Tuesday, March 13, 2018
Last time we started the conversation on precision manure application and some of the challenge of variable rate manure application, this time we’ll dive into an example and see how the economics play out.
Precision agricultural methods and variable rate application can improve nutrient management and help reduce environmental impact. We talked last time about doing this with nitrogen and the challenges it presents, but as manures also provide phosphorus and potassium. These nutrients and their need for upcoming crops can be well predicted by soil sampling. This means grid soil sampling can be used to tailor phosphorus and potassium recommendations across the field and put down a sufficient, but not an excess amount anywhere. In some cases, this may allow us to cover more acres with manure and save the purchase of commercial fertilizer for those additional acres.
The process of soil sampling and developing the “to apply” maps are similar to what would be done for commercial phosphorus or potassium fertilizers. The first main difference from commercial fertilizer is you get a guaranteed analysis, whereas with manure you have to sample, sample, sample to get a handle on its composition. This could range from testing every load to taking a composite sample, the key being you have to trust the analysis to have less variability than the rate change over the field. In some cases, this may be easy, if the manure was well mixed as it is loaded and stockpiled it will be more uniform than if it was loaded from different areas of a pen. Getting a handle on this variability is critical to make variable rate application a success.
A study by ISU on variable rate manure application showed it wasn’t unusual for fields to span four to five soil test phosphorus classes within a field. By varying the manure application rate across the field they were able to positively impact yield similar to what was obtained with a fixed application rate, not apply manure to areas that were optimal or high in soil test P and in so doing, save manure to be utilized in other areas. Moreover, the variable application rate decreased soil test variability, reducing soil P in areas that were high (and as a result more susceptible to phosphorus loss) and increasing phosphorus content in areas that were low, and the phosphorus in the soil positively impacted future crops.The variable rate allowed for better manure management by conserving manure where it wasn’t needed and placing it where more value could be obtained while also reducing the risk of phosphorus delivery from the field to water resources.
Thursday, February 15, 2018
With the very idea of the topic, questions begin to emerge: what, why, and how to use the technology. We will try to walk through a few of these questions to address what we do and don’t know. With today’s technology, including things like GPS location guidance, flow controllers, or weigh scales on manure spreaders it is possible to make maps of how many gallons per acre are applied.
In terms of solid manure, where decisions are often made based on phosphorus management, grid sampling can be used to determine current soil phosphorus levels. A map is generated of how much phosphorus we want to add to hit a certain level and this prescription map used to determine manure application rates on the go. Some current equipment even has the capability of using these prescription maps on-the-go to change the rate as you move through the field. This is effectively how variable-rate of application other commercial fertilizers has been done for a while, but there are some additional challenges with manures.
However, the question when using manure as the fertilizer source substantially increases these questions. Things like how accurately do we know the manure nutrient content, how variable is the nutrient content during application, how accurately can you hit rate, how uniform is the application, how good is the application method, and we are left with questions about if we can control these variables accurately enough to make variable rate application pay . If we try to extend this to nitrogen, it can get even more complicated as we now need to consider additional factors such as the quality of injection/incorporation throughout the field and its impact on ammonia volatilization and the variation in nitrogen mineralization and variability. This is to say, getting a firm grasp on these details would be the first step towards working towards a variable-rate manure application.
In terms of variable rate nitrogen application with manure, the first step would be determining what we parameter we want to vary nitrogen application rate based on. Some ideas that have been proposed, include previous year’s yield maps, soil type, or soil organic carbon levels. Two weeks from now we will take a closer look at each of these potential methods, why they may be considered, and science available behind how well it works.
Wednesday, December 20, 2017
Research has indicated that organic matter content in the prairie regions of the United States have declined by 50-90 percent since the land was first cultivated; for soils in Iowa this was approximately a decline from 10% to around 5% organic matter. As soil organic matter can serve as a significant source of fertility, this has led to increased interest in understanding the mechanisms that stabilize organic carbon within soils and management practices that promote building soil carbon levels.
Researcher have hypothesized that soils could be used to sequester additional carbon and prompted researchers to investigate soil carbon storage efficiencies and to evaluate if there is an upper limit to a soil’s carbon stabilization capacity. This has typically been done by applying differing C-inputs to field plots and then measuring C-stocks in the soil. The results in many cases have shown a linear increase in soil carbon with increasing carbon inputs (Huggins et al., 1998b; Kong et al., 2005; Paustian et al., 1997); however, in some long-term agroecosystem experiments little to no change in soil carbon stocks has been detected with changing carbon input levels (Reicosky et al., 2002; Huggins et al., 1998a; Huggins and Fuchs, 1997; Huggins et al., 1998). These investigations have lead researchers to propose soil carbon saturation theory (Six et al., 2002; Stewart et al., 2008; Gulde et al., 2008).
As proposed by Stewart et al. (2007), soil carbon saturation is a soil’s unique limit to stabilize carbon, in other words the maximum amount of organic carbon the soil can accumulate. This concept implies that even with increasing levels of organic matter inputs, the amount of organic matter within the soil would not accumulate. In addition to studying soil organic C stocks under various carbon loading rates researchers have also intensively investigated the dynamics of specific pools in relation to saturation theory (Six et al., 2002; Stewart et al., 2008; Gulde et al., 2008). Three main mechanisms, chemical stabilization, physical protection, and biochemical stabilization (Christensen, 1996; Stevenson, 1994, Six et al., 2002; Sollins et al., 1996; Baldock and Skjemstad, 2000), of carbon stabilization have been proposed. Chemical stabilization refers to intermolecular interactions between organic and inorganic substances (Guggenberger and Kaiser, 2003), physical protection to the accumulation of organic matter due to physical barriers or exclusion of microbes and their enzymes from the organic matter (Jastrow et al., 1996; Six et al., 2004), and biological recalcitrance to preservation of the organic matter due to structures inherently stable against biological attack (Krull et al., 2003; Poirier et al., 2003). This theory is especially significant for interpreting the results of experiments regarding soil organic matter accumulation as a result of manure application.
When compared to commercial synthetic fertilizers manure nutrient content is relatively dilute. Thus, to achieve a desired nutrient mass application a greater amount of mass of manure than mineral fertilizer needs to be applied. As an example, in Iowa approximately 112-168 kg N/ha (100 to 150 lbs. N/acre) is recommended for corn after soybeans. If our fertilizer source is anhydrous ammonia this translates to an application rate of 136-204 kg anhydrous ammonia per hectare. If manure from a swine facility using concrete storage structures is used to meet nitrogen requirements then an application rate of 16,000-24,000 kg manure per hectare are required (based on average nitrogen content of 58.1 lb N/1000 gallons from Lorimor and Kohl, 1997). At these application rates approximately 1100 and 1650 kg/ha of solids will be applied, of which between half to three quarters (550 – 825 kg/ha) would be organic in nature.
In terms of soil formation and developmen, the application of this organic matter with the manure is most closely associated with the vegetation component. By applying manure, we are adding to the amount of organic residue the soil receives and also adjusting the array and quantity of specific organic compounds that are processed by the soil microorganisms. In general, the amount of land applied organic residue is small in comparison to the amount of residue returned to the soil with a typical corn crop (roughly 18,000 kg/ha of above ground biomass) when applied at an agronomic rate, and yet reports of manures impacts on soil tilth and organic matter levels persist (Nowak et al., 2002). It is possible for small increases in carbon inputs to cause large increases in soil organic carbon levels (see figure 2 diagramming Stewart et al.’s model of soil carbon dynamics); however, this generally requires that the mineral associated pool, i.e., the physio-chemically protected pool to not be saturated. Although work in this area is far from comprehensive, it generally appears that this pool is saturated in most agricultural systems (see Hassink., 1997; Six et al., 2002).
Figure 2. Conceptual model the relationship between annual carbon inputs and soil organic carbon content (based on Stewart et al., 2007)
Despite the relatively low levels of organic matter addition, manures may have the ability to improve soil aggregation, aggregate stability and tilth. The work of Celik et al. (2004) showed that the mean weighted diameter of water –stable aggregates was 65% greater for manure and compost amended soils than in soils that received no organic amendment. Similarly, Wortmann and Shapiro (2008) found that large aggregates were increased by 200% or more by both manure and compost application within 15 days after application, with the effect persisting for seven months. In their study Wortmann and Shapiro (2008) used Bray extractable phosphorus levels to track the new inputs of compost and manure. Using this technique, they noted that the manure and compost generally served to consolidate smaller aggregates into macro-aggregates and that this occurred to a greater extent in the compost amended soil than in the manure amended soil. This indicates that the hierarchical storage structure proposed by Six et al. (2002), who suggested that organic matter would first accumulate in the physiochemical pools and then in aggregate protected fraction, is correct.
This hierarchical storage also supports the theory the layering model for the growth of organic matter in soil of Sollins et al. (2009). In their conceptual model Sollins et al. (2009) suggest that the innermost layer is protein rich as proteins can for exceptionally strong bonds with mineral surfaces (Kleber et al., 2007). Organic molecules can then interact with these surface coatings to bind the particles together as aggregates. One argument working in favor of this hypothesis is that the application of manure or compost is known to increase microbial activity (Spiehs et al., 2010). These microbes produce binding agents that anchor the cells and often coat them with enzymes. The remaining organic matter from the manure or compost can then interact with these enzymes and cement the soil particles together. Using this theory, aggregates can be formed quickly if the surfaces of particles are conditions to bind to the organic matter, would be relatively water stable as it is held together by organic matter, but effects would break down as the organic materials mineralize.
Extending this theory, we’d hypothesize that this would imply that compost application should have greater and longer lasting impacts than fresh manure at an equal carbon loading as the compost would be more stabilized against microbial brake-down than the fresh manure. This additional stability of aggregates in compost amended soils was noted by Wortmann and Shapiro (2008) and provides support for short term improvements in soil tilth and structure from manure application argument. Additionally, we’d expect that tillage would reduce or eliminate these impacts as it allows oxidation of the applied organic matter and that including a cover crop in the rotation would further enhance aggregate stabilization. Both of these practices interaction with manure application were tested by Spiehs et al. (2010), although their survey of hydraulic properties was limited, they did suggest that the benefits of manure application were enhanced in no-till and cover cropping systems.
Overall, these results paint a picture that manure, when managed correctly, can be a beneficial fertilizer that not only supplies nutrients needed to support crop production, but also can be part of a system to improve soil tilth, health, and hydraulic properties.
Tuesday, November 21, 2017
Of late, there has been greater interest in soil health, agricultural sustainability, and improving the robustness of our soils to occurrences of drought or heavy rainfall. These concepts often have one thing in common, a focus on increasing soil organic matter as a way to improve soil tilth and structure. This is the case because research has shown that soil organic matter is related to many important soil hydraulic properties, including porosity, hydraulic conductivity, and soil water retention.
Manure application is often credited with improving soil physical properties and associated benefits such as reduced runoff and erosion (Gilley and Risse, 2000; Wortmann and Wlaters, 2006). In most literature the phrase “improved tilth” is cited in manure application studies. Celik et al. (2004) found that five years of manure or compost application increased hydraulic conductivity, porosity, and that available water holding capacity increased by 85 and 56% for the compost and manure application treatments respectively as compared to the control. Many other studies have reported similar increases in soil water retention (Hafez, 1974; Unger and Stewart, 1974; Salter and Williams, 1969; Mbagwu, 1989; Schjonning et al., 1994; Benbi et al., 1998) from the application of feedlot or barnyard manure. Martens and Frankenberger (1992) measured seasonal changes in gravimetric soil water content and found that application of hog manure increased soil water content 3% during the growing season when compared to the soils that didn’t receive the amendment. These improvements in soil water holding capacity and storage have been attributed to several factors including soil aggregation and structure improvements, an increase in total porosity, the direct effect of the addition of high specific surface area material, and even changes in soil texture (Khaleel et al., 1981; Sweeten and Mathers, 1985; Boyle et al., 1989; Haynes and Naidu, 1998).
A comprehensive study by Miller et al. (2002) evaluated the impact of long-term cattle manure application on the hydrologic properties of a clay loam soil. They found that manure significantly increased soil water retention, increased ponded infiltration rates by more than 200%, and saturated hydraulic conductivity increased, but found that manure had little to no effect on the unsaturated hydraulic conductivity of the soil. Similarly, Bhattacharyya et al. (2006) found that manure application increased infiltration rates. They attributed the changes to a better pore size distribution, which appeared to infer an increase in larger pores, but which isn’t clearly articulated within the manuscript. Based on this sampling of literature, it appears there is a general consensus that manure application has neutral to beneficial impacts on soil hydraulic properties, but questions as to the cause of these modifications remain.
In general, these changes are similar to those that would be suggested with increased soil organic matter content, as these studies suggested that manure leads to improved tilth, greater porosity, hydraulic conductivity, and increased soil water holding capacity. In the next Manure Scoop we’ll take a look at the evidence to support that manure is building soil organic matter and then do some back of the envelope math to evaluate what this may mean for Iowa soils.
Tuesday, October 31, 2017
As we get to the heart of land application season my thoughts always drift to the same concepts. How can we do better at moving manure from farmstead to field, quickly, safely, and environmentally consciously? Manure has long been considered a valuable input to the soil for crop production and in its broadest sense manure management is the science of figuring out the most appropriate use of animal manure and how to get the most benefit for the least expense while protecting air, soil, and water quality. When it comes to manure utilization it seems like every year is a discussion of how we can get 10-billion gallons or so of liquid manure applied quickly, safety, accurately, and as cost effectively as possible. There are several ways to do this: bigger equipment, more people in the manure business, extending application seasons either by planting crops with different harvest windows or developing technologies that allow application during the season.
Today I’m going to focus on just one little aspect though – nutrient delivery rates with drag line systems for dairies and pig finishing manure. My costs are all approximate as lots of factors can influence cost, but right now we are going to take a look at why application rate may be important.
Say we have two farms, one a dairy and the other a finishing swine farm, who each generate the same amount of available nitrogen for land application every year. Let’s say this is a 4800-head swine farm so it will generate about 1.75 million gallons of manure a year or about enough manure from 695 acres (approximately 60 lb N/1000 gallons). At this farm we’d have an application rate of about 2500 gallons per acre. At a dairy the manure would have closer to 10 pounds of N per 1000 gallons so we’d apply right around 15,000 gallons per acre and would be dealing with closer to 10 million gallons of manure.
For illustrative purposes, I’m going to ballpark $500,000 in equipment costs (pumps, hose, drags, and a toolbar) but that is all dependent on what you are using. In the case of swine manure let’s assume we have a 30-foot bar and can drive through the field at 7 mph, this means they can cover an 0.42 acres per minute and to get 2500 gallons per acre the flow rate would be about 1060 gpm. This means to get all 1.75 million gallons applied would take 27.5 hours and assuming the crew was about 50% efficient it would take about 55 hours overall. Just for fun in estimating, let’s assume run time costs about $500 an hour (tractors, fuel, wear and tear, etc.). If we figure a 5-year equipment life and that 1.75 million gallons is about 10% of the total gallons they apply every year, then or cost for manure here would be about $37,500 or about $0.02 a gallon of manure applied or about $0.36 per pound of N applied.
Now let’s take a look at the case of the dairy. Here we are covering the same number of acres and would have the same number of sets so let’s assume that setup time was again 27.5 hours, however we have lots more gallons to apply so the application will take a bit longer. In this case we can probably pump around 3000 a minute if everything is set up well so we’d take about 57 hours of application time so with setup time we’d have about 84 hours in application time. As we are applying more gallons this might represent 50% of the annual gallons this crew would apply. If you work this about we have about $42,000 in variable rate cost related to application time and about $50,000 in equipment depreciation for a total of $92,000. This would work about to about a $0.01 per gallon application cost or about $0.88 per pound of nitrogen applied.
So when you think about what your manure application, remember there is a lot that goes into that per gallon price and application rates can play a big role in that, but it’s important to also think in terms of fertilizer benefit you are providing.
Dragline manure application getting set for its next field.
Wednesday, September 20, 2017
I often get asked the question what does the future of the manure industry look like. I typically give a little thought and then reply, a lot like it does now, we’ll continue to try to get better at finding ways to more quickly and accurately apply the manure nutrients so we can better capture the fertilizer value. I say this because I mean it; manure can be a great fertilizer resource on a farm and when we think about, livestock production is a critical component of sustainability as the majority of nitrogen, phosphorus, and potassium we feed ends up in the manure and needs to be recycled.
Today I’m going to stop and consider this number a little for you – we are going to focus on liquid manure in Iowa. There is somewhere around 10 billion gallons of manure produced annually (give or take a billion here or there depending on rainfall and the accuracy of my animal populations, the production systems I assume farmers are using, and general variation). It’s a bit hard to fathom this number but I’m going to try a couple ways. The first is if we think of a 40-acre field the manure would be 767 feet tall, or just a little more than the 801 Grand (previously The Principal Building which as far as I can tell is the tallest building in Iowa. Of course Iowa really has around million acres so if we tried to put or manure on all of them each acre would only get around 500 gallons (or you know a little less than 0.02”).
As interesting as that is, today I wanted to take a look at slightly different topic, manure application logistics. So we know we are working with approximately 10-billion gallons of manure and if we look in the fall we have approximately 75-days between October and mid-December and then another 30 days of potential application in the spring. So we are looking at somewhere around 105 application days in a given year (give or take depending on the exact day we start applying and the number of days unsuitable due to soil and weather conditions). That means to get all our manure applied we need to apply somewhere in the neighborhood of 100-million gallons per day!
So what does the typical logistics of application look like?
If we think about a drag-line system, when it’s flowing we are probably in the neighborhood of 1500 gpm for a flow rate; however, there is some setup time involved as we move to new fields. Just for fun let’s figure that we are somewhere around 50% efficient with this system, that is it is running half the time and being reset the other half of the time. If this is true we’d average around 750 gpm or about 45,000 gallons per hour. Assuming 12-hours days (some companies run longer but I need some time to clean and move from farm to farm) we’d need about 18,500 days to finish all the manure in Iowa! Luckily there are lots of companies out there to help with this big task.
Figure 1. Manure application with low-disturbance injectors into covercrop.
Similarly, if a manure tanker is used (let’s just say it is a 7300-gallon tank and we get it 95% full with each load). Let’s say we are hauling three loads an hour then every hour we are moving 20,000 gallons. To finish hauling all the manure in Iowa in those 105-days we’d need somewhere around 400 manure spreaders going not stop 12 hours a day.
Luckily Iowa farmers and commercial manure applicators have recognized this challenge and continuously are purchasing new and better equipment to help ensure they are moving manure from farm to field as cost effectively and responsibly as possible.
Friday, August 11, 2017
I received a question the other day about my blog post from mid-July dealing with uncertainty in manure application rate selection. If you recall, I talked about the concept of insurance Nitrogen (N) and why it wasn’t advisable. That’s where I said something a little controversial, with uncertainty in inputs to our decision, such as manure nitrogen content, the ideal nitrogen rate goes down (just a little bit, but still down). This week I was asked how I made that conclusion and if there was different uncertainty from different types of manure.
Since the second part is a little easier, I’ll start with that one: Is there uncertainty for different types of manure (swine, solid cattle, liquid dairy) or are they all equally variable? The data I have suggests the coefficient of variation (standard deviation divided by the average) in nitrogen content of hog, dairy, layer, and beef manures were about 23, 40, 30, and 33%.
Keep in mind this only focuses on uncertainty in the actual nutrient content of the manure – there are actually numerous things that cause uncertainty in what we actually apply. Things like the amount of volatilization that occurs during agitation and application, the availability of nitrogen in the manure, how accurately we are hitting the desired application rate, how uniformly we are applying manure, and even when we apply the manure relative to crop need. Some of these we can control, some of these we can reduce the impact of by picking the right type of equipment, and in some cases we can get a better idea through sampling, but there will always be some uncertainty remaining (You can read more about dealing with uncertainty here, the value of manure sampling here, and about rate control here I know I hit on these 4R topics a lot, but while achieving the Iowa Nutrient Reduction Strategy is going to require more than just the 4R’s, they are R’s that impact the value we get from our manure helping make manure a more valuable commodity for our livestock producers.
Now the hard part of this question, why did I say uncertainty lowered the ideal manure application rate? The simple answer I created a model, liked the assumptions I made, and believed it. However, I recognize that is a very unsatisfactory answer to a curious farmer, a consultant that wants to give better information to a farmer, and even this extension engineer who is trying to provide the answer. So I looked back at my work and thought, there has to be an easier way to say this is true. Then in that moment a light bulb, I should be able to do this graphically (and who doesn’t like a picture!).
So a little bit to help to get us started, I need to go over two pictures then we’ll work on putting them together (excuse my lack of graphical design). The first is the Maximum Return to Nitrogen graph; the one shown in figure 1 is for Southeast Iowa for corn in a corn-soybean rotation with estimated nitrogen prices of $0.30 a pound and a value of corn at $3.50 per bushel. In case you haven’t seen the Maximum Return to Nitrogen Tool before you can find it here http://cnrc.agron.iastate.edu/About.aspx, but briefly its six states’ (Illinois, Iowa, Michigan, Minnesota, Ohio, and Wisconsin) approach to recommending nitrogen application rates. There are three lines plotted on the curve: the first (blue) is the gross return to nitrogen – this is the price of corn per bushel times the estimated number of bushel we’d expect from different nitrogen application rates (this is based on years of data and numerous research plots in those regions). The second (green) is the cost of fertilizer, it is the fertilizer price multiplied by the number of units of N we applied. Finally, we get the third line (red) which is the difference between the gross return and a fertilizer cost. This line shows us the point (the highlighted diamond) where that unit of nitrogen resulted in just enough corn yield to cover the cost of buying that last bit of nitrogen.
The second picture I’m going to show you is a normal distribution. I know what you are thinking the same thing my dad, Mr. Manure, would say, “That’s Greek to me.”(now you know where these terrible jokes come from!). Essentially there are a few key points from this figure we need to know. If you were told to guess one value to pick on this curve you’d want to pick the one at the peak, or the mean (its where you’d be most likely to be right) denoted with the Greek letter µ. The next is the shape of this curve (how wide or narrow that bell curve looks) is controlled by the standard deviation, denoted with the Greek letter σ. A big standard deviation leads to short, wide curves and while small standard deviations lead to narrow, high peaked curves. This standard deviation gives us our uncertainty – you see, about 68% of the time we’ll be within one standard deviation of the mean (the light blue area in figure 2), 95% of the time we’ll be within two standard deviations (the light blue and the dark blue in figure 2), and 99.7% of the time we’ll be within three standard deviations.
Figure 2. Illustration of a normal distribution.
Now the fun part – the math I did to get my original answer. I simply put this normal distribution onto our Net Return to N curve and looked for the point on the net return curve where the area under the net return to N curve of the left-half of the normal distribution and the right-half of the normal distribution are equal (the math intensive part is they have to balance when weighting this area by the probability of that N application rate occurring).
Figure 3. Normal distribution overlaid onto the maximum return to N curve (for most of Iowa, corn in a corn-soybean rotation).
What the uncertainty does is basically flatten out the yield curve. Say you are trying to put on 140 lb N/acre. There is a chance you hit this rate, there is also a chance that you only put on 100 lb N/acre and similarly there is a chance you actually put on 180 lb N/acre.
If you think about what happens at low application rates (below MRTN), there is a chance that there was more N in the manure than you anticipated. This would work to your advantage because we are in an extremely sensitive part of the yield response curve where just a little more nitrogen results in a lot more yield. If you think about, this is exactly what MRTN was designed to say; if we are below MRTN the benefit of a little extra N is worth it.
If you are on the right side of the curve (above MRTN) it works the opposite way. A little less N only causes minimal yield drop because the yield curve is relatively flat here, but a little more wastes the value of the nitrogen and gives you essentially no yield gain. Again, this makes sense because it is effectively what MRTN was designed to tell you.
Also, it’s reasonable any uncertainty we have is going to make us less profitable than if we know perfectly what we put on. It’s like playing the lottery, if we knew the winning number beforehand we could be sure to pick it every time. Even if we were trying for the right amount there is some probability that we missed that “ideal rate” and as a result either over applied nitrogen or under applied just a little.
Why did I say it was slightly more profitable to under apply than over apply? The difference between the two rates is marginal (about 5-10 pounds an acre). What I think is that as you get close to the MRTN rate even though you are a little below MRTN, the yield curve has already flattened out quite a bit. This puts us in a situation where if we are just a little low it doesn’t really change our yield, but if we are over that amount it’s costing us $0.30/lb N that could have been used elsewhere. I tried to show you why this would happen pictorially in figure 3). If you place a normal distribution over the Net Return to N (with the red dot representing the ideal point), you’ll see that the net return fell off a bit more quickly on the right side of the distribution then on than it rose on the left side of the distribution. This would mean if we have uncertainty, our ideal rate is actually to the left of the MRTN with no uncertainty.
However, you’ll also note the shape of the distribution matters. If it was narrower, the MRTN with and without uncertainty might be the same point. If the uncertainty is bigger, it might even move us to the right, that is a higher application rate than MRTN. This would happen if our distribution is wide enough that our uncertainty curve (that normal distribution) encompasses part of the yield response curve where yield responds rapidly to increases in nitrogen (figure 4).
Figure 4. Maximum return to nitrogen for corn in a corn-soybean rotation for Southeastern Iowa with normal distribution with high uncertainty overlaid on the curve.