Fundamentals and Perspectives on Soil Moisture Measurements

Master the fundamentals of soil mechanics.

In this webinar, Dr. Paolo Castiglione presents on soil mechanics and the theory behind soil moisture measurements.

Topics covered are:

  • The energy properties of soil and water.
  • Differences in TDR and capacitance measurements.
  • How to convert from dielectric permittivity to water content in soils.
  • Textural and environmental effects on soil moisture sensor measurements and how to overcome them.

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Our scientists have decades of experience helping researchers and growers measure the soil-plant-atmosphere continuum.


Dr. Paolo Castiglioni is a METER Group environmental scientist.


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Hello, and welcome to our seminar on soil moisture measurements. While there are many technologies that are available nowadays for measuring soil water content, in this seminar, we will focus specifically on those methods that rely on direct measurements, which by the way, represent the vast majority of the technology available on the market. We do so, for the very good reason that the soil dielectric properties are strongly affected by the presence of water. The rationale behind this is that the three components of soil or solid particle and water display very different. There are two properties we will talk at length and define what dielectric permittivity is, but if you accept for now, the fact that water has a value of dielectric permittivity much higher than the value of the other two components, air and solid particles. Then it is intuitive that the amount of water present in soil should somehow affect the overall permittivity of soil. This is the explanation that you may have heard over and over in your soil physics class or at seminars around the world, and it works well for explaining this relationship between soil dielectric permittivity and water content.

However, this explanation does not account for a number of problems that we often incur into when taking soil moisture measurements. In particular, one of the greatest problem is that water is not the only factor that affects soil dielectric permittivity. We will see other factors such as temperature or salinity may also have an effect and those represent the most common cause for errors in our measurements. Another aspect that is often overlooked is that we have mentioned the dielectric permittivity of water and stated that is much higher than the permittivity of the other component. In doing so, we may be thinking of the water that is contained in this beaker which we will refer to as free water. While it is important to remember that the water when is inside the soil, this displays physical properties which are very different in particular, the dielectric permittivity which may be very different than those corresponding to free water. Also, it is important to notice that the dielectric permittivity of soil is in general frequency dependent. We say the soil is a dispersion system. The result is that if we take measurements with different technology, each operating at a specific frequency, we will obtain different results. And so, we have to be careful when comparing results that are in fact obtained from different techniques. To explain all those factors and eventually to have a better understanding on how those measurements work, and eventually to obtain better measurements, it is important to go beyond the simple explanation we have given so far which you may be already familiar with, and take a closer look at what the dielectric permittivity of soil is.

So, it is my hope that by the end of this seminar, you will have a good understanding of what dielectric permittivity is, and in particular the dielectric permittivity of soil. Also, you should be able to have a fair understanding of the two main technologies we will be discussing today which are time domain reflectometry and capacitance sensors. We will talk about the influence of additional factors besides water content, and in particular we will examine one by one the effects of soil texture, salinity, and temperature. Also we will try to assess what is this expected accuracy- what is the accuracy we can expect from our measurements. And we will talk very briefly if we have time about calibration procedures, and other important yet not so technical aspects of soil moisture measurements such as installation procedure and data transmission. Before everything, we better understand what dielectric permittivity is.

Now, to have a good understanding, I like to compare our dielectric material with something we’re all familiar with, which is a conductor. Now, if we apply an electric field in a conductor, as you may know, there are particles that are free to move. For example, we can think of metal. Many of the electrons are indeed free. And so, upon the influence of an electric field, these electrons which of course, the charge will start moving, and this is what we call electric current. Now, let us consider the case of a dielectric material. Or if you like a material, well, we will refine this definition, but let’s think of something that does not conduct. Now, in this material, also, we have charged particles, positive and negative particles. The sum of it will be zero, so, the material overall is neutral. Now, when we apply an electric field, in this case, particles are not free to move, yet they undergo some sort of stretching, they deform. We can show these one more time. And you see how the particles are stretching.

Now, I’m going to take a close up of those particles, and in particular, I will be considering a neutral atom where the nucleus is surrounded by an electron cloud around it. Of course, the nucleus represents the positive charge and the electron cloud the negative. Now, when we apply an electric field, well, these two bodies with opposite charge will move in opposite directions. The result is that positive and negative charge, although their sum is zero, they are stretched. They are now located, they’re already organized in such a way that the center of mass of the two charges does no longer coincide. The result is what we call a dipole. We define the dipole moment as the product of the charges by their distance. If we understand what a dipole is, then we can define the dielectric permittivity as the ability of a material to form dipoles, or if you prefer to polarize under the influence of an electric field.

Here is the formula that relates the dipole moment to the dielectric permittivity of material. You will see we refer to epsilon naught as the permittivity of air or in vacuum, and the epsilon sub r is the relative permittivity. It’s developed permittivity relative to the value it attains in volume. Now, what you have seen so far is a one specific mechanism for the particles, the charged particles to reorganize under the factor of electric field, but not the only one, let us consider the important case of a water molecule. Now, as you may know water molecule is a dipolar molecule. That means that the water displays a permanent dipole, even though it is neutral, the arrangement of positive and negative charge in this case is such that a permanent dipole is formed. Now, if we consider under the effect a molecule under the effect of an electric field, we should expect some reorientation of this molecule. Of course, in the real reality, the orientation of the molecule is not as dramatic as displayed in my presentation, for it takes a very, very intense electric field to reorient the water molecule only a few degrees, but I think this is more intuitive to show it this way. So we have seen the behavior of one molecule.

Let’s consider now a group of other molecules, which have symbolized here with the arrows, each molecule represent an arrow, which is the dipole movement. And as you can see, although an individual with a molecule displays a dipole movement, if we take a group of molecules, and those molecules are oriented random, their dipole, the average dipole movement is zero as indicated here. That is the case when no electric field is present. But if we apply an electric field, then its molecule will orient in the same direction. The result is that now the average the electric field pardon me, the average dipole movement of this group of molecules is positive, is no longer zero. And so, this is a second mechanism of polarization. Now, a third and most interesting mechanism for polarization is what is known as the Maxwell Wagner polarization and it is a typical of heterogeneous systems.

Now, here we have an image showing soil where you can see the soil particles, I hope it’s clear enough and the water and air which is the white bubble right in the middle. Now, let’s take a closer look at the portion of this system that highlights all three phases. So, the soil particles the water and air, as you may know, soil water is far from being pure, there is a large number of soil dissolved in it. And here I have indicated with these two different colors, these soils have different charges. So ions and cations for applying electric field, you will expect the particles of different charge move in different directions and they will do so until they reach the interface whether it is the water gas interface or the water solid interface and in doing so, it is clear that a large dipole is formed because now we have a distribution of charge such that the center of mass of positive and negative and this is different and these dipoles can be very large compared for example to the permanent dipole of the water molecule. If you imagine that not only the amount of charge, but also the distance is an order of magnitude larger than the distance within one single water molecule.

This mechanism is also known as interfacial polarization because of the charges traveling until they find an interface. Now, these three mechanisms that we have described the polarization by the formation, orientation, or the interfacial, or Maxwell Wagner polarization, they all have something in common which is worth to mention here and that is that in each case, it takes energy to polarize our system. In other words, if we do not supply energy, for example, that molecule will not deform or if we consider an ensemble of water molecules, unless we do something, unless we supply energy, those molecules will be oriented at random and likewise the cations and anions in a water solution that will be distributed uniformly within it. And so, you can think of the polarization mechanism as a form of storing energy, very much like you can store energy when you compress a spring by applying a force. This is typical of polarization phenomena as opposed to that, in conduction phenomena, energy is not conserved. Energy is in fact dissipated. And this is another main difference between conduction and polarization phenomena. Something I would like to remark at this point is the distinction between conductors and dielectrics that is often to mark in perhaps for historical reasons. What I mean is that most of the materials are not perfectly conducted, or they don’t display the electric behavior exclusively, yet, they display both. They can polarize but also somewhat conduct current and so, it is one of them. So, it is definitely displays a strong dielectric behavior, and yet it can be sometimes a good conductor as well.

Another important aspect of polarization is the fact that this phenomenon is not instantaneous. To polarize it takes time. So, it is important to understand how the polarization phenomena will look like when we apply electrical field which are not constant in time, which is always the case. We will never apply a DC electric field. So, let us consider again the polarization by deformation example. And that let’s pay attention to slow down the process on purpose. So, let us pay attention to how long it takes for the system to polarize, you see, it takes a finite time. Now, if we excite the system with a different input, such as this one displayed to the left, where the electric field oscillates between, say a value of one and zero, a periodic interval, this is what we call a square wave, well then, let’s see what happens.

The deformation begins, but before it can complete, now, the field it goes back to zero. And so, the polarization cannot proceed any further. And the molecule that charges doesn’t have to go back to the original position and then follow up until you follow the field. So, the result is that the maximum amount of polarization here is less than that we were observed before. And this is because, simply we did not or the electrical field that was stimulating our system did not give our system enough time to polarize to the full extent. So, the message here is that the amount of polarization, it depends strongly on the frequency of the applied electric field.

The first technology we will be discussing now is the time domain reflectometry which is known as a TDR. Now, the rationale behind that technology is the very simple fact that the velocity of propagation of an electromagnetic wave through medium, it depends on the dielectric permittivity of such system through a formula, that simple formula that you’ve see before, that you see below where we have of course, the propagation velocity in a vacuum and the square root of the relative permittivity. So, based on that, if we want to measure the dielectric permittivity, all we need to do is to measure the propagation velocity of a given wave into the system. To do so, we usually, or TDR and TDR technology, we have a waveguide, a system where waves can propagate through.

In the waveguide in the case of TDR probably looks like this. And this is a typical setup of a TDR system where we recognize a pulse generator and we’d be not trying to get a dean input signal that travels in direction of the sample which is connected to the pulse generator through a coaxial cable. Once the signal reaches the sample it propagates through the end of the sample is reflected back. So, it travels back as indicated by the signal r. And in all these traveling back and forth all the voltage signals, we record the voltage at a given point. And we record these over time and this is why the technology is called time domain reflectometry (TDR). And here is a nice image that show the propagation of these bolts that signal. Pay attention to the shaded area that goes from the cable tester onto the sample. And you can see how it travels back is reflected and is sampled and the correspondingly the signal that we obtain looks like this. And that’s our wave going back and forth.

Now, how do we in practice measure the propagation velocity? Well we do so through something known as a travel time analysis, here again is a typical bolted signal from TDR system and we take a close look at a portion of the signal. And so, the beginning like or if you like the first reflection of the signal correspond to the time when the voltage signal first enters the sample. And this is a point in time that we can easily pinpoint. And the second reflection, where eventually the voltage signal goes up corresponds to the time when the wave reaches the end of the probe. And we usually pinpoint that time drawing two tangents on the curve and eventually we can obtain the travel time which have indicated with delta t or the time that it takes for the signal to go from the beginning of the probe to the end, since the length of the probe is known, and then we can easily estimate the propagation velocity because we know the travel time and therefore the dielectric permittivity which comes out with this simple formula.

And here you can see typical TDR signals obtained with systems at higher and higher water content. And so, in particular, we compare air dried sand with a fully saturated sand system and the third TDR signal corresponds to water or pure water. And so, you can see that as the dielectric permittivity or these three system becomes higher and higher. The travel time also indicated here with the L sub a becomes longer and longer. Another very important feature of TDR systems is that it allows to measure the electrical conductivity or sample. And here we consider four TDR waveforms. We are now exploring a time range larger than what we have before. So in particular, we’re considering the signal at a very long time and we know this that the signal reaches a plateau reaches a steady value and this value happens to be dependent on the electrical conductivity of the sample. Therefore, if we can measure that value of the signal a long time, we can estimate rather easily the electrical conductivity of the sample.

Another important aspect that needs to be kept in mind is that as the conductivity of the system becomes larger and larger, then this the signal undergoes energy dissipation, and this is the case and simply because as the signal as a voltage propagates, the voltage if the system is conductive, we will eventually induce electric current and to have it, it takes energy to have an electrical current. All this energy eventually is dissipated from the signal. The result is that if the system conductivity is too high, the signal becomes dissipated to the point that when it reaches the end of the probe, there is very little energy left and there is no reflection. There is too little energy for the reflection to take place. In that case the technology fields we cannot take TDR measurements when our sample is too salty or too conductive, and that is perhaps the most important limitation of TDR technology.

Now, let us describe briefly the other main technology that is available for measuring soil water content, which is the capacitance sensor. Now, the capacitance is defined as the ability to store electric charge into any arrangement of electrodes, when of course, a voltage difference is applied in between and so, here we consider for example, two plate electrodes and we have a different voltage in between and we observe some charge accumulated at the electrodes, and the ratio between charge and voltage is what define the capacitance of the system. Now, let us consider the same system, but let’s put some dielectric material in between. Now, if you remember what the polarization phenomena we have discussed before, it wouldn’t surprise you that in this case the electric field is lower than it was before, simply because the formation of dipoles within the electrical material neutralizes part of the surface charge that has naturally formed on electrodes. And the overall effect we may say that is to reduce the voltage, the effective voltage between the plates and therefore, the overall capacity of the system has gone up.

So, the introduction of a dielectric material in general has the effect to increase the capacity and there is a proportional relationship between the electoral property and the capacity that you see is present here. The proportionality constant is what we call the cell constant or geometry factor. Now, one important thing is that this geometry factor as the name suggests, depends on the geometry of the electrodes exclusively. And now we can consider two electrodes just like the ones that we saw before for TDR and in a cross section, the electric field will look like that, but we can consider or for example, the electric field as you have seen it in the example before, the one that is formed between two play capacitors or there are different configuration of electrodes like such as this one where electrodes, each electrode is a ring, and the electric field will look something completely different.

This is another remarkable difference of capacitance technology compared to TDR. In capacitance sensor we have the freedom to arrange our electrodes as it is most convenient as opposed to that with TDR, there are severe constraints on the shape that you can give to the electrodes. They must allow the propagation of the wave in a certain way. Once it is understood what capacitance is we may wonder how we can measure it. There are different kinds of capacitance sensors and different technologies. We will consider one specific and most common kind of sensors, the ones that measure the charging time. Now to better understand the functioning of such kind of capacitance sensors. It is helpful to consider the analogy between electric phenomena and hydraulic phenomena. In that case we may think rather than to have charge, we may think of water and so, the electric currents becomes water flow. And what we referred to as voltage in electric phenomena becomes of course pressure which is the driving force orders for water movement.

So, let us consider this a simple example that I have that I propose here, which is an empty container whose capacitance then represents the volume or if you prefer the cross section that is connected to a very large container through a pipe. That container to the left is so large that if water comes out of it, the height of the water level will not change. So let’s see what happens when we open the Dow that I have depicted here. Well, our tank fills up and it takes a certain time to fill up. So, now, let us consider a smaller thing. So, a system where the capacitance is smaller, and if we open the valve, again we fill it, but it takes less time. So, the idea is that if we want to measure the size of our tank, one possible way of doing so is by measuring the charging time we may set up a certain arbitrary threshold value and wonder value per meter of water level and we may wonder how long it takes before that water level is reached. And in doing so, we will recognize that the larger the capacitance and the longer it takes for the tank to fill up.

So, what happens when our sample is also conductive? It displays electrical conductivity. Well, in literature a sample that is conductive, it is often referred to as a leaky capacitor and that is a very appropriate definition. So, let us create a leak in our system by drilling a hole in our tank. And let’s see what happens when we try to fill it. As you can see, because of the leak or if, because of the electrical conductivity of the sample, the water level does not reach the same value it did before, also it takes longer. So, our method, the method that we have chosen, the one that base, the one that measures capacitance through measurements of the charging time, it runs into problems when our sample is conducted, because the quantity, the very quantity that we measure that is the charging time indeed is affected by the conductivity of the center. It’s important to remark this difference between TDR and capacitance sensor which is a main one.

With TDR technology what we measure is the travel time. As this image indicates we’re two signals or waveforms in two samples, one conductive and one non conductive are illustrated. The travel time that is not influenced if not a minimum in a way that is probably negligible by the conductivity of the sample. Another fundamental difference between TDR and capacitance technology is represented by the frequency at which these two technologies operate. Now with capacitance sensors, the frequency is quite precisely determined by the frequency at which the input signal operates, and so it is a fixed the well determined quantity. In modern capacitance sensors we are talking about a few tenths of megahertz. For example, the sensors that we produce at Decagon work at 70 megahertz, but it is not uncommon to see sensors on the market they may operate at 100 megahertz or so.

Unlike capacitance technologies TDR does not operate at a very specific frequency. This is because the effective frequency of a TDR system depends not only on the input signal that is applied to our system, but also depends on the electric and dielectric properties of the sample, and also on the hardware. In particular, it is strongly affected by the length of the TDR probe. As a result, we cannot speak of, well, determine effective frequency, but rather we can speak of a frequency range at which TDR operates, and values reported in literature and also some numerical tests that have been that I had performed myself in the past they indicate that reasonable range for the TDR system is in between .5 and 2 gigahertz. Once it is understood how the electric permittivity is measured, whether with TDR or capacitance sensor, we need to determine how okay, once it is clear how permittivity measurements are taken, whether with TDR or capacitance technology, we need to understand how those measurements can be used to estimate water content. In other words we need to investigate what is the relationship between the electric permittivity and water content.

The data that you see in this image represents the results from a very famous scientist Dr. Clark Topp who was pioneering soil water content measurements with TDR technology 1980. And the data correspond to four different soils, mostly coarse soils, although a fine soil was also included in the dataset. And also they were obtained with low values of pore water conductivity. Well, here we see a very strong correlation between water content and permittivity, which may induce to think that we could obtain some sort of universal relationship between the two quantities. Well, these are the dreams for a universal calibration function between permittivity and water content were perhaps broken a few years later, when Dr. Malicki 1996 published his data, which were obtained with different kinds of soils, and with the moderate to high values of salinities as well as clay content. Here we see a much larger scatter. And that indicates that a universal relationship between the two quantities is unlikely.

What is the reason for it, where the TDR sensor used by Dr Malicki perform in less than the one used by Dr topp, certainly not. It is simply the data appear like this simply because Dr Malicki in this experiment, he was considering different kinds of soils and was exploring certainly different kinds of bulk densities and salinities and clay content. So, it was adding additional factors to his experiments and apparently, the single measurement of permittivity cannot explain all those factors. So, let us formalize the problem by stating that the measured value of permittivity whether it is obtained through TDR or capacitance does not depend only on water content.

There are additional factors which I have listed here and we definitely must include the texture of our soil which can be represented by the particle size distribution or a better effective parameter maybe the specific surface area and also the bulk density certainly affects the permittivity. And these two quantities, temperature and bulk density typically do not change with time. I will refer to those as structural variables as opposed to those we have qualities that change with time under normal condition and I will refer to those as environmental variables. Among those we have water content of course, and also the electrical conductivity of the soil or if you prefer the salt concentration in the soil water and soil like any other material displays a relative permittivity which depends on temperature.

The problem that we’re facing is that a relationship between estimated permittivity and water content that works equally well for all values of structural or environmental variables simply does not exist. And this is because to put it in simple words, the single estimate, the permittivity at one single frequency does not contain enough information to allow us to estimate water contents under all these different conditions. So, there is an error that is intrinsic in our measurements and there is little we can do about it other than trying to assess this error. It is important to give us confidence in our measurements and to estimate what the expected accuracy could be. It is important for the analysis we will be developing here to understand the properties of water in proximity of the surface. Depending on the literature you are reading this water can be referred to as confined water or bound water or sometimes these are referred to as the absorbed water.

Whatever name we give to it, it is clear that this water behaves in a way that is different than the water away from the surface which is known as a bulk water and here we have an image in displaying an ensemble of water molecules and it is intuitive that the electrostatic and the thunderbolt forces at the surface somehow must affect the water which the water molecules which are in proximity with it. And here you see that the molecules are oriented in a way that if you like more organized is less chaotic compared to the organization that they have in bulk water. The structure of water molecules in proximity of the surface in fact, resembles somewhat the structure of ice. And in fact, often what we call to bound water is referred to ice at least as far as the electric permittivity goes.

And now, it is rather intuitive to expect the polarization phenomena in the groundwater to be slower than those that occurs in bulk water and this is due to these additional constraints that is represented by the surface water are not as free to move as they are in bulk water and therefore, whatever depolarization mechanism it will probably be slowed down by the presence of the surface. And so, if we consider that fact and also the fact that in a fine soil, the amount of surface is larger than in a coarse soil or if you like the specific surface area is much larger in a fine than in a coarse soil. And then you can expect dielectric permittivity spectrum, such as the one depicted here, where I compare the spectrum for a fine of course, with the spectrum observed in bulk water. Well as you can see, for fine soils, we have the relaxation or relaxation frequency much smaller than what it is observed for a coarse soil or for bulk.

In order to quantify the effect of the surface or the effect of soil textures, just like effects of the other additional factors we will be discussing here, it is important to avail ourselves of a model that can predict somehow the macroscopic permittivity of soil. I will be using in this presentation a simplified model that I have developed in the past and I will very briefly describe it here and by no means that this is meant to be a detailed description. So in our model the soil particle is represented by an ellipsoid and each solid particle is is surrounded by a water shell. What you see here is one individual particle and the soil is imagined to be formed by an ensemble of particles all identical, which are randomly oriented and are within an air background.

Now, the interesting aspects of the this model is that we can account for the different permittivity that bound water displays compared to the bulk water and in fact, here the water shell surrounding the particle is added one monomolecular layer at a time and each monomolecular layer displays specific permittivity or the two properties which depend from the distance to the surface and of course, also on temperature just like bulk water does. Now, if I and then going back to the model to work here we have represented our soil it may be worth the mention that the technique that was used to obtain the microscopic permittivity is known as a DEM which stands for differential effective medium is a technique proposed by Bruggeman in 1935. Now, we can use the model and we can predict the effects of texture on our permittivity spectrum. Here you see some 10 spectra representing different soils which vary from coarse to fine. All other variables are kept constant in the simulation and only the texture of our system is what we have changed.

So, what our measurements would look like in the systems that are represented by such spectrum. Again remember TDR and capacitance operate at different frequencies. It is apparent from this image that the frequency at which capacitance sensors operate, again we are choosing here 70 megahertz is such that as the texture changes, the estimates of permittivity change very little. Unlike capacitance sensors, TDR operates at a higher frequency range right where the variations are visible. And so, it is expected that the estimates through TDR technology display a larger scatter compared to capacitance sensors and this is in fact what we see here. Again, those are synthetic data, those are obtained through the model I have described before. One point that is worth remarking here is that, whether we estimate it through capacitance or TDR, the data reproduce quite closely the results that were obtained by Topp’s. I have reproduced here with a red line, the Topp’s equation and so, the fact that we were able to reproduce these results from first principle, get some confidence to our modeling efforts and to the analysis that we are proposing here.

Again, we may conclude that TDR suffers more than capacitance sensors when it comes to texture variability. Now, let us examine the remaining additional factor, let’s begin with the salinity effects or with the variability in soil electrical conductivity due to water content or to soil variations. Now, the effects of varying sample electrical conductivity is rather clear. The main effect is low frequencies and this is because the relaxation frequency for the Maxwell Wagner polarization turns out to depend quite strongly on the electrical conductivity and there is also a less pronounced effect in the high frequency range and this is because also the changing conductivity affects also the behavior of the bound water. Again, we want to- we’re interested in comparing estimates through TDR and capacitance sensors. So, again the typical frequency range is depicted and the results are shown here.

We see as expected that the largest effects are now seen through capacitance measurements and this is because it operates in the lower frequency range and therefore, it is most sensitive to interfacial polarization phenomena, which are then affected by EC. TDR estimates are barely affected by changing sample conductivity. And I have here indicated, I have shaded the portion of the graph as a reminder that the results here again are obtained through modeling. Those are synthetic data. In the real world, TDR technology will not work for salinities higher for sample conductivity higher than two to three decisiemens per meter. And so, I chose to cut to indicate a threshold line at two and a half decisiemens per meter indicating that TDR won’t work any way above those values. Capacitance estimates will work.

However, those estimates will be strongly affected by the conductivity. It is important to notice that the effect of sample EC is not the same. It changes if we go from a wet to a dry soil and also if we consider a coarse versus a fine soil. And these represent a major problem because of whatever the extent of the salinity effect is, is very hard to correct for unless independent information on soil texture or on soil moisture is available. Let us now spend a few words to discuss temperature effects, which are a big witness in field measurements and account for the large part of Earth that we observe in soil water content estimates. Now temperature affects soil permittivity in at least three ways. The first way is that temperature affects the permittivity of the water face, and as you may or you may not know, it does so with negative correlation. In other words, as the temperature goes up, the dielectric permittivity of water decreases. Also, it affects the conductivity of the water face, this time through a positive correlation. And this is important because the electrical conductivity will affect permittivity itself through the interfacial polarization phenomena. But also, it is important to remember that the fraction between bound water and bulk water is also somehow affected by temperature.

And now, this is better understood if we consider one more time the image is showing the difference between bulk water and free water. Whatever is the forces that attract the water molecules at the surface, it is intuitive to understand that such forces, such attraction is somewhat loosened when the temperature goes up. And so here the analogy between bound water and free water. It comes pretty handy. And so again, the distinction between bound and free water is not a sharp one. There are different degrees about water. But if we let such distinction to be dramatic and consider like two separate systems bound and free water. Now, it’s easy to imagine that when temperature goes up, the effects, the attraction from the surface is somewhat loosened. And so, some of that bound water starts to behave as a free water. A way to put it, if we consider the bomb water as a sheet of ice, we can see that when temperature goes up, these layer of ice becomes thinner and thinner, because some ice eventually melts into liquid water. Likewise, when temperature goes down, and then those attraction forces become more pronounced, and that means more and more water behaves as bound water or in other words, more and more liquid water becomes ice, becomes frozen water, which is what typically happens when temperature goes down.

Now, we have combined these three mechanisms that we have described the effects on the water permittivity and water conductivity and also the effect on the volume fraction about the free water and we have included all these in the model. And the result is what do you have displayed here, what do you see displayed here like when temperature goes up, in general, we observed a shift to the right of the relaxation frequency all the while the spectrum and the higher frequency tends to lower its values. And so again, let us compare the predicted estimates through TDR and capacitance.

These are the results, with TDR what we have here, we have chosen a reference value of permittivity which as obtained corresponds to the permittivity of 20 Celsius. And so, we just consider the variation of that estimate relative to the value 20 C when temperature changes between zero to 40 degrees. Now for TDR systems, the temperature effect may have a positive or a negative sign. In other words, the permittivity may go up or may go down as temperature increases. Typically, we find that in fine systems, especially when there is little water, the temperature effects are positive and this is because of the three mechanisms, the dominant one in those systems, where there is a lot of surface is the effects on the volume fraction of the bound water relative to free water. Whereas, when there is a little surface around the effects tend to be like those displayed by free water which means a negative effect. These results confirm many theoretical studies that have been proposed in the past by well great scientists and also confirms that the behavior is quite different for capacitance sensors in this case, the behavior is a lot more similar among the four cases that we have considered here compared to what happens for TDR. This is an advantage because if we were to attempt to correct for temperature effects, and then we’ll do so more successfully and without having to estimate the texture or the initial moisture of the system independently.

So with this we have concluded this sort of comparison between TDR and capacitance sensors. I am often asked when I go around and talk to scientists or to customers, whether TDR technologies is superior to capacitance and this seems to be the $1 million question. I don’t have the answer. I don’t think there is an answer because they perform so differently, and they have some negative aspects in some areas and positive in others. For example, capacitance sensors. The greatest problem is that they suffer very strongly from salinity effects. On the other hand, the TDR technology seems to cope little with the texture variability. And so it depends on the specific applications. But it is important to remember that capacitance sensors have evolved a great deal since the beginning of this technology, which it was about 20 years ago. And the fact is that the early sensors that were available, they were operating at frequencies that were very little, too little. And therefore, they were sensitive to the salinity effects, because again of the interfacial polarization phenomena in a way that was unacceptable. And to explain that behavior, I have reproduced the behavior of those early days sensors. In this case, I have used the frequency of 20 megahertz, but I’m told that some of the sensors were operating frequencies as little as one megahertz or 10 megahertz.

Now, as you can see, when that frequency is so little, and then the scatter between the permittivity and water content, it becomes very large and so, the expected error, it probably makes that technology unsuited for most practical application. So, the result is that if I may say the capacitance technology enjoys some bad reputation because of the first prototypes. It is clear now that the higher frequencies are beneficial and then so, as you can see, if we operate at 70 megahertz and if you look closely into the picture, that includes like the variability for all possible factors. That includes your variability of texture, salinity, temperature, and also soil density. And yet the model predicts an accuracy for these datasets, which is a +-5%, which is probably acceptable for most purposes.

I would like to conclude this presentation by spending just a few words on the installation process, which may account for a good portion of the costs of soil monitoring setup. In fact, most often the cost associated with installation is superior to the cost of the equipment itself. So, it’s some aspects that should always be kept in mind. There are many different options available and depending on the specific application and field condition and kind of measurements that are desired. And here I have shown some which I refer to as a permanent installation example.

But also it is possible to take measurements through non permanent installations such as the push and read sensors, or like profile probes, which are typically non permanent, they’re installed in the ground through an access tube. So that the sensor itself can be removed easily and brought to different locations. Now, in each case, it is important in my opinion, one of the most important aspects to consider is the gap between electrodes and soil. What is to be avoided at all cost is the formation of air gaps. In other words, we need a very firm contact between the metal electrodes and the soil. And here I have some image of a contraption that I have developed in the past for installing probes up to two meters underground. And we were here trying to assess the performance of a capillary barrier on the landfill and with the proper setup and of course, this is a rather expensive setup, because we were featuring about 29 sensors from surface about two meters, but, we were successful in what we could monitor the very movement of water through the soil layer and eventually through the capillary barrier. And this makes it for today.

So to sum it up, we have seen that dielectric sensors offer reliable measurements of soil water content in most situations. And we have also pointed out that a unique relationship, or if you like a universal relationship between the soil dielectric, whether it is estimated through TDR, capacitance, and water content, a relationship that works well for all soils and under any environmental condition simply does not exist. So, our measurements are inherently subject to Earth. We have also seen that the way TDR and capacitance sensors respond to environmental or structural variability is different. And also we have shown that in some cases, especially for the environmental factors, the earth induced by salinity and temperature variability, may be if not corrected, at least mitigated through independent estimates of soil, electrical conductivity and temperature, which are in fact available in both sensors. And there is little we can do at this point to mitigate the variability that comes from the natural variability in soil texture and bulk density. And in those cases, if improved measurements are necessary, one has to resort to soil specific calibration procedure. I hope you have enjoyed the seminar and I will be looking forward for further comments requested. Thank you very much.

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