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Posts from the ‘Ecology’ Category

A different approach to stream restoration

University of Idaho graduate student, Adrianne Zuckerman, is taking a different approach to stream restoration than the traditional approach, channel manipulation, which often requires heavy equipment and major disruption to the riparian area.

Zuckerman set out to understand how vegetation lining the stream bank impacts habitat quality for anadromous salmon and steelhead in Washington’s Methow River, which flows through the eastern Cascades. Zuckerman wanted to know how tree species composition affects the amount of nutrients available to the benthic insect community, since they are a critical food source for young salmonid fish.

When Zuckerman began investigating methods for measuring leaf contribution to the stream, she found that leaf litter traps were the standard equipment. Leaf litter traps are time-consuming to set and maintain, and data analysis consists of frequent visits to the field followed by extensive time in the lab processing leaf material.

Stream with rocks and trees

Looking for an alternative method, she discovered the LP-80 ceptometer: a lightweight, field-portable instrument for measuring leaf area index. Using the LP-80, Zuckerman was able to rapidly assess the leaf area contribution of each tree species along the riparian corridor. Using this information, it was relatively straightforward for her to estimate the contribution of each tree species to the stream food web.

Zuckerman’s research will help land managers and other researchers understand the importance of riparian vegetation for maximizing the food available to salmonid fish species. Improvement and maintenance of optimal stream-side vegetation composition should ultimately help to enhance salmon populations in the Pacific Northwest.

How To Estimate the Impact of Radiation Sources in the Environment

What impact does direct solar radiation have on the overall radiation balance? Dr. Colin Campbell, WSU Environmental Biophysics professor and METER scientist, shows you how to do the calculations in our latest chalk talk.


Hi, I’m Dr. Colin Campbell. And this is a METER Chalk Talk.

Have you ever been outside on a hot day walking in the full sun and then stepped into the shade? The relief is almost immediate. And I was thinking about that a lot when I was looking at this graph here, the estimated crop water loss on one of my experiments.

So this is an ET zero, meaning a reference ET. But since I was working grass, that was actually the estimated water loss from this grass crop. And what I noticed was that the shape of this curve kind of went up, and then went down. And it kind of matched right here, the solstice, the summer solstice. And in my mind, I thought, you know, what impact is direct solar radiation have on the overall radiation balance? Well, we can quickly just jump down and look at the equation that talks about how we might estimate the evapotranspiration from a crop. I’m not going to be able to have time here to get into what each of these variables mean.

But as you see, solar absorbed radiation, R abs is a strong component of that overall calculation. Now, when we talk about absorbed radiation, we need to understand that it’s not just all direct sunlight. In fact, if you assumed that, you’d be off in the weeds quite a bit, because it contains components of both longwave radiation, which is radiation that’s coming from your terrestrial surroundings, and shortwave radiation, that which is coming from predominantly the sun.

So let’s talk about that for a minute. With absorbed radiation, we have shortwave radiation. This is radiation that’s less than four micrometers. And we have longwave radiation. This is not surprisingly, from wavelengths greater than four micrometers. Now, this shortwave radiation, this comes from the sun longwave radiation comes from other sources, like trees, the sky, ground, just other objects that are around the temperature that we expect in the natural environment. Now, the truth of the matter is to get R abs, we need to combine both of these things into a single number. And it actually gets even more complex than that. So bear with us as we go on to the next equation.

R abs is a function of both shortwave radiation and long wave radiation. And when we calculate our radiation balance to get absorbed radiation, we have to actually take all of this into account. Now, you might be wondering, what are the other pieces in this equation, we’re going to spend a little time going over that. So you might understand how we can get from all of these numbers, all of these potential sources of radiation to a final number of R abs.

This portion of the equation here is shortwave radiation. And we’re going to talk about the variables in that equation. The first one we see is alpha s. It’s a number between zero and one. It signifies the percentage of shortwave radiation that the object can absorb. The other parameters in the equation include some F’s and some S’s. The F’s we call view factors, we’ll discuss view factors in more detail in another chalk talk. But suffice it to say that these essentially are parameters to estimate the amount of radiation that our object can see in its surroundings.

S stands for shortwave radiation. And this comes from several different sources. They include p: this is radiation that’s coming directly from the sun. That’s the one I mentioned earlier, that we feel if we’re standing in the direct sun, versus if we walk into the shade. But there are a couple of others. One is diffuse. This is the radiation that’s scattered as light comes into our atmosphere and it’s scattered by the atmosphere.

Finally, there’s R. This is reflected radiation, radiation that when it comes in, hits a surface, it reflects off that surface and comes and impinges on our object. Think about snow. If you’ve ever been skiing or out on the snow, you know, on a sunny day, you’re getting a lot of radiation that’s being reflected back. This portion of the equation over here is our longwave portion. Similar to our shortwave, it contains many of the same symbols, but they’re a little bit different.

The alpha L is the absorbed radiation. Now in the long wave that also goes from zero to one. The F is our view factor again, but now the view factor of longwave radiation, and L stands for that longwave radiation. This time, the subscripts A, that stands for atmosphere, and G stands for ground. If we put together all components in this equation, we’ll be able to solve for absorbed radiation. But that’s going to take a little bit of work. First, we need to understand the absorptivity of our surface both in the shortwave and the longwave.

The shortwave typically is calculated just from tables from looking out on the internet. For example, if I wanted to look at the absorptivity of a maple leaf, that’s typically around 50%. But it’s something that’s probably been calculated in literature. For our longwave radiation, almost all objects absorb long wave radiation at about 97 to 98% of the possible total.

So it’s pretty easy to estimate these absorptivities for objects that are fairly common. Calculating solar radiation and long wave radiation take a little bit more time. And especially understanding the view factors or how much of a particular surface our object sees, is going to take a whole chalk talk on its own. We’re going to leave this discussion here and leave for next time an opportunity to talk about how to calculate our shortwave radiation, or long wave radiation, and then get to the complicated discussion of view factors.

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How to calculate the angle of the sun

Listen to Dr. Colin Campbell, WSU environmental biophysics professor, as he discusses how to calculate the angle of the sun, or solar zenith angle.


Hi, I’m Dr. Colin Campbell. And this is a METER Chalk Talk. A couple of years ago, I was heading out into the backcountry and we wanted to figure out what kind of gear we should take along. A friend suggested we should just check the wind chill factor. But when I looked into it, we found out that it doesn’t even consider solar radiation in that calculation. Our exchange of energy in the environment is highly dependent on radiation, particularly solar radiation. And today, we’re going to talk a little bit more about that. Now the first thing to know about solar radiation is where the sun is in the sky. In fact, our absorbed radiation really depends on it. Interestingly, it’s one of the few things in life you can really count on.

With a few equations, we can figure out where the sun is in the sky at any time of the day. And I’m going to take you through some of these equations, one of the things I want you to know first is, they’re a little complicated, so don’t get stressed. In fact, if you just want to stop the video at a certain point. And check out these equations for a moment and write them down. That’s just fine. Now let’s just jump into it.

So here on my screen, I’m showing a graph of where the sun might be, at any point in a day if you were standing on the equator. Now in the middle, I’m going to draw this blue line across there, that is at the equinox. Now at the two solstices the sun might be here tracking across the sky, or here. And of course, this diagram is really showing kind of a fisheye picture of where that sun might be. There are two ways to describe where the sun is. One is a zenith angle. The zenith angle has a symbol, we call psi. In fact, the angle to the Earth’s surface from the perpendicular or normal, so this would be that zenith angle. Now there’s another angle we might be interested in, it’s called the Azmuth angle. But for our purposes of today, I just want to focus on this zenith angle because it’s the most important as we consider the radiation impact in an object that we’re interested in.

So to calculate the zenith angle, we’re going to go down and discuss the equation where this right here is zenith angle. And this here is the equation that we use to calculate that. Now you recognize the sines and cosines. And there’s just a couple other things in here. Of course, we’ve got t, which is time. And then a few other variables, phi. This is the latitude. Delta, this we call the solar declination, and finally, t zero, this is solar noon. Now before we get too crazy and worried about this equation, all we have to do is put in a few things into here, and we’ll be able to calculate that. So the first thing we need to know is the time of day.

Then we need to know the day of year. Now we actually call this a special name. This is called a Julian day. And it starts counting from January 1. The other things we need to know is of course, latitude, and longitude. And I’ll get to why in just a moment. The first parameter we’re going to try to find is called the solar declination. The solar declination equation looks pretty crazy. And anytime you see an equation like this in a book or something, the first assumption you should make is this is an empirical equation. As I look out on the internet and study other materials, I find that these equations actually are fairly common out there. And this isn’t exactly the way you see it in every piece of literature. But let me talk you through it here.

Really, there’s only one thing we need to know. It is the Julian day and we can go on the internet and calculate these a lot of programs just have those hard coded in like Excel. And all we need to do is just put that Julian day in for each of these values-here into here, and then we can eventually calculate the delta value. And then we can go put it back in this equation. So as long as we know the declination here, this is just the latitude. Let’s say my latitude is about 47 degrees. We just put that right here. All we need to know now is this t zero or solar noon. So what did we do for that?

Well, solar noon is calculated like this: t zero is equal to 12. That’s solar noon, and then we change it for wherever we are with respect to entered Meridian. And we call that the LC longitudinal correction, and then we also subtract off this equation of time t. We can start with the equation of time here. That’s this equation right here. And that’s not very small. In fact, not only is it not small, but it has a whole bunch of f’s in it. You can see f, here, this two times f, this is three times f, this is four times f. And now in the cosine or sines, then we have cosines here. So what is that?

Well, f is another one of these little bit long equations it is two point, or sorry, 279.575 plus 0.98565 times the Julian day. Now, if you get that, you just plug it back in here. And you can calculate your equation of time. And this is a number much smaller than one that you can plug in to this equation right here. Now, what about the longitudinal correction?

Well, the longitudinal correction Lc, that’s pretty straightforward. It’s essentially for every degree east of this of the standard meridian, you add 115. So for example, where I live, I’m at one 117.2 degrees, longitude, our standard meridian 120 degrees. And so the difference is, we’re east of that 2.8 degrees, and therefore the longitudinal correction, LC is just 2.8 over 15, or equal to 0.19h. So essentially, what I do is take that right there, and plug it in up here for the longitudinal correction. So essentially, we take 12, and we subtract off the longitudinal correction, and then with our equation of time, we get this value and eventually have t zero.

So what does all this mean? What does it sum up to? Well, there’s a lot of numbers in here. But if we go back to our initial equation, all we’re going to need to do now is simply this. We have our solar noon, we plug our time in. And then we use our solar declination here that we calculated on the first part of this discussion, our latitude here, and then suddenly, we’re able to calculate the Zenith Angle. And I’m going to try to link to a little calculation spreadsheet I did in Excel onto the sheet or onto the this video and then you can go ahead and look at that, how it’s done, and do your own calculations. For more content like this, check out our YouTube channel or head over to Thanks for watching a METER Chalk Talk.

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Building a National Water Potential Network

Champions of water potential

Drs. Kim Novick and Jessica Guo team up to discuss the vital role water potential measurement plays in both plant and soil sciences and the work they are doing to establish the first-of-its-kind nationwide water potential network. Join their discussion to understand how a communal knowledge of these measurements could impact what we know about climate change and ecology as a whole.

A water potential measurement network could increase our understanding of climate change and ecology.

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Dr. Kim Novick is a professor, Paul H. O’Neill Chair, Fischer Faculty Fellow, and director of the Ph.D. Program in Environmental Sciences at Indiana University.  She earned her bachelor’s and Ph.D. in environmental science at Duke University’s Nicholas School of the Environment. Her research areas span ecology and conservation, hydrology and water resources, and sustainability and sustainable development, with specific interests in land-atmosphere interactions, terrestrial carbon cycling, plant ecophysiology, and nature-based climate solutions.

Dr. Jessica Guo is a plant ecophysiologist and data scientist who studies plant-environment interactions under extreme climate conditions. She earned her bachelor’s in environmental biology from Columbia University and her Ph.D. in biological sciences from Northern Arizona University.  She is currently at the University of Arizona, where she blends her passion for reproducible workflows, interactive visualizations, and hierarchical Bayesian models with her expertise in plant water relations.

Links to learn more about Dr. Kim Novick

Links to learn more about Dr. Jessica Guo


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The views and opinions expressed in the podcast and on this posting are those of the individual speakers or authors and do not necessarily reflect or represent the views and opinions held by METER.

Understanding the Language of Plants

Like a silent battle cry, plants call out to signal they are under siege as a warning to other plants and to call in reinforcements to fend off the invasion.

How does this communication work? What else are plants doing to protect themselves from disease and predators alike? In our latest podcast, Natalie Aguirre, a PhD candidate and plant physiology and chemical ecology researcher at Texas A&M University, dives into her research on pathogen infection, water stress, and how plants communicate and defend themselves.



Natalie Aguirre graduated with a degree in biology from Pepperdine University, where she completed an honors thesis conducting research on the interaction of drought stress and pathogen infection in chaparral shrubs. She then spent a year as a Fulbright scholar in Spain, studying the effect of water stress on Dutch Elm Disease. Most recently, Natalie worked for the Everglades Foundation, creating educational programs and materials about the Florida Everglades.

Links to learn more about Natalie Aguirre

Publications by Natalie Aguirre

Natalie Aguirre on Loop Open Science Research Network


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


The views and opinions expressed in the podcast and on this posting are those of the individual speakers or authors and do not necessarily reflect or represent the views and opinions held by METER.

Determining drought tolerance in plants: How to do it right.


Abiotic stress in plants: How to assess it the right way

As a plant researcher, you need to effectively assess crop performance, whether you’re  selecting the best variety, trying to understand abiotic stress tolerance, studying disease resistance, or determining climate resilience. But if you’re only measuring weather data, you might be missing key performance indicators. Water potential is underutilized by plant researchers in abiotic stress studies even though it is the only way to assess true drought conditions when determining drought tolerance in plants. Learn what water potential is and how it can improve the quality of your plant study.

Soil directly impacts plant growth via nutrient availability, disease pressure, root growth, and water availability.

Quantitative genetics in plant breeding: why you need better data

If you’ve studied plant populations, you’re probably familiar with the simplified equation in Figure 1 that represents how we think about the impact of genetics and the environment on observable phenotypes.

Figure 1. Phenotype = Genotype + Environment

This equation breaks down the observed phenotype (plant height, yield, kernel color, etc.) into the effects from the genotype (the plants underlying genetics) and the effects of the environment (rainfall, average daily temperature, etc.). You can see from this equation that the quality of your study directly depends on the kind of environmental data you collect. Thus, if you’re not measuring the right type of data, the accuracy of your entire study can be compromised.

Water potential: the secret to understanding water stress in plants

Drought studies are notoriously difficult to replicate, quantify, or even design. That’s because there is nothing predictable about drought timing, intensity, or duration, and it’s difficult to make comparisons across sites with different soil types. We also know that looking at precipitation alone, or even volumetric water content, doesn’t adequately describe the drought conditions that are occurring in the soil.

Figure 2. The TEROS 21 is a field sensor used to measure soil water potential

Soil water potential is an essential tool for quantifying drought stress in plant research because it allows you to make quantitative assessments about drought and provides an easy way to compare those results across field sites and over time. Let’s take a closer look to see why.

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Chalk Talk: How Many Soil Moisture Measurements Do I Need?

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


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. 

TEROS 12 soil moisture sensor

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?” 

Soil water content will vary from place to place.

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. 

Why We Live Or Die By Soil Health

In our latest podcast, Dr. Cristine Morgan, one of the US’s premier soil scientists and Chief Scientific Officer at the Soil Health Institute shares her views on soil health: what it is, how to quantify it, what’s the payoff, and why it’s so critical to our success as a society.

“Our soils support 95 percent of all food production, and by 2060, our soils will be asked to give us as much food as we have consumed in the last 500 years.” (Credit:

Her thoughts? “We all live or die by soil, literally. We just have to remind people that it’s about quality of life. It’s about the food that you eat. It’s about the safety and welfare of your children.” 



Dr. Cristine Morgan is the Chief Scientific Officer at the Soil Health Institute in North Carolina. Learn more about the Soil Health Institute on their website. 


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The views and opinions expressed in the podcast and on this posting are those of the individual speakers or authors and do not necessarily reflect or represent the views and opinions held by METER.

Chalk talk: How to model air temperature variation with height

In his latest chalk talk, Dr. Colin Campbell, environmental scientist at METER Group, teaches how to model vertical variation in temperature and how to estimate sensible heat flux.

Video transcript

Hello, everyone. My name is Dr. Colin Campbell, and I’m a senior research scientist here at METER Group. For today’s chalk talk, we’ll be talking about modeling vertical variation in temperature. In Figure 1, I’ve put together a graph that shows the maximum and minimum temperature with height and depth in the soil at some snapshot in time at a particular place. 

Figure 1. Maximum and minimum temperature with height and depth at a snapshot in time, in a particular place

It’s interesting to note that the change in temperature with depth in the soil is much faster than the change in temperature with height, whether we’re talking about a maximum or minimum. And the reason is that even though air is a good insulator, it also mixes really well. And that mixing is caused by eddies. And there’s a little more to that story. It depends specifically on surface heating by the sun through radiation and the cover type, whether it’s plants, rocks, boulders, straight soil, snow, or wind.

Equation 1

If we were going to model that, we would start by writing an equation (Equation 1) where a temperature at sun height, Z, above the surface (see variables noted in Figure 1), is equal to an aerodynamic surface temperature, T0, minus the sensible heat flux, divided by 0.4 times rho, CP, which is the volume specific heat of the air, times a variable called u*, which is the friction velocity. We multiply all that by the logarithm of z, the height above the surface minus d, which is the zero plane displacement, divided by z h, which is a roughness parameter. You might notice up here in the list of variables, that the zero plane displacement is 0.6 times H. H is the canopy height in meters. The rough roughness parameter can be estimated as 0.02 times the canopy height or times H. Now we have an equation that will help us model temperature with height. 

However, often we don’t know things like H, our sensible heat flux, and u*, our friction velocity. One of the things that we notice about this equation is that it’s set up somewhat like a linear equation. As you know, an example of a linear equation is something like Equation 2.

Equation 2

Figure 1 isn’t written quite that way, but if we look closely at the example below (Equation 3), this value could be our b, and this value our m, and this value could be our x. And if we do that, we actually can get some use out of graphing temperature with height. 

Equation 3

So we went out one day and measured this with a METER Group set of environmental sensors set up at certain heights above the surface. Here we placed sensors at 0.2 m, 0.4 m, 0.8 m, and 1.6 m above the ground. 

Table 1

To visualize this, in Figure 2 we graphed height on the y axis and temperature on the x axis, similar to the graph in Figure 1.

Figure 2. Graph showing the relationship between height and temperature

We know from Equation 1 that the axes for temperature and height should be switched because temperature is the dependent variable, and height is the independent variable. So if we switch axes it would look like the graph in Figure 3.

Figure 3. Graph showing the relationship between height and temperature where temperature is the dependent variable and height is the independent variable.

Figure 3 is graphed with the independent variable on the x axis and height on the y axis. If we fit this curve with today’s calculators, it would be fairly easy to get a curve that would fit that. But since it’s a linear equation, we can take the temperature data from Table 1 and the In ((Z-d)/ZH) data from Table 1 and graph them together.

Figure 4. Relationship between temperature and In Z-d/zh

Figure 4 is a graph that shows what happens when we do that. Notice that, just like we suggested, it creates a linear equation (Equation 4). 

Equation 4

We learned in Figure 1 the B value was equal to t0 (our aerodynamic surface temperature). Since we know our surface temperature is 34.5 degrees, we can estimate what the temperature is down here at the surface, even though we only measured down 0.2 m. 

We also know from Equation 4 that our M value is equal to -2.01. And if we look at Equation 1, our slope value is below.

Equation 5 (the slope value from Equation 1)

So we can write

Equation 6

How to estimate sensible heat flux

Now, if we were interested in the sensible heat flux, which we often are, we can simply rearrange this equation to be

Equation 7

And in Figure 1, I forgot to give you this value, but for an air temperature of 20 degrees celsius, 

Equation 8

And then finally, a typical unit for friction velocity, which should be measured in the field over the specific canopy you are in, is about 0.2 meters per second.

Equation 9

So if we did this calculation, we would learned that there’s about 193 watts per meter squared of sensible heat flux coming off that surface. 

Equation 10

So if we can measure temperature at a few heights, we can estimate what the heat flux is coming off the surface assuming we know something about our canopy. Learn more about measuring and modeling environmental parameters at If you have any questions feel free to email Dr. Campbell at [email protected].

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