How Do You Calculate Variable Phosphorus and Potassium Rates?

Grid sampling method. For this method, samples are taken in specific areas of the field. Their coordinates are recorded, and, based on the laboratory testing, specialists predict the nutrient content throughout the field.

How reliable is this method? Take a look at this example. These are two maps of the same 20-ha field in Belarus. The map on the left is based on a sampling density of 100 meters; the one on the right shows a field with a sampling density of 50 meters.

These maps are clearly different, and the one with a higher sampling density is more accurate. But high sampling density also means it costs more to conduct a soil nutrient analysis. Let’s say we have a 40-ha field. With a grid of at least 0.9 ha, we’ll have to take about 44 samples. On average, it costs between $ 45 and $ 80 to analyze one sample (depending on the country and many other factors). So the complete soil analysis will amount to about $ 2000−3500. Not every farmer can spend this much on an analysis. But if we apply fertilizer based on the map with a lower density, we’ll only increase the spatial heterogeneity of phosphorus and potassium, which would make the yield unpredictable.

The grid sampling method can be either expensive (with a dense sampling grid) or risky (if the density is low).

Sampling-by-zone method. With this method, the field is divided either into equal rectangles or into zones by relief, yield, conductivity, and other indicators. A mixed soil sample is taken in each of these zones and analyzed.

How reliable is this method? In my experience, it’s not very reliable. I’ve been testing different methods of selecting zones in the field since 2014. I’ve tested various methods that agricultural consulting companies practice. That would include selecting zones by conductivity, relief, and humus content maps, by soil maps, and by a grid of equal-sized rectangles.

According to my data, the zones obtained for the field aren’t homogeneous in terms of phosphorus and potassium content, regardless of the method chosen. For example, even the 1.5-ha area with homogeneous humus content has segments with high and low potassium and phosphorus content. The same is true for zones selected by all other methods.

That’s why I don’t trust this method and recommend that you approach it with caution.

When calculating fertilizers by productivity zones, we don’t rely on the difference in soil nutrient content; instead, we look at how yields change in the field.

This makes sense for two reasons. First, the yield isn’t always limited by phosphorus and potassium content. For example, you put phosphorus and potassium in the field, expecting to get a yield of 8 t/ha, but instead, you get 2 t/ha each year in some areas. I doubt a shortage of phosphorus and potassium is the reason for it. The cause most likely lies in a lack of moisture, low humus content, or soil acidity that also lowers yield. That’s why it’s important not just to determine the fertilizer rate accurately but also to find and eliminate limiting factors.

Secondly, this method is simpler and less expensive. Lots of combine manufacturers equip their machinery with sensors. These sensors record the weight of the grain that hits the elevators and links that value to field coordinates. To compile a productivity zone map for a field, we need to collect yield data for the past four years and compare each year’s data. In high productivity zones, soil nutrient removal is always higher than in low productivity zones. When focusing on these differences, we can accurately identify the rate of phosphorus and potassium for each area of the field.

Another way to do this, if you don’t have specialized equipment or can’t collect yield data, is to identify productivity zones and calculate fertilizer rates in the OneSoil web app.

To calculate variable-rate phosphorus and potassium fertilizer application using OneSoil, you first need to register in the web app. Registering in and using OneSoil is free for everyone, always. Here's what's next:

To define productivity zones, we learned how to model relative yield values. In other words, we don’t know how many tons were harvested from this or that part of the field, but we do know a specific area’s productivity relative to the entire field. For example, if the crop yield for the whole field was 10 tons, and area X yielded 2 tons, its relative yield is 20%.

Now let’s talk about how the calculation is made. To learn how to restore yield data, we used several years' worth of Sentinel-2 satellite images and the database that we’ve compiled on over 40,000 hectares of fields. Our team compared these actual yield figures and vegetation indices in various stages of plant development and found a pattern among them. Armed with this information, we created an algorithm to calculate relative yield in a field.

How reliable is this? Let’s use an example to get to the bottom of this. Just below are four years' worth of yield maps. We modeled the maps for 2014 and 2016. The ones for 2015 and 2017 are based on actual data collected using a combine.

Despite the difference in the weather and the crops being cultivated, most of the field is stable in terms of its yield numbers, while the locations of productivity zones in the field are consistent year after year. What that tells us is that we can trust the maps with modeled yield data.