Prescription maps for Variable Rate Application

Agriculture
1

Based on a youtube video (https://www.youtube.com/watch?v=wWOifd3Xzo4), I tried to make a variable fertilizer application map.

Everything is explained very well, but the formula at the end of the video is quite confusing.

Anyone know the meaning of the ‘‘spread’’ parameter in the formula?

For example, if I have made 3 zones for VRA, how can I can calculate correct amount of fertilizer needed if I want to use a dose of 200 kg/ha?

Thanks in advance,
Rados

2

Choosing the Formula

You have two options:

  1. Homogenize: Rate zone = Rate flat - [Rate flat * (Zone value - Field average) / Field average * Spread]
  • This applies more fertilizer to zones with lower index values (below average) and less fertilizer to zones with higher index values (above average). This is typical for nitrogen, aiming to bring lower-performing areas up.
  1. Heterogenize: Rate zone = Rate flat + [Rate flat * (Zone value - Field average) / Field average * Spread]
  • This applies more fertilizer to zones with higher index values and less to zones with lower index values. This might be used to push high-potential areas even further or for specific inputs other than standard NPK.

For typical variable rate fertilizer application aiming to correct deficiencies, the Homogenize formula is usually the one you’d use.

Example Calculation

Let’s set up your scenario:

  • Number of Zones: 3
  • Planned Average Rate (Rate flat): 200 kg/ha
  • Strategy: Homogenize (apply more to lower index zones, less to higher index zones)

Now, we need some hypothetical index values for your zones (these would come from your Zonation analysis in PIX4Dfields, often based on NDVI or similar vegetation indices):

  • Assume Zone 1 (Low Productivity): Zone value = 0.5
  • Assume Zone 2 (Medium Productivity): Zone value = 0.7
  • Assume Zone 3 (High Productivity): Zone value = 0.9
  1. Calculate the Field Average Index Value (Field average): Field average = (0.5 + 0.7 + 0.9) / 3 = 2.1 / 3 = 0.7
  2. Choose a Spread Value: This is subjective and depends on your agronomic strategy. Let’s choose Spread = 1.0 for this example. This means the percentage adjustment to the rate will be equal to the percentage deviation of the zone’s index from the field average index.
  3. Calculate the Rate for Each Zone using the Homogenize Formula:
  • Zone 1 (Index = 0.5): Rate zone1 = 200 - [200 * (0.5 - 0.7) / 0.7 * 1.0] Rate zone1 = 200 - [200 * (-0.2) / 0.7 * 1.0] Rate zone1 = 200 - [200 * -0.2857 * 1.0] Rate zone1 = 200 - [-57.14] Rate zone1 = 200 + 57.14 = **257.14 kg/ha**
  • Zone 2 (Index = 0.7): Rate zone2 = 200 - [200 * (0.7 - 0.7) / 0.7 * 1.0] Rate zone2 = 200 - [200 * 0 / 0.7 * 1.0] Rate zone2 = 200 - 0 = **200 kg/ha** (The zone with the average index gets the average rate)
  • Zone 3 (Index = 0.9): Rate zone3 = 200 - [200 * (0.9 - 0.7) / 0.7 * 1.0] Rate zone3 = 200 - [200 * (0.2) / 0.7 * 1.0] Rate zone3 = 200 - [200 * 0.2857 * 1.0] Rate zone3 = 200 - 57.14 = **142.86 kg/ha**

Summary of Example Results (Spread = 1.0):

  • Zone 1 (Low Index): 257.14 kg/ha
  • Zone 2 (Medium Index): 200.00 kg/ha
  • Zone 3 (High Index): 142.86 kg/ha

If you chose a different Spread, say Spread = 0.5, the adjustments would be halved:

  • Zone 1: 200 + (57.14 / 2) = 228.57 kg/ha
  • Zone 2: 200 kg/ha
  • Zone 3: 200 - (57.14 / 2) = 171.43 kg/ha

If you chose Spread = 2.0, the adjustments would be doubled:

  • Zone 1: 200 + (57.14 * 2) = 314.28 kg/ha
  • Zone 2: 200 kg/ha
  • Zone 3: 200 - (57.14 * 2) = 85.72 kg/ha

In conclusion: The ‘Spread’ parameter allows you to fine-tune how aggressively your application rates vary based on the index differences between your zones. You’ll need to select a value that aligns with your agronomic goals for the field.

3

Julius, thank you very much for your detailed answer. Everything is explained very well!

But I have to ask something more about the parameter “Spread”.

As you mentioned in the first example where you would use a “Spread” value of 1, using that value makes no sense since it is the same as removing the “Spread” value from the formula. On the other hand, if we put a “Spread” value of 1.1, it changes things quite a bit. That’s why I’m a little confused by that “Spread” value.

To be clear, we are talking about differences in the values ​​of the NDVI (or if we used some other vegetation index) index by zones, actually it is the mean index value!?

If so, since it is related on the index differences, can some correlation be made depending on how much the difference in the indexes is on how much should the “Spread” value be?

In my case I have 3 zones with values ​​of 0.245; 0.350 and 0.529? What would be a realistic “Spread” value and how can I calculate it? I ask all this because changing these values affects the amount of fertilizer used?

Finally, one more question, is there a limit from which the “Spread” value should not be higher or lower? Because if, for example, in my case, for the zone that has a value of 0.529, I put the “Spread” value = 3, the amount of fertilizer that I need to apply goes into the minus??

Thanks in advance,
Rados

4

Yes you can remove “Spread” if you just want to change your inputs the same order of magnitude as the vegetation index varies across the zones. But from experience a 10% change in NDVI for example will not mean a 10% change in biomass or final yield, it would be much more.

To be clear, we are talking about differences in the values ​​of the NDVI (or if we used some other vegetation index) index by zones, actually it is the mean index value!

Yes thats the average per zone. You can see the values here in this screenshot:

image
image1920×1259 192 KB

If so, since it is related on the index differences, can some correlation be made depending on how much the difference in the indexes is on how much should the “Spread” value be?

Finally, one more question, is there a limit from which the “Spread” value should not be higher or lower? Because if, for example, in my case, for the zone that has a value of 0.529, I put the “Spread” value = 3, the amount of fertilizer that I need to apply goes into the minus??

Hard to say its and agronomic decision. But I would propably go with 1.5 to 2 for the Spread, otherwise it will have no difference compared to flat rate.

5

Anyway, thanks for the clarifications, it’s much clearer to me now!