Calculate critical-nitrogen allowances with the Schulte-Uebbing method.
Source:R/critical_n_reproduce.R
calculate_critical_n.RdComputes the critical nitrogen input and surplus of every 0.5-degree cell
with the equations of Schulte-Uebbing et al. (2022, Nature 610, 507-512,
doi:10.1038/s41586-022-05158-2, Supplementary Information Eqs. 1-36),
instead of reading the fixed 2010 layers of their archive
(doi:10.5281/zenodo.6395016) as read_critical_n() does by default. The
critical input is the fertiliser and manure that keeps each of three
impacts at its threshold, plus the constant fixation and the deposition it
implies:
"de": deposition at the critical load of the cell's biome (5 to 20 kg N/ha of cell area, SI Supplementary Table 2);"sw": 5 mg N/l in runoff to surface water (SI Eq. 12);"gw": 11.6 mg NO3-N/l in water leaching from agricultural soil (SI Eq. 29);"mi": the lowest of the three, land use by land use (SI Eqs. 31-32).
Fertiliser and manure change in their current proportion (SI Eq. 3);
fixation, the non-agricultural sources and extensive grassland stay at
their current values. Where the non-agricultural sources alone exceed a
threshold, fertiliser and manure are set to zero (critical_rule
"non_agricultural_floor"). Where the threshold allows more than crops can
use, the input is cut off at the input needed for the regional yield
potential at current nitrogen use efficiency, capped at 0.8 (Methods
Eqs. 1-2; "yield_potential_cap"). The critical surplus is input minus
uptake (SI Eqs. 5-6).
With the archive's own 2010 inputs the result reproduces the deposited
layers closely but not exactly, because the source does not print every
rule it applied (see the section below). Supplying inputs from another
year or model applies the same method to them.
Arguments
- inputs
Optional tibble with one row per cell and the IMAGE-GNM quantities listed by
whep:::.critn_input_specs():cell_id,lon,lat, areas in hectares (area_total_ha,area_arable_ha,area_intensive_ha,area_extensive_ha,area_natural_ha), the IMAGEbiomeandimage_regioncodes,runoff_l(litres per year) and the nitrogen flows in kg N per cell per year. Fertiliser and manure are net of NH3, as the archive deposits them. WhenNULL(default) the 2010 inputs are read from the archive'sInput_files.- dir
Optional archive directory, resolved as in
read_critical_n(). Ignored wheninputsis supplied.- verify_source
If
TRUE(default), the archive's input rasters are checked against the package's content manifest before they are read. Ignored wheninputsis supplied.- example
If
TRUE, return the result for a small fixture of four cells instead of reading data. Defaults toFALSE.
Value
A tibble with one row per cell, threshold and land-use scope:
cell_id, lon, lat, image_region, critical_threshold ("de",
"sw", "gw" or "mi"), critical_land_use ("ara", "igl" or
"all"), area_ha (the hectares of that scope), the critical
critical_n_input_kgn_ha and critical_n_surplus_kgn_ha, the current
current_n_input_kgn_ha and current_n_surplus_kgn_ha (all kg N per
hectare per year), critical_rule ("environmental_threshold",
"non_agricultural_floor" or "yield_potential_cap"; NA for "all")
and method_critical_n = "reproduced". A cell whose land use has no
current fertiliser or manure, no crop uptake, or no agricultural leaching
has no critical value there, as in the archive.
Rules recovered from the deposited layers
The SI prints the equations for cells with one reducible agricultural land use and states that cells combining arable land with grassland follow "slightly different" formulas. The rules for those cells, and several values the text leaves out, were recovered by recomputing the archive's outputs from its inputs: fertiliser and manure enter gross of their NH3 emission; the groundwater limit is 11.6 mg NO3-N/l (the article's Methods print 11.3); ice cells get 5 kg N/ha of critical deposition (Supplementary Table 2 prints "n.a."); the fertiliser share is clipped to [1e-4, 1 - 1e-4]; the regional yield-gap ratios carry three decimals (each rounds to the two printed in Supplementary Table 5). The cut-off binds where uptake at the critical input (with the deposition of every land use in the cell) reaches uptake at yield potential; with NUE above 0.8 this raises the input to the cut-off input. In cells with both arable land and intensive grassland, the NH3 the critical deposition leaves room for is shared by their current NH3 emission, and both land uses are scaled by one factor for the surface-water threshold. For groundwater there, each land use is held to its area share of the critical leaching and the one that must fall further is solved first; this rule is a reconstruction, and those cells carry the remaining differences.
One departure is deliberate: "mi" is the lowest of the three thresholds
as SI Eq. 31 defines it. In 57 arable cells where deposition and
groundwater both sit at the non-agricultural floor, the deposited
all-impacts layer carries the higher surface-water value instead.
Examples
calculate_critical_n(example = TRUE)
#> # A tibble: 36 × 13
#> cell_id lon lat image_region critical_threshold critical_land_use area_ha
#> <int> <dbl> <dbl> <int> <chr> <chr> <dbl>
#> 1 89786 72.8 27.8 18 de ara 45604.
#> 2 61368 -96.2 47.2 2 de ara 49086.
#> 3 59642 121. 48.8 20 de ara 28095
#> 4 59642 121. 48.8 20 de igl 118959
#> 5 61591 15.2 47.2 11 de igl 59438.
#> 6 89786 72.8 27.8 18 de all 45604.
#> 7 61368 -96.2 47.2 2 de all 49086.
#> 8 59642 121. 48.8 20 de all 147054
#> 9 61591 15.2 47.2 11 de all 59438.
#> 10 89786 72.8 27.8 18 sw ara 45604.
#> # ℹ 26 more rows
#> # ℹ 6 more variables: critical_n_input_kgn_ha <dbl>,
#> # critical_n_surplus_kgn_ha <dbl>, current_n_input_kgn_ha <dbl>,
#> # current_n_surplus_kgn_ha <dbl>, critical_rule <chr>,
#> # method_critical_n <chr>