Wednesday, June 9, 2021

How does uncertainty impact the manure nitrogen application rate you select?

 Selecting an appropriate nitrogen fertilizer rate is critical for optimizing profit from cornfields. Applying too little N reduces profit by reducing grain yield; too much N and you don’t get a return on the nitrogen you bought and can cause damage to the environment. In Iowa, most manure management plans are filled out using the yield goal method, with current university guidelines suggesting the use of the maximum return to nitrogen approach. If you are a long-time reader of this blog, you’ve probably seen both of these discussed before, so don’t worry, that isn’t the topic today. Instead, I’m focusing on uncertainties in the application and what that means for how we make decisions.

A lot of uncertainties exist when using manure as a fertilizer. Some examples include:

 · Nitrogen need of the crop (every growing season is a bit different)

· Spatial variation in nitrogen need to support crop production (because all soils aren’t the same)

· Nutrient content of the manure

· Nutrient variation from start to finish of manure application

· Application Rate Control and Variation in Application Rate

· Availability of the manure nitrogen to the crop

· Amount of nitrogen lost to volatilization

· Non-uniformity in application rate

 For now, I want to look at the manure application parts of this uncertainty and assume we know the crop response to nitrogen perfectly. How do all the variations and uncertainty impact the nitrogen application rate we should select? To answer this question, I first parameterized the yield response curve from the maximum return to nitrogen. The price of corn was set at $5.65 a bushel and nitrogen price at $0.40 a pound, which in a corn-soybean rotation gave an optimal nitrogen rate of 150 lb N/acre.

 The manure nitrogen content was set at 40 lbs N/1000 gallon, nitrogen availability at 95%, the nitrogen volatilization coefficient at 98%, and the desired application rate of 3706 gallons/acre calculated. A Monte Carlo simulation was then performed. For each variable that added uncertainty (manure N/content, Application rate, Volatilization coefficient, Nitrogen availability, and the knife-to-knife coefficient of variation), a normal distribution was constructed using the average value listed above and standard deviations of 2.75 lb N/1000 gallons, 250 gallons/acre, 0.01 % volatilization, and 0.05 % availability, respectively. Knife-to-knife variation varied between 0 and 100% were evaluated. I then performed 3500 simulations drawing randomly from the distributions I created to determine the nitrogen application rate for each knife (for distributions with natural limits, such as volatilization coefficient, no values over 100% were allowed).

 A lost value from application variability and uncertainty was calculated. If the actual amount of available N applied was greater than the MRTN rate of 150 lb N/acre, the value was set at the differences between the amount of N used minus 150 lb N/acre times a nitrogen price of $0.40 a pounds. If the nitrogen application rate was less than the MRTN rate, the value was set at the difference between corn yield at MRTN and the projected corn yield at the N rate applied times a corn price of $5.65 a bushel. The average loss in profit for all 400 knife simulations for each of the 3500 simulations was calculated, and then the average and standard deviation of the 3500 simulations were calculated.

A maximum return curve was calculated by taking the profit that would have been generated with perfect information (200 bu/acre x $5.65/bu – 150 lb N/acre x $0.40/lb N) minus the profit lost from uncertainty and application variability using the procedure listed above. Here we see an interesting trend – the uncertainty of ammonia volatilization and nitrogen availability and the variation in volumetric application rate and manure nitrogen content during the application, make it advisable to apply six pounds more available nitrogen per acre than if we didn’t have these variations. This occurs as the economics of nitrogen application is non-symmetrical, with the cost of being a pound short greater than being a pound heavy. Suppose we factor in any knife-to-knife application variability. The story gets more interesting, with the ideal application rate first increasing (until we reach a knife-to-knife application variability of about 40%, where the ideal rate is 167 pounds of N/acre, or 17 pounds/acre higher than the known nitrogen response curve we put in. Ideal nitrogen rate then decreasing to 137 lb available N/acre.


Figure 1. Impact of knife-to-knife variability of the effects of the maximum return to nitrogen for spring-applied swine manure to corn in a corn-soybean rotation. The ideal rate varies with our machinery variation.


But what about a fall application? As the MRTN curve is based on spring nitrogen applications, I added a term to the model to account for N-loss from fall to spring. For fall applications, I assumed an average of 15 lbs N/acre with a standard deviation of 15 lb N/acre and performed the same Monte Carlo simulation as above (but with the available N corrected for estimated nitrogen loss.

Figure 2. Impact of knife-to-knife variability on the impact of the maximum return to nitrogen for a fall and spring-applied swine manure to corn in a corn-soybean rotation and continuous corn rotations. The ideal rate varies with our machinery variation.

Almost all the curves looked the same. For example, the Maximum Return to Nitrogen in a continuous corn rotation was approximately 50 pounds higher in the continuous corn rotation than in the corn-soybean rotation, whether the manure was applied in the fall or the spring. The difference was impacted slightly by the knife-to-knife variability of the application equipment, but only slightly. Similarly, while the nitrogen loss from fall application was set at 15 lb N/acre, the fall application rates were on average 22 lb N/acre higher to hit the optimal rate.

So overall, where does this leave us. There is uncertainty and variability in every decision we make. The more confident we are about our equipment and manure, the closer our rate should be to the “true” MRTN. However, from an economic perspective, if there is uncertainty or variability in what we are doing, the right rate for us sneaks upward just slightly. This insurance N helps us in years we’d otherwise be short. And this is why we still talk about the 4Rs of right rate, right place, right timing, and the right type of fertilizer.