VM0010 Starter Script

1. Process data
2. Compute Equations
Appendix
- A.1 DataMaid audit

1. Process data

The following workflow provides a starter script for quantifying greenhouse gas emissions reduction of projects designed under the VCS Methodology VM0010.

Import dummy data

set.seed(333)
dataset_raw <- read_excel("./R/assets/dataset_raw.xlsx")
write.csv(dataset_raw, "./R/assets/dataset_tidy.csv", row.names = FALSE)
dataset_tidy <- read.csv("./R/assets/dataset_tidy.csv")
dataset_tidy |> kbl() |> kable_styling()

Stratum...i.	Plot..sp.	Species..j.	Tree..l.	Volume..V_.l.j.I.sp..
1	1	Sp1	t1	3.30
1	1	Sp1	t2	4.80
1	1	Sp1	t3	4.08
1	2	Sp4	t1	1.50
1	2	Sp4	t2	1.68
2	1	Sp1	t1	1.38
2	1	Sp2	t2	3.24
2	1	Sp3	t3	3.72
2	1	sp4	t4	2.94
2	1	Sp5	t5	3.36

Review dummy data

str(dataset_tidy)
dplyr::count(dataset_tidy, Species..j.)

saveHTML(dataMaid::makeDataReport(
  dataset_tidy,
  output = "html",
  codebook = TRUE,
  onlyProblematic = TRUE,
  visuals = setVisuals(all = "basicVisual"),
  replace = TRUE
  )
) # output "dataMaid_dataset_tidy.html" shown in Appendix A.1

'data.frame':   10 obs. of  5 variables:
 $ Stratum...i.         : int  1 1 1 1 1 2 2 2 2 2
 $ Plot..sp.            : int  1 1 1 2 2 1 1 1 1 1
 $ Species..j.          : chr  "Sp1" "Sp1" "Sp1" "Sp4" ...
 $ Tree..l.             : chr  "t1" "t2" "t3" "t1" ...
 $ Volume..V_.l.j.I.sp..: num  3.3 4.8 4.08 1.5 1.68 1.38 3.24 3.72 2.94 3.36

Species..j.	n
Sp1	4
Sp2	1
Sp3	1
Sp4	2
Sp5	1
sp4	1

Tidy dummy data

Clean dataset and relabel to match VM0010 Verra Methodology and Tidyverse style guide

data.table::setnames(dataset_tidy, old = "Stratum...i.", new = "stratum_i", skip_absent = TRUE)
data.table::setnames(dataset_tidy, old = "Species..j.", new = "species_j", skip_absent = TRUE)
data.table::setnames(dataset_tidy, old = "Plot..sp.", new = "plot_sp", skip_absent = TRUE)
data.table::setnames(dataset_tidy, old = "Tree..l.", new = "tree_l", skip_absent = TRUE)
data.table::setnames(dataset_tidy, old = "Volume..V_.l.j.I.sp..", new = "volume", skip_absent = TRUE)
dataset_tidy$species_j[dataset_tidy$species_j == "sp4"] <- "Sp4"
dataset_tidy$species_j  = as.factor(dataset_tidy$species_j)
dataset_tidy$stratum_i  = as.factor(dataset_tidy$stratum_i)

Compute new variables & save copy of cleaned dataset_tidy.csv

dataset_tidy$bcef_r     = 0.7
dataset_tidy$cf         = 0.5
dataset_tidy$d          = 0.5
dataset_tidy$a_sp       = 0.1
dataset_tidy$a_sp_m2    = dataset_tidy$a_sp * 10000

dataset_tidy = dataset_tidy %>%
  group_by(stratum_i) %>%
  mutate(a_I_m2 = sum(a_sp_m2), a_I_ha = sum(a_sp)) 

write.csv(dataset_tidy, "./R/assets/dataset_tidy.csv", row.names = FALSE)
dataset_tidy |> kbl() |> kable_styling()

stratum_i	plot_sp	species_j	tree_l	volume	bcef_r	cf	d	a_sp	a_sp_m2	a_I_m2	a_I_ha
1	1	Sp1	t1	3.30	0.7	0.5	0.5	0.1	1000	5000	0.5
1	1	Sp1	t2	4.80	0.7	0.5	0.5	0.1	1000	5000	0.5
1	1	Sp1	t3	4.08	0.7	0.5	0.5	0.1	1000	5000	0.5
1	2	Sp4	t1	1.50	0.7	0.5	0.5	0.1	1000	5000	0.5
1	2	Sp4	t2	1.68	0.7	0.5	0.5	0.1	1000	5000	0.5
2	1	Sp1	t1	1.38	0.7	0.5	0.5	0.1	1000	5000	0.5
2	1	Sp2	t2	3.24	0.7	0.5	0.5	0.1	1000	5000	0.5
2	1	Sp3	t3	3.72	0.7	0.5	0.5	0.1	1000	5000	0.5
2	1	Sp4	t4	2.94	0.7	0.5	0.5	0.1	1000	5000	0.5
2	1	Sp5	t5	3.36	0.7	0.5	0.5	0.1	1000	5000	0.5

2. Compute Equations

Note all four equations that follow derive estimates according to specific species, whether measured at the plot level, stratum or globally. Hence, caution is advised when computing initial, absolute estimates and when deriving or applying hectare expansion factors.

On page 19 of VM0010 Methodology, ‘equation 1’ calculates merchantable timber volume in cubic meters using the following:

EQ1: Plot biomass

$$V_{j,i|sp} = \sum_{l = 1}^{L} V_{l,j,i,sp}$$

where $V_{j,i|sp}$ refers to the sum of merchantable volume of species j from plot sp in stratum i, as computed in the following.

dataset_tidy = dataset_tidy |>
  group_by(species_j, stratum_i, plot_sp) |>
  mutate(vji_sp_m3 = sum(volume))

# compute new variable 'vji_sp_m3'
data.table::setDT(dataset_tidy)[, .(
  vji_sp_m3 = sum(volume)
  ),
  by = .(stratum_i, plot_sp, species_j)
] |> kbl() |> kable_styling()

stratum_i	plot_sp	species_j	vji_sp_m3
1	1	Sp1	12.18
1	2	Sp4	3.18
2	1	Sp1	1.38
2	1	Sp2	3.24
2	1	Sp3	3.72
2	1	Sp4	2.94
2	1	Sp5	3.36

EQ2: Strata biomass

On page 19 of the VM0010 Methodology, ‘equation 2’ provides calculation of merchantable timber volume of a species at the stratum level:

$$V_{j,i|BSL} = \displaystyle \frac{1}{SP} \sum_{sp=1}^{sp} \displaystyle \frac{V_{j,i,sp}}{A_{sp}}$$

where $V_{j,i|BSL}$ refers to the mean merchantable timber volume of species j measured across all plots within stratum i in the baseline scenario. Volume estimates are derived in terms of m³/ha^-1 using an expansion factor derived as the ratio of plot area 1,000m² to 10,000m², as follows.

dataset_tidy = dataset_tidy |>
  group_by(stratum_i, species_j) |>
  mutate(vji_ha_m3 = mean(vji_sp_m3) * 10)

data.table::setDT(dataset_tidy)[, .(
  vji_sp_m3,
  vji_ha_m3
  ),
  by = .(stratum_i, species_j)
] |> kbl() |> kable_styling()

stratum_i	species_j	vji_sp_m3	vji_ha_m3
1	Sp1	12.18	121.8
1	Sp1	12.18	121.8
1	Sp1	12.18	121.8
1	Sp4	3.18	31.8
1	Sp4	3.18	31.8
2	Sp1	1.38	13.8
2	Sp2	3.24	32.4
2	Sp3	3.72	37.2
2	Sp4	2.94	29.4
2	Sp5	3.36	33.6

EQ3: Harvest carbon

On page 20 of the VM0010 Methodology, ‘equation 3’ provides calculation of carbon stock of harvested timber volumes for species i in stratum i.

In the absence of harvest plan data, carbon stocks of commercial timber will be derived from the full inventory dataset_tidy.

This differs to ‘equation 3’ below, which measures mean carbon stock from volumes of ‘harvested biomass’ $C_{HB,j,i|BSL}$ comprised of volumes estimates from extracted timber that is destined off-site for market sales, in addition to volume estimates from extracted timber that is remaining on-site due to damage or use during site operations and road construction. The difference in destinations of these carbon stocks means that alternative carbon factors must be applied in their calculation, as indicated in following two equations

$$C_{HB,j,i|BSL} = (V_{EX,j,i|BSL} + V_{EX,INF,j,i|BSL} ) * BCEF_{R} * CF_{j}$$

Carbon estimates are calculated in units of metric tons per hectare (tC/ha^-1) by multiplying mean volume per hectare of extracted timber of species i from stratum j by the carbon fraction $CF$ (default = 0.5) and biomass conversion and expansion factor $BCEF_{R}$ of that species. If needed, VM0010 methoodology provides guidance on approriate literature source for defining CF with prioritiy of local forest types over national and regional forest types, over forest types from neighboring countries. However, if defaulting to global forest type values, recommendations point to chapter four of (Krey et al., n.d.) that cite value of 1.11. We rely on the provided value of 0.7.

dataset_tidy <- dataset_tidy %>%
  mutate(chb_ha_tC = vji_ha_m3 * bcef_r * cf)

data.table::setDT(dataset_tidy)[, .(
  vji_sp_m3,
  vji_ha_m3,
  chb_ha_tC
  ),
  by = .(stratum_i, species_j)
] |> kbl() |> kable_styling()

stratum_i	species_j	vji_sp_m3	vji_ha_m3	chb_ha_tC
1	Sp1	12.18	121.8	42.63
1	Sp1	12.18	121.8	42.63
1	Sp1	12.18	121.8	42.63
1	Sp4	3.18	31.8	11.13
1	Sp4	3.18	31.8	11.13
2	Sp1	1.38	13.8	4.83
2	Sp2	3.24	32.4	11.34
2	Sp3	3.72	37.2	13.02
2	Sp4	2.94	29.4	10.29
2	Sp5	3.36	33.6	11.76

EQ4: Extracted carbon

“Not all of the harvested biomass leaves the forest because the timber harvested has two components: 1) wood removed to market (extracted timber) and 2) wood remaining in the forest as a result of harvest” (VM0010, 2024:21).

To account for all harvest removals, ‘equation 4’ computes mean carbon of species i in stratum j by adding mean timber to market ($V_{EX,j,i|BSL}$) and mean timber used in harvest infrastructure ($V_{EX,INF,j,i|BSL}$). This sum is then multiplied by the wood density $D$ and carbon fraction $CF$ of that species and reported in units of tC.ha^-1 using the following formula:

$$C_{EX,j,i|BSL} = (V_{EX,j,i|BSL} + V_{EX,INF,j,i|BSL} ) * D_{j} * CF_{j}$$

dataset_tidy <- dataset_tidy %>%
  mutate(cex_ha_tC = vji_ha_m3 * d * cf)

data.table::setDT(dataset_tidy)[, .(
  vji_sp_m3,
  vji_ha_m3,
  chb_ha_tC,
  cex_ha_tC
  ),
  by = .(stratum_i, species_j)
] |> kbl() |> kable_styling()

stratum_i	species_j	vji_sp_m3	vji_ha_m3	chb_ha_tC	cex_ha_tC
1	Sp1	12.18	121.8	42.63	30.45
1	Sp1	12.18	121.8	42.63	30.45
1	Sp1	12.18	121.8	42.63	30.45
1	Sp4	3.18	31.8	11.13	7.95
1	Sp4	3.18	31.8	11.13	7.95
2	Sp1	1.38	13.8	4.83	3.45
2	Sp2	3.24	32.4	11.34	8.10
2	Sp3	3.72	37.2	13.02	9.30
2	Sp4	2.94	29.4	10.29	7.35
2	Sp5	3.36	33.6	11.76	8.40

EQ5: Slash carbon

$$∆C_{DWSLASH_,i,p|BSL} = \sum_{i=1}^{j} \space [C_{HB,j,i|BSL} - C_{EX,j,i|BSL} + C_{RSD,j,i|BSL} + C_{notHB,inf,j,i|BSL}]$$

Equation 5 computes carbon change produced by slash as “the difference between the total carbon stock of the harvested biomass and the carbon stock of the extracted timber, plus the residual stand damage and biomass of trees left to decay as a result forestry infrastructure establishment”. Specifically, values of $C_{notHB,inf,j,i|BSL}$ are computed by applying a fractional value of timber used in harvesting infrastructure development ($F_{V,INF,HWP}$), which may be provided by project proponent, and if missing will be conservatively assumed as 0.0%.

EQ6: Damaged carbon

$C_{RSD,j,i|BSL}$ is defined in units of tC·ha^-1 as mean carbon change from residual stand damage as computed in the following:

$$C_{RSD,j,i|BSL} = C_{EX,j,i|BSL} \times F_{RSD|BSL}$$ where $F_{RSD|BSL}$ represents a dimensionless value for the factor of “residual stand damage” per species in that area. On page 56 of the VM0010 document, an example reference is cited for sourcing residual stand damage values (Winjum, Brown, and Schlamadinger 1998). We apply the reported value of Congo operations of 1.74 t compute the following:

dataset_tidy = dataset_tidy %>%
  mutate(f_rsd = 1.74)

dataset_tidy = dataset_tidy %>%
  mutate(c_rsd = cex_ha_tC * f_rsd)

data.table::setDT(dataset_tidy)[, .(
  vji_sp_m3,
  vji_ha_m3,
  chb_ha_tC,
  c_rsd
  ),
  by = .(stratum_i, species_j)
] |> kbl() |> kable_styling()

stratum_i	species_j	vji_sp_m3	vji_ha_m3	chb_ha_tC	c_rsd
1	Sp1	12.18	121.8	42.63	52.983
1	Sp1	12.18	121.8	42.63	52.983
1	Sp1	12.18	121.8	42.63	52.983
1	Sp4	3.18	31.8	11.13	13.833
1	Sp4	3.18	31.8	11.13	13.833
2	Sp1	1.38	13.8	4.83	6.003
2	Sp2	3.24	32.4	11.34	14.094
2	Sp3	3.72	37.2	13.02	16.182
2	Sp4	2.94	29.4	10.29	12.789
2	Sp5	3.36	33.6	11.76	14.616

EQ7: Undamaged carbon

Equation 7 computes mean carbon volume of biomass that was not extracted during the construction of harvest infrastructure as follows:

$$C_{notHB,inf,j,i|BSL} = V_{notEX,inf,j,i|BSL} \times BCEF_R \times CF_j$$

EQ8: Wood products

Sampling criteria indicate that carbon of wood products is quantified in terms of its volume at time of harvest, while applying conversion factors provided in Winjum et al (1998):

$$C_{EX,i|BSL} = \sum_{j=1}^{J} C_{EX,j,i|BSL}$$

At this stage, It is advised to assign gross percentages of volume extracted to wood product classes on the basis of local expert knowledge of harvest activities and markets. Wood product classes may include sawnwood, panels, roundwood, paper, etc. In addition, the amount of carbon stored in wood products that would decay within three years after harvest are assumed to be emitted at the time of harvest

EQ9: HWP carbon loss ^year-0

Equation 9 calculates mean carbon immediately emmited from harvested volumes at the time of harvest, as follows:

$$ ∆C_{WP0,i|BSL} = \sum \space (C_{EX,i,k|BSL} \times WW_k + SLF_k) $$

where input variables $SLF_f$ and $WW_k$ are derived as the fraction of carbon immediately emitted from specific short-lived wood products, and the fraction of carbon immediately emitted from wood waste, respectively.

EQ10: HWP carbon store

Alternatively, equation 10 computes mean carbon not immediately emitted from harvest volumes at the time of harvest (year=0), as follows:

$$ C_{WP,i|BSL} = \sum \space (C_{EX,i,k|BSL} - ∆C_{WP0,i|BSL}) $$

EQ11: HWP carbon loss ^year-100

Equation 11 computes carbon stored in wood products that are assumed to be retired between 3 - 100 years after harvest from stratum i in land parcel p (tC ha^-1), where $OF_k$ provides the fraction of biomass carbon for wood product type k that is assumed to be emitted to the atmosphere between 3 and 100 years of timber harvest. Winjum, Brown, and Schlamadinger (1998) gives annual oxidation fractions for each class of wood products split by forest region (boreal, temperate and tropical), which is estimated to provide the fraction of carbon that is oxidized between the 3rd and the 100th year after initial harvest, as follows:

$$ ∆C_{WP100,i,p|BSL} = \sum \space (C_{WP,i|BSL} \times OF_k) $$

where $OF_k$ is defined in VM0010 documentation as the fraction of biomass carbon per product type k that is emitted to atmosphere in 100 years following timber harvest:

EQ12: Fuel emissions

Total fuel emissions are derived from all sources presented in Table 2 on page 12 of [VM0010](https://verra.org/wp-content/uploads/2024/10/VM0010_IFM_LtPF_v1.4_Clean_10282024.pdf). Specific emissions variables are defined in subsequent equations:

$$C_{FUEL} = \frac{E_{HARVEST} + E_{HAULING} + E_{TRANSPORT} + E_{PROCESSING}} {\frac{44}{12}}$$

EQ13: Harvesting fuel emissions

$$ E_{HARVEST} = FC_{HARVEST} \times EF_{FUEL} \times \sum_{j,i,p} \space V_{EX,j,i|BSL} \times A_i $$

where $FC_{HARVEST}$ derives volume of fuel consumed by harvest operators per m³ of extracted log (kL/m^-3) and $EF_{FUEL}$ represents a fuel emission factor (tCO2_e kL^-1). These input variables must be derived through the common practice pathway method. The following sources of information are permitted for this: • Data from other forest management companies in the region; or • Data from peer reviewed literature (or published by government agency)

EQ14: Hauling fuel emissions

$$ E_{HAULING} = FC_{HAULING} \times EF_{FUEL} \times V{EX,j,i|BSL} \times A_i $$

EQ15: Transport fuel emissions

$$ N_{TRUCKS-TRANSPORT} = \frac{\sum_{j,i} V_{EX,j,i|BSL} \times A_i}{CAP_{TRUCK}}$$

Appendix

A.1 DataMaid audit

htmltools::includeHTML("dataMaid_dataset_tidy.html")

devtools::session_info()

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 [1] /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library

──────────────────────────────────────────────────────────────────────────────

Krey, Volker, Hans Lofgren, Toshihiko Masui, Ritu Mathur, Joana Portugal Pereira, Benjamin Kenneth Sovacool, Maria Virginia Vilariño, et al. n.d. “1 Chapter 4: Mitigation and Development Pathways in the 2 Near- to Mid-Term.”

Winjum, Jack K., Sandra Brown, and Bernhard Schlamadinger. 1998. “Forest Harvests and Wood Products: Sources and Sinks of Atmospheric Carbon Dioxide.” Forest Science 44 (2): 272–84. https://doi.org/10.1093/forestscience/44.2.272.

Name		Name	Last commit message	Last commit date
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R		R
VM0010-starter_files/libs		VM0010-starter_files/libs
.gitignore		.gitignore
README.md		README.md
VM0010-starter.R		VM0010-starter.R
VM0010-starter.Rproj		VM0010-starter.Rproj
VM0010-starter.html		VM0010-starter.html
VM0010-starter.qmd		VM0010-starter.qmd

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VM0010 Starter Script

1. Process data

Import dummy data

Review dummy data

Tidy dummy data

2. Compute Equations

EQ1: Plot biomass

EQ2: Strata biomass

EQ3: Harvest carbon

EQ4: Extracted carbon

EQ5: Slash carbon

EQ6: Damaged carbon

EQ7: Undamaged carbon

EQ8: Wood products

EQ9: HWP carbon loss ^year-0

EQ10: HWP carbon store

EQ11: HWP carbon loss ^year-100

EQ12: Fuel emissions

EQ13: Harvesting fuel emissions

EQ14: Hauling fuel emissions

EQ15: Transport fuel emissions

Appendix

A.1 DataMaid audit

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seamusrobertmurphy/VM0010-starter

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VM0010 Starter Script

1. Process data

Import dummy data

Review dummy data

Tidy dummy data

2. Compute Equations

EQ1: Plot biomass

EQ2: Strata biomass

EQ3: Harvest carbon

EQ4: Extracted carbon

EQ5: Slash carbon

EQ6: Damaged carbon

EQ7: Undamaged carbon

EQ8: Wood products

EQ9: HWP carbon loss year-0

EQ10: HWP carbon store

EQ11: HWP carbon loss year-100

EQ12: Fuel emissions

EQ13: Harvesting fuel emissions

EQ14: Hauling fuel emissions

EQ15: Transport fuel emissions

Appendix

A.1 DataMaid audit

About

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EQ9: HWP carbon loss ^year-0

EQ11: HWP carbon loss ^year-100

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