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eason of this is the fact that water particles are bound by soil solid phase, which decreases the mobility of water dipoles. The equations (70), (71), (73) and (74) present four models describing the soil refractive index, n, in the function of selected soil properties. These models were verified by the comparison of model calculated values of n with the experimental ones measured with the use of Time Domain Reflectometry technique. Fig. 29 displays the results of this verification. The values of R 2 and S yx and the convergence of the trend line with the 1 : 1 line is the best for model III. This model generates the n values, which are closest to the measured ones. Model I, presently used as a calibration basis [29] in TDR soil water content measurement, generates values with the poorest correlation with the measured ones. Models II and IV are in the middle as far as goodness of fit is analyzed. The best of the analyzed models is the model III described by (73). Taking into account the soil bulk density, ρ, decreases the standard deviation, S yx , almost twice as much as in the model I, which has only soil water content, θ, as the independent variable. Model IV with two independent variables: soil water content, θ, and porosity, φ, generates theoretical values of n slightly worse correlated with the measured values than model III. The presented models allow determination of soil water content from the measurement of soil refractive index. The relation θ(n), with only one independent variable, can be found by conversion of (70), ie from the model I: θ = 0.134n − 0.182 (75) TDR _ I Relation θ (n,ρ) can be found by conversion of the (71), ie from the model III: 0.573 − 0.582ρ θ _ = n − TDR III (76) 7.755 + 0.792ρ with two independent variables: n and ρ. The equation (76) is proposed as the calibration formulae of the TDR soil water content because of the best correlation of data. Fig. 30B presents the comparison of the soil water content values, θ TDR , received from the model III with the reference values, θ, and measured by the thermo-gravimetric method. The slope equal to one, almost no offset of the trend line and low value of the standard error of estimation, S yx , verifies model III as the calibration equation of the reflectometric measurement of volumetric water 77
content. The similar values for model I presented in Fig. 30A show bigger dispersion of results generated by the actually used calibration function (70). 1,2 1,2 A θ TDR_I = 0,996θ + 0,002 θ TDR_III = θ + 2E-05 1,0 R 2 = 0,924, S yx = 0,055 R 2 1,0 = 0,984, S yx = 0,024 B 0,8 0,8 θ TDR_I 0,6 θ TDR_III 0,6 0,4 0,4 0,2 0,0 1 : 1 line trend line 0,0 0,2 0,4 0,6 0,8 1,0 1,2 θ 0,2 1 : 1 line trend line 0,0 0,0 0,2 0,4 0,6 0,8 1,0 1,2 θ Fig. 30. Comparison of the values of soil water content, θ TDR , calculated from the measured values of soil refractive index, n, for model I – A and model III – B with the reference values determined by the thermogravimetric method Equation (77) presents the soil water content values determined by TDR on the base of model I as the function of directly measured values of time distance between the appropriate reflections from the TDR probe. c t θ TDR = 0.134 − 0.182 (77) 2L The derivative of (77) on time, t, is: c ∆θ TDR = 0.134 ∆t (78) 2L where: ∆θTDR = ( θTDR −θ ) is the absolute error of the TDR measured soil water content, and ∆t is the absolute error of the propagation time measurement. For the practical TDR sensor length L =10 -1 m, and the absolute error of time measurement ∆ t=30·10 -12 [s], the absolute error of soil water content measurement resulted from the hardware and software imperfections of TDR meter is: 78
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TDR METHOD FOR THE MEASUREMENT OF W
Page 4 and 5:
PREFACE The importance of water for
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CONTENTS 1. Status of water as an s
Page 8 and 9:
12.2. New prototype version of FOM/
Page 10 and 11:
that stimulate the phenomena and pr
Page 12 and 13:
The solution to the problem of elec
Page 14 and 15:
3. ELECTRICAL MEASUREMENTS METHODS
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v = c 1 2L = = ( θ ) n ∆t ε (2)
Page 18 and 19:
The TDR probe consists of two waveg
Page 20 and 21:
ε a =1 and φ=0.5 the Eq. (10) has
Page 22 and 23:
The experiment description is given
Page 24 and 25:
Results obtained with the discussed
Page 26 and 27:
Notice that at C s = 0, ie when dis
Page 28 and 29: water orientation polarization [s],
Page 30 and 31: Fig. 8. Frequency dispersion of the
Page 32 and 33: The measurements were performed in
Page 34 and 35: 5. EVALUATION OF DIELECTRIC MIXING
Page 36 and 37: ε α = ∑V α iε i (29) i where
Page 38 and 39: where SAND and CLAY are percents of
Page 40 and 41: Below the transition value, the soi
Page 42 and 43: To verify the observations concerni
Page 44 and 45: 6. TEMPERATURE EFFECT ON SOIL DIELE
Page 46 and 47: chamber and the freezer, only one w
Page 48 and 49: The user interface on the main comp
Page 50 and 51: soil sample volumetric water conten
Page 52 and 53: close vicinity of the analyzed obje
Page 54 and 55: process of measurement is non-destr
Page 56 and 57: dielectric permittivity change caus
Page 58 and 59: The values of the refractive index
Page 60 and 61: The relative, ∆n/∆T, and absolu
Page 62 and 63: Fig. 25. The temperature effect on
Page 64 and 65: The temperature effect of TDR soil
Page 66 and 67: The purpose of the above discussion
Page 68 and 69: ( ,25 + T )( 45 + T ) 49 9 f rel =
Page 70 and 71: 8. THE ACCURACY OF SOIL WATER CONTE
Page 72 and 73: gravimetric method and the soil ref
Page 74 and 75: where: a 0 ÷ a 6 are coefficients
Page 76 and 77: values of p F calculated for the re
Page 80 and 81: 9 ∆θ = 0,2 ⋅10 ⋅ ∆t = 0.00
Page 82 and 83: values of θ rel for lower values o
Page 84 and 85: 9. COMPARISON OF OPEN-ENDED COAX AN
Page 86 and 87: ε" = EC ε d " + (82) 2π fε wher
Page 88 and 89: dielectric permittivity, the dielec
Page 90 and 91: The applied lumped capacitance mode
Page 92 and 93: stainless steel wires soldered to t
Page 94 and 95: ε’ Open Coax and ε b-TDR , exce
Page 96 and 97: − − The difference of the imagi
Page 98 and 99: Integrated Circuit) recently introd
Page 100 and 101: 10.2. Electromechanical microwave s
Page 102 and 103: RF1. Two PIN diodes in series in ea
Page 104 and 105: The significant aspect of the proto
Page 106 and 107: visible for lower values of soil el
Page 108 and 109: In the TDR method the signal propag
Page 110 and 111: description of functional and techn
Page 112 and 113: MASTER modules are wireless transce
Page 114 and 115: time the Real Time Clock module wak
Page 116 and 117: ase station distinguishes A SLAVE d
Page 118 and 119: sensor, format the data received fr
Page 120 and 121: 12. SOIL WATER STATUS MONITORING DE
Page 122 and 123: D-LOG/mpts is a moisture/pressure/t
Page 124 and 125: For compatibility reasons it uses t
Page 126 and 127: D-LOG/mts (Fig. 59) is a TDR (Time-
Page 128 and 129:
12.4. FP/m, FP/mts - Field Probe fo
Page 130 and 131:
inside of a separate polyethylene b
Page 132 and 133:
differential water capacity and the
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− maximum number of LP/p probes t
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12.7. LP/t - Laboratory Probe for s
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From the collected data set, after
Page 140 and 141:
25. de Loor G.P.: Dielectric proper
Page 142 and 143:
TDR. Symposium on Time Domain Refle
Page 144 and 145:
100. Whalley W.R.: Considerations o
Page 146 and 147:
Fig. 14. Fig. 15. Fig. 16. Fig. 17.
Page 148 and 149:
Fig. 38. The three-rod TDR probe -
Page 150 and 151:
Fig. 67. A set of LP/ms and LP/p LO
Page 152:
Table 17. An example of the executa
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