66.3 m 2 erosion plot at Research Centre Foulum in 1994. Measurements of water content for the 0–20 cm profile (vertical probe) and at a depth of 5 cm (horizontal probe) are shown together with water level measurements made in a 1.35 m 2 collection tank and local measurements of rainfall. Time resolution is 2 h for all measurements.
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6. Summary and conclusions Initial calibration of a prototype TDR probe for measuring water depth showed that water depth could be measured with sufficient accuracy — both with short and long sensor cables — for field application in water erosion studies. Surface runoff and water erosion are typically short duration processes most readily monitored by a system integrating both measurements of soil moisture and runoff dynamics. The specialised TDR probe resembling a balanced soil moisture probe can be made in a moderately equipped workshop and has proven reliable in the field under adverse winter conditions. Measurements are however degraded when the water in runoff collection tanks starts to freeze because of the low dielectric constant of ice relative to that of unfrozen water. A quality commercial acoustic water level probe performed equally well — or slightly better — under laboratory conditions, but has shown degraded performance in the field because of temperature sensitivity although the instrument corrects for temperature and is rated for low temperature operation. References Baker, J.M., Allmaras, R.R., 1990. System for automating and multiplexing soil moisture measurements by time domain reflectometry. Soil Sci. Soc. Am. J. 54, 1–6. Dowding, C.H., Huang, F.-C. 1994. Ground water pressure measurement with time domain reflectometry. Proceedings of the Symposium and Workshop on Time Domain Reflectometry in Environmental, Infrastructure, and Mining Applications, Northwestern University, Evanston, IL, September 7–9, 1994. Hansen, B., Sibbesen, E., Schjønning, P., Thomsen, A., Hasholt, B.
1996. Surface runoff, erosion and loss of sediment and phosphorous — Danish plot studies. In: Kronvang, B., Svendsen, L.M., Sibbesen, E. (Eds.), Phosphorus and sediment. Erosion and delivery, transport and fate of sediments and sediment-associated nutrients in watersheds. Proceedings from an International Workshop held in Silkeborg, Denmark, October 9–12, 1995. Ministry of Environment and Energy. 150pp. NERI Technical Report No. 178, pp. 29–32. Heimovaara, T.J., Bouten, W., 1990. A computer-controlled 36-channel time domain reflectometry system for monitoring soil water contents. Water Resour. Res. 26, 2311–2316. Jacobsen, O.H., Schjønning, P., 1993. A laboratory calibration of time domain reflectometry for soil water measurement including effects of bulk density and texture. J. Hydrol. 151, 147–157. Roth, C.H., Malicki, M.A., Plagge, R., 1992. Empirical evaluation of the relationship between soil dielectric constant and volumetric water content as the basis for calibrating soil moisture measurements by TDR. J. Soil Sci. 43, 1–13. Spaans, E.J.A., Baker, J.M., 1993. Simple baluns in parallel probes for time domain reflectometry. Soil Sci. Soc. Am. J. 57, 668–673. Tektronix 1987. Tektronix metallic TDRs for cable testing. Application Note. Tektronix Inc., Redmond, OR, USA. Thomsen, A. 1994. Program AUTOTDR for making automated TDR measurements of soil water content. User’s Guide. SP Report No. 38, Danish Institute of Agricultural Sciences, Tjele, Denmark. Thomsen, A., Thomsen, H., 1994. Automated TDR measurements: control box for Tektronix TSS 45 relay scanners. SP-Report No. 10, Danish Institute of Agricultural Sciences, Tjele, Denmark. Topp, G.C., Davis, J.L., Annan, A.P., 1980. Electromagnetic determination of soil water content: measurement in coaxial transmission lines. Water Resour. Res. 16, 574–582. Topp, G.C., Davis, J.L., Bailey, W.G., Zebchuck, W.D., 1984. The measurement of soil water content using a portable TDR hand probe. Can. J. Soil Sci. 64, 313–321. Zegelin, S.J., White, I., Jenkins, D.R., 1989. Improved field probes for soil water content and electrical conductivity measurement using time domain reflectometry. Water Resour. Res. 25, 2367–2376.
Technical note
Application of TDR to water level measurement A. Thomsen*, B. Hansen, K. Schelde Danish Institute of Agricultural Sciences, Department of Crop Physiology and Soil Science, PO Box 50, DK-8830 Tjele, Denmark Received 2 March 2000; accepted 14 July 2000
Abstract A specialised time domain reflectometry (TDR) probe for measuring water level in tanks collecting surface runoff was developed, calibrated and field-tested. The water level probe — in the form of a slightly modified soil moisture probe — was developed as part of a TDR measuring system designed for continuous monitoring of soil water content and surface runoff in plot studies of water erosion and sediment transport. A computer algorithm for the analysis of TDR traces from the new probe was developed and incorporated into existing software for automated acquisition and analysis of TDR data. Laboratory calibration showed that water level could be measured with sufficient accuracy (standard deviation ⬍2 mm) for a range of applications in hydrology. Soil erosion is typically a short duration process closely linked to soil moisture content and rainfall intensity. A major benefit of integrating time critical measurements of surface runoff and soil moisture into a single system is the synchronisation of measurements. Measurements were made on a regular schedule except during rainfall events when the measuring rate depended on rainfall intensity. In a parallel calibration study it was shown that the performance of the TDR probe was comparable to a commercial ultrasonic liquid level sensor used for measuring runoff at an erosion site not instrumented for automated TDR measurements. 䉷 2000 Elsevier Science B.V. All rights reserved. Keywords: Time domain reflectometry; Water depth; Water level; Water erosion; Probe design
1. Introduction Time domain reflectometry (TDR) instrumentation is widely used in hydrology and soil science for accurate and flexible measurement of soil water content. Water content is measured using suitable measuring probes of varying design (Topp et al., 1984; Zegelin et al., 1989), with the ‘global’ Topp (Topp et al., 1980) or a locally derived calibration function (Roth et al., 1992; Jacobsen and Schjønning, 1993) relating TDR measured soil dielectric constant to volumetric water content. TDR measurements can be made manually or automatically using computer * Corresponding author. Fax: ⫹45-89-991-619. E-mail address: [email protected] (A. Thomsen).
software (Baker and Allmaras, 1990; Heimovaara and Bouten, 1990; Thomsen, 1994). Only automated TDR systems are practical for projects where short duration processes such as surface runoff and water erosion are investigated. The development of a new type of TDR probe for measuring water level was initiated in order to integrate time critical measurements of near surface water content and volume of surface runoff into a single automated system. The water level probe — in the form of a slightly modified two-wire soil moisture probe — was designed for measuring water level in square tanks placed below ground level at the downslope end of field plots. Plot layout, soil tillage, crops and selected results of the field erosion studies are discussed by Hansen et al. (1996).
0022-1694/00/$ - see front matter 䉷 2000 Elsevier Science B.V. All rights reserved. PII: S0022-169 4(00)00305-X
A. Thomsen et al. / Journal of Hydrology 236 (2000) 252–258
Water level was determined by measuring the distance between the probe head placed at a known distance above the bottom level and the water level in the tank. Because of impedance changes at the beginning of the probe and at the air–water interface, the length of probe above water level could be estimated from the recorded TDR trace using suitable software. Employing much longer transmission lines in the form of insulated cables or wires, Dowding and Huang (1994) were able to measure ground water pressure in piezometric tubes up to 15 m deep, using a similar approach to locate both the air–water interface and the end of the transmission line. An alternative approach would have been to design a probe for measuring water depth directly with reference level below the water surface. This approach would have been preferable because of the much lower propagation velocity of the TDR pulse in water than in air (1:9) and the limited time resolution of the Tektronix 1502 cable tester (Tektronix Inc., Beaverton, OR, USA) used as TDR instrument. Direct measurement of water depth is however not feasible when the medium is a mixture of water and sediments with unknown pulse propagation velocity instead of sediment-free water with known dielectric properties. Further, the pulse propagation velocity in water is temperature dependent requiring the temperature to be monitored and corrected for in the analysis. The accumulation of silt on the bottom of the tanks also complicated the use of other submerged sensors such as pressure transducers that were considered because of their simplicity and moderate costs.
253
significant negative slope whether water is present or not simplifying software development. The probe is connected to the cable tester or the multiplexer of a multiprobe system using 50 V coaxial cable (Belden no. 9907, Belden, Richmond, IN, USA). The coaxial cable and probe rods made from 3 mm stainless steel wire are connected using a 50/200 V (1:4) balun transformer made as described by Spaans and Baker (1993). The balun transformer is included in order to match the impedances of the coaxial cable and the probe and convert from unbalanced to balanced transmission lines. An approximate matching of the impedances is important for reducing signal losses. Spaans and Baker (1993) provide a detailed discussion of baluns in TDR probes. Probes of lengths up to 1.2 m have been tested, but longer probes are possible because of the small transmission losses in air. The probe head is made from polyoxymethylene (POM; generally available as Delrin), machined to hold the probe components in place during assembly. After soldering, the cavity is filled with a twocomponent adhesive to bond the probe together and waterproof it. In Fig. 2a the trace produced by the probe is shown together with the other graphical output produced by the acquisition and
2. Probe design and trace analysis The water level probe shown in Fig. 1a was designed much like a two-wire balanced soil moisture probe (Topp et al., 1984), the only difference being the probe rods forming a closed loop instead of an open fork that allows insertion into the soil. The closed loop probe was chosen because of mechanical stability (no spacers necessary for lengths up to 1.2 m) and the similarity of signals from the shorted end of the probe and an air–water interface. The end reflection has a
Fig. 1. (a) Isometric drawing of water level probe. Materials are Delrin plastic and 3 mm stainless steel wire. An impedance matching (50/200 V) pulse transformer is placed between the coaxial cable and probe wires in a cavity machined in the Delrin block. The cavity is filled with a two-component adhesive after parts have been soldered together. The placement of the probe in the collection tank and an idealised trace are shown in (b) and (c), respectively.
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A. Thomsen et al. / Journal of Hydrology 236 (2000) 252–258
analysis software used with the water level probe, as well as with soil moisture probes of several designs (Thomsen, 1994). The end of the probe section measuring in air is located at the intersection of two short regression lines fitted to trace segments bordering the signal from the air– water interface as discussed by Heimovaara and Bouten (1990). If the tank is empty, the end reflection is similar and the same procedure can be applied. The beginning of the probe is located at the intersection of a regression line and a horizontal line through the local trace maximum (not shown in
Fig. 2a). The beginning of the probe is located at the impedance discontinuity where cable, balun transformer and probe rods are soldered together rather than at the face of the Delrin block, necessitating probe calibration. Maximum and minimum points on the first derivative trace are used for locating the trace segments used for fitting the regression lines. After the beginning of probe and the air–water interface have been located, the length of probe above the water surface is calculated assuming a relative pulse velocity of 1 as for vacuum.
Fig. 2. (a) An example of a TDR trace recorded during laboratory calibration of the water level probe. The trace is shown together with other output from the software developed for general TDR acquisition and analysis (details provided in the main text). The beginning and end of the active trace are shown using vertical lines. The probe was attached to the cable tester using a short (1 m) coaxial cable. (b) The same data as shown in (a); the only difference is 15 m of coaxial extension cable added to the 1 m probe cable used in (a). The trace has been analysed using the same software parameters as used in (a). The heavily filtered look of the recorded trace is due to dispersion in the long cable of the step pulse generated by the TDR instrument.
A. Thomsen et al. / Journal of Hydrology 236 (2000) 252–258
3. Calibration of TDR probe and acoustic water level probe Erosion plots were located at two sites with contrasting soil types (Hansen et al., 1996). Only one of the sites could be instrumented with an automated TDR station due to the relatively high costs of TDR equipment. The other site was instrumented with ultrasonic liquid level probes connected to a conventional data logger for continuous recording of water levels. Soil water content was monitored periodically using manual TDR measurements (Thomsen, 1994). A calibration study was planned in order to calibrate and evaluate the two approaches to water level measurements. A prototype 1 m long TDR water level probe was placed in a 1.3 m tall, clear Plexiglas cylinder with an inside diameter of 25 cm. A steel measuring tape was placed inside the cylinder with the scale clearly readable through the Plexiglas wall. An ultrasonic liquid level probe, PL-396 (Milltronics, Peterborough, Ontario, Canada) was placed at the centre of the top of the same cylinder for calibration and comparison with TDR. The acoustic instrument outputs a 4–20 mA current proportional to measuring distance. No calibration function was available for the instrument. Transducer output was recorded as a voltage difference across a 100 V shunt resistor using a quality multimeter as readout instrument. Water was gradually added to the cylinder and water depth visually read to the nearest millimetre using the measuring tape and recorded together with the voltage output from the acoustic sensor and TDR measurements made with five replications. In Fig. 3a mean TDR measured water depth is shown together with the depth visually measured using the steel tape placed inside the cylinder. TDR measurements were converted from distance between probe head and water surface to water depth directly by subtracting individual measurements from an initial measurement made before any water was added. As water was added and the length of probe in air was reduced, the cable tester settings were gradually changed so the active trace occupied most of the screen (and the digitised trace acquired by the PC software). In Fig. 3a, a second-order polynomial has been least-
255
squares fitted to the data and plotted together with the residuals. Standard error was 1.6 mm with no apparent trend in the residuals. The fitting of a first-order polynomial resulted in a higher standard error (2.5 mm) and a trend in the residuals. This effect is likely due to the non-systematic changing of trace analysis parameters with changing trace resolution. In a later version of the software, an option will allow the parameters to be automatically scaled according to the settings of the cable tester. In Fig. 3b measurements made using the acoustic sensor have been analysed analogous to the TDR measurements. Standard error was 1.4 mm for a second-order polynomial comparable to TDR measurements. No systematic trend in the residuals was evident.
4. Effects of long sensor cables From experimentation with TDR probes for measuring soil water content, it was known that cable length strongly affects the waveform of a given probe due to degraded rise time of the reflected pulse from long cables (Tektronix, 1987). In Fig. 2a and b the waveforms of the TDR depth probe with 1 m of coaxial cable and 15 m of additional cable are shown together. It is seen how the longer rise time due to the longer cable resulted in traces with a smoothed appearance. Both traces shown in Fig. 2 were analysed using the computer algorithm previously discussed and identical parameters. From a limited experiment, it was concluded that the additional 15 m of sensor cable did not seriously degrade measurements if the parameters of the algorithm were optimised for the degraded trace. The length (vertical projection) of the regression lines shown in Fig. 2 was found to be especially critical and should be increased to compensate for the lower slope of degraded traces. For applications where cables longer than the 15 m used in this study are required, standard RG 58 coaxial cable should be replaced by more expensive low loss cable. Tests have shown that traces from a relatively short soil moisture probe connected to the TDR instrument using 50 m of RG 214 coaxial cable were well defined and could readily be analysed. The tanks to be monitored in the field erosion
256
A. Thomsen et al. / Journal of Hydrology 236 (2000) 252–258
Fig. 3. (a) Depth measurements (closed symbols) made under laboratory conditions. TDR measurements are shown together with manual measurements of water depth made in a clear Plexiglas cylinder. A second-order polynomial has been least-squares fitted to the measurements. Standard error is 1.6 mm. There is no apparent trend in the residuals (open symbols). (b) Depth measurements (voltage output) made together with the measurements shown in (a), using a commercial ultrasonic liquid level probe (‘The Probe’, Milltronics PL-396). Standard error using a second-order polynomial is 1.4 mm. There is no apparent trend in the residuals (open symbols).
project had a spacing requiring up to 15 m long cables. To simplify trace analysis, the four TDR depth probes to be used in the experiment were all made with 15 m long sensor cables. After workshop assembly the four depth probes were calibrated in the laboratory as previously discussed for the prototype probe. Measurements were made using the multiplexed TDR system (Thomsen and Thomsen, 1994) and associated control software to be installed in the field after probe calibration. Initially the cable tester controls were adjusted manually so that the trace from
the probes placed together in the empty calibration cylinder extended across the entire display. During calibration the settings were left unchanged to resemble the field measuring situation. The major calibration results are given in Table 1. Both firstand second-order polynomials were fitted to the data resulting in negligible differences in standard deviations. No trend in the residuals was found. This result supports the discussion of the trend in residuals observed in the calibration of the prototype probe.
A. Thomsen et al. / Journal of Hydrology 236 (2000) 252–258 Table 1 Calibration of four identical water depth probes with 15 m of standard RG 58 coaxial sensor cables. Regression relationship: Water depth in cm a ⫹ b × TDR measured distance from probe head to water surface in cm. The b value is less than 1 for all probes. This can partly be explained by the relative velocity of the TDR pulse in atmospheric air being slightly less than unity as was assumed in the calculation of TDR distance. The standard error (Std) in cm is relatively high because of the long sensor cables Probe no.
a
b
Std
1 2 3 4
92.87 94.53 93.47 93.22
⫺0.991 ⫺0.993 ⫺0.984 ⫺0.988
0.29 0.24 0.34 0.25
Although the probes were carefully made to have identical dimensions, Table 1 shows that the total TDR measured length (a) of the probes differs by more than 1 cm. Most of this spread is due to length differences inside the probe head where the cable, the unwieldy balun transformer and the probe rods are connected. The standard deviations are larger than
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found in the initial calibration experiment because the cable tester was not adjusted here for maximum trace resolution and because of the long sensor cables and multiplexing used.
5. Field measurements Fig. 4 shows soil moisture and water level measurements during three days for one of the erosion field plots. The TDR system was connected to a tipping bucket-type rain gauge and the sampling interval was reduced from 2 h to 15 min during and for some time after — depending on the intensity — rainfall events. In Fig. 4 TDR and rainfall data are shown using a common 2 h resolution for direct comparison. During periods with sub-zero temperatures and the formation of significant ice cover in the collection tanks, the measurements were seriously degraded because of the much lower contrast in dielectric constant between air and ice than between air and free water.
Fig. 4. Three days of selected measurements made in a 66.3 m 2 erosion plot at Research Centre Foulum in 1994. Measurements of water content for the 0–20 cm profile (vertical probe) and at a depth of 5 cm (horizontal probe) are shown together with water level measurements made in a 1.35 m 2 collection tank and local measurements of rainfall. Time resolution is 2 h for all measurements.
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6. Summary and conclusions Initial calibration of a prototype TDR probe for measuring water depth showed that water depth could be measured with sufficient accuracy — both with short and long sensor cables — for field application in water erosion studies. Surface runoff and water erosion are typically short duration processes most readily monitored by a system integrating both measurements of soil moisture and runoff dynamics. The specialised TDR probe resembling a balanced soil moisture probe can be made in a moderately equipped workshop and has proven reliable in the field under adverse winter conditions. Measurements are however degraded when the water in runoff collection tanks starts to freeze because of the low dielectric constant of ice relative to that of unfrozen water. A quality commercial acoustic water level probe performed equally well — or slightly better — under laboratory conditions, but has shown degraded performance in the field because of temperature sensitivity although the instrument corrects for temperature and is rated for low temperature operation. References Baker, J.M., Allmaras, R.R., 1990. System for automating and multiplexing soil moisture measurements by time domain reflectometry. Soil Sci. Soc. Am. J. 54, 1–6. Dowding, C.H., Huang, F.-C. 1994. Ground water pressure measurement with time domain reflectometry. Proceedings of the Symposium and Workshop on Time Domain Reflectometry in Environmental, Infrastructure, and Mining Applications, Northwestern University, Evanston, IL, September 7–9, 1994. Hansen, B., Sibbesen, E., Schjønning, P., Thomsen, A., Hasholt, B.
1996. Surface runoff, erosion and loss of sediment and phosphorous — Danish plot studies. In: Kronvang, B., Svendsen, L.M., Sibbesen, E. (Eds.), Phosphorus and sediment. Erosion and delivery, transport and fate of sediments and sediment-associated nutrients in watersheds. Proceedings from an International Workshop held in Silkeborg, Denmark, October 9–12, 1995. Ministry of Environment and Energy. 150pp. NERI Technical Report No. 178, pp. 29–32. Heimovaara, T.J., Bouten, W., 1990. A computer-controlled 36-channel time domain reflectometry system for monitoring soil water contents. Water Resour. Res. 26, 2311–2316. Jacobsen, O.H., Schjønning, P., 1993. A laboratory calibration of time domain reflectometry for soil water measurement including effects of bulk density and texture. J. Hydrol. 151, 147–157. Roth, C.H., Malicki, M.A., Plagge, R., 1992. Empirical evaluation of the relationship between soil dielectric constant and volumetric water content as the basis for calibrating soil moisture measurements by TDR. J. Soil Sci. 43, 1–13. Spaans, E.J.A., Baker, J.M., 1993. Simple baluns in parallel probes for time domain reflectometry. Soil Sci. Soc. Am. J. 57, 668–673. Tektronix 1987. Tektronix metallic TDRs for cable testing. Application Note. Tektronix Inc., Redmond, OR, USA. Thomsen, A. 1994. Program AUTOTDR for making automated TDR measurements of soil water content. User’s Guide. SP Report No. 38, Danish Institute of Agricultural Sciences, Tjele, Denmark. Thomsen, A., Thomsen, H., 1994. Automated TDR measurements: control box for Tektronix TSS 45 relay scanners. SP-Report No. 10, Danish Institute of Agricultural Sciences, Tjele, Denmark. Topp, G.C., Davis, J.L., Annan, A.P., 1980. Electromagnetic determination of soil water content: measurement in coaxial transmission lines. Water Resour. Res. 16, 574–582. Topp, G.C., Davis, J.L., Bailey, W.G., Zebchuck, W.D., 1984. The measurement of soil water content using a portable TDR hand probe. Can. J. Soil Sci. 64, 313–321. Zegelin, S.J., White, I., Jenkins, D.R., 1989. Improved field probes for soil water content and electrical conductivity measurement using time domain reflectometry. Water Resour. Res. 25, 2367–2376.