In mbask/fertplan: Compute Components Of NPK Fertilization Plans

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>")
library(data.table)
library(fertplan)

This document will walk you through a simulation of a real fertilization plan for phosphorus ($P_2O$) and potassium ($K_2O_5$) nutrients. Both fertplan and this document depend on package data.table but its usage is not in any way mandatory.

Fertilization plan balances

This estimation of phospohorus (P) and potassium (K) fertilization concentrations for erbaceous and tree crops will strictly follow the indications formulated in the regulation drawn up by the Italian Region of Lazio [@guidelines2020], hereafter the guidelines.

Fertilization concentrations in kg/ha are estimated as the net resultant of a balance between the phosphorus or potassium pool available for the crops and the phosphorus or potassium losses.

Phosphorus

The P balance involves 3 flow components. Similarly to N plans, flows that increase P availability to the crop are > 0 (positive sign). Flows that deplete soil P pool or PN availability for the crop are < 0 (negative sign).

The P flow components include:

• $f_{P,a}$ Crop demand for phosphorus on the basis of its expected yield and its phosphorus absorption coefficient in percent. Absorption coefficients are tabled per a number of different crops in the guidelines
• $f_{P,b}$ Phosphorus concentration currently in the soil due to its fertility. Three multiplicative sub-components contribute to this flow: soil depth, apparent soil density, and offset from average "normal" soil P concentration. fertplan estimates "normal" soil phosphorus concentration from Table 10 of the guidelines (page 32) by considering the average value of the P ranges for each crop class and soil texture. As an example the tabled normal P concentration range for Sunflower in loam soil is [18,25] whereas the average range value 21.5 mg/kg is used by fertplan for further elaboration.
• $f_{P,c}$ Phosphorus immobilized by limestone (Calcium). Limestone has a potential to immobilize phosphorus in soil and let it become unavailable for crop take up.

The final phosphorus balance is computed as: $$B_P = f_{P,a} + f_{P,b} \cdot f_{P,c}$$

Potassium

The K balance involves 3 flow components. Similarly to N plans, flows that increase K availability to the crop are > 0 (positive sign). Flows that deplete soil K pool or PN availability for the crop are < 0 (negative sign).

The K flow components include:

• $f_{K,e}$ Crop demand for potassium
• $f_{K,f}$ Potassium concentration currently in the soil due to its fertility. Three multiplicative sub-components contribute to this flow: soil depth, apparent soil density, and offset from average "normal" soil K concentration.
• $f_{K,g}$ Potassium immobilized due to clay content
• $f_{K,h}$ Potassium lost due to leaching as a function of soil texture (specifically clay content)

The final potassium balance is computed as: $$B_K = f_{K,e} + f_{K,f} \cdot f_{K,g} + f_{K,h}$$

First step: load soil analyses

Let's begin with some minimal data from soil physical and chemical analyses on a few sampling points in the field.

data(soils)
soil_dt <- soils[, c("id", "P_ppm", "Limestone_pc", "K_ppm", "Clay_pc")]
knitr::kable(soil_dt)

The table shows the soil chemical and physical status before the planned crop sowing. The soil analyses elements that will be fed the phosphorus balance estimation are:

• P_ppm, Total phosphorus content in ppm (eg. mg/kg)
• Limestone_pc, Limestone content in %

The soil analyses elements that will be fed the potassium balance estimation are:

• K_ppm, Total potassium content in ppm (eg. mg/kg)
• Clay_pc, Clay content in %

The id feature is not relevant to the balance estimation.

Second step: variable configuration

A few environmental and crop-related variables need to be set. Some variables need to match those set out in the guidelines tables, while a few others have to be derived from external sources.

Let's first translate the guidelines tables into english:

fertplan::i18n_switch("lang_en")

Matching-variables are:

• Crop, this is the name of the crop to be sown and will be used to look up its phosphorus or potassium demand in table 15.2 (page 63) of the guidelines to contribute to $f_{P,a}$ or $f_{K,e}$ components. The name must match one of the following crop names available. Partial matching is not allowed. Note that fertplan implementation of the table has separated the crop column into two features, the actual "crop" and "part" (eg fruits, whole plant, and so on). The available crops are:

knitr::kable(fertplan::get_available("crop"))

• Crop part, this is the part of the crop to be sown that will contribute to $f_{P,a}$ or $f_{K,e}$ components. Note that the nutrient demand by crops may greatly differ upon the crop part considered. As an example P and K coefficients for "sunflower" crop are:

knitr::kable(fertplan:::tables_l$all_01_dt[crop == "Sunflower" & element %in% c("P2O5", "K2O"), ])

As a reference crop parts include:

knitr::kable(fertplan::get_available("part"))

• Texture, soil texture, one of r paste0("'", get_available("soil texture"), "'", collapse = ", "). Soil texture enters in a $f_{P,b}$ and $f_{P,c}$ or $f_{K,f}$ flows of the P or K balances.

• Crop class, this is the class of crop to be sown to be looked up in table 10 (page 32) of the guidelines. It is used to estimate the "normal" phosphorus supply in soil. Crop class contributes to the $f_{P,b}$ component. Available crop classes are:

knitr::kable(fertplan::get_available("crop class"))

Environmental and crop-related variables include:

• Expected yield, it contributes to $f_{P,a}$ component, unit of measure kg/ha. It can be estimated from statistical estimates of crop areas and yields at province, regional, or national level. As an example, wheat expected yield is 2,900 kg/ha in the province of Rome, based on 2019 Istat estimates.

• Soil depth, depth of soil tillage practise, in $cm$. This is usually 30 or 40 cm, for shallow tillage (the former) or deep tillage (the latter). A soil depth coefficient measured as depth / 10 enters the $f_{P,b}$ or $f_{K,f}$ flow components as a multiplicative coefficient (eg 3 for shallow tillage or 4 for deep tillage).

Let's now set the variables values and bind them to the soil analysis table. Let's suppose the values are constant among all soil samples, as it may be the case when all sampling points come from a uniform field that will be sown with the same crop:

soil_l <- list(
    crop                 = "Durum wheat",
    part                 = "Seed",
    crop_class           = "Durum wheat",
    expected_yield_kg_ha = 2900L,
    texture              = "Loam",
    soil_depth_cm        = 30L)

Third step: estimate the components of P or K balance

Let's estimate the $f_{P,a|b|c}$ and $f_{K,e|f|g|h} components:

nutrient_dt <- demand_nutrient(
  soil_dt, 
  soil_l, 
  nutrient  = c("phosphorus", "potassium"), 
  blnc_cmpt = TRUE)
knitr::kable(nutrient_dt)

All components were estimated. Remember that positive values are demand pools of nutrient in soil or nutrient flows leaving the field; negative values are current nutrient pools in the soils that are available for assimilation to the crop or that will be available during the time-frame of crop growth.

The phosprorus components are:

fertzl_dt <- cbind(nutrient_dt, soil_dt)
fertzl_p_cols <- grep(
  pattern = "^[A-Z]_P_kg_ha$", 
  x       = colnames(fertzl_dt), 
  value   = TRUE)
knitr::kable(fertzl_dt[, ..fertzl_p_cols])

The potassium components are:

fertzl_k_cols <- grep(
  pattern = "^[A-Z]_K_kg_ha$", 
  x       = colnames(fertzl_dt), 
  value   = TRUE)
knitr::kable(fertzl_dt[, ..fertzl_k_cols])

Fourth step: estimate P or K demand

We are finally arrived to the last step of assembling all components of the P or K balance. Let's compute the balance following the previous balance equation:

fertzl_dt[, p_demand_kg_ha := A_P_kg_ha + B_P_kg_ha * C_P_kg_ha]
fertzl_dt[, k_demand_kg_ha := E_K_kg_ha + F_K_kg_ha * G_K_kg_ha + H_K_kg_ha]
knitr::kable(fertzl_dt[, c("id", "p_demand_kg_ha", "k_demand_kg_ha")])

All sampling points end up needing a supply of phosphorus of r fertzl_dt[, mean(p_demand_kg_ha)] kg/ha and of r fertzl_dt[, mean(k_demand_kg_ha)] on average.

Alternative pathway

A more direct pathway to get to B_P or B_K estimation is to set argument blnc_cmpt of demand_nutrient function to FALSE (the default setting). This will have the effect of returning directly B_P or B_K instead of its balance components thereby skipping the fourth step:

nutrient_dt <- demand_nutrient(
  soil_dt, 
  soil_l, 
  nutrient = c("phosphorus", "potassium"), 
  blnc_cmpt = FALSE)
knitr::kable(nutrient_dt)

That's it as far as phosphorus and potassium fetilization plans are concerned.

References

mbask/fertplan documentation built on July 3, 2020, 12:01 p.m.