Performance Evaluation of Volumetric Water Content and Relative Permittivity Models

Table 1

Summary of all equations of 𝜀-𝜃 relationship.

Equations	Source	Experimental method	Soil type	Properties of soil
				Porosity; (cm^3cm^−3)	Bulk density; (g cm^−3)	Particle density; (g cm^−3)
Model with one parameter
(1a)			(i) Mineral soil; (ii) Organic soil; (iii) Vermiculite; (iv) Glass beads	—	(i) 1.04–1.44; (ii) 0.422; (iii) 1.08; (iv) 1.49–1.61	—
(1b)	Topp et al. [22]	ε: using TDR Tektronik Model 7S12 to perform 18 experiments with different treatments; θ: using gravimetric technique
(1c)			Organic soil	—	0.422	—
(1d)			450 μm glass beads	—	1.60–1.61	—
(2a)	Roth et al. [21]	ε: TDR miniprobe 250 ps rise time needle pulse; θ: gravimetric technique	9 Mineral soils	0.418–0.482	1.26–1.55	2.28–2.67
(2b)			7 Organic soils	0.527–0.785	0.2–0.77	0.70–1.63
(3)	Ferré et al. [25]	Using model of inverse averaging for TDR method by analysing the mixing model	—	—	—	—
(4)	Schaap et al. [29]	ε: TDR Tektronix 1502B; θ: gravimetric technique	25 samples of forest floors	—	0.086–0.263	1.3
(5)	Curtis [18]	Coaxial Transmission/reflection apparatus controlled by a Hewlett-Packard 8510C Vector Network Analyzer system 45 MHz to 26.5 GHz	—	—	—	—
(6)	Wu et al. [20]	ε: based on capacitance measurement; θ: gravimetric technique	Quartz sand	—	—	—
Model with two parameters
(7a)	Wang and Schmugge [30]	Modelling using data from other studies [34–36]	22 different samples	0.4–0.6	1.1–1.7	2.6–2.75
(7b)
(8a)	Roth et al. [21]	TDR	From 11 different field sites
(8b)
(9)	Malicki et al. [23]	TDR CAMI	62 kinds of soil samples	0.33–0.95	0.13–1.66	1.06–2.7
(10)	Gardner et al. [19]	Capacitance probe 80–150 MHz	(i) Brown earths; (ii) Silica materials	—	(i) 1.08–1.49; (ii) 1.24–1.63	—
(11)	Robinson et al. [14]	TDR Tektronix 1502B	Coarse grained, quartz grain, sandy soil	—	—	—