In this chalk talk video, world-renowned soil physicist, Dr. Gaylon Campbell, discusses how many measurements researchers and growers need to characterize soil moisture at a field or research site. He explores the question: What is the relationship between the measurements that you make and the underlying value of water content in the field?
Dr. Gaylon S. Campbell has been a research scientist and engineer at METER for 19 years following nearly 30 years on faculty at Washington State University. Dr. Campbell’s first experience with environmental measurement came in the lab of Sterling Taylor at Utah State University making water potential measurements to understand plant water status. Dr. Campbell is one of the world’s foremost authorities on physical measurements in the soil-plant-atmosphere continuum. His book written with Dr. John Norman on Environmental Biophysics provides a critical foundation for anyone interested in understanding the physics of the natural world. Dr. Campbell has written three books, over 100 refereed journal articles and book chapters, and has several patents.
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We quite often get a question from customers about how many measurements we need to characterize soil moisture at a site. And so that’s what I want to talk about today. A number of years ago, I knew a man who was wanting to provide a business of making soil moisture measurements for the purpose of irrigation scheduling for farmers. And he came to me wondering how many samples he should take. He figured that he wanted a fairly simple way of determining soil moisture.
So, he thought he would go into the field and he would collect soil samples from the field, he would take them back to the laboratory, he would dry them and weigh them and dry them and determine water content. And he wondered how many samples would be required to determine the water content to provide this information for a farmer.
Now, that’s not so different from the kinds of information that are often required either for practical applications like irrigation scheduling, or for research purposes. We can see the broader applications of the question of, “what’s the relationship between the measurements that we take and the underlying value of water content in the field?”
I think you can see that the same thing would apply whether we were taking samples and bringing them back to the laboratory, or if we were putting in soil moisture sensors, and wanting to monitor soil moisture in the field. So, the first thing we need to talk about soil moisture is a random variable, we need some vocabulary for talking about that. Two terms are important: mean and standard deviation.
If we were to collect many samples of water content from a field, and we were to plot the number of samples versus the water content of the samples, we would obtain a relationship something like this. We would get the most samples around some central value, and that central value is the mean.
The standard deviation is a measure of the dispersion around the mean. 68% of the values that we take would be within plus or minus one standard deviation of that mean value. 95% would be within plus or minus two standard deviations of the mean value.
So, let’s say that we walked out here in the field, and we took a sample and made a measurement on it. And let’s say out of that sample, we determined the water content was 27%. Now let’s say that we assume or we know from some means that the standard deviation is 3%. Then, by these ideas, we would know that the mean value – the expected value for the water content – is or at least there would be a 95% probability that the mean value of the water content would be somewhere between 21% and 33%. The mean value plus two times the standard deviation and the mean value minus two times the standard deviation.
Now we may say, “well that’s not good enough. We need better values than that. So what do we do? We need to take more samples. And so we take a number of samples and average them. And so we can know what the result of averaging several samples is, with a simple relationship. The uncertainty in the average value that we get–the standard deviation of the mean–is the standard deviation, divided by the square root of the number of samples.
So let’s say that we went out in the field, and we took 100 samples. Then the standard deviation of the mean, would be our standard deviation that we assumed before, divided by the square root of 100. The square root of 100, of course, is 10. And so that would be 0.3%. If we determined a value of 28% for that mean of the 100 samples, then with 95% confidence, we can say that the water content is between 27.4 (2 standard deviations below the mean), and 28.6.
Now we’re getting closer then to our quest of determining the number of samples that we need to take. We start out with that equation that we just had that the standard deviation of the mean is equal to the standard deviation divided by the square root of the number of samples. We can rearrange that to say that the number of samples that we need is equal to the standard deviation divided by the standard deviation of the mean, and that value squared. So, the error that we normally would talk about in the measurement–if we’re again talking about 95% confidence–the error is half of the standard deviation of the mean.
This number of samples is two times the standard deviation over the air, and that all squared. So, if we work through a little problem with that, how many samples would we need in order to know the water content within 1%? If the standard deviation is 3%, the way we’ve assumed.
So, the standard deviation is 3%. The error value that we want to get to is 1%. We want to take enough samples so that we have 95% confidence that we’re within 1%. And so the number of samples is 2 times 3%, divided by the air, 1%, and that’s all squared. And that comes out to be 36 samples. Well, when we see that number, typically we get pretty discouraged. That’s more samples than we want to take. More samples probably than we can afford to take.
To see how that relates to reality, we did a little experiment. Here we have a soccer field out behind the METER (formerly Decagon) building. We went out and took one of our sensors, the GS3, and hooked it up to our little handheld device. And we set up three transects 20 meters long, parallel with each other and spaced a meter apart. We went along and took samples every meter along these transects. And I have a little video here that shows how that sampling went. The result of that sampling is shown in this next slide.
This slide shows the result of that set of measurements that we made. And you can see it looks about like you would expect it to. We’ve got some variation, we show a mean value and some variation around it. The transects, again, showed variability but seemed to be showing about the same result for each transect. We had 60 samples there.
The average water content that we computed was 38.6%. The standard deviation was not 3%, but 5%. So, the situation is even worse than we imagined with these calculations that we just did here. With a standard deviation of 5%, if we want to know the water content within 1%, we would need 100 samples to do that. And so even with our 60 samples, here, our standard deviation of the mean is 0.65%. And so our field water content is somewhere between 37.3 and 39.9.
Well, as I say that usually is discouraging when we get to that point and see how many samples are needed to make a set of measurements, but the thing is that quite often, the thing that we need to know is not an accurate value for the average water content. Quite often, what we want to know is how much the water content is changing. And that we can know in other ways, accurately enough, so that we don’t need that many samples.
That person that I started out talking about who was wanting to schedule irrigation would need to know water content with an accuracy of 1%. Well, at least with a precision of 1% or better. But that could be achieved much more readily by installing a sensor in situ, where you’re not dealing with the spatial variability in the soil and monitoring that.
Here I’ve shown some data that we took in the field with one of our 5TE sensors hooked up to a data logger. The water content is sampled every minute, it’s averaged over hour intervals, and the plot that you see here is a plot of the water content measured each hour. Then, you can see a period of time where the soil is drying, because the plants are using water. You can see an increase in water content that results from adding water through irrigation or rain. And then again, the water content decreasing as the water is used. And you see very little variation in those data.
Now if this guy that wanted to provide the irrigation scheduling service, had wanted to do this same thing by sampling, the next slide shows the result that he would have gotten if he had gone out every hour and taken one soil sample and plotted the result.
This is what he would have gotten; the blue lines that you see. And you can see that it’s about what you would expect: that the highest values are about 10% higher than the mean value, the lowest values are about 10% lower, and the standard deviation we said is about 5. So, that’s about what we would expect. But from these kinds of data, there’s no possibility that you could ever tell when you should irrigate.
In the next slide, I show the result that you would have gotten if you went out and took 10 samples every hour. And here you can see the pattern to some extent of when the drying and wetting occur, but there’s still an awful lot of variation.
The next slide shows the result of taking 100 samples every hour, a ridiculous thought, but again, there’s still some variation in it. It still doesn’t look anywhere near as good as the in situ sample. When we’re just looking for the changes in water content, the water storage, and water use, in situ measurements make a lot more sense than soil moisture sampling.
So, let me conclude just by a few points that I hope to have made in this. First of all, the soil water content varies from place to place; that’s inherent in nature. It’s something that we expect anytime we go out to measure soil moisture. We usually need to take an average of moisture at several locations in order to know what the water content of a field is, or an experimental site. We usually can’t afford to take enough measurements to really know what it is to have it within the accuracy that we would like to have it. And so we can go through this exercise that I’ve gone through here, we can determine the number that we need, but usually, our budget won’t allow us to put in that many and so we end up compromising to some extent.