The conversion of light energy and atmospheric carbon dioxide to plant biomass is fundamentally important to both agricultural and natural ecosystems.
The detailed biophysical and biochemical processes by which this occurs are well understood. At a less-detailed level, however, it is often useful to have a simple model that can be used to understand and analyze parts of an ecosystem. Such a model has been provided by Monteith (1977). He observed that when biomass accumulation by a plant community is plotted as a function of the accumulated solar radiation intercepted by the community, the result is a straight line. Figure 1 shows Monteith’s results.
Figure 1. Total dry matter produced by a crop as a function of total intercepted radiation (from Monteith, 1977).
In the conclusion of our three-part series on improving NDVI sensor data (see part 2), we discuss how to correct for limitations which occur in high leaf area index (LAI) conditions.
Where there’s a large amount of vegetation, NDVI tends to saturate.
NDVI Limitations – High LAI
NDVI is useful in the midrange of LAI’s as long as you don’t have strong soil effects, but as you approach an LAI above 4, you lose sensitivity. In figure 6, loss of sensitivity is primarily due to a saturation in the red band. Measurements were taken in a wheat canopy and a maize canopy. The near-infrared reflectance is sensitive across the entire spectrum of the wheat and maize canopies, but the red saturates relatively quickly. Where the red starts to saturate is where the NDVI starts to saturate.
Figure 6: Gitelson (2004) J. Plant Phys
Note: NDVI saturates at high LAI’s, however, if your purpose is to get at the fractional interception of light, NDVI tends not to have the saturation issue. In Figure 7, Fpar or the fractional interception of light of photosynthetically radiation is nearly complete far before NDVI saturates. This is because canopies are efficient at intercepting light, and once we get to an LAI of about 4, most of the light has been intercepted or absorbed by the canopy. Thus, incremental increases in LAI don’t significantly affect the FPar variable.
Figure 7: Fractional interception of light is near complete at an LAI around 4. (Gamon et al. (1995) Eco. Apps)
Solution 3- WDRVI
One solution for the NDVI saturation issue is called the Wide Dynamic Range Vegetation Index (WDRVI). Its formulation is similar to NDVI, except for a weighting coefficient that can be used to reduce the disparity between the contribution of the near infrared and red reflectance.
In the WDRVI, a is multiplied by the near-infrared reflectance to reduce its value and bring it closer to the red reflectance value. In doing so, it balances out the red and the near-infrared contribution to the vegetation index.
Figure 8: (Gitelson (2004) J. Plant Phys)
a can range anywhere from 0 to 1. Figure 8 shows that as we use a smaller value of a, we get an increasing linear response of the wide dynamic vegetation index to LAI.
The only drawback of the WDRVI is that the selection of a is subjective. It’s something that you experiment on your own until you find a value for a that is optimal for your solution. People tend to err on the side of a very low value simply because they’ll get closer and closer to a linear response to LAI as a decreases.
Solution 4 – Enhanced Vegetation Index
The enhanced vegetation index (EVI) was designed to enhance sensitivity in high biomass ecosystems, but it also attempts to reduce atmospheric influences. This was a vegetation index created for the purposes of a satellite-based platform. There’s a lot of atmosphere to look through from a satellite to the ground, and sometimes the aerosols in the atmosphere affect the reflectances in the red and the near infrared regions causing spurious observations. The EVI also tries to reduce sensitivity of the index to soil. Thus the EVI is a kind of solution to both extremes.
In the EVI equation, the two major inputs are near infrared and red reflectances. C1 , C2, and L are all parameters that can be estimated, but the blue band is something that has to be measured. Most NDVI sensors are two band sensors, so you don’t have that information in the blue. Plus, with satellites, the blue band is relatively noisy and doesn’t always have the best quality data, thus EVI has limited value.
Solution 6: EVI2 (Enhanced Vegetation Index 2)
Those problems led a scientist named Jiang to come up with a solution. Jiang observed quite a bit of autocorrelation between the red band and the blue band, so he decided to try and formulate EVI without the blue band in what he called the EVI2 (Enhanced Vegetation Index 2). if you’re interested in the mathematics, we encourage you to read his paper, but here we give you the equation in case you’re interested in using it.
When Jiang calculated his EVI2 and compared it to the traditional EVI (Figure 9), it was nearly a one to one relationship. For all intents and purposes EVI2 was equivalent to EVI. Since this avoids blue band, it offers some exciting possibilities as it reduces to just using the two inputs of NIR and red bands to calculate NDVI.
NDVI Sensor Summary
NDVI measurements have considerable value, and though there are extremes where NDVI performs poorly, even in these cases there are several solutions. These solutions all use the near infrared and the red bands, so you can take an NDVI sensor, obtain the raw values of NIR and red reflectances and reformulate them in one of these indices (there are several other indices available that we haven’t covered). So if you’re in a system with extremely high or low LAI, try to determine how near infrared and red bands can be used in some type of vegetation index to allow you to research your specific application.
Last week we discussed Normalized Difference Vegetation Index (NDVI) sampling across a range of scales both in space and in time, from satellites sampling the entire earth’s surface to handheld small sensors that measure individual plants or even leaves (see part 1). This week, learn about NDVI applications, limitations, and how to correct for those limitations.
Limitations of the Normalized Difference Vegetation Index tend to occur at the extremes of the spectrum.
People use NDVI to infer things like leaf area index (LAI) or fractional light interception (FPAR) of a canopy. Some scientists also associate NDVI with biomass or yield of a crop. People also use NDVI to get a sense of phenology (general temporal patterns of greenness), as well as where vegetation occurs or how much vegetation is in a particular location.
In Figure 4, you can see how the reflectance spectrum at a given canopy LAI changes with leaf area index, decreasing in the visible range while increasing in the near infrared.
At very low LAI’s, the reflectance spectrum is relatively undifferentiated between red and NIR (black line), but when LAI is high, there’s a strong absorption of red light by chlorophyll with a strong reflectance in the NIR. In fact, as LAI increases, there’s an ever-increasing reflectance in the near infrared around 800 nm.
Limitations of the Normalized Difference Vegetation Index tend to occur at the extremes of the spectrum. Any time there’s very low vegetation cover (majority of the scene is soil), NDVI will be sensitive to that soil. This can confound measurements. On the other extreme, where there’s a large amount of vegetation, NDVI tends to saturate. Notice the negligible difference between spectra at a leaf area index (LAI) of 3 (purple) versus 6 (green). Indeed, in a tropical forest, NDVI will not be sensitive to small changes in the LAI because LAI is already very high. However, several solutions exist.
Solution 1-Soil Adjusted Vegetation Index
Figure 5 shows the results of a study taking spectral measurements of different vegetation indices across a transect of bare soil. Moving from dry clay loam to wet clay loam, we see a very strong response of NDVI due to the wetness of the soil; undesirable if we’re measuring vegetation. We’re not interested in an index that’s sensitive to changes in soil or soil moisture. However, there are a few other indices plotted in figure 5 with much lower sensitivities to variations in the soil across the transect.
Figure 5: Qi et al. (1994) Rem. Sens. Env.
The first one of those indices is the Soil Adjusted Vegetation Index (SAVI). The equation for SAVI is similar to NDVI. It incorporates the same two bands as the NDVI—the near infrared and the red.
Soil Adjusted Vegetation Index (Huete (1988) Rem. Sens. Env.)
The only thing that’s different, is the L parameter. L is a soil adjustment factor with values that range anywhere from 0 to 1. When vegetation cover is 100%, L is 0 because there’s no need for a soil background adjustment. However, when vegetation cover is very low, that L parameter will approach one. Because it is difficult to measure exactly how much vegetation cover you have without using NDVI, we can modify the NDVI so it’s not sensitive to soil by guessing beforehand what L should be. It’s common practice to set L to an intermediate value of 0.5. You can see in Figure 5 the Soil Adjusted Vegetation Index or SAVI has a much lower sensitivity to the soil background.
Solution 2- Modified SAVI
The next vegetation index is the modified SAVI (MSAVI). The SAVI equation contains an L parameter that we have to estimate—not an accurate way of handling things. So a scientist named Key developed a universal optimum for L. We won’t get into the math, but he was able to simplify the SAVI equation to where there’s no longer a need for the L parameter, and the only inputs required are the reflectances in the near infrared and the red.
Modified SAVI (Qi et al. (1994) Rem. Sens. Env.)
This was a pretty significant advance as it circumvented the need to estimate or independently measure L. When Key compared SAVI to MSAVI, there was virtually no difference between the two indices in terms of their sensitivity to the amount of vegetation and their response to the soil background.
MSAVI compares well with SAVI in terms of dynamic range and noise level (Qi et al. (1994) Rem. Sens. Env.)
In Haiti, untreated human waste contaminating urban areas and water sources has led to widespread waterborne illness. Sustainable Organic Integrated Livelihoods (SOIL) has been working to turn human waste into a resource for nutrient management by turning solid waste into compost. Read more…
Estimating the relative humidity in soil? Most people do it wrong…every time. Dr. Gaylon S. Campbell shares a lesson on how to correctly estimate soil relative humidity from his new book, Soil Physics with Python, which he recently co-authored with Dr. Marco Bittelli. Read more.…
“How many soil moisture sensors do I need?” is a question that we get from time to time. Fortunately, this is a topic that has received substantial attention by the research community over the past several years. So, we decided to consult the recent literature for insights. Here is what we learned.
Globally, the number one reason for data loggers to fail is flooding. Yet, scientists continue to try to find ways to bury their data loggers to avoid constantly removing them for cultivation, spraying, and harvest. Chris Chambers, head of Sales and Support at Decagon Devices always advises against it. Read more…
During a recent semester at Washington State University, a film crew recorded all of the lectures given in the Environmental Biophysics course. The videos from each Environmental Biophysics lecture are posted here for your viewing and educational pleasure. Read more…
Soil moisture sensors belong in the soil. Unless, of course, you are feeling creative, curious, or bored. Then maybe the crazy idea strikes you that if soil moisture sensors measure water content in the soil, why couldn’t they be used to measure water content in a tree? Read more…
University of Georgia researcher, Shuyang Zhen, wanted to find out if she could optimize greenhouse irrigation with reference evapotranspiration calculated from environmental factors and a crop coefficient, using NDVI measurements to adjust for canopy size (see part 1). Learn the results of the experiment and how fast growth and flowering caused problems with the NDVI measurement.
Shuyang’s experimental setup.
Fast Growth Causes Problems
Shuyang says because the plants grew so large, the canopy filled in beyond what the sensor could see. That meant there was additional leaf area that participated in vapor loss which wasn’t identified by the NDVI sensor. As the canopies approached moderate-to-high canopy densities, Shuyang observed that the NDVI readings became less responsive to increases in canopy size. To work around this problem, Shuyang tried to calculate a vegetation index called the Wide Dynamic Range Vegetation index with the spectral reflectance outputs of the two wavebands measured by the NDVI sensor. Shuyang says, “This index was supposed to improve the sensitivity at higher canopy density, so I transformed all my data and was surprised that it actually improved the sensitivity when the canopy density was lower. But at a higher canopy density it wasn’t as effective.”
The red flowers reflected a lot of red light compared to the leaves, which confused the NDVI measurement.
Plant flowering also caused problems with the NDVI measurement. Shuyang explains, “We had one cultivar of petunia with red flowers which formed on top of the canopy. The red flowers reflected a lot of red light compared to the leaves, which confused the NDVI measurement. The NDVI value gradually decreased when the plants started to flower. There was no way I could get around that issue, so in some of the replicates, I removed the flowers, and in some I kept the flowers so I could compare the different responses and characterize why it happened.”
The NDVI was very sensitive to the increase in crop size when the canopy was relatively small, but when you reach a certain canopy size and the canopy closure was nearly complete, then the sensitivity decreased.
Summary and Future Studies
During the early stages of growth, the research team saw a linear relationship between NDVI and crop coefficient. However, when the crop coefficient reached higher values, the response leveled off. Shuyang says, “The response failed to change with further increases in the crop coefficient. The NDVI was very sensitive to the increase in crop size when the canopy was relatively small, but when you reach a certain canopy size and the canopy closure was nearly complete, then the sensitivity decreased.”
Lack of NDVI sensitivity during canopy closure and flowering translated to a problem with under-irrigation,
Shuyang adds that the lack of NDVI sensitivity during canopy closure and flowering translated to a problem with under-irrigation, so the team is thinking about developing separate models for different canopy stages. She explains, “When the canopy reaches high canopy closure we may have to add an additional coefficient to compensate for that underestimation, but it’s difficult to evaluate what kind of coefficient we should use without more data. We need to do more studies to get an idea of what kind of adjustments will make the prediction more precise.”
In contrast to the majority of the literature on soil physics, this text focuses on solving, not deriving, differential equations for transport. Numerical methods convert differential equations into algebraic equations, which can be solved using conventional methods of linear algebra. Here, Dr. Campbell interviews about this update to his classic book Soil Physics with BASIC.
Why did you write the first book, Soil Physics with BASIC?
Soil physics classes were always frustrating for me because you would spend time writing fancy equations on the chalkboard, and in the end, you couldn’t do anything with them. You couldn’t solve any of the problems because, even though they involved difficult mathematics, the math was still so simplified that it didn’t apply to anything that went on in nature.
When I taught my first graduate soil physics class, I determined that we were going to be able to do something by the time we finished. Luckily, in the mid-1970s, personal computers were being developed, and I realized this was the answer to my problem. Numerical methods could solve any problem with any geometry in it. It wasn’t limited to problems that fit the assumptions needed to derive a complex differential equation. I could write computer programs that simplified the mathematics for the students and teach them how to solve those problems using numerical methods. By the end of the semester, my students would have a set of tools that they could use to solve problems in the real world.
Did this book come from class notes or some other source?
I wrote two textbooks and they both came the same way. When I first started teaching, I had a textbook that was inadequate, so I began writing notes of my own and handing them out to the students. After two years, I turned these notes into An Introduction toEnvironmental Biophysics. Soil Physics with BASIC came about by the same process, but I enlisted the help of my daughter, Julia, to type it up. It was in the early days of word processing so entering equations was quite difficult. It all went well for her until chapter eight, which was a nightmare of greek symbols. After she finished slogging for days through the material, we somehow lost the chapter. She retyped it, and we lost it again, making her type it three times! We didn’t have spreadsheets then either, so the figures were all hand-drawn by my daughter, Karine.
Marco [Bitteli] has added two and three-dimensional flow problems, so you can model whole landscapes and water behavior in an entire terrain.
What does Soil Physics with Python add to the conversation?
First, it updates the programming language. BASIC was a language invented at Dartmouth and intended to be a simple teaching language. It was never supposed to be a scientific computer language. Python (13:26.) is a newer language, and there are many open source programs for it, making it a better language to use for science.
Secondly, the old book had one-dimensional flow problems in it for the most part, but Marco [Bitteli] has added two and three-dimensional flow problems, so you can model whole landscapes and water behavior in an entire terrain.
In addition, Dr. Bitteli describes the process and analysis of soil treated as fractals as well as soil image analysis. There are a lot of extensions and updates that weren’t in the original book.
Will it be accessible across all disciplines?
To some extent, different disciplines speak different languages. A soil physicist talks about water potential, and a geotechnical engineer talks about soil suction. Thus, there may be some translation of discipline-specific terms, but it’s intended to be a book that people in the plant sciences can use along with people in the soil sciences.
Dr. Marco Bitteli earned his PhD at Washington State University and was Dr. Campbell’s former student. This book is a product of their continued collaboration. Dr. BBitteli is now a professor at University of Bologna, the oldest university in operation in the world. Soil Physics with Python is available at Amazon.com.