Package {wefnexus}

Type:	Package
Title:	Water-Energy-Food-Nutrient-Carbon Nexus Analysis for Agronomic Systems
Version:	1.1.0
Description:	Provides functions for analysing Water-Energy-Food-Nutrient-Carbon (WEFNC) nexus interactions in agricultural production systems. Includes functions for computing water use efficiency (WUE), water productivity (WP), and water footprint (WF) including green, blue, and grey components following the methodology of Hoekstra et al. (2011, ISBN:9781849712798). Includes energy budgeting tools for energy use efficiency (EUE), energy return on investment (EROI), net energy (NE), and energy productivity (EP). Computes nutrient use efficiency (NUE) metrics including agronomic efficiency (AE), physiological efficiency (PE), recovery efficiency (RE), and partial factor productivity (PFP) as defined by Dobermann (2007) https://digitalcommons.unl.edu/agronomyfacpub/316/ and Congreves et al. (2021) <doi:10.3389/fpls.2021.637108>. Estimates carbon footprint (CF), greenhouse gas (GHG) emissions, soil organic carbon (SOC) stocks, and global warming potential (GWP) using Intergovernmental Panel on Climate Change (IPCC) Sixth Assessment Report (AR6) default values (CH4 = 27, N2O = 273) as reported in Forster et al. (2021) <doi:10.1017/9781009157896.009>. Computes composite Water-Energy-Food-Nutrient-Carbon (WEFNC) nexus indices, trade-off correlation matrices, and generates radar and heatmap visualizations for comparing agricultural treatments. Supports conservation agriculture (CA), irrigated and rain-fed systems, and arid and semi-arid production environments. Methods follow Lal (2004) <doi:10.1016/j.envint.2004.03.005> for carbon emissions from farm operations, and Hoover et al. (2023) <doi:10.1016/j.scitotenv.2022.160992> for water use efficiency indicators. Version 1.1.0 adds a one-call workflow for replicated field trials, analysis of variance with standard error of mean (SEm), critical difference (CD) and coefficient of variation (CV), objective indicator weights by the entropy, CRITIC (Diakoulaki et al. (1995) <doi:10.1016/0305-0548(94)00059-H>) and principal component methods, TOPSIS ranking of treatments (Hwang and Yoon, 1981), and energy budgeting from physical input quantities with an editable table of energy equivalents.
License:	GPL (≥ 3)
URL:	https://github.com/lalitrolaniya/wefnexus, https://lalitrolaniya.github.io/wefnexus/
BugReports:	https://github.com/lalitrolaniya/wefnexus/issues
Encoding:	UTF-8
LazyData:	true
Depends:	R (≥ 4.0.0)
Imports:	stats, graphics, grDevices, rlang
Suggests:	ggplot2 (≥ 3.4.0), knitr, rmarkdown, testthat (≥ 3.0.0)
VignetteBuilder:	knitr
Config/testthat/edition:	3
NeedsCompilation:	no
Config/roxygen2/version:	8.1.1
Packaged:	2026-11-09 08:43:24 UTC; root
Author:	Lalit Kumar Rolaniya [aut, cre], Hemant Poonia [aut] (deceased), Ram Lal Jat [aut], Monika Punia [aut] (deceased), Raja Ram Choudhary [aut]
Maintainer:	Lalit Kumar Rolaniya <lalitrolaniya@gmail.com>
Repository:	CRAN
Date/Publication:	2026-11-09 10:00:02 UTC

wefnexus: Water-Energy-Food-Nutrient-Carbon Nexus Analysis for Agronomic Systems

Description

Provides functions for analysing Water-Energy-Food-Nutrient-Carbon (WEFNC) nexus interactions in agricultural systems. The package provides five core modules and a nexus integration layer:

Water

Water use efficiency (WUE), water productivity (WP), water footprint (WF) with green/blue/grey components, irrigation efficiency, crop water stress index (CWSI), and crop water productivity (CWP).

Energy

Energy budgeting including input-output analysis, energy use efficiency (EUE), energy return on investment (EROI), energy productivity (EP), net energy (NE), specific energy, and energy profitability.

Food

Food productivity indices, harvest index (HI), land equivalent ratio (LER), system productivity index (SPI), caloric and protein yield, and production efficiency index (PEI).

Nutrient

Nutrient use efficiency (NUE) metrics including agronomic efficiency (AE), physiological efficiency (PE), recovery efficiency (RE), partial factor productivity (PFP), internal utilization efficiency (IUE), and nutrient harvest index (NHI).

Carbon

Carbon footprint (CF) with source-wise breakdown, greenhouse gas (GHG) emission estimation, soil organic carbon (SOC) stocks, carbon sequestration rate (CSR), and global warming potential (GWP) using IPCC AR6 values.

Nexus

Normalization, composite nexus index, objective weights (nexus_weights: entropy, CRITIC, PCA), TOPSIS ranking (nexus_topsis), trade-off matrix, weight sensitivity, radar and heatmap plots.

Workflow

nexus_analysis runs the full analysis on replicated field data; nexus_anova gives treatment means with SEm, CD, CV and letter groups; energy_budget converts physical input quantities to energy with energy_coefficients.

Set options(wefnexus.verbose = FALSE) to silence the informational messages of all functions.

Author(s)

Maintainer: Lalit Kumar Rolaniya lalitrolaniya@gmail.com (ORCID)

Authors:

• Lalit Kumar Rolaniya lalitrolaniya@gmail.com (ORCID)

• Hemant Poonia pooniaheman80@gmail.com (ORCID) (deceased)

• Ram Lal Jat khokharagro1986@gmail.com (ORCID)

• Monika Punia monikapunia02@gmail.com (ORCID) (deceased)

• Raja Ram Choudhary rajaramchoudhary26@gmail.com

See Also

Useful links:

• https://github.com/lalitrolaniya/wefnexus

• https://lalitrolaniya.github.io/wefnexus/

• Report bugs at https://github.com/lalitrolaniya/wefnexus/issues

Agronomic Efficiency (AE)

Description

Increase in economic yield per unit of nutrient applied.

Usage

agronomic_efficiency(
  yield_treated,
  yield_control,
  nutrient_applied,
  verbose = getOption("wefnexus.verbose", TRUE)
)

Arguments

Details

AE = \frac{Y_f - Y_0}{F}

Value

Numeric vector. Agronomic efficiency (kg grain per kg nutrient).

References

Dobermann, A. (2007). Nutrient use efficiency: measurement and management. In Fertilizer Best Management Practices, IFA, Paris, pp. 1-28. https://digitalcommons.unl.edu/agronomyfacpub/316/

Fixen, P. et al. (2015). Nutrient/fertilizer use efficiency: Measurement, current situation and trends. In Managing Water and Fertilizer for Sustainable Agricultural Intensification, IFA/IWMI/IPNI/IPI, pp. 8-38.

Congreves, K.A. et al. (2021). Nitrogen use efficiency definitions of today and tomorrow. Frontiers in Plant Science, 12, 637108. doi:10.3389/fpls.2021.637108

Examples

agronomic_efficiency(yield_treated = 4500, yield_control = 3000,
                     nutrient_applied = 120)

Arid Pulse Nexus Dataset

Description

A sample dataset with six conservation agriculture treatments in an arid pulse-based cropping system from western Rajasthan, India. Includes water, energy, food, nutrient, and carbon data for WEFNC nexus analysis.

Usage

arid_pulse_nexus

Format

A data frame with 6 rows and 26 variables:

treatment

Character. Treatment combination name

tillage

Character. Tillage method: CT (conventional), ZT (zero), PB (permanent beds)

irrigation

Character. Irrigation method: Flood, Sprinkler, Drip, or SSDI (sub-surface drip)

residue

Logical. Whether crop residue was retained

grain_yield

Numeric. Grain yield (kg/ha)

straw_yield

Numeric. Straw yield (kg/ha)

irrigation_applied

Numeric. Irrigation water applied (mm)

effective_rainfall

Numeric. Effective rainfall (mm)

total_water

Numeric. Total water consumed (mm)

crop_et

Numeric. Crop evapotranspiration (mm)

energy_input

Numeric. Total energy input (MJ/ha)

energy_output_grain

Numeric. Energy output from grain (MJ/ha)

energy_output_straw

Numeric. Energy output from straw (MJ/ha)

n_applied

Numeric. Nitrogen applied (kg/ha)

p_applied

Numeric. Phosphorus applied (kg P2O5/ha)

k_applied

Numeric. Potassium applied (kg K2O/ha)

n_uptake

Numeric. Total plant nitrogen uptake (kg/ha)

p_uptake

Numeric. Total plant phosphorus uptake (kg/ha)

grain_n_uptake

Numeric. Grain nitrogen uptake (kg/ha)

diesel_use

Numeric. Diesel consumption (L/ha)

electricity_kwh

Numeric. Electricity consumption (kWh/ha)

soc_pct

Numeric. Soil organic carbon (percent)

bulk_density

Numeric. Soil bulk density (Mg/m3)

ghg_emission

Numeric. Total GHG emission (kg CO2-eq/ha)

cost_cultivation

Numeric. Cost of cultivation (INR/ha)

gross_return

Numeric. Gross return (INR/ha)

Source

Simulated dataset based on typical experimental data from ICAR-Indian Institute of Pulses Research, Regional Centre, Bikaner, Rajasthan, India.

Examples

data(arid_pulse_nexus)
str(arid_pulse_nexus)

Replicated Arid Pulse Trial Dataset

Description

A plot-level dataset from a simulated randomized complete block design with the six conservation agriculture treatments of arid_pulse_nexus and three replications. Intended for examples of nexus_analysis and nexus_anova.

Usage

arid_pulse_trial

Format

A data frame with 18 rows and 11 variables:

treatment

Character. Treatment combination name

replication

Character. Block (R1 to R3)

grain_yield

Numeric. Grain yield (kg/ha)

straw_yield

Numeric. Straw yield (kg/ha)

total_water

Numeric. Total water consumed (mm)

energy_input

Numeric. Total energy input (MJ/ha)

energy_output

Numeric. Energy output of grain and straw (MJ/ha), using 14.7 and 12.5 MJ/kg

n_applied

Numeric. Nitrogen applied (kg/ha)

n_uptake

Numeric. Total plant nitrogen uptake (kg/ha)

grain_n_uptake

Numeric. Grain nitrogen uptake (kg/ha)

ghg_emission

Numeric. Total GHG emission (kg CO2-eq/ha)

Source

Simulated around the treatment means of arid_pulse_nexus; the script is in the package source (data-raw/make_data.R).

Examples

data(arid_pulse_trial)
aggregate(grain_yield ~ treatment, data = arid_pulse_trial, FUN = mean)

Caloric Yield

Description

Total caloric output per hectare from crop production.

Usage

caloric_yield(
  yield,
  caloric_value,
  verbose = getOption("wefnexus.verbose", TRUE)
)

Arguments

Details

Formula:

CY = Yield \times Caloric Value

Value

Numeric vector. Caloric yield (kcal/ha).

Examples

caloric_yield(yield = 4500, caloric_value = 3400)

Carbon Efficiency

Description

Crop yield per unit of greenhouse gas emitted.

Usage

carbon_efficiency(
  yield,
  carbon_emission,
  verbose = getOption("wefnexus.verbose", TRUE)
)

Arguments

Details

Formula:

CE = \frac{Yield}{Carbon Footprint}

Value

Numeric vector. Carbon efficiency (kg yield per kg CO2-eq). Higher values indicate more yield per unit emission.

Examples

carbon_efficiency(yield = 4500, carbon_emission = 2500)

Carbon Footprint of Crop Production

Description

Estimates the carbon footprint from major emission sources in crop production, with source-wise breakdown and yield-scaled intensity. Uses IPCC AR6 default GWP values.

Usage

carbon_footprint(
  diesel_use = 0,
  electricity_use = 0,
  n_fertilizer = 0,
  p_fertilizer = 0,
  k_fertilizer = 0,
  pesticide_use = 0,
  seed_rate = 0,
  n2o_direct = NULL,
  ch4_emission = 0,
  yield = NULL,
  ef_diesel = 2.68,
  ef_electricity = 0.727,
  ef_n_manufacture = 4.96,
  ef_p_manufacture = 1.61,
  ef_k_manufacture = 0.57,
  ef_pesticide = 10.97,
  ef_seed = 0.58,
  gwp_n2o = 273,
  gwp_ch4 = 27,
  ef_n2o = 0.01,
  verbose = getOption("wefnexus.verbose", TRUE)
)

Arguments

Details

Formula:

CF = \sum_i A_i \times EF_i

in kg CO2-eq/ha, where A_i is the activity (input use) and EF_i its emission factor; N2O and CH4 are converted with the GWP values. When yield is given, the carbon intensity CF / Y (kg CO2-eq/kg) is also returned.

Value

A list with components:

total_cf

Numeric. Total carbon footprint (kg CO2-eq/ha)

cf_intensity

Numeric. Carbon footprint intensity (kg CO2-eq/kg yield), returned only when yield is provided and positive

breakdown

Data frame with columns: source, emission_kg_CO2eq, and share_pct showing the contribution of each emission source

References

Lal, R. (2004). Carbon emission from farm operations. Environment International, 30(7), 981-990. doi:10.1016/j.envint.2004.03.005

Central Electricity Authority (2024). CO2 Baseline Database for the Indian Power Sector, Version 20.0. Ministry of Power, Government of India, New Delhi.

Forster, P. et al. (2021). The Earth's energy budget, climate feedbacks, and climate sensitivity. In Climate Change 2021: The Physical Science Basis (IPCC AR6 WGI Chapter 7). doi:10.1017/9781009157896.009

IPCC (2019). 2019 Refinement to the 2006 IPCC Guidelines for National Greenhouse Gas Inventories. Volume 4: Agriculture, Forestry and Other Land Use. ISBN:978-4-88788-232-4.

Examples

cf <- carbon_footprint(
  diesel_use = 60, electricity_use = 200,
  n_fertilizer = 120, p_fertilizer = 60, k_fertilizer = 40,
  pesticide_use = 1.5, seed_rate = 100, yield = 4500
)
cf$total_cf
cf$cf_intensity
cf$breakdown

Carbon Sequestration Rate

Description

Annual rate of soil carbon change between two measurement time points.

Usage

carbon_sequestration_rate(
  soc_initial,
  soc_final,
  years,
  verbose = getOption("wefnexus.verbose", TRUE)
)

Arguments

Details

Formula:

CSR = \frac{SOC_{final} - SOC_{initial}}{Years}

Value

Numeric vector. Carbon sequestration rate (Mg C/ha/year). Positive values indicate net sequestration; negative values indicate net emission from soil.

References

Minasny, B. et al. (2017). Soil carbon 4 per mille. Geoderma, 292, 59-86. doi:10.1016/j.geoderma.2017.01.002

Examples

carbon_sequestration_rate(soc_initial = 28.5, soc_final = 31.2,
                          years = 5)

Carbon Sustainability Index (CSI)

Description

Ratio of yield to net carbon emission, accounting for carbon sequestration by the soil.

Usage

carbon_sustainability_index(
  yield,
  carbon_emission,
  carbon_sequestered = 0,
  verbose = getOption("wefnexus.verbose", TRUE)
)

Arguments

Details

Formula:

CSI = \frac{Y}{E - S}

where Y is yield (kg/ha), E is GHG emission and S is carbon sequestered (both kg CO2-eq/ha).

Value

Numeric vector. Carbon sustainability index. Higher values indicate better carbon sustainability. Returns NA where net emission is zero or negative (net sequestration exceeds emission).

References

Brentrup, F. et al. (2004). Environmental impact assessment of agricultural production systems using the life cycle assessment methodology. European Journal of Agronomy, 20(3), 247-264. doi:10.1016/S1161-0301(03)00024-8

Examples

carbon_sustainability_index(yield = 4500, carbon_emission = 2500,
                             carbon_sequestered = 500)

Crop Water Productivity (CWP)

Description

Computes crop water productivity as the ratio of yield to total evapotranspiration, analogous to the "more crop per drop" concept.

Usage

crop_water_productivity(
  yield,
  et,
  verbose = getOption("wefnexus.verbose", TRUE)
)

Arguments

Details

CWP = \frac{Y}{ET \times 10}

The factor 10 converts mm to m3/ha.

Value

Numeric vector. Crop water productivity (kg/m3).

References

Zwart, S.J. & Bastiaanssen, W.G.M. (2004). Review of measured crop water productivity values for irrigated wheat, rice, cotton and maize. Agricultural Water Management, 69(2), 115-133. doi:10.1016/j.agwat.2004.04.007

Examples

crop_water_productivity(yield = 4500, et = 400)

Crop Water Stress Index (CWSI)

Description

Computes the Crop Water Stress Index from the ratio of actual to potential evapotranspiration (the evapotranspiration form of the index described by Jackson et al., 1981).

Usage

crop_water_stress_index(
  actual_et,
  potential_et,
  verbose = getOption("wefnexus.verbose", TRUE)
)

Arguments

Details

CWSI = 1 - \frac{ET_a}{ET_p}

Value

Numeric vector. CWSI values between 0 (no stress) and 1 (maximum stress). Values close to 0 indicate well-watered conditions; values close to 1 indicate severe water deficit.

References

Jackson, R.D., Idso, S.B., Reginato, R.J. & Pinter, P.J. (1981). Canopy temperature as a crop water stress indicator. Water Resources Research, 17(4), 1133-1138. doi:10.1029/WR017i004p01133

Idso, S.B. et al. (1981). Normalizing the stress-degree-day parameter for environmental variability. Agricultural Meteorology, 24, 45-55. doi:10.1016/0002-1571(81)90032-7

Examples

crop_water_stress_index(c(4.5, 3.8, 3.0, 2.2), c(5.0, 5.0, 5.0, 5.0))

Crop Yield Index (CYI)

Description

Relative yield performance compared to a check or control treatment.

Usage

crop_yield_index(
  yield,
  check_yield,
  verbose = getOption("wefnexus.verbose", TRUE)
)

Arguments

Details

Formula:

CYI = \frac{Y}{Y_{check}}

Multiply by 100 to express as a percentage of the check.

Value

Numeric vector. Yield index where 1.0 equals the check yield. Values above 1 indicate superiority over check.

Examples

crop_yield_index(yield = c(4500, 4200, 3800), check_yield = 4000)

Depleted Fraction (DF)

Description

Ratio of water beneficially consumed (crop ET) to total water inflow, used to assess basin-level water allocation.

Usage

depleted_fraction(
  crop_et,
  total_inflow,
  verbose = getOption("wefnexus.verbose", TRUE)
)

Arguments

Details

Formula:

DF = \frac{ET_{actual}}{Water_{supplied}}

Value

Numeric vector. Depleted fraction (proportion, 0 to 1).

References

Perry, C., Steduto, P., Allen, R.G. & Burt, C.M. (2009). Increasing productivity in irrigated agriculture: Agronomic constraints and hydrological realities. Agricultural Water Management, 96(11), 1517-1524. doi:10.1016/j.agwat.2009.05.005

Examples

depleted_fraction(crop_et = 320, total_inflow = 500)

Energy Budget from Physical Input Quantities

Description

Converts physical quantities of inputs (litres of diesel, kg of fertilizer, labour hours, and so on) and outputs (grain and straw) to energy using the equivalents in energy_coefficients or a user-supplied table. Returns input energy by source, direct and indirect energy, renewable and non-renewable energy, and, when outputs are given, the main energy efficiency indicators.

Usage

energy_budget(
  data,
  coefficients = wefnexus::energy_coefficients,
  yield_col = "grain",
  verbose = getOption("wefnexus.verbose", TRUE)
)

Arguments

Details

Energy of each item is quantity multiplied by its energy equivalent (MJ per unit). Shares are percentages of total input energy. When outputs are present the summary also includes energy output, net energy, energy use efficiency (output/input), energy productivity (kg/MJ) and energy intensity (MJ/kg).

Value

An object of class energy_budget: a list with

summary

Data frame, one row per treatment: identifier columns, total_input_MJ, direct_MJ, indirect_MJ, renewable_MJ, non_renewable_MJ, their percentage shares, and (if outputs are present) total_output_MJ, net_energy_MJ, EUE, energy_productivity_kg_MJ and energy_intensity_MJ_kg.

detail

Long data frame with the energy of every item per treatment and its share of total input energy.

unmatched

Character vector of numeric columns not found in coefficients.

See Also

energy_coefficients, energy_input, energy_use_efficiency

Examples

inputs <- data.frame(
  treatment = c("CT", "ZT"),
  human_labour_man = c(320, 240),
  diesel = c(65, 38),
  electricity = c(180, 75),
  nitrogen = c(20, 20),
  phosphorus = c(40, 40),
  seed = c(20, 20),
  herbicide = c(0, 0.75),
  grain = c(980, 1280),
  straw = c(1450, 1850)
)
eb <- energy_budget(inputs)
eb
eb$summary

# Use your own energy equivalent for diesel
my_coef <- energy_coefficients
my_coef$mj_per_unit[my_coef$input == "diesel"] <- 47.8
energy_budget(inputs, coefficients = my_coef, verbose = FALSE)$summary

Energy Equivalents of Agricultural Inputs and Outputs

Description

A reference table of typical energy equivalents used in energy budgeting of crop production, for use with energy_budget.

Usage

energy_coefficients

Format

A data frame with 20 rows and 7 variables:

input

Character. Item name; use these as column names in the data passed to energy_budget.

unit

Character. Physical unit of the item.

mj_per_unit

Numeric. Energy equivalent (MJ per unit).

type

Character. "input" or "output".

form

Character. "direct" or "indirect" energy.

source

Character. "renewable" or "non-renewable".

note

Character. Short description.

Details

Energy equivalents differ between sources, regions and years. These are commonly used values in Indian and international crop energy studies and are provided as a starting point. Check them against the reference you cite and edit a copy of the table where needed (see the examples in energy_budget).

Source

Values compiled from commonly cited energy budgeting literature, including Mittal, J.P. & Dhawan, K.C. (1988). Research Manual on Energy Requirements in Agricultural Sector. ICAR, New Delhi; and Pimentel, D. (Ed.) (1980). Handbook of Energy Utilization in Agriculture. CRC Press, Boca Raton.

Examples

energy_coefficients
subset(energy_coefficients, type == "input" & form == "direct")

Total Energy Input

Description

Computes total energy input for a cropping system from individual input components with energy equivalents.

Usage

energy_input(
  seed = 0,
  fertilizer_n = 0,
  fertilizer_p = 0,
  fertilizer_k = 0,
  fym = 0,
  pesticide = 0,
  diesel = 0,
  electricity = 0,
  human_labour = 0,
  machinery = 0,
  irrigation = 0,
  micronutrient = 0,
  biofertilizer = 0,
  solar_energy = 0,
  other = 0,
  verbose = getOption("wefnexus.verbose", TRUE)
)

Arguments

Details

Formula:

EI = \sum (Input_i \times EE_i)

Value

Numeric. Total energy input (MJ/ha), computed as the sum of all individual energy input components.

References

Mittal, V.K. & Dhawan, K.C. (1988). Research manual on energy requirements in agricultural sector. Punjab Agricultural University, Ludhiana, India.

Chaudhary, V.P. et al. (2009). Energy auditing of diversified rice-wheat cropping systems in the Indo-Gangetic Plains. Energy, 34(9), 1091-1096. doi:10.1016/j.energy.2009.04.017

Examples

energy_input(seed = 250, fertilizer_n = 3600, fertilizer_p = 500,
             diesel = 2800, human_labour = 180, machinery = 1200,
             irrigation = 1500)

Energy Intensity

Description

Energy consumed per unit of crop yield.

Usage

energy_intensity(
  energy_in,
  yield,
  verbose = getOption("wefnexus.verbose", TRUE)
)

Arguments

Details

Formula:

EI = \frac{Energy Input}{Yield}

Value

Numeric vector. Energy intensity (MJ/kg). Lower values indicate more energy-efficient production.

Examples

energy_intensity(energy_in = 12000, yield = 4500)

Total Energy Output

Description

Computes total energy output from grain and straw/stover yields using crop-specific energy coefficients.

Usage

energy_output(
  grain_yield,
  straw_yield = 0,
  grain_energy_coeff = 14.7,
  straw_energy_coeff = 12.5,
  verbose = getOption("wefnexus.verbose", TRUE)
)

Arguments

Details

E_{out} = (Y_g \times C_g) + (Y_s \times C_s)

where Y_g and Y_s are grain and straw yields, and C_g and C_s are their respective energy coefficients.

Value

Numeric vector. Total energy output (MJ/ha).

References

Devasenapathy, P., Senthilkumar, G. & Shanmugam, P.M. (2009). Energy management in crop production. Indian Journal of Agronomy, 54(1), 80-90.

Examples

energy_output(grain_yield = 4500, straw_yield = 5500)
energy_output(grain_yield = 1500, straw_yield = 2000,
              grain_energy_coeff = 14.3, straw_energy_coeff = 12.5)

Energy Productivity

Description

Crop yield produced per unit of energy input.

Usage

energy_productivity(
  yield,
  energy_in,
  verbose = getOption("wefnexus.verbose", TRUE)
)

Arguments

Details

Formula:

EP = \frac{Yield}{Energy Input}

Value

Numeric vector. Energy productivity (kg/MJ). Higher values indicate better yield per unit energy invested.

Examples

energy_productivity(yield = 4500, energy_in = 12000)

Energy Profitability

Description

Economic return per unit of energy invested.

Usage

energy_profitability(
  gross_return,
  energy_in,
  verbose = getOption("wefnexus.verbose", TRUE)
)

Arguments

Details

Formula:

EPr = \frac{GR}{E_{in}}

where GR is gross return (currency/ha) and E_{in} is energy input (MJ/ha). The energy-based ratio (output - input) / input is net_energy(out, in) / in, or EUE minus 1.

Value

Numeric vector. Energy profitability (currency/MJ).

Examples

energy_profitability(gross_return = 112500, energy_in = 12000)

Energy Use Efficiency (EUE)

Description

Ratio of total energy output to total energy input.

Usage

energy_use_efficiency(
  energy_out,
  energy_in,
  verbose = getOption("wefnexus.verbose", TRUE)
)

Arguments

Details

EUE = \frac{E_{out}}{E_{in}}

Value

Numeric vector. Energy use efficiency (dimensionless ratio). Values greater than 1 indicate a positive energy balance.

Examples

energy_use_efficiency(energy_out = 135000, energy_in = 12000)

Energy Return on Investment (EROI)

Description

Computes the Energy Return on Investment, a key metric for assessing whether an agricultural system produces more energy than it consumes. EROI is mathematically identical to energy use efficiency (EUE) but is the preferred term in energy and sustainability science literature.

Usage

eroi(
  energy_out,
  energy_in,
  include_solar = FALSE,
  verbose = getOption("wefnexus.verbose", TRUE)
)

Arguments

Details

EROI = \frac{E_{out}}{E_{in}}

EROI is the fundamental metric of net energy analysis. In agricultural contexts, EROI typically ranges from 2 to 15 for conventional cropping systems, with higher values for low-input or conservation agriculture systems.

Value

Numeric vector. EROI values (dimensionless ratio). Interpreted as follows:

EROI > 5

Highly energy-profitable system

1 < EROI < 5

Energy-positive but moderate return

EROI = 1

Break-even: energy output equals input

EROI < 1

Energy sink: system consumes more than it produces

References

Hall, C.A.S., Lambert, J.G. & Balogh, S.B. (2014). EROI of different fuels and the implications for society. Energy Policy, 64, 141-152. doi:10.1016/j.enpol.2013.05.049

Murphy, D.J. & Hall, C.A.S. (2010). Year in review - EROI or energy return on (energy) invested. Annals of the New York Academy of Sciences, 1185(1), 102-118. doi:10.1111/j.1749-6632.2009.05282.x

Murphy, D.J. et al. (2022). Energy return on investment of major energy carriers: Review and harmonization. Sustainability, 14(12), 7098. doi:10.3390/su14127098

Examples

# Conservation agriculture with low input
eroi(energy_out = 59800, energy_in = 8500)

# Conventional tillage with high input
eroi(energy_out = 40800, energy_in = 12500)

# Multiple treatments
eroi(energy_out = c(40800, 50500, 59800),
     energy_in = c(12500, 9800, 8500))

Food Productivity Index (FPI)

Description

Computes a composite food productivity index considering yield relative to potential, and optionally nutritional quality.

Usage

food_productivity_index(
  yield,
  reference_yield,
  protein_content = NULL,
  caloric_value = NULL,
  verbose = getOption("wefnexus.verbose", TRUE)
)

Arguments

Details

Without protein and caloric values,

FPI = \min(Y / Y_{ref}, 1)

With both supplied,

FPI = 0.5 \min(Y / Y_{ref}, 1) + 0.25 \min(P / 40, 1) + 0.25 \min(C / 400, 1)

where P is protein (percent) and C is caloric value (kcal/100 g); 40 percent protein and 400 kcal/100 g are the upper reference values. The index is on a 0 to 1 scale.

Value

Numeric vector. Food productivity index on a 0 to 1 scale. When protein and caloric values are provided, weights are 0.50 for yield ratio, 0.25 for protein, and 0.25 for caloric content.

Examples

food_productivity_index(yield = 4500, reference_yield = 6000,
                        protein_content = 12.5, caloric_value = 340)

GHG Emission Estimation from Field Operations

Description

Quick estimation of greenhouse gas emissions (N2O, CH4, CO2) from agricultural field operations using IPCC Tier 1 default factors.

Usage

ghg_emission(
  n_applied,
  residue_burned = FALSE,
  residue_amount = 0,
  paddy_days = 0,
  tillage = "conventional",
  gwp_n2o = 273,
  gwp_ch4 = 27,
  ef_n2o = 0.01,
  ef_ch4_paddy = 1.3,
  combustion_factor = 0.8,
  ef_ch4_burn = 2.7,
  ef_n2o_burn = 0.07,
  include_burn_co2 = FALSE,
  verbose = getOption("wefnexus.verbose", TRUE)
)

Arguments

Details

Formula:

GHG = \sum (Activity_i \times EF_i)

where EF is the emission factor for each activity.

Residue burning follows IPCC (2006, Vol. 4, Ch. 2): mass burnt = residue x combustion factor; CH4 and N2O = mass burnt x emission factor (g/kg dry matter). CO2 from burning crop residue is biogenic and, as in IPCC inventories, is reported but left out of the total unless include_burn_co2 = TRUE. Versions before 1.1.0 added that CO2 to the total and omitted burning CH4 and N2O.

The tillage CO2 values (150, 100 and 50 kg CO2/ha for conventional, reduced and zero tillage) are rough screening values. When diesel use is known, carbon_footprint gives a better estimate.

Value

For a single observation, a data frame with columns source, gas, emission_kg, CO2_eq_kg and counted (whether the row enters the total); the total is stored in attr(, "total_CO2eq"). For several observations (any input of length > 1), a data frame with one row per observation and a total_CO2eq column.

References

IPCC (2006). 2006 IPCC Guidelines for National Greenhouse Gas Inventories. Volume 4, Chapter 2: Generic methodologies applicable to multiple land-use categories (Tables 2.5 and 2.6). IGES, Japan.

IPCC (2019). 2019 Refinement to the 2006 IPCC Guidelines for National Greenhouse Gas Inventories. Volume 4, Chapter 11: N2O emissions from managed soils, and CO2 emissions from lime and urea application. ISBN:978-4-88788-232-4.

Examples

ghg_emission(n_applied = 120, tillage = "zero")
ghg_emission(n_applied = 150, paddy_days = 90)
ghg_emission(n_applied = 100, residue_burned = TRUE,
             residue_amount = 5000)
ghg_emission(n_applied = c(20, 40, 60), ef_n2o = 0.005)

Global Warming Potential (GWP)

Description

Converts individual greenhouse gas emissions to CO2 equivalents using IPCC AR6 Global Warming Potential values.

Usage

global_warming_potential(
  co2 = 0,
  ch4 = 0,
  n2o = 0,
  gwp_ch4 = 27,
  gwp_n2o = 273,
  time_horizon = "100yr",
  verbose = getOption("wefnexus.verbose", TRUE)
)

Arguments

Details

Formula:

GWP = CO_2 + CH_4 \times 27 + N_2O \times 273

IPCC AR6 100-year GWP values (with climate-carbon feedbacks): CH4 = 27, N2O = 273.

IPCC AR6 20-year GWP values for non-fossil (biogenic) methane, as emitted by agriculture: CH4 = 79.7, N2O = 273. With time_horizon = "20yr" these replace the defaults, unless you supply gwp_ch4 or gwp_n2o yourself. Versions before 1.1.0 used 81 for CH4.

Note: Previous IPCC AR5 100-year values were CH4 = 34, N2O = 298 (with climate-carbon feedbacks) or CH4 = 28, N2O = 265 (without).

Value

Numeric. Total global warming potential (kg CO2-eq/ha).

References

Forster, P. et al. (2021). The Earth's energy budget, climate feedbacks, and climate sensitivity. In Climate Change 2021: The Physical Science Basis (IPCC AR6 WGI Chapter 7), Table 7.15. doi:10.1017/9781009157896.009

Examples

global_warming_potential(co2 = 500, ch4 = 50, n2o = 2)
global_warming_potential(co2 = 500, ch4 = 50, n2o = 2,
                         time_horizon = "20yr")

Harvest Index (HI)

Description

Proportion of economic yield to total above-ground biological yield.

Usage

harvest_index(
  economic_yield,
  biological_yield,
  verbose = getOption("wefnexus.verbose", TRUE)
)

Arguments

Details

HI = \frac{Y_{econ}}{Y_{biol}}

Value

Numeric vector. Harvest index as a proportion (0 to 1). A warning is issued if any value exceeds 1.

References

Hay, R.K.M. (1995). Harvest index: A review of its use in plant breeding and crop physiology. Annals of Applied Biology, 126(1), 197-216. doi:10.1111/j.1744-7348.1995.tb05015.x

Examples

harvest_index(economic_yield = 4500, biological_yield = 10000)

Human Energy Profitability

Description

Ratio of energy output to human labour energy input, measuring the degree of human labour amplification by the farming system.

Usage

human_energy_profitability(
  energy_out,
  human_energy,
  verbose = getOption("wefnexus.verbose", TRUE)
)

Arguments

Details

Formula:

HEP = \frac{Energy Output}{Human Energy Input}

Value

Numeric vector. Human energy profitability (dimensionless ratio).

Examples

human_energy_profitability(energy_out = 135000, human_energy = 180)

Internal Utilization Efficiency (IUE)

Description

Yield produced per unit of total nutrient in the plant.

Usage

internal_utilization_efficiency(
  yield,
  total_uptake,
  verbose = getOption("wefnexus.verbose", TRUE)
)

Arguments

Details

Formula:

IE = \frac{Yield}{Total Nutrient Uptake}

Value

Numeric vector. Internal utilization efficiency (kg yield per kg nutrient uptake).

Examples

internal_utilization_efficiency(yield = 4500, total_uptake = 100)

Irrigation Efficiency

Description

Computes multiple irrigation efficiency metrics: conveyance, application, overall, and consumptive use efficiency.

Usage

irrigation_efficiency(
  water_delivered,
  water_diverted,
  water_stored = NULL,
  crop_et = NULL,
  verbose = getOption("wefnexus.verbose", TRUE)
)

Arguments

Details

Formula:

IE = \frac{Water_{crop}}{Water_{applied}} \times 100

Value

A data frame with efficiency metrics expressed as percentages. Columns depend on inputs provided:

conveyance_eff

Conveyance efficiency (percent), always computed

application_eff

Application efficiency (percent), if water_stored is provided

overall_eff

Overall efficiency (percent), if water_stored is provided

consumptive_eff

Consumptive use efficiency (percent), if crop_et is provided

References

Grafton, R.Q. et al. (2018). The paradox of irrigation efficiency. Science, 361(6404), 748-750. doi:10.1126/science.aat9314

Examples

irrigation_efficiency(water_delivered = 400, water_diverted = 500,
                      water_stored = 350, crop_et = 320)

Land Equivalent Ratio (LER)

Description

Evaluates the productivity advantage of intercropping systems over sole cropping.

Usage

land_equivalent_ratio(
  yield_inter_a,
  yield_sole_a,
  yield_inter_b,
  yield_sole_b,
  verbose = getOption("wefnexus.verbose", TRUE)
)

Arguments

Details

LER = \frac{Y_{iA}}{Y_{sA}} + \frac{Y_{iB}}{Y_{sB}}

Value

Numeric vector. LER values. Values greater than 1 indicate an intercropping advantage; less than 1 indicates a disadvantage.

References

Mead, R. & Willey, R.W. (1980). The concept of a land equivalent ratio and advantages in yields from intercropping. Experimental Agriculture, 16(3), 217-228. doi:10.1017/S0014479700010978

Examples

land_equivalent_ratio(yield_inter_a = 3500, yield_sole_a = 4500,
                      yield_inter_b = 800, yield_sole_b = 1200)

Net Energy

Description

Difference between total energy output and total energy input.

Usage

net_energy(
  energy_out,
  energy_in,
  verbose = getOption("wefnexus.verbose", TRUE)
)

Arguments

Details

Formula:

NE = Energy Output - Energy Input

Value

Numeric vector. Net energy (MJ/ha). Positive values indicate net energy gain; negative values indicate net energy loss.

Examples

net_energy(energy_out = 135000, energy_in = 12000)

Complete Nexus Analysis from Replicated Field Data

Description

Runs the full WEFNC workflow on plot-level data in one call: computes plot-level indicators, compares treatments by ANOVA (with SEm, CD and CV), builds the composite nexus index from treatment means with equal or objective weights, and ranks treatments by TOPSIS.

Usage

nexus_analysis(
  data,
  treatment,
  yield,
  water,
  energy_in,
  energy_out,
  emission,
  n_applied = NULL,
  n_uptake = NULL,
  block = NULL,
  weights = "equal",
  nutrient_metric = NULL,
  carbon_basis = c("intensity", "emission"),
  alpha = 0.05,
  verbose = getOption("wefnexus.verbose", TRUE)
)

Arguments

Details

Plot-level indicators are WUE (kg/ha/mm), EUE, the nutrient indicator (PFP or IUE, kg/kg) and carbon intensity (kg CO2-eq/kg). The nexus index and TOPSIS ranking use treatment means of the raw variables. ANOVA is skipped when treatments are not replicated.

Value

An object of class nexus_analysis: a list with

plot_data

Input data with plot-level indicator columns WUE, EUE, NUE and CI added.

treatment_means

Treatment means of the raw variables.

nexus

A nexus_result from nexus_summary on the treatment means.

anova

A nexus_anova object for yield and the four indicators, or NULL without replication.

topsis

TOPSIS ranking from nexus_topsis.

weights

Named weights used for the nexus index.

See Also

nexus_summary, nexus_anova, nexus_weights, nexus_topsis

Examples

data(arid_pulse_trial)
res <- nexus_analysis(
  arid_pulse_trial, treatment = "treatment", block = "replication",
  yield = "grain_yield", water = "total_water",
  energy_in = "energy_input", energy_out = "energy_output",
  emission = "ghg_emission", n_uptake = "n_uptake",
  weights = "entropy"
)
res
res$anova

plot(res$nexus)

ANOVA Table for Nexus Indicators (CRD or RCBD)

Description

Runs a one-way analysis of variance for each indicator, in a completely randomized design (CRD) or randomized complete block design (RCBD), and returns the statistics usually reported in agronomy papers: treatment means, standard error of mean (SEm), critical difference (CD, the least significant difference), coefficient of variation (CV) and letter groups.

Usage

nexus_anova(
  data,
  response,
  treatment,
  block = NULL,
  alpha = 0.05,
  digits = 2,
  verbose = getOption("wefnexus.verbose", TRUE)
)

Arguments

Details

For each response the model y ~ block + treatment (RCBD) or y ~ treatment (CRD) is fitted with aov; in an RCBD the treatment F test is adjusted for blocks. With error mean square MSE, r replications and error degrees of freedom df_e:

SEm = \sqrt{MSE / r}, \quad SEd = \sqrt{2 MSE / r}

CD = t_{1 - \alpha/2,\, df_e} \times SEd, \quad CV = 100 \sqrt{MSE} / \bar{y}

Treatment means are least-squares means: in an RCBD with missing plots they are adjusted for blocks, and with complete data they equal the raw means. Letters follow Fisher's LSD: every pair of treatments is compared with its own standard error of the difference, and the compact letter display is built with the insert-and-absorb algorithm of Piepho (2004), so treatments sharing a letter do not differ at level alpha and treatments that differ share no letter. With equal replication this is the familiar single CD. With unequal replication or missing plots the single SEm, SEd and CD in the table use the harmonic mean of replications and are approximate, while the letters remain exact. Beyond 26 groups the letters continue with capitals and then numbered letters.

When the treatment F test is not significant, all treatments get the letter "a" and the CD is shown as "NS" in the formatted table. Treatments with no observations for a response are shown as missing.

Value

An object of class nexus_anova: a list with

means

Data frame of treatment means (treatments in rows, responses in columns).

letters

Data frame of letter groups in the same layout.

se

Data frame of the standard error of each treatment mean (standard deviation / sqrt(n)), in the same layout.

stats

Data frame, one row per response: F_value, p_value, significant, MSE, df_error, SEm, SEd, CD, CV_pct, grand_mean, balanced.

table

Character data frame ready for a manuscript: means with letters, followed by SEm, CD and CV rows.

models

List of fitted aov objects.

alpha

The significance level used.

Use plot() on the result for a bar chart with error bars and letters (plot.nexus_anova).

References

Gomez, K.A. & Gomez, A.A. (1984). Statistical Procedures for Agricultural Research, 2nd ed. John Wiley & Sons, New York.

Piepho, H.-P. (2004). An algorithm for a letter-based representation of all-pairwise comparisons. Journal of Computational and Graphical Statistics, 13(2), 456-466. doi:10.1198/1061860043515

Examples

data(arid_pulse_trial)
res <- nexus_anova(arid_pulse_trial,
                   response = c("grain_yield", "n_uptake"),
                   treatment = "treatment", block = "replication")
res
res$stats

Nexus Heatmap

Description

Creates a heatmap showing nexus dimension scores across treatments.

Usage

nexus_heatmap(
  scores,
  row_labels = NULL,
  col_labels = NULL,
  title = "WEFNC Nexus Heatmap",
  color_palette = NULL
)

Arguments

Value

Invisibly returns the input scores matrix. Called primarily for the side effect of generating a heatmap plot.

Examples

scores <- matrix(c(0.85, 0.70, 0.90, 0.65, 0.80,
                    0.72, 0.80, 0.85, 0.70, 0.60),
                 nrow = 2, byrow = TRUE)
nexus_heatmap(scores,
  row_labels = c("Conservation", "Conventional"),
  col_labels = c("Water", "Energy", "Food", "Nutrient", "Carbon"))

Nexus Heatmap (ggplot2)

Description

Publication-quality heatmap using ggplot2 for WEFNC nexus scores.

Usage

nexus_heatmap_gg(
  scores,
  treatment_names = NULL,
  dim_labels = c("Water", "Energy", "Food", "Nutrient", "Carbon"),
  title = "WEFNC Nexus Heatmap",
  colours = NULL
)

Arguments

Value

A ggplot2 object.

Examples

if (requireNamespace("ggplot2", quietly = TRUE)) {
  scores <- matrix(c(0.85, 0.70, 0.90, 0.65, 0.80,
                      0.72, 0.80, 0.85, 0.70, 0.60),
                   nrow = 2, byrow = TRUE)
  nexus_heatmap_gg(scores, treatment_names = c("CA", "CT"))
}

WEFNC Nexus Index

Description

Computes a weighted composite Water-Energy-Food-Nutrient-Carbon nexus sustainability index from normalized dimension scores.

Usage

nexus_index(
  water_score,
  energy_score,
  food_score,
  nutrient_score,
  carbon_score,
  weights = rep(0.2, 5),
  verbose = getOption("wefnexus.verbose", TRUE)
)

Arguments

Details

NI = w_W S_W + w_E S_E + w_F S_F + w_N S_N + w_C S_C

Value

Numeric vector. Composite nexus index on a 0 to 1 scale, where higher values indicate better overall sustainability.

Examples

nexus_index(water_score = c(0.85, 0.72), energy_score = c(0.70, 0.80),
            food_score = c(0.90, 0.85), nutrient_score = c(0.65, 0.70),
            carbon_score = c(0.80, 0.60))

Nexus Radar Plot

Description

Creates a radar (spider/web) chart showing the WEFNC nexus profile of one or more treatments.

Usage

nexus_radar(
  scores,
  labels = c("Water", "Energy", "Food", "Nutrient", "Carbon"),
  treatment_names = NULL,
  colors = NULL,
  title = "WEFNC Nexus Profile",
  fill = TRUE,
  alpha = 0.2
)

Arguments

Value

Invisibly returns the input scores matrix. Called primarily for the side effect of generating a radar plot.

Examples

scores <- matrix(c(0.85, 0.70, 0.90, 0.65, 0.80,
                    0.72, 0.80, 0.85, 0.70, 0.60),
                 nrow = 2, byrow = TRUE)
nexus_radar(scores,
  treatment_names = c("CA+SSDI", "CT+Flood"))

Nexus Radar Plot (ggplot2)

Description

Publication-quality radar chart using ggplot2 for WEFNC nexus profiles.

Usage

nexus_radar_gg(
  scores,
  treatment_names = NULL,
  dim_labels = c("Water", "Energy", "Food", "Nutrient", "Carbon"),
  title = "WEFNC Nexus Profile",
  facet = FALSE,
  reference = TRUE,
  colours = NULL,
  ncol = NULL
)

Arguments

Details

Overlaid radars become hard to read beyond three or four treatments; use facet = TRUE for more.

Value

A ggplot2 object.

Examples

if (requireNamespace("ggplot2", quietly = TRUE)) {
  scores <- matrix(c(0.85, 0.70, 0.90, 0.65, 0.80,
                      0.72, 0.80, 0.85, 0.70, 0.60),
                   nrow = 2, byrow = TRUE)
  nexus_radar_gg(scores, treatment_names = c("CA", "CT"))
  nexus_radar_gg(scores, treatment_names = c("CA", "CT"), facet = TRUE)
}

Compare Treatment Rankings Across Weighting Methods

Description

Ranks treatments eight ways (composite index and TOPSIS, each with equal, entropy, CRITIC and PCA weights) and measures how far the rankings agree. A ranking that holds across methods is a stronger basis for a recommendation than one that depends on a single choice of weights.

Usage

nexus_rank_compare(
  data,
  benefit = NULL,
  treatment_names = NULL,
  methods = c("equal", "entropy", "critic", "pca"),
  verbose = getOption("wefnexus.verbose", TRUE)
)

Arguments

Details

For each weighting method, the composite index is the weighted sum of min-max normalized indicators (inverted where benefit = FALSE), and TOPSIS is computed with nexus_topsis. Agreement among the m rankings of n treatments is summarised by Kendall's coefficient of concordance with correction for ties,

W = \frac{12 S}{m^2 (n^3 - n) - m \sum T}

where S is the sum of squared deviations of the treatment rank sums from their mean and T = \sum (t^3 - t) over tied groups. W runs from 0 (no agreement) to 1 (identical rankings). The chi-square statistic \chi^2 = m (n - 1) W with n - 1 degrees of freedom is reported for reference only: the eight rankings come from the same data and are not independent judges, so its p-value is not a formal test of robustness. Read W itself, and look at which treatments change rank and under which method.

Value

An object of class rank_compare: a list with

ranks

Data frame: treatment, one rank column per method, mean_rank and consensus (rank of the mean rank).

scores

Data frame of index values and TOPSIS closeness.

weights

Matrix of weights (methods x indicators).

kendall_w

Kendall's W.

chisq, df, p_value

Chi-square test of W.

spearman

Matrix of Spearman correlations between rankings.

References

Kendall, M.G. & Babington Smith, B. (1939). The problem of m rankings. The Annals of Mathematical Statistics, 10(3), 275-287. doi:10.1214/aoms/1177732186

See Also

nexus_weights, nexus_topsis, nexus_sensitivity

Examples

data(arid_pulse_nexus)
d <- arid_pulse_nexus
ind <- data.frame(
  WUE = d$grain_yield / d$total_water,
  EUE = (d$energy_output_grain + d$energy_output_straw) / d$energy_input,
  Yield = d$grain_yield,
  IUE = d$grain_yield / d$n_uptake,
  CF = d$ghg_emission
)
rc <- nexus_rank_compare(ind, benefit = c(TRUE, TRUE, TRUE, TRUE, FALSE),
                         treatment_names = d$treatment)
rc
if (requireNamespace("ggplot2", quietly = TRUE)) plot(rc)

Nexus Weight Sensitivity Analysis

Description

Evaluates how the composite nexus index changes as the weight of one dimension varies from 0 to its maximum feasible value, with remaining weight distributed equally among the other four dimensions.

Usage

nexus_sensitivity(
  water_score,
  energy_score,
  food_score,
  nutrient_score,
  carbon_score,
  treatment_names = NULL,
  steps = 20,
  verbose = getOption("wefnexus.verbose", TRUE)
)

Arguments

Value

A data frame with columns: dimension, weight, treatment, and nexus_index showing how the index changes as each dimension's weight varies.

Examples

sa <- nexus_sensitivity(
  water_score = c(0.9, 0.5), energy_score = c(0.6, 0.8),
  food_score = c(0.8, 0.7), nutrient_score = c(0.7, 0.6),
  carbon_score = c(0.5, 0.9),
  treatment_names = c("CA", "CT"), steps = 10
)
head(sa)

Nexus Summary

Description

Generates a comprehensive one-call nexus analysis from raw agronomic field data, computing all dimension metrics, normalizing, and producing the composite index.

Usage

nexus_summary(
  yield,
  water_consumed,
  energy_input,
  energy_output,
  n_applied = NULL,
  n_uptake = NULL,
  carbon_emission,
  treatment_names = NULL,
  weights = rep(0.2, 5),
  nutrient_metric = c("pfp", "iue"),
  carbon_basis = c("emission", "intensity"),
  verbose = getOption("wefnexus.verbose", TRUE)
)

Arguments

Details

Each dimension indicator is min-max normalized across the treatments supplied (carbon is inverted, so lower emission scores higher). Scores are therefore relative to the set of treatments being compared; with only two treatments every score is 0 or 1. Min-max scaling stretches any spread to the full 0 to 1 range, so a small absolute difference (for example 2 percent in IUE) can look as large as a big one; check the raw indicators before interpreting. When every treatment receives the same N, PFP is proportional to yield, so the function warns and nutrient_metric = "iue" is the better choice.

Value

A data frame of class nexus_result with one row per treatment and columns:

treatment

Character. Treatment name

yield_kg_ha

Numeric. Crop yield

WUE_kg_mm

Numeric. Water use efficiency

EUE_ratio

Numeric. Energy use efficiency ratio

EROI

Numeric. Energy return on investment

net_energy_MJ

Numeric. Net energy balance

PFP_kg_kgN

Numeric. Partial factor productivity of N (NA when N applied is missing or zero)

carbon_eff

Numeric. Carbon efficiency

carbon_intensity

Numeric. Carbon intensity

W_score

Numeric. Normalized water score

E_score

Numeric. Normalized energy score

F_score

Numeric. Normalized food score

N_score

Numeric. Normalized nutrient score

C_score

Numeric. Normalized carbon score

nexus_index

Numeric. Composite nexus index

IUE_kg_kgN

Numeric. Internal utilization efficiency of N (NA when n_uptake is not supplied)

rank

Integer. Rank by nexus index (1 = best)

The weights used are stored in attr(result, "weights").

Examples

nexus_summary(
  yield = c(4500, 4200, 3800),
  water_consumed = c(450, 400, 350),
  energy_input = c(12000, 11000, 9500),
  energy_output = c(135000, 125000, 112000),
  n_applied = c(150, 120, 90),
  n_uptake = c(100, 90, 80),
  carbon_emission = c(2500, 2200, 1800),
  treatment_names = c("CA+Drip", "CT+Sprinkler", "ZT+Rainfed")
)

# Legume without fertilizer N, carbon scored per kg grain
nexus_summary(
  yield = c(950, 870, 780),
  water_consumed = c(260, 240, 220),
  energy_input = c(5200, 4800, 4100),
  energy_output = c(36000, 33000, 29500),
  n_applied = c(0, 0, 0),
  n_uptake = c(62, 57, 50),
  carbon_emission = c(610, 560, 470),
  nutrient_metric = "iue", carbon_basis = "intensity"
)

Nexus Sustainability Score

Description

Comprehensive sustainability score with categorization based on user-defined thresholds.

Usage

nexus_sustainability_score(
  water_score,
  energy_score,
  food_score,
  nutrient_score,
  carbon_score,
  weights = rep(0.2, 5),
  thresholds = c(0.4, 0.6, 0.8),
  verbose = getOption("wefnexus.verbose", TRUE)
)

Arguments

Details

Formula:

NSS = \sum_{i=1}^{5} w_i S_i

where S_i are the dimension scores and w_i the weights (equal weights give the mean).

Value

A data frame with columns:

nexus_score

Numeric. Composite sustainability score (0 to 1)

category

Character. Sustainability category: Unsustainable, Low Sustainability, Moderately Sustainable, or Highly Sustainable

water

Numeric. Water dimension input score

energy

Numeric. Energy dimension input score

food

Numeric. Food dimension input score

nutrient

Numeric. Nutrient dimension input score

carbon

Numeric. Carbon dimension input score

Examples

nexus_sustainability_score(
  water_score = c(0.85, 0.60, 0.45),
  energy_score = c(0.70, 0.55, 0.35),
  food_score = c(0.90, 0.80, 0.50),
  nutrient_score = c(0.65, 0.70, 0.40),
  carbon_score = c(0.80, 0.50, 0.30)
)

TOPSIS Ranking of Treatments

Description

Ranks treatments by the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) using several nexus indicators at once. Unlike nexus_index, TOPSIS works on raw indicators in their own units and handles "lower is better" indicators directly.

Usage

nexus_topsis(
  data,
  weights = "equal",
  benefit = NULL,
  treatment_names = NULL,
  verbose = getOption("wefnexus.verbose", TRUE)
)

Arguments

Details

Each column is vector-normalized, r_{ij} = x_{ij} / \sqrt{\sum_i x_{ij}^2}, and multiplied by its weight. The ideal solution takes the best value of each column and the anti-ideal the worst. The closeness coefficient is C_i = D_i^- / (D_i^+ + D_i^-), where D^+ and D^- are Euclidean distances to the ideal and anti-ideal. C_i lies between 0 and 1; higher is better.

Value

A data frame of class topsis_result with columns treatment, d_ideal, d_anti_ideal, closeness and rank (1 = best). The weights used are stored in attr(, "weights"). Use plot() for a ranked bar chart.

References

Hwang, C.L. & Yoon, K. (1981). Multiple Attribute Decision Making: Methods and Applications. Springer, Berlin.

See Also

nexus_weights

Examples

data(arid_pulse_nexus)
d <- arid_pulse_nexus
ind <- data.frame(
  WUE = d$grain_yield / d$total_water,
  EUE = (d$energy_output_grain + d$energy_output_straw) / d$energy_input,
  Yield = d$grain_yield,
  IUE = d$grain_yield / d$n_uptake,
  CF = d$ghg_emission
)
nexus_topsis(ind, weights = "entropy",
             benefit = c(TRUE, TRUE, TRUE, TRUE, FALSE),
             treatment_names = d$treatment)

Nexus Trade-off Matrix

Description

Computes pairwise correlation matrix among nexus dimensions to identify synergies (positive) and trade-offs (negative).

Usage

nexus_tradeoff(
  data,
  method = "pearson",
  verbose = getOption("wefnexus.verbose", TRUE)
)

Arguments

Value

A numeric correlation matrix with pairwise correlations. When all indicators are higher-is-better, positive values suggest synergies and negative values trade-offs; for a lower-is-better indicator (such as carbon footprint) the reading reverses. The p-values of the pairwise correlation tests (cor.test) and the number of complete pairs are attached as attr(, "p_values") and attr(, "n"). The result has class tradeoff_matrix and behaves as an ordinary matrix; plot() or plot_tradeoff draws it.

Examples

df <- data.frame(WUE = c(8.5, 7.2, 6.5, 9.0, 7.8),
                 EUE = c(11.2, 12.5, 9.8, 10.5, 11.0),
                 Yield = c(1500, 1380, 1250, 1650, 1580),
                 NUE = c(25, 23, 20.8, 27.5, 26.3),
                 CF = c(2500, 3000, 1800, 2800, 2200))
nexus_tradeoff(df)

Objective Weights for Nexus Indicators

Description

Derives dimension weights from the data instead of assigning them by judgement. Supports equal weights, the Shannon entropy weight method, the CRITIC method and PCA-based weights. The result can be passed directly to the weights argument of nexus_index, nexus_sustainability_score, nexus_summary or nexus_topsis.

Usage

nexus_weights(
  data,
  method = c("entropy", "critic", "pca", "equal"),
  benefit = NULL,
  verbose = getOption("wefnexus.verbose", TRUE)
)

Arguments

Details

Indicators are first min-max normalized to 0 to 1 (inverted where benefit = FALSE). With m treatments and n indicators:

Entropy. p_{ij} = x_{ij} / \sum_i x_{ij}, e_j = -\frac{1}{\ln m} \sum_i p_{ij} \ln p_{ij} (with 0 \ln 0 = 0), and w_j = (1 - e_j) / \sum_j (1 - e_j). Indicators that vary more between treatments get more weight.

CRITIC. C_j = \sigma_j \sum_k (1 - r_{jk}) and w_j = C_j / \sum_j C_j, where \sigma_j is the standard deviation of the normalized indicator and r_{jk} the Pearson correlation between indicators. Indicators that vary more and overlap less with others get more weight.

PCA. Principal components of the standardized indicators are computed and components with eigenvalue of at least 1 are kept (at least one). The weight of indicator j is proportional to \sum_k \lambda_k |v_{jk}|, where \lambda_k is the eigenvalue and v_{jk} the loading.

Constant indicators receive zero weight under entropy, CRITIC and PCA. With very few treatments (fewer than about five) data-driven weights are unstable and should be reported with a sensitivity analysis (nexus_sensitivity).

Value

A named numeric vector of weights summing to 1, with the method stored in attr(, "method").

References

Hwang, C.L. & Yoon, K. (1981). Multiple Attribute Decision Making: Methods and Applications. Springer, Berlin.

Diakoulaki, D., Mavrotas, G. & Papayannakis, L. (1995). Determining objective weights in multiple criteria problems: The CRITIC method. Computers & Operations Research, 22(7), 763-770. doi:10.1016/0305-0548(94)00059-H

See Also

nexus_topsis, nexus_sensitivity

Examples

data(arid_pulse_nexus)
d <- arid_pulse_nexus
ind <- data.frame(
  WUE = d$grain_yield / d$total_water,
  EUE = (d$energy_output_grain + d$energy_output_straw) / d$energy_input,
  Yield = d$grain_yield,
  IUE = d$grain_yield / d$n_uptake,
  CF = d$ghg_emission
)
nexus_weights(ind, method = "entropy",
              benefit = c(TRUE, TRUE, TRUE, TRUE, FALSE))
nexus_weights(ind, method = "critic",
              benefit = c(TRUE, TRUE, TRUE, TRUE, FALSE))

Normalize Data (Min-Max)

Description

Min-max normalization to scale values between 0 and 1.

Usage

normalize_minmax(x, inverse = FALSE)

Arguments

Details

Formula:

X_{norm} = \frac{X - X_{min}}{X_{max} - X_{min}}

Value

Numeric vector normalized to the 0 to 1 range. Returns 0.5 for all elements if the input has zero range.

Examples

normalize_minmax(c(10, 20, 30, 40, 50))
normalize_minmax(c(10, 20, 30, 40, 50), inverse = TRUE)

Normalize Data (Z-score)

Description

Standardization to z-scores (mean = 0, standard deviation = 1).

Usage

normalize_zscore(x)

Arguments

Details

Formula:

Z = \frac{X - \mu}{\sigma}

Value

Numeric vector of z-scores. Returns all zeros if standard deviation is zero.

Examples

normalize_zscore(c(10, 20, 30, 40, 50))

Nutrient Balance Sheet

Description

Input-output nutrient balance for major nutrients (N, P, K).

Usage

nutrient_balance(
  n_input,
  p_input,
  k_input,
  n_output,
  p_output,
  k_output,
  verbose = getOption("wefnexus.verbose", TRUE)
)

Arguments

Details

Formula:

NB = Nutrient Applied - Nutrient Removed

Zero inputs are allowed (for example no K applied), giving a negative balance that shows nutrient mining.

Value

A data frame with five columns:

nutrient

Character. Nutrient name: N, P, or K

input_kg_ha

Numeric. Total nutrient input (kg/ha)

output_kg_ha

Numeric. Total nutrient output (kg/ha)

balance_kg_ha

Numeric. Balance: input minus output (kg/ha). Positive = surplus; negative = depletion

output_input_ratio

Numeric. Output to input ratio (NA when the input is zero)

Examples

nutrient_balance(n_input = 120, p_input = 60, k_input = 40,
                 n_output = 95, p_output = 25, k_output = 80)
# No potassium applied: balance shows K mining
nutrient_balance(n_input = 20, p_input = 40, k_input = 0,
                 n_output = 56.8, p_output = 8.2, k_output = 45)

Nutrient Harvest Index (NHI)

Description

Proportion of total plant nutrient partitioned to grain.

Usage

nutrient_harvest_index(
  grain_nutrient_uptake,
  total_nutrient_uptake,
  verbose = getOption("wefnexus.verbose", TRUE)
)

Arguments

Details

Formula:

NHI = \frac{U_{grain}}{U_{total}}

where U_{grain} is nutrient uptake in grain and U_{total} is total plant nutrient uptake (kg/ha).

Value

Numeric vector. Nutrient harvest index (proportion, 0 to 1).

Examples

nutrient_harvest_index(grain_nutrient_uptake = 75,
                       total_nutrient_uptake = 100)

Comprehensive Nutrient Use Efficiency (NUE)

Description

Computes all major nutrient use efficiency metrics for a given nutrient in a single call.

Usage

nutrient_use_efficiency(
  yield_treated,
  yield_control,
  nutrient_applied,
  uptake_treated,
  uptake_control,
  nutrient_name = "N",
  grain_uptake = NULL,
  verbose = getOption("wefnexus.verbose", TRUE)
)

Arguments

Details

Returns agronomic efficiency (AE), physiological efficiency (PE), recovery efficiency (RE), partial factor productivity (PFP), internal utilization efficiency (IUE) and nutrient harvest index (NHI). See the individual functions for formulas. Versions before 1.1.0 returned a fixed NHI of 0.75; NHI is now computed from grain_uptake.

Value

A data frame with one row and seven columns:

nutrient

Character. Nutrient name

agronomic_eff

Numeric. Agronomic efficiency (kg/kg)

physiological_eff

Numeric. Physiological efficiency (kg/kg)

recovery_eff

Numeric. Recovery efficiency (proportion)

partial_factor_prod

Numeric. Partial factor productivity (kg/kg)

internal_util_eff

Numeric. Internal utilization efficiency (kg/kg)

nutrient_harvest_idx

Numeric. Nutrient harvest index (grain uptake / total uptake). NA when grain_uptake is not supplied.

References

Dobermann, A. (2007). Nutrient use efficiency: measurement and management. In Fertilizer Best Management Practices, IFA, Paris, pp. 1-28. https://digitalcommons.unl.edu/agronomyfacpub/316/

Congreves, K.A. et al. (2021). Nitrogen use efficiency definitions of today and tomorrow. Frontiers in Plant Science, 12, 637108. doi:10.3389/fpls.2021.637108

Examples

nutrient_use_efficiency(
  yield_treated = 4500, yield_control = 3000,
  nutrient_applied = 120, uptake_treated = 100,
  uptake_control = 60, nutrient_name = "N", grain_uptake = 72
)

Partial Factor Productivity (PFP)

Description

Total yield per unit of nutrient applied, without deduction of control yield.

Usage

partial_factor_productivity(
  yield,
  nutrient_applied,
  verbose = getOption("wefnexus.verbose", TRUE)
)

Arguments

Details

PFP = \frac{Y}{F}

Value

Numeric vector. Partial factor productivity (kg yield per kg nutrient applied).

Examples

partial_factor_productivity(yield = 4500, nutrient_applied = 120)

Physiological Efficiency (PE)

Description

Yield increase per unit of nutrient uptake increase.

Usage

physiological_efficiency(
  yield_treated,
  yield_control,
  uptake_treated,
  uptake_control,
  verbose = getOption("wefnexus.verbose", TRUE)
)

Arguments

Details

PE = \frac{Y_f - Y_0}{U_f - U_0}

Value

Numeric vector. Physiological efficiency (kg grain per kg nutrient uptake). Returns NA where uptake difference is zero.

Examples

physiological_efficiency(yield_treated = 4500, yield_control = 3000,
                         uptake_treated = 100, uptake_control = 60)

Plot method for cf_result

Description

Plot method for cf_result

Usage

## S3 method for class 'cf_result'
plot(x, ...)

Arguments

Value

No return value, called for the side effect of generating a horizontal bar plot showing carbon footprint by emission source.

Plot method for energy_budget

Description

Stacked horizontal bars of input energy for each treatment, split by input item, by direct and indirect energy, or by renewable and non-renewable energy.

Usage

## S3 method for class 'energy_budget'
plot(
  x,
  type = c("items", "form", "source"),
  percent = FALSE,
  top = 7,
  title = NULL,
  ...
)

Arguments

Value

A ggplot2 object.

Examples

if (requireNamespace("ggplot2", quietly = TRUE)) {
  inputs <- data.frame(
    treatment = c("CT", "ZT"),
    human_labour_man = c(320, 240), diesel = c(65, 38),
    electricity = c(180, 75), nitrogen = c(20, 20),
    phosphorus = c(40, 40), seed = c(20, 20), herbicide = c(0, 0.75)
  )
  eb <- energy_budget(inputs, verbose = FALSE)
  plot(eb)
  plot(eb, type = "source", percent = TRUE)
}

Plot method for nexus_analysis

Description

Quick access to the main figures of a nexus_analysis.

Usage

## S3 method for class 'nexus_analysis'
plot(x, which = c("radar", "anova", "topsis", "heatmap"), ...)

Arguments

Value

A ggplot2 object.

Examples

if (requireNamespace("ggplot2", quietly = TRUE)) {
  data(arid_pulse_trial)
  res <- nexus_analysis(
    arid_pulse_trial, treatment = "treatment", block = "replication",
    yield = "grain_yield", water = "total_water",
    energy_in = "energy_input", energy_out = "energy_output",
    emission = "ghg_emission", n_uptake = "n_uptake", verbose = FALSE)
  plot(res)
  plot(res, which = "anova")
}

Plot method for nexus_anova

Description

Draws treatment means as horizontal bars with error bars and the letter groups from nexus_anova, one panel per response.

Usage

## S3 method for class 'nexus_anova'
plot(
  x,
  response = NULL,
  error = c("se", "sem", "none"),
  labels = NULL,
  ncol = NULL,
  title = NULL,
  ...
)

Arguments

Details

Panels for responses whose treatment F test is not significant are marked "(ns)" and show no letters.

Value

A ggplot2 object.

Examples

if (requireNamespace("ggplot2", quietly = TRUE)) {
  data(arid_pulse_trial)
  res <- nexus_anova(arid_pulse_trial,
                     response = c("grain_yield", "n_uptake"),
                     treatment = "treatment", block = "replication",
                     verbose = FALSE)
  plot(res, labels = c(grain_yield = "Grain yield (kg/ha)",
                       n_uptake = "N uptake (kg/ha)"))
}

Plot method for nexus_result

Description

Plot method for nexus_result

Usage

## S3 method for class 'nexus_result'
plot(x, type = c("radar", "heatmap"), ...)

Arguments

Value

Invisibly returns the scores matrix. Called for the side effect of generating a radar or heatmap plot.

Plot method for rank_compare

Description

Rank chart: each line follows one treatment across the eight rankings, so stable and unstable treatments are easy to see.

Usage

## S3 method for class 'rank_compare'
plot(x, title = NULL, ...)

Arguments

Value

A ggplot2 object.

Plot method for topsis_result

Description

Ranked horizontal bars of the TOPSIS closeness coefficient, with the best treatment highlighted.

Usage

## S3 method for class 'topsis_result'
plot(x, highlight = 1, title = NULL, ...)

Arguments

Value

A ggplot2 object.

Examples

if (requireNamespace("ggplot2", quietly = TRUE)) {
  data(arid_pulse_nexus)
  d <- arid_pulse_nexus
  ind <- data.frame(WUE = d$grain_yield / d$total_water,
                    Yield = d$grain_yield, CF = d$ghg_emission)
  ts <- nexus_topsis(ind, benefit = c(TRUE, TRUE, FALSE),
                     treatment_names = d$treatment, verbose = FALSE)
  plot(ts)
}

Plot method for tradeoff_matrix

Description

Plot method for tradeoff_matrix

Usage

## S3 method for class 'tradeoff_matrix'
plot(x, ...)

Arguments

Value

A ggplot2 object.

Plot Nexus Sensitivity Analysis (ggplot2)

Description

Visualises the output of nexus_sensitivity as faceted line plots showing how the nexus index changes with dimension weights.

Usage

plot_sensitivity(sa, title = "Nexus Weight Sensitivity")

Arguments

Value

A ggplot2 object.

Examples

if (requireNamespace("ggplot2", quietly = TRUE)) {
  sa <- nexus_sensitivity(
    water_score = c(0.9, 0.5), energy_score = c(0.6, 0.8),
    food_score = c(0.8, 0.7), nutrient_score = c(0.7, 0.6),
    carbon_score = c(0.5, 0.9),
    treatment_names = c("CA", "CT"), steps = 10
  )
  plot_sensitivity(sa)
}

Plot a Nexus Trade-off Matrix

Description

Draws the correlation matrix from nexus_tradeoff as a heatmap with a diverging scale (blue positive, red negative, grey near zero). Cells show the coefficient and significance stars. Supply benefit to orient the indicators so that blue always means a synergy and red a trade-off.

Usage

plot_tradeoff(
  cor_mat,
  p_values = attr(cor_mat, "p_values"),
  benefit = NULL,
  triangle = c("lower", "full"),
  digits = 2,
  title = NULL
)

Arguments

Details

Stars: * p < 0.05, ** p < 0.01, *** p < 0.001 (orienting changes only the sign, not the p-value). Without benefit, a negative correlation is not necessarily a trade-off: lower GHG emission with higher yield is a synergy. With few treatments, correlations are imprecise; interpret them with care.

Value

A ggplot2 object.

Examples

if (requireNamespace("ggplot2", quietly = TRUE)) {
  data(arid_pulse_trial)
  d <- arid_pulse_trial
  ind <- data.frame(Yield = d$grain_yield,
                    WUE = d$grain_yield / d$total_water,
                    EUE = d$energy_output / d$energy_input,
                    IUE = d$grain_yield / d$n_uptake,
                    GHG = d$ghg_emission)
  tm <- nexus_tradeoff(ind, verbose = FALSE)
  plot_tradeoff(tm)
  # GHG is lower-is-better: orient so blue = synergy, red = trade-off
  plot_tradeoff(tm, benefit = c(TRUE, TRUE, TRUE, TRUE, FALSE))
}

Print method for cf_result

Description

Print method for cf_result

Usage

## S3 method for class 'cf_result'
print(x, ...)

Arguments

Value

Invisibly returns the input object x. Called for the side effect of printing a formatted carbon footprint summary to the console.

Print method for energy_budget

Description

Print method for energy_budget

Usage

## S3 method for class 'energy_budget'
print(x, ...)

Arguments

Value

Invisibly returns x. Called for the side effect of printing the energy budget summary.

Print method for nexus_analysis

Description

Print method for nexus_analysis

Usage

## S3 method for class 'nexus_analysis'
print(x, ...)

Arguments

Value

Invisibly returns x. Called for the side effect of printing the ranking of treatments.

Print method for nexus_anova

Description

Print method for nexus_anova

Usage

## S3 method for class 'nexus_anova'
print(x, ...)

Arguments

Value

Invisibly returns x. Called for the side effect of printing the formatted comparison table.

Print method for nexus_result

Description

Print method for nexus_result

Usage

## S3 method for class 'nexus_result'
print(x, ...)

Arguments

Value

Invisibly returns the input object x. Called for the side effect of printing a formatted nexus analysis summary to the console.

Print method for rank_compare

Description

Print method for rank_compare

Usage

## S3 method for class 'rank_compare'
print(x, ...)

Arguments

Value

Invisibly returns x. Called for the side effect of printing the ranks and the concordance statistics.

Print method for sustainability_result

Description

Print method for sustainability_result

Usage

## S3 method for class 'sustainability_result'
print(x, ...)

Arguments

Value

Invisibly returns the input object x. Called for the side effect of printing sustainability scores and categories to the console.

Print method for tradeoff_matrix

Description

Print method for tradeoff_matrix

Usage

## S3 method for class 'tradeoff_matrix'
print(x, ...)

Arguments

Value

Invisibly returns x. Called for the side effect of printing the correlation matrix.

Production Efficiency Index (PEI)

Description

Yield produced per unit of production cost, measuring economic efficiency of crop production.

Usage

production_efficiency_index(
  yield,
  cost,
  verbose = getOption("wefnexus.verbose", TRUE)
)

Arguments

Details

Formula:

PEI = \frac{Y}{C}

where Y is yield (kg/ha) and C is the total cost of production (currency/ha).

Value

Numeric vector. Production efficiency index (kg/currency unit).

Examples

production_efficiency_index(yield = 4500, cost = 28500)

Protein Yield

Description

Total protein output per hectare from crop production.

Usage

protein_yield(
  yield,
  protein_content,
  verbose = getOption("wefnexus.verbose", TRUE)
)

Arguments

Details

Formula:

PY = Yield \times Protein Content / 100

Value

Numeric vector. Protein yield (kg/ha).

Examples

protein_yield(yield = 4500, protein_content = 12.5)

Recovery Efficiency (RE)

Description

Proportion of applied nutrient that is recovered in crop biomass.

Usage

recovery_efficiency(
  uptake_treated,
  uptake_control,
  nutrient_applied,
  verbose = getOption("wefnexus.verbose", TRUE)
)

Arguments

Details

RE = \frac{U_f - U_0}{F}

Value

Numeric vector. Recovery efficiency as a proportion (0 to 1, but can exceed 1 due to priming effects or added benefits).

Examples

recovery_efficiency(uptake_treated = 100, uptake_control = 60,
                    nutrient_applied = 120)

Soil Organic Carbon Stock (SOC)

Description

Estimates soil organic carbon stock for a given soil depth.

Usage

soil_carbon_stock(
  soc_pct,
  bulk_density,
  depth = 30,
  coarse_fraction = 0,
  verbose = getOption("wefnexus.verbose", TRUE)
)

Arguments

Details

SOC = SOC_{pct} \times BD \times D \times (1 - CF)

where SOC_pct is organic carbon (percent), BD is bulk density (Mg/m3), D is depth (cm) and CF is the coarse fragment fraction. The product of percent, Mg/m3 and cm is already Mg C/ha: (SOC/100) x BD x (D/100 m) x 10000 m2/ha.

Versions before 1.1.0 multiplied by an extra factor of 0.1, which gave kg C/m2 while labelling the result Mg C/ha, so stocks were 10 times too low.

Value

Numeric vector. SOC stock (Mg C/ha, equivalent to t C/ha).

References

Batjes, N.H. (1996). Total carbon and nitrogen in the soils of the world. European Journal of Soil Science, 47(2), 151-163. doi:10.1111/j.1365-2389.1996.tb01386.x

Examples

soil_carbon_stock(soc_pct = 0.65, bulk_density = 1.45, depth = 30)

Specific Energy

Description

Energy input per unit area per unit time, useful for comparing cropping systems of different durations.

Usage

specific_energy(
  energy_in,
  duration,
  verbose = getOption("wefnexus.verbose", TRUE)
)

Arguments

Details

Formula:

SE = \frac{E_{in}}{d}

where E_{in} is energy input (MJ/ha) and d is crop duration (days).

Note that much of the energy budgeting literature uses "specific energy" for energy input per kg of produce (MJ/kg). That quantity is returned by energy_intensity.

Value

Numeric vector. Specific energy (MJ/ha/day).

Examples

specific_energy(energy_in = 12000, duration = 150)

Summary method for nexus_result

Description

Summary method for nexus_result

Usage

## S3 method for class 'nexus_result'
summary(object, ...)

Arguments

Value

Invisibly returns the input object object. Called for the side effect of printing a detailed dimension-wise summary to the console.

System Productivity Index (SPI)

Description

Converts yields from a cropping system to a common crop-equivalent yield based on economic value.

Usage

system_productivity_index(
  yields,
  prices,
  base_price,
  verbose = getOption("wefnexus.verbose", TRUE)
)

Arguments

Details

SPI = \frac{\sum(Y_i \times P_i)}{P_{base}}

Value

Numeric. System productivity expressed as base crop equivalent yield (kg/ha).

Examples

system_productivity_index(yields = c(5000, 4500),
                          prices = c(22, 25), base_price = 25)

Water Footprint (WF)

Description

Computes the water footprint of crop production decomposed into green, blue, and grey components following the Water Footprint Assessment framework.

Usage

water_footprint(
  green_water,
  blue_water,
  grey_water = 0,
  yield,
  area = 1,
  per_ton = FALSE,
  verbose = getOption("wefnexus.verbose", TRUE)
)

Arguments

Details

The water footprint per unit mass of product is:

WF = \frac{CWU \times 10}{Y}

where CWU is crop water use (mm) and Y is yield (kg/ha). The factor 10 converts mm over 1 ha to m3.

Value

A data frame with four numeric columns:

green_wf

Green water footprint (m3/kg or m3/ton)

blue_wf

Blue water footprint (m3/kg or m3/ton)

grey_wf

Grey water footprint (m3/kg or m3/ton)

total_wf

Total water footprint (m3/kg or m3/ton)

References

Hoekstra, A.Y., Chapagain, A.K., Aldaya, M.M. & Mekonnen, M.M. (2011). The Water Footprint Assessment Manual: Setting the Global Standard. Earthscan, London. ISBN:9781849712798.

Mialyk, O. et al. (2024). Water footprints and crop water use of 175 individual crops for 1990-2019 simulated with a global crop model. Scientific Data, 11, 200. doi:10.1038/s41597-024-03051-3

Examples

water_footprint(green_water = 300, blue_water = 200,
                grey_water = 50, yield = 4000)

Water Productivity (WP)

Description

Computes physical or economic water productivity per unit of water used.

Usage

water_productivity(
  yield,
  water_applied,
  price = NULL,
  unit = "mm",
  verbose = getOption("wefnexus.verbose", TRUE)
)

Arguments

Details

Physical water productivity:

WP = \frac{Y}{W_{m3}}

Economic water productivity:

WP_{econ} = \frac{Y \times P}{W_{m3}}

When unit = "mm", water is converted to m3/ha using 1 mm = 10 m3/ha.

Value

Numeric vector. Physical water productivity in kg/m3 when price is NULL, or economic water productivity in currency/m3 when price is specified.

References

Molden, D. et al. (2010). Improving agricultural water productivity: Between optimism and caution. Agricultural Water Management, 97(4), 528-535. doi:10.1016/j.agwat.2009.03.023

Examples

water_productivity(4500, 500, unit = "mm")
water_productivity(4500, 500, price = 25, unit = "mm")

Water Use Efficiency (WUE)

Description

Computes water use efficiency as the ratio of economic yield to total water consumed (evapotranspiration or irrigation plus rainfall).

Usage

water_use_efficiency(
  yield,
  water_consumed,
  verbose = getOption("wefnexus.verbose", TRUE)
)

Arguments

Details

Water use efficiency is defined as:

WUE = \frac{Y}{W}

where Y is economic yield (kg/ha) and W is total water consumed (mm).

Value

Numeric vector. Water use efficiency in kg/ha/mm. Higher values indicate more efficient use of water for crop production.

References

Hoover, D.L. et al. (2023). Indicators of water use efficiency across diverse agroecosystems and scales. Science of the Total Environment, 864, 160992. doi:10.1016/j.scitotenv.2022.160992

Examples

# Wheat yield with different irrigation levels
yield <- c(4500, 4200, 3800, 3500)
water <- c(450, 400, 350, 300)
water_use_efficiency(yield, water)