Sensitivity analysis of REDD+ emissions and emission reductions (delta method)

Sensitivity of the reference level, monitoring emissions and emission reductions to the independent model inputs (activity data, carbon elements, carbon fraction, degradation ratios), with the same model as the Monte Carlo chain (fct_combine_mcs_E(), fct_combine_mcs_P(), fct_combine_mcs_ER()): carbon elements are shared by all transitions of a land use, and EF = C_i - C_f.

Delta method: for independent inputs and a first-order expansion, \(Var(Y) \approx \sum_i (\partial Y / \partial X_i)^2 \sigma_i^2\). The share \((\partial Y / \partial X_i \cdot \sigma_i)^2 / Var(Y)\) is the first-order Sobol index of input \(i\). Shares are summed by input group, and by input type: activity data (AD) vs emission factors (EF: carbon stocks, carbon fraction, degradation ratios). The AD x EF interaction is second order and not included.

The AD tornado swings each AD source across \(mean \pm z \cdot se\), all other inputs at their mean. Outputs are linear in each AD, so the swing is exact and the AD shares add up to the AD group share.

Usage

fct_sensitivity2(.checked_data)

Arguments

.checked_data

The list returned by fct_checkinput().

Value

A list with: outputs (mean, delta-method se and U\ variance (share of variance per output, input type and group, in \ ad_tornado (one row per output and AD source: low / high output value, swing and share of variance, sorted by swing), split (emissions per period type and REDD+ activity, with uncertainty) and gg_variance (stacked bar chart of the variance shares). Outputs are named as in the app: reference type (e.g. "REF"), "E-" and "ER-".

Examples

path <- system.file("extdata/mocaredd-templatev2-simple.xlsx", package = "mocaredd")
checked <- fct_checkinput(.path = path)
#> Loading data... - progress: 0%.
#> ✓ Tables loaded successfully from template v2
#> Checking column names... - progress: 14%.
#> ✓ Column names: all required columns present
#> Checking table dimensions... - progress: 29%.
#> ✓ Table sizes: all tables have sufficient rows
#> Checking column data types... - progress: 43%.
#> ✓ Data types: all columns have correct data types
#> Checking category values... - progress: 57%.
#> ✓ Category values: all categories are valid
#> Checking unique IDs... - progress: 71%.
#> ✓ Unique IDs: no duplicates or missing IDs found
#> Checking cross-table and intra_table consistency... - progress: 86%.
#> ✓ Cross-table consistency: all references match
#> -- All checks passed.

sa <- fct_sensitivity2(.checked_data = checked)
sa$variance
#> # A tibble: 12 × 4
#>    output  input_type group             contribution_pct
#>    <chr>   <chr>      <chr>                        <dbl>
#>  1 REF     EF         Carbon stock                43.3  
#>  2 REF     EF         Degradation ratio           48.9  
#>  3 REF     AD         Activity data                7.20 
#>  4 REF     EF         Carbon fraction              0.624
#>  5 E-MON1  EF         Carbon stock                38.2  
#>  6 E-MON1  EF         Degradation ratio           56.3  
#>  7 E-MON1  AD         Activity data                4.84 
#>  8 E-MON1  EF         Carbon fraction              0.682
#>  9 ER-MON1 EF         Carbon stock                42.3  
#> 10 ER-MON1 EF         Degradation ratio           40.8  
#> 11 ER-MON1 AD         Activity data               16.4  
#> 12 ER-MON1 EF         Carbon fraction              0.536
fct_tornado(sa$ad_tornado, .output = "ER-MON1")