Derive the binding critical-nitrogen threshold per cell. — build_critical_n

Identifies, for every 0.5-degree cell, the impact threshold whose critical nitrogen surplus is lowest among the three threshold-specific surfaces of Schulte-Uebbing et al. (2022): atmospheric deposition ("de"), groundwater nitrate ("gw") and surface-water eutrophication ("sw"). That threshold is the one that binds. The archive's own threshold-exceedance map (read_critical_n() with var = "threshold_exceedance") is a different quantity: it records which thresholds the 2010 surplus exceeds.

binding_threshold is "deposition", "groundwater", "surface_water", a two-way tie, "yield_potential_cap" or "non_agricultural_floor". A two-way tie is recorded explicitly by joining both tied thresholds with + in that fixed order, for example "groundwater+surface_water". Ties are exact equalities of the deposited values: on the real archive no surface lies within 1e-6 kg N/ha of the cell minimum without equalling it, so a tolerance would change nothing. A cell missing from any of the three surfaces gets NA.

A cell where all three critical surpluses are equal has no environmental threshold that binds on its own. Schulte-Uebbing et al. (2022, Nature 610, Methods) set such a threshold-independent value by one of two rules, and the label names which one:

"non_agricultural_floor": all three thresholds are exceeded (each threshold-specific exceedance of the critical surplus is positive) or the tied critical surplus is negative. The source's "Aggregation to regional and planetary boundaries" section states: "Where N losses from non-agricultural sources alone exceeded thresholds, critical N inputs from fertilizer and manure were set to zero." The critical input is then the fixation and deposition left over, the same for every threshold.
"yield_potential_cap": every other tie. Step 4 of the source's Methods reads: "for areas with no threshold exceedance, cut off critical inputs and surplus at a maximum value, set to the input level required to obtain crop yield potentials", with Nin(crit,max) = Nup(Yp) / NUE(act), where Nup(Yp) is crop nitrogen uptake at potential yield and NUE(act) the current nitrogen use efficiency, "capped ... at 0.8".

A tie whose critical surplus is not negative and whose exceedance is missing on any threshold cannot be assigned to either rule and gets NA. On the real archive the three critical inputs are identical in every tied cell. The two labels count 293 floor and 8,895 cap cells of 28,573 for "ara", 293 and 9,138 of 28,881 for "all", and 0 and 1,727 of 11,740 for "igl". The split matches the archive's threshold-exceedance map exactly: every floor cell carries code 8 and every cap cell code 1. The 293 floor cells include 3 with a negative critical surplus (minimum -21.78 kg N/ha), and their median critical input is 38.7 kg N/ha against 90.7 for the "all" cap cells.

When the deposited minimum-of-all-media surface ("mi") is supplied, binding_matches_mi reports whether it equals the lowest of the three threshold-specific surpluses. Where it does not, the relation between "mi" and the three surfaces is undetermined: "mi" differs from min(de, gw, sw) there and the source text does not explain why. On the real archive this happens in 1,623 of 28,573 cells for "ara" (maximum gap 159.5 kg N/ha), 1,540 of 28,881 for "all" (159.5 kg N/ha) and 1,480 of 11,740 for "igl" (479.1 kg N/ha), with "mi" above the minimum in some cells and below it in others. binding_threshold still names the argmin of the three surfaces in those cells.

Usage

build_critical_n_binding(
  critical = NULL,
  exceedance = NULL,
  land_use = c("all", "ara", "igl"),
  dir = NULL,
  example = FALSE
)

Arguments

critical: Optional named list of read_critical_n() critical-surplus layers (var = "critical_n_surplus") with elements de, gw and sw, and optionally mi, each stamped with its own threshold and with land_use. When NULL (default) the four layers are read from the archive with read_critical_n(), together with exceedance.
exceedance: Named list of read_critical_n() exceedance layers (var = "exceedance") with elements de, gw and sw, used only to tell the two kinds of three-way tie apart. Required when critical is supplied; read from the archive when both are NULL (default).
land_use: Land-use scope: "all", "ara" or "igl", as in read_critical_n(). Supplied layers must carry this scope.
dir: Optional archive directory passed to read_critical_n() when critical is NULL.
example: If TRUE, return a small fixture instead of reading data. Defaults to FALSE.

Value

A tibble with one row per cell: cell_id, lon, lat, critical_land_use, the three threshold-specific critical surpluses critical_de_kgn_ha, critical_gw_kgn_ha, critical_sw_kgn_ha (kg N per hectare per year), their exceedances exceedance_de_kgn_ha, exceedance_gw_kgn_ha, exceedance_sw_kgn_ha, the minimum critical surplus binding_critical_kgn_ha, the binding_threshold label, the deposited critical_mi_kgn_ha and the logical binding_matches_mi (both NA when mi is not supplied).

Examples

build_critical_n_binding(example = TRUE)
#> # A tibble: 5 × 14
#>   cell_id   lon   lat critical_land_use critical_de_kgn_ha critical_gw_kgn_ha
#>     <int> <dbl> <dbl> <chr>                          <dbl>              <dbl>
#> 1  128521  0.25  0.75 ara                               50                 45
#> 2  128522  0.75  0.75 ara                               90                 90
#> 3  128523  1.25  0.75 ara                                4                  4
#> 4  129241  0.25  0.25 ara                               12                 40
#> 5  129242  0.75  0.25 ara                               60                 18
#> # ℹ 8 more variables: critical_sw_kgn_ha <dbl>, exceedance_de_kgn_ha <dbl>,
#> #   exceedance_gw_kgn_ha <dbl>, exceedance_sw_kgn_ha <dbl>,
#> #   binding_critical_kgn_ha <dbl>, binding_threshold <chr>,
#> #   critical_mi_kgn_ha <dbl>, binding_matches_mi <lgl>