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# Why TDR vs. capacitance may be missing the point

## When considering which soil water content sensor will work best for any application, it’s easy to overlook the obvious question: what is being measured?

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When considering which soil water content sensor will work best for any application, it’s easy to overlook the obvious question: what is being measured?  Time domain reflectometry (TDR sensor) vs. capacitance sensor technology is the right question for a researcher who is looking at the dielectric permittivity across a wide measurement frequency spectrum (called dielectric spectroscopy). There is important information in these data, like the ability to measure bulk density along with water content and electrical conductivity. If this is the desired measurement, currently only one technology will do: TDR. The reflectance of the electrical pulse that moves down the conducting rods contains a wide range of frequencies. When digitized, these frequencies can be separated by the fast Fourier transform and analyzed for additional information.

The objective for the majority of scientists, however, is to simply monitor soil water content instantaneously or over time, with good accuracy, which means a complex and costly TDR sensor system may not be necessary.

## The theory behind both techniques

Capacitance sensor and TDR sensor techniques are often grouped together because they both measure the dielectric permittivity of the surrounding medium. In fact, it is not uncommon for individuals to confuse the two, suggesting that a given probe measures water content based on TDR sensor technology when it actually uses capacitance sensor technology. Below is a clarification of the difference between the two techniques.

The capacitance sensor technique determines the dielectric permittivity of a medium by measuring the charge time of a capacitor, which uses that medium as a dielectric. We first define a relationship between the time, t, it takes to charge a capacitor from a starting voltage, Vi to a voltage Vf with an applied voltage, Vf.

where R is the series resistance and C is the capacitance. The charging of the capacitor is illustrated in Figure 1:

If the resistance and voltage ratio are held constant, then the charge time of the capacitor, t, is related to the capacitance according to

For a parallel plate capacitor, the capacitance is a function of the dielectric permittivity (k) of the medium between the capacitor plates and can be calculated by

where A is the area of the plates and S is the separation between the plates. Because A and S are also fixed values, the charge time on the capacitor is a simple linear function (ideally) of the dielectric permittivity of the surrounding medium.

Soil probes are not parallel plate capacitors, but the relationship shown in Equation 3 is valid whatever the plate geometry. Time domain reflectometry (a TDR sensor) determines the dielectric permittivity of a medium by measuring the time it takes for an electromagnetic wave to propagate along a transmission line that is surrounded by the medium. The transit time (t) for an electromagnetic pulse to travel the length of a transmission line and return is related to the dielectric permittivity of the medium, k , by the following equation

where L is the length of the transmission line and c is the speed of light (3 x 108 m s in a vacuum). Thus, the dielectric permittivity is calculated

Therefore, the propagation time of the electromagnetic wave along the TDR sensor is only a function of the square of the transit time and a fixed value (c/2L). Because c and L are a constant and a fixed length, respectively, TDR sensor measurements are theoretically less susceptible to soil and environmental conditions compared to capacitance sensors. However, the interpretation of TDR sensor output can be a considerable source of error when high salinity diminishes the reflectance waveform or temperature changes the endpoint.

## Frequency makes a difference in accuracy

An oscillating voltage must be applied to a TDR sensor or capacitance sensor to measure the reflection or charge time in the medium. The frequency of the oscillation is important because it is widely accepted that low frequencies (<10 MHz) are highly susceptible to changes in salinity and temperature. Because there is no limit on the possible input frequencies for either technique, it is important to verify the frequency of the soil moisture device used.

Capacitance sensors manufactured by METER use high frequencies to minimize the effects of soil salinity on readings.  The frequencies used, however, are quite a bit lower than for TDR, typically 50 to 100 MHz.  The high frequency of the capacitance probes “sees” all of the water in the soil, while being high enough to escape most of the errors from soil salinity present in older capacitance probes. The circuitry in a capacitance sensor can be designed to resolve extremely small changes in volumetric water content, so much so, that NASA used capacitance sensor technology to measure water content on Mars. Capacitance sensors are lower in cost as they don’t require a lot of circuitry, allowing more measurements per dollar.

Like a TDR sensor, a capacitance sensor is reasonably easy to install. The measurement prongs tend to be shorter than a TDR sensor so they can be less difficult to insert into a hole. Capacitance sensors tend to have lower energy requirements and may last for years in the field powered by a small battery pack in a data logger.

## Errors are due to poor installation methods

In summary, though the theory behind the measurements is somewhat different, a TDR sensor and a capacitance sensor both measure dielectric permittivity to obtain volumetric water content. From a historic perspective, both TDR and capacitance have gained widespread acceptance, although some may perceive greater value in TDR compared to capacitance because of the extreme price difference. In general, reasonable measurements of volumetric water content can be obtained using either technique, and errors in measurements are often due more to poor installation methods than limitations in the techniques themselves.

## Questions?

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## New tool mistake-proofs sensor installation

The new TEROS Borehole Installation Tool reduces data uncertainty by mistake-proofing soil moisture sensor installation. Watch the video to see how it works.

Because of its mechanical advantage, the tool delivers consistent, flawless installation into any soil type (even hard clay) while minimizing site disturbance. Sensors are installed straight in and perpendicular with uniform pressure then gently released to prevent air gaps and preferential flow. This means the TEROS line of capacitance soil moisture sensors is able to deliver more accuracy with less uncertainty than similar sensors on the market.

## Installation tips for higher accuracy

Poor installation is the most common source of error in soil moisture data, but there are techniques that will ensure a perfect installation every time. Sensor installation expert, Chris Chambers, explains why you need a smarter soil moisture sensor installation and how to achieve it. Learn:

• What good soil moisture data look like
• How various installation issues show up in your data (i.e, air gaps, a loose sensor, soil type change, depths crossing)
• How to ensure an accurate installation
• How the new TEROS Borehole Installation Tool reduces air gaps and site disturbance while improving consistency
• What other scientists are doing to ensure a correct installation

## Get the complete picture

Everything you need to know about measuring soil moisture—all in one place.

## Take our soil moisture master class

Six short videos teach you everything you need to know about soil water content and soil water potential—and why you should measure them together.  Plus, master the basics of soil hydraulic conductivity.

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