Theoretical Basis: IPCC Tier 2 Methodology

Introduction

The herdr package performs environmental impact assessments based on the 2019 Refinement to the 2006 IPCC Guidelines. The core of the model is the Energy Balance, where Gross Energy (GE) intake is derived from the animal’s physiological requirements.

I. Net Energy for Maintenance ( $NE_m$ ) (Eq. 10.3)

$NE_m$ is the energy required to maintain the animal’s energy balance without gain or loss of weight.

Formula: $NE_m = Cf_i \cdot \text{Weight}^{0.75}$

Variable	Description	Source in the Package
$NE_m$	Net energy for maintenance (MJ/day)	Calculated
$Cf_i$	Maintenance coefficient based on animal species/status	`ipcc_coefficients.csv`
Weight	Live weight of the individual animal (kg)	`weights.csv`

II. Net Energy for Activity ( $NE_a$ )

$NE_a$ represents energy used for grazing, walking, or other activities.

Cattle: $NE_a = C_a \cdot NE_m$ (Eq. 10.4)
Sheep and Goats: $NE_a = C_a \cdot \text{Weight}$ (Eq. 10.5)

Variable	Description	Source in the Package
$NE_a$	Net energy for activity (MJ/day)	Calculated
$C_a$	Activity coefficient (varies by feeding situation)	`ipcc_coefficients.csv`
$NE_m$	Maintenance energy	Result of Eq. 10.3
Weight	Live weight of the animal (kg)	`weights.csv`

III. Net Energy for Growth ( $NE_g$ )

Energy required for tissue deposition (weight gain).

Cattle and Buffalo: (Eq. 10.6) $NE_{g} = 22.02 \cdot \left( \frac{BW}{C \cdot MW} \right)^{0.75} \cdot WG^{1.097}$
Sheep and Goats: (Eq. 10.7) $NE_g = \frac{WG_{lamb/kid} \cdot (a + 0.5b(BW_i + BW_f))}{365}$

Variable	Description	Source in the Package
$BW$	Average live body weight of the animal (kg)	`weights.csv`
$MW$	Mature body weight of an adult female (kg)	`weights.csv`
$WG$	Daily weight gain (kg/day)	`weights.csv`
$C, a, b$	IPCC species-specific growth constants	`ipcc_coefficients.csv`
$BW_i / BW_f$	Initial and final weight for the period (kg)	`weights.csv`

IV. Net Energy for Lactation ( $NE_l$ )

Energy required for milk production based on volume and fat content.

Cattle: $NE_l = \text{Milk} \cdot (1.47 + 0.40 \cdot \text{Fat})$ (Eq. 10.8)
Sheep and Goats: $NE_l = \text{Milk} \cdot EV_{milk}$ (Eq. 10.9)

Variable	Description	Source in the Package
$NE_l$	Net energy for lactation (MJ/day)	Calculated
Milk	Average daily milk yield (kg/day)	`livestock_definitions.csv`
Fat	Milk fat content percentage (%)	`livestock_definitions.csv`
$EV_{milk}$	Energy required to produce 1 kg of milk (MJ/kg)	`ipcc_coefficients.csv`

V. Net Energy for Work, Wool, and Pregnancy

Work ( $NE_{work}$ ): $NE_{work} = 0.10 \cdot NE_m \cdot \text{Hours}$
Wool ( $NE_{wool}$ ): $NE_{wool} = \frac{\text{Pr}_{wool} \cdot EV_{wool}}{365}$
Pregnancy ( $NE_p$ ): $NE_p = C_{pregnancy} \cdot NE_m$

Variable	Description	Source in the Package
Hours	Number of hours worked per day (draft animals)	`livestock_definitions.csv`
$\text{Pr}_{wool}$	Annual wool production (kg/year)	`livestock_definitions.csv`
$EV_{wool}$	Energy per kg of wool (IPCC default 24 MJ/kg)	Constant
$C_{pregnancy}$	Pregnancy energy coefficient	`ipcc_coefficients.csv`

VI. Efficiency Ratios ( $REM$ and $REG$ )

Based on IPCC Equations 10.14 and 10.15, derived from feed digestibility ( $DE$ ):

For Maintenance ( $REM$ ): $REM = \left[ 1.123 - (4.092 \cdot 10^{-3} \cdot DE) + (1.126 \cdot 10^{-5} \cdot (DE)^2) - \left( \frac{25.4}{DE} \right) \right]$
For Growth ( $REG$ ): $REG = \left[ 1.164 - (5.16 \cdot 10^{-3} \cdot DE) + (1.308 \cdot 10^{-5} \cdot (DE)^2) - \left( \frac{37.4}{DE} \right) \right]$

Variable	Description	Source in the Package
$REM$	Efficiency of digestible energy for maintenance	Calculated
$REG$	Efficiency of digestible energy for growth	Calculated
$DE$	Digestibility of feed as % of gross energy	`feed_characteristics.csv`

VII. Gross Energy (GE)

Gross Energy (GE) is the total daily energy intake required to sustain all physiological functions.

Formula: $GE = \frac{\left( \frac{NE_m + NE_a + NE_l + NE_{work} + NE_p}{REM} + \frac{NE_g + NE_{wool}}{REG} \right)}{DE/100}$

Variable	Description	Source in the Package
$GE$	Total daily gross energy requirement (MJ/day)	Calculated
$NE_x$	Various net energy requirements calculated above	Calculated Results
$REM/REG$	Efficiency ratios	Results of Eq. 10.14/10.15
$DE$	Feed digestibility (%)	`feed_characteristics.csv`

VIII. Methane Module: Enteric Fermentation ( $CH_4$ )

Methane Emission Factor ( $EF$ ) (Eq. 10.21)

$EF = \frac{GE \cdot \left( \frac{Y_m}{100} \right) \cdot 365}{55.65}$

Variable	Description	Source in Package
$EF$	Methane emission factor (kg $CH_4$ /head/year)	Calculated
$GE$	Daily gross energy intake (MJ/day)	Result of Section VII
$Y_m$	Methane conversion factor (%)	`feed_characteristics.csv`
55.65	Energy content of methane (MJ/kg $CH_4$ )	Constant

Total Enteric Emissions ( $E_T$ ) (Eq. 10.19)

$E_T = \sum_{(P)} EF_{(T,P)} \cdot \left( \frac{N_{(T,P)}}{10^6} \right)$

Variable	Description	Source in Package
$E_T$	Total emissions from category $T$ (Gg $CH_4$ /year)	Calculated
$N_{(T,P)}$	Number of animals in category $T$	`livestock_census.csv`

IX. Methane Module: Manure Management ( $CH_{4(mm)}$ )

Volatile Solid Excretion Rates ( $VS$ ) (Eq. 10.24)

$VS = \left[ GE \cdot \left( 1 - \frac{DE}{100} \right) + (UE \cdot GE) \right] \cdot \left[ \frac{1 - ASH}{18.45} \right]$

Variable	Description	Source in Package
$VS$	Daily volatile solid excretion (kg VS/day)	Calculated
$UE$	Urinary energy excretion fraction (default 0.04)	`ipcc_coefficients.csv`
$ASH$	Ash content of the feed (fraction)	`feed_characteristics.csv`
18.45	Energy content of dietary dry matter (MJ/kg)	Constant

Manure Emission Factor ( $EF$ ) (Eq. 10.23)

$EF_{(T)} = (VS_{(T)} \cdot 365) \cdot \left[ B_{0(T)} \cdot 0.67 \cdot \sum_{S,k} \frac{MCF_{S,k}}{100} \cdot AWMS_{(T,S,k)} \right]$

Variable	Description	Source in Package
$B_{0(T)}$	Maximum methane producing capacity ( $m^3/kg VS$ )	`ipcc_coefficients.csv`
$MCF_{S,k}$	Methane conversion factor for system $S$ (%)	`ipcc_mm.csv`
$AWMS$	Fraction of manure handled in system $S$	`manure_management.csv`
0.67	Conversion factor ( $m^3 CH_4$ to kg $CH_4$ )	Constant

X. N₂O Module: Nitrogen-Based Emissions

I. Nitrogen Balance & Excretion

1. Nitrogen Intake ( $N_{intake}$ ) (Eq. 10.31/10.32)

$N_{intake} = \left( \frac{GE}{18.45} \right) \cdot \left( \frac{CP/100}{6.25} \right)$

Variable	Description	Source in Package
$N_{intake}$	Total nitrogen ingested (kg N/day)	Calculated
$CP$	Crude Protein content of the diet (%)	`feed_characteristics.csv`
6.25	Conversion factor from N to Protein	Constant

2. Nitrogen Retention ( $N_{retention}$ )

Reflects the logic used in the herdr codebase: * Cattle: $Milk_{protein} = 1.9 + 0.4 \cdot Fat_{content}$ $N_{retention} = \left[ \frac{Milk \cdot Milk_{protein}}{6.38} \right] + \left[ \frac{WG \cdot (268 - (7.03 \cdot \frac{NE_g}{WG})) / 1000}{6.25} \right]$

Variable	Description	Source in Package
$Fat_{content}$	Milk fat percentage (%)	`livestock_definitions.csv`
$Milk$	Daily milk yield (kg/day)	`livestock_definitions.csv`
$WG$	Daily weight gain (kg/day)	`weights.csv`
6.38 / 6.25	Specific N-to-Protein conversion factors	Constants

3. Annual Excretion ( $N_{excreted}$ )

Sheep/Goats: $N_{excreted} = (N_{intake} \cdot (1 - 0.1)) \cdot 365$
Cattle: $N_{excreted} = (N_{intake} - N_{retention}) \cdot 365$

II. Direct $N_2O$ Emissions (Eq. 10.25)

$N_2O_{direct} = N_{(T,P)} \cdot N_{excreted} \cdot Allocation \cdot EF_3 \cdot \left( \frac{44}{28} \right)$

Variable	Description	Source in Package
$Allocation$	Fraction of N managed in a specific system	`manure_management.csv`
$EF_3$	Direct $N_2O$ emission factor for the system	`ipcc_mm.csv`
44/28	Stoichiometric ratio of $N_2O$ to $N_2$	Constant

XI. N₂O Module: Indirect Emissions

I. Nitrogen Losses from Manure

1. Volatilization ( $N_{volatilization-MMS}$ ) (Eq. 10.26)

$N_{vol-MMS} = \sum \left[ (N \cdot Nex \cdot AWMS) \cdot Frac_{GasMS} \right]$

2. Leaching and Runoff ( $N_{leaching-MMS}$ ) (Eq. 10.27)

$N_{leach-MMS} = \sum \left[ (N \cdot Nex \cdot AWMS) \cdot Frac_{LeachMS} \right]$

Variable	Description	Source in Package
$Frac_{GasMS}$	Fraction of N lost as volatilized gas ( $NH_3 + NO_x$ )	`ipcc_mm.csv`
$Frac_{LeachMS}$	Fraction of N lost via leaching into water	`ipcc_mm.csv`

II. Indirect $N_2O$ Calculation (Eq. 10.28/10.29)

From Volatilization: $N_2O_{G(mm)} = (N_{vol-MMS} \cdot EF_4) \cdot \frac{44}{28}$
From Leaching: $N_2O_{L(mm)} = (N_{leach-MMS} \cdot EF_5) \cdot \frac{44}{28}$

Variable	Description	Source in Package
$EF_4$	Indirect $N_2O$ factor for volatilization	`ipcc_coefficients.csv`
$EF_5$	Indirect $N_2O$ factor for leaching	`ipcc_coefficients.csv`

📚 References

IPCC (2019). Refinement to the 2006 IPCC Guidelines for National Greenhouse Gas Inventories. Volume 4: AFOLU, Chapter 10.

Introduction

I. Net Energy for Maintenance (NEmNE_m) (Eq. 10.3)

II. Net Energy for Activity (NEaNE_a)

III. Net Energy for Growth (NEgNE_g)

IV. Net Energy for Lactation (NElNE_l)

V. Net Energy for Work, Wool, and Pregnancy

VI. Efficiency Ratios (REMREM and REGREG)

VII. Gross Energy (GE)

VIII. Methane Module: Enteric Fermentation (CH4CH_4)

Methane Emission Factor (EFEF) (Eq. 10.21)

Total Enteric Emissions (ETE_T) (Eq. 10.19)

IX. Methane Module: Manure Management (CH4(mm)CH_{4(mm)})

Volatile Solid Excretion Rates (VSVS) (Eq. 10.24)

Manure Emission Factor (EFEF) (Eq. 10.23)