Clay minerals, smectites above all, have a very large specific surface, and the first layers of water adsorbed on it are not free to rotate with the field. Their permittivity is far below that of bulk water, so a given sensor reading corresponds to more water in a clay than in a sand (Saarenketo, 1998). Clays also conduct electricity through their exchangeable cations. At the frequencies used by capacitive sensors, which are commonly well below those of time domain reflectometry, conduction and interfacial polarisation add to the apparent permittivity, and the effect grows as frequency falls (Robinson et al., 2003). Laboratory work on a widely used low-cost sensor found its response to electrical conductivity and temperature to be small at its operating frequency of 70 MHz (Kizito et al., 2008), but sensors that run at lower frequencies are less well protected, and an independent evaluation of a sensor of this class reported measurable effects of temperature, conductivity and supply voltage (Bogena et al., 2007).

Temperature acts in two directions. The permittivity of free water falls as it warms, while bound water is released from surfaces and conductivity rises, so the net temperature response of a clay can be positive where that of a sand is negative (Wraith and Or, 1999). A sensor at shallow depth therefore shows a daily wave that is not a change in water content. An evaluation of a 50 MHz sensor likewise found that its response differed between soils, most of all in those rich in clay, which points to soil-specific calibration (Seyfried and Murdock, 2004).

A swelling clay changes volume as it dries. Over much of the range the loss of volume nearly equals the volume of water lost, the soil surface subsides, and cracks open (Bronswijk, 1988). Two consequences follow. A crack or a thin air gap beside an electrode lowers the reading sharply, because the sensor is most sensitive to the material closest to it. And the dry bulk density of the soil matrix rises as water content falls, so the conversion from gravimetric to volumetric water content, which multiplies by bulk density, cannot use a single value measured once (Grossman and Reinsch, 2002). A calibration for a clay must determine volume and mass on the same sample every time.

Sensors of one model do not respond identically. Before installation each sensor is read in air and in water at a recorded temperature, and where possible in one or two liquids of intermediate permittivity, following the approach used to quantify sensor-to-sensor variability (Rosenbaum et al., 2010). Sensors whose readings fall well outside the group are set aside. The spread of the remainder is kept, because it sets a floor under the uncertainty of any calibration that will be applied to sensors other than those calibrated.

Installation is done when the soil is moist and plastic, so that the prongs can be pressed into the wall of a small pit or the base of an auger hole without leaving a gap. At least three sensors are placed at each depth of interest, far enough apart for cores to be taken between them later. A soil temperature sensor is installed at the same depth. The pit is backfilled in layers to its original density, and the site is left through one wetting event before sampling starts, so that the soil closes around the sensors.

The calibration is only as wide as the range of water contents sampled. The plot is wetted to saturation by ponding, then allowed to dry under the crop or under a rain shelter, and cores are taken on six to ten occasions spread from the wettest to the driest condition the sensors will meet. On each occasion two or three cores are cut with thin-walled rings of known volume at the depth of the sensors and within a short horizontal distance of them, in the manner laid down for volumetric sampling (ISO, 2001). The sensor output and the soil temperature are logged at the moment of sampling, and the readings are taken at the same hour each time to limit the diurnal temperature effect. When cracks have formed, cores are taken from the intact soil between cracks, and the presence and width of cracks near the sensors are noted.

Each core is sealed in the field, weighed moist, dried in a ventilated oven at 105 °C until its mass is constant, and weighed again. Gravimetric water content is the mass of water lost divided by the oven-dry mass, bulk density is the oven-dry mass divided by the ring volume, and volumetric water content is their product divided by the density of water (Gardner, 1986). Because the ring fixes the volume at the moment of sampling, the bulk density obtained is the one that applied at that water content. Smectitic clays retain some structural water at 105 °C and take a long time to reach constant mass. The convention is kept nonetheless, so that results are comparable with other work, and the drying time actually needed is established on a few trial cores.

The paired values of sensor output and volumetric water content are plotted before anything is fitted. Three forms are then compared: a straight line in raw output, a second-order polynomial, and a line in the square root of apparent permittivity where the sensor reports it, which corresponds to the refractive index mixing model and has been used to calibrate a common capacitive sensor in sands from two reference points (Sakaki et al., 2008). Soil temperature is tested as an additional term and retained only if it clearly reduces the residual scatter. The simplest equation whose residuals show no trend with water content is preferred. Higher-order polynomials are avoided, since they behave unpredictably at the ends of the range, which are the conditions that trigger irrigation decisions.

A calibration judged on the data used to fit it looks better than it is. Before fitting, the cores from one or two sampling occasions near the middle of the range, or from one of the replicate sensors, are set aside. The fitted equation is applied to these and the differences between predicted and gravimetric values are summarised by their mean, which estimates bias, and by the root mean square error. A plot of each difference against the mean of the two values, with limits of agreement, shows whether the error depends on wetness (Bland and Altman, 1986). The same statistics are computed for the manufacturer's equation, so that the gain from calibrating is stated and not assumed.

The report gives the soil classification, clay content and mineralogy if known, the sensor model and firmware, the range of water content and temperature covered, the bulk density at each sampling, the equation with the standard errors of its coefficients, and the validation statistics. The uncertainty of the reference itself, which combines the tolerances of the ring volume and the balance with the scatter between replicate cores, is stated following the conventions of the international guide (JCGM, 2008). An equation is not to be used outside the range of water contents over which it was fitted, and the report says so.