ReboundTools
Matthew Kuperus Heun
2024-07-09
ReboundTools.RmdIntroduction
ReboundTools is an R package that provides
functions to analyze energy rebound, the unanticipated reduction of the
benefits of energy efficiency due to behavior change and economy-wide
effects. Many functions perform analysis calculations to move from known
parameters to rebound estimates. Graphing functions (described in the
Graphs vignette) create rebound path graphs in energy,
expenditure, and consumption spaces. Other graphing functions create
sensitivity graphs. The functions in this package were used for the
analyses and graphs in the paper **********.
Getting started
The first step in a rebound analysis is specifying parameters for the
energy efficiency upgrade (EEU) and rebound analysis, typically in a
Excel spreadsheet. The path to an example spreadsheet can be found with
the function sample_eeu_data_path(). Data can be loaded
into a data frame as follows:
eeu_data <- sample_eeu_data_path() %>%
load_eeu_data() # Uses the readxl package internally.
dplyr::glimpse(eeu_data)
#> Rows: 3
#> Columns: 28
#> $ Reference <chr> "None yet", "None yet", "None yet"
#> $ Case <chr> "Car", "Lamp", "Car, r = 0"
#> $ Original <chr> "Ford Fusion", "Incandescent", "Ford Fusion"
#> $ Upgrade <chr> "Ford Fusion Hybrid", "LED", "Ford Fusion Hybrid"
#> $ r <dbl> 0.03, 0.03, 0.00
#> $ service_unit <chr> "mile", "lm-hr", "mile"
#> $ energy_engr_unit <chr> "gal", "W-hr", "gal"
#> $ `MJ/energy_engr_unit` <dbl> 126.6216, 0.0036, 126.6216
#> $ I_E <dbl> 3.389339, 3.389339, 3.389339
#> $ k <dbl> 1, 1, 1
#> $ p_E_engr_units <dbl> 2.2100000, 0.0001355, 2.2100000
#> $ e_qs_ps_UC_orig <dbl> -0.1, -0.4, -0.1
#> $ e_qs_M <dbl> 1, 1, 1
#> $ e_qo_M <dbl> 1, 1, 1
#> $ eta_engr_units_orig <dbl> 25.000000, 8.833333, 25.000000
#> $ eta_engr_units_star <dbl> 42.0, 81.8, 42.0
#> $ q_dot_s_orig <dbl> 14425, 580350, 14425
#> $ M_dot_orig <dbl> 27401.28, 27401.28, 27401.28
#> $ C_cap_orig <dbl> 28216.10, 1.88, 28216.10
#> $ C_cap_star <dbl> 27523.40, 1.21, 27523.40
#> $ C_dot_om_orig <dbl> 2861.134, 0.000, 2861.134
#> $ C_d_orig <dbl> 100, 0, 100
#> $ C_dot_om_star <dbl> 2774.668, 0.000, 2774.668
#> $ C_d_star <dbl> 101, 0, 101
#> $ E_emb_orig <dbl> 34000.0, 2.2, 34000.0
#> $ t_life_orig <dbl> 14.0, 1.8, 14.0
#> $ E_emb_star <dbl> 40000.0, 6.5, 40000.0
#> $ t_life_star <dbl> 14, 10, 14Variable names (columns in the EEU spreadsheet) are described by
various constants in the package, including
eeu_base_params, key_analysis_vars, and
rebound_stages. Get help on any of those constants to see
descriptions of parameters, variables, and stages.
Rows of the EEU spreadsheet should describe the cases to be analyzed.
The example file at sample_eeu_data_path() contains two
cases: a car and an electric lamp. Columns of the EEU spreadsheet should
contain rebound parameters for each case. Required columns are shown in
the example file and in the eeu_data data frame.
colnames(eeu_data)
#> [1] "Reference" "Case" "Original"
#> [4] "Upgrade" "r" "service_unit"
#> [7] "energy_engr_unit" "MJ/energy_engr_unit" "I_E"
#> [10] "k" "p_E_engr_units" "e_qs_ps_UC_orig"
#> [13] "e_qs_M" "e_qo_M" "eta_engr_units_orig"
#> [16] "eta_engr_units_star" "q_dot_s_orig" "M_dot_orig"
#> [19] "C_cap_orig" "C_cap_star" "C_dot_om_orig"
#> [22] "C_d_orig" "C_dot_om_star" "C_d_star"
#> [25] "E_emb_orig" "t_life_orig" "E_emb_star"
#> [28] "t_life_star"Rows can be used for sensitivity analysis, varying one or many parameters in each row of the spreadsheet.
Performing the analysis
After data are loaded, rebound analyses can be performed. A rebound
analysis consists of calculating all rebound terms and intermediate
results, once for each row of the EEU data frame. A convenient function
to perform the rebound analysis is named, aptly,
rebound_analysis(). Columns for intermediate and final
results are added to the right of the data frame.
rebound_data <- rebound_analysis(eeu_data)
dplyr::glimpse(rebound_data)
#> Rows: 3
#> Columns: 256
#> $ Reference <chr> "None yet", "None yet", "None yet"
#> $ Case <chr> "Car", "Lamp", "Car, r = 0"
#> $ Original <chr> "Ford Fusion", "Incandescent", "Ford Fus…
#> $ Upgrade <chr> "Ford Fusion Hybrid", "LED", "Ford Fusio…
#> $ r <dbl> 0.03, 0.03, 0.00
#> $ service_unit <chr> "mile", "lm-hr", "mile"
#> $ energy_engr_unit <chr> "gal", "W-hr", "gal"
#> $ `MJ/energy_engr_unit` <dbl> 126.6216, 0.0036, 126.6216
#> $ I_E <dbl> 3.389339, 3.389339, 3.389339
#> $ k <dbl> 1, 1, 1
#> $ p_E_engr_units <dbl> 2.2100000, 0.0001355, 2.2100000
#> $ e_qs_ps_UC_orig <dbl> -0.1, -0.4, -0.1
#> $ e_qs_M <dbl> 1, 1, 1
#> $ e_qo_M <dbl> 1, 1, 1
#> $ eta_engr_units_orig <dbl> 25.000000, 8.833333, 25.000000
#> $ eta_engr_units_star <dbl> 42.0, 81.8, 42.0
#> $ q_dot_s_orig <dbl> 14425, 580350, 14425
#> $ M_dot_orig <dbl> 27401.28, 27401.28, 27401.28
#> $ C_cap_orig <dbl> 28216.10, 1.88, 28216.10
#> $ C_cap_star <dbl> 27523.40, 1.21, 27523.40
#> $ C_dot_om_orig <dbl> 2861.134, 0.000, 2861.134
#> $ C_d_orig <dbl> 100, 0, 100
#> $ C_dot_om_star <dbl> 2774.668, 0.000, 2774.668
#> $ C_d_star <dbl> 101, 0, 101
#> $ E_emb_orig <dbl> 34000.0, 2.2, 34000.0
#> $ t_life_orig <dbl> 14.0, 1.8, 14.0
#> $ E_emb_star <dbl> 40000.0, 6.5, 40000.0
#> $ t_life_star <dbl> 14, 10, 14
#> $ R_alpha_orig <dbl> 1.203271, 1.011811, 1.000000
#> $ R_omega_orig <dbl> 0.7955036, 0.9593840, 1.0000000
#> $ p_E <dbl> 0.01745357, 0.03763889, 0.01745357
#> $ p_E_orig <dbl> 0.01745357, 0.03763889, 0.01745357
#> $ eta_orig <dbl> 0.1974386, 2453.7036944, 0.1974386
#> $ E_dot_s_orig <dbl> 73060.68, 236.52, 73060.68
#> $ C_dot_cap_orig <dbl> 2015.435714, 1.044444, 2015.435714
#> $ R_alpha_C_dot_cap_orig <dbl> 2425.114596, 1.056781, 2015.435714
#> $ p_s_orig <dbl> 8.840000e-02, 1.533962e-05, 8.840000e-02
#> $ C_dot_s_orig <dbl> 1275.17000, 8.90235, 1275.17000
#> $ C_dot_d_orig <dbl> 7.142857, 0.000000, 7.142857
#> $ R_omega_C_dot_d_orig <dbl> 5.682169, 0.000000, 7.142857
#> $ C_dot_omd_orig <dbl> 2866.816, 0.000, 2868.277
#> $ C_dot_o_orig <dbl> 20834.18, 27391.32, 21242.39
#> $ f_Cs_orig <dbl> 0.0576756075, 0.0003249007, 0.0566300134
#> $ e_qo_ps_UC_orig <dbl> -0.0550851141, -0.0001950038, -0.0540265…
#> $ e_qs_ps_C_orig <dbl> -0.04232439, -0.39967510, -0.04336999
#> $ e_qo_ps_C_orig <dbl> 0.0025904933, 0.0001298969, 0.0026034779
#> $ sigma <dbl> 0.04491489, 0.39980500, 0.04597346
#> $ rho <dbl> -21.264334, -1.501219, -20.751678
#> $ E_dot_emb_orig <dbl> 2428.571429, 1.222222, 2428.571429
#> $ N_dot_orig <dbl> 0, 0, 0
#> $ R_alpha_star <dbl> 1.203271, 1.138160, 1.000000
#> $ R_omega_star <dbl> 0.7955036, 0.8468981, 1.0000000
#> $ eta_star <dbl> 3.316969e-01, 2.272222e+04, 3.316969e-01
#> $ eta_ratio <dbl> 1.680000, 9.260377, 1.680000
#> $ S_dot_dev <dbl> 29572.1802, 210.9789, 29572.1802
#> $ G_dot <dbl> 516.140238, 7.941012, 516.140238
#> $ p_E_star <dbl> 0.01745357, 0.03763889, 0.01745357
#> $ p_s_star <dbl> 5.261905e-02, 1.656479e-06, 5.261905e-02
#> $ q_dot_s_star <dbl> 14425, 580350, 14425
#> $ C_dot_cap_star <dbl> 1965.957, 0.121, 1965.957
#> $ R_alpha_C_dot_cap_star <dbl> 2365.5784841, 0.1377174, 1965.9571429
#> $ E_dot_emb_star <dbl> 2857.143, 0.650, 2857.143
#> $ C_dot_s_star <dbl> 759.0297619, 0.9613377, 759.0297619
#> $ C_dot_d_star <dbl> 7.214286, 0.000000, 7.214286
#> $ R_omega_C_dot_d_star <dbl> 5.738991, 0.000000, 7.214286
#> $ C_dot_omd_star <dbl> 2780.407, 0.000, 2781.882
#> $ M_dot_star <dbl> 27401.28, 27401.28, 27401.28
#> $ N_dot_star <dbl> 662.085664, 8.860075, 652.013517
#> $ C_dot_o_star <dbl> 20834.18, 27391.32, 21242.39
#> $ E_dot_s_star <dbl> 43488.50030, 25.54108, 43488.50030
#> $ f_Cs_star <dbl> 3.515132e-02, 3.509521e-05, 3.449912e-02
#> $ e_qs_ps_UC_star <dbl> -0.1, -0.4, -0.1
#> $ e_qo_ps_UC_star <dbl> -0.0550851141, -0.0001950038, -0.0540265…
#> $ e_qs_ps_C_star <dbl> -0.04232439, -0.39967510, -0.04336999
#> $ e_qo_ps_C_star <dbl> 0.0025904933, 0.0001298969, 0.0026034779
#> $ t_life_hat <dbl> 14, 10, 14
#> $ R_alpha_hat <dbl> 1.203271, 1.138160, 1.000000
#> $ R_omega_hat <dbl> 0.7955036, 0.8468981, 1.0000000
#> $ eta_engr_units_hat <dbl> 42.0, 81.8, 42.0
#> $ eta_hat <dbl> 3.316969e-01, 2.272222e+04, 3.316969e-01
#> $ p_E_hat <dbl> 0.01745357, 0.03763889, 0.01745357
#> $ p_s_hat <dbl> 5.261905e-02, 1.656479e-06, 5.261905e-02
#> $ C_dot_cap_hat <dbl> 1965.957, 0.121, 1965.957
#> $ R_alpha_C_dot_cap_hat <dbl> 2365.5784841, 0.1377174, 1965.9571429
#> $ E_dot_emb_hat <dbl> 2857.143, 0.650, 2857.143
#> $ M_dot_hat <dbl> 27401.28, 27401.28, 27401.28
#> $ q_dot_s_hat <dbl> 14749.25, 1412809.74, 14757.28
#> $ E_dot_s_hat <dbl> 44466.06000, 62.17745, 44490.24608
#> $ C_dot_s_hat <dbl> 776.09167, 2.34029, 776.51381
#> $ C_d_hat <dbl> 101, 0, 101
#> $ C_dot_d_hat <dbl> 7.214286, 0.000000, 7.214286
#> $ R_omega_C_dot_d_hat <dbl> 5.738991, 0.000000, 7.214286
#> $ C_dot_om_hat <dbl> 2774.668, 0.000, 2774.668
#> $ C_dot_omd_hat <dbl> 2780.407, 0.000, 2781.882
#> $ C_dot_o_hat <dbl> 20811.86, 27386.95, 21219.52
#> $ f_Cs_hat <dbl> 3.595023e-02, 8.544544e-05, 3.530244e-02
#> $ e_qs_ps_C_hat <dbl> -0.04330019, -0.39977083, -0.04435049
#> $ e_qo_ps_C_hat <dbl> 1.614700e-03, 3.416152e-05, 1.622976e-03
#> $ e_qs_ps_UC_hat <dbl> -0.07925041, -0.39985628, -0.07965293
#> $ e_qo_ps_UC_hat <dbl> -3.433553e-02, -5.128393e-05, -3.367947e…
#> $ N_dot_hat <dbl> 667.34404, 11.85078, 657.40189
#> $ M_dot_hat_prime <dbl> 21587.95, 27389.29, 21996.04
#> $ t_life_bar <dbl> 14, 10, 14
#> $ R_alpha_bar <dbl> 1.203271, 1.138160, 1.000000
#> $ R_omega_bar <dbl> 0.7955036, 0.8468981, 1.0000000
#> $ eta_engr_units_bar <dbl> 42.0, 81.8, 42.0
#> $ eta_bar <dbl> 3.316969e-01, 2.272222e+04, 3.316969e-01
#> $ p_E_bar <dbl> 0.01745357, 0.03763889, 0.01745357
#> $ p_s_bar <dbl> 5.261905e-02, 1.656479e-06, 5.261905e-02
#> $ C_dot_cap_bar <dbl> 1965.957, 0.121, 1965.957
#> $ R_alpha_C_dot_cap_bar <dbl> 2365.5784841, 0.1377174, 1965.9571429
#> $ E_dot_emb_bar <dbl> 2857.143, 0.650, 2857.143
#> $ M_dot_bar <dbl> 27401.28, 27401.28, 27401.28
#> $ q_dot_s_bar <dbl> 15205.19, 1413421.03, 15198.33
#> $ E_dot_s_bar <dbl> 45840.63067, 62.20435, 45819.93891
#> $ C_dot_s_bar <dbl> 800.082844, 2.341303, 799.721698
#> $ C_d_bar <dbl> 101, 0, 101
#> $ C_dot_d_bar <dbl> 7.214286, 0.000000, 7.214286
#> $ R_omega_C_dot_d_bar <dbl> 5.738991, 0.000000, 7.214286
#> $ C_dot_om_bar <dbl> 2774.668, 0.000, 2774.668
#> $ C_dot_omd_bar <dbl> 2780.407, 0.000, 2781.882
#> $ C_dot_o_bar <dbl> 21455.21, 27398.80, 21853.72
#> $ f_Cs_bar <dbl> 3.595023e-02, 8.544544e-05, 3.530244e-02
#> $ e_qs_ps_UC_bar <dbl> -0.07925041, -0.39985628, -0.07965293
#> $ e_qo_ps_UC_bar <dbl> -3.433553e-02, -5.128393e-05, -3.367947e…
#> $ e_qs_ps_C_bar <dbl> -0.04330019, -0.39977083, -0.04435049
#> $ e_qo_ps_C_bar <dbl> 1.614700e-03, 3.416152e-05, 1.622976e-03
#> $ N_dot_bar <dbl> 0, 0, 0
#> $ t_life_tilde <dbl> 14, 10, 14
#> $ R_alpha_tilde <dbl> 1.203271, 1.138160, 1.000000
#> $ R_omega_tilde <dbl> 0.7955036, 0.8468981, 1.0000000
#> $ eta_engr_units_tilde <dbl> 42.0, 81.8, 42.0
#> $ eta_tilde <dbl> 3.316969e-01, 2.272222e+04, 3.316969e-01
#> $ p_E_tilde <dbl> 0.01745357, 0.03763889, 0.01745357
#> $ p_s_tilde <dbl> 5.261905e-02, 1.656479e-06, 5.261905e-02
#> $ C_dot_cap_tilde <dbl> 1965.957, 0.121, 1965.957
#> $ R_alpha_C_dot_cap_tilde <dbl> 2365.5784841, 0.1377174, 1965.9571429
#> $ E_dot_emb_tilde <dbl> 2857.143, 0.650, 2857.143
#> $ M_dot_tilde <dbl> 27401.28, 27401.28, 27401.28
#> $ q_dot_s_tilde <dbl> 15205.19, 1413421.03, 15198.33
#> $ E_dot_s_tilde <dbl> 45840.63067, 62.20435, 45819.93891
#> $ C_dot_s_tilde <dbl> 800.082844, 2.341303, 799.721698
#> $ C_dot_om_tilde <dbl> 2774.668, 0.000, 2774.668
#> $ C_d_tilde <dbl> 101, 0, 101
#> $ C_dot_d_tilde <dbl> 7.214286, 0.000000, 7.214286
#> $ R_omega_C_dot_d_tilde <dbl> 5.738991, 0.000000, 7.214286
#> $ C_dot_omd_tilde <dbl> 2780.407, 0.000, 2781.882
#> $ C_dot_o_tilde <dbl> 21455.21, 27398.80, 21853.72
#> $ f_Cs_tilde <dbl> 3.595023e-02, 8.544544e-05, 3.530244e-02
#> $ e_qs_ps_UC_tilde <dbl> -0.07925041, -0.39985628, -0.07965293
#> $ e_qo_ps_UC_tilde <dbl> -3.433553e-02, -5.128393e-05, -3.367947e…
#> $ e_qs_ps_C_tilde <dbl> -0.04330019, -0.39977083, -0.04435049
#> $ e_qo_ps_C_tilde <dbl> 1.614700e-03, 3.416152e-05, 1.622976e-03
#> $ N_dot_tilde <dbl> 0, 0, 0
#> $ Delta_t_life_star <dbl> 0.0, 8.2, 0.0
#> $ Delta_R_alpha_star <dbl> 0.0000000, 0.1263491, 0.0000000
#> $ Delta_R_omega_star <dbl> 0.0000000, -0.1124859, 0.0000000
#> $ Delta_eta_engr_units_star <dbl> 17.00000, 72.96667, 17.00000
#> $ Delta_eta_star <dbl> 1.342583e-01, 2.026852e+04, 1.342583e-01
#> $ Delta_p_s_star <dbl> -3.578095e-02, -1.368314e-05, -3.578095e…
#> $ Delta_q_dot_s_star <dbl> 0, 0, 0
#> $ Delta_p_E_star <dbl> 0, 0, 0
#> $ Delta_E_dot_s_star <dbl> -29572.1802, -210.9789, -29572.1802
#> $ Delta_E_dot_emb_star <dbl> 428.5714286, -0.5722222, 428.5714286
#> $ Delta_C_dot_s_star <dbl> -516.140238, -7.941012, -516.140238
#> $ Delta_C_dot_cap_star <dbl> -49.4785714, -0.9234444, -49.4785714
#> $ Delta_R_alpha_C_dot_cap_star <dbl> -59.5361117, -0.9190632, -49.4785714
#> $ Delta_C_dot_om_star <dbl> -86.46614, 0.00000, -86.46614
#> $ Delta_C_d_star <dbl> 1, 0, 1
#> $ Delta_C_dot_d_star <dbl> 0.07142857, 0.00000000, 0.07142857
#> $ Delta_R_omega_C_dot_d_star <dbl> 0.05682169, 0.00000000, 0.07142857
#> $ Delta_C_dot_omd_star <dbl> -86.40931, 0.00000, -86.39471
#> $ Delta_C_dot_o_star <dbl> 0, 0, 0
#> $ Delta_N_dot_star <dbl> 662.085664, 8.860075, 652.013517
#> $ Delta_M_dot_star <dbl> 0, 0, 0
#> $ Delta_t_life_hat <dbl> 0, 0, 0
#> $ Delta_R_alpha_hat <dbl> 0, 0, 0
#> $ Delta_R_omega_hat <dbl> 0, 0, 0
#> $ Delta_eta_engr_units_hat <dbl> 0, 0, 0
#> $ Delta_eta_hat <dbl> 0, 0, 0
#> $ Delta_p_s_hat <dbl> 0, 0, 0
#> $ Delta_q_dot_s_hat <dbl> 324.2535, 832459.7380, 332.2760
#> $ Delta_p_E_hat <dbl> 0, 0, 0
#> $ Delta_E_dot_s_hat <dbl> 977.55969, 36.63637, 1001.74577
#> $ Delta_E_dot_emb_hat <dbl> 0, 0, 0
#> $ Delta_C_dot_s_hat <dbl> 17.061911, 1.378952, 17.484044
#> $ Delta_C_dot_cap_hat <dbl> 0, 0, 0
#> $ Delta_R_alpha_C_dot_cap_hat <dbl> 0, 0, 0
#> $ Delta_C_dot_om_hat <dbl> 0, 0, 0
#> $ Delta_C_d_hat <dbl> 0, 0, 0
#> $ Delta_C_dot_d_hat <dbl> 0, 0, 0
#> $ Delta_R_omega_C_dot_d_hat <dbl> 0, 0, 0
#> $ Delta_C_dot_omd_hat <dbl> 0, 0, 0
#> $ Delta_C_dot_o_hat <dbl> -22.320290, -4.369659, -22.872418
#> $ Delta_N_dot_hat <dbl> 5.258380, 2.990707, 5.388374
#> $ Delta_M_dot_hat <dbl> 0, 0, 0
#> $ Delta_t_life_bar <dbl> 0, 0, 0
#> $ Delta_R_alpha_bar <dbl> 0, 0, 0
#> $ Delta_R_omega_bar <dbl> 0, 0, 0
#> $ Delta_eta_engr_units_bar <dbl> 0, 0, 0
#> $ Delta_eta_bar <dbl> 0, 0, 0
#> $ Delta_p_s_bar <dbl> 0, 0, 0
#> $ Delta_q_dot_s_bar <dbl> 455.9408, 611.2937, 441.0550
#> $ Delta_p_E_bar <dbl> 0, 0, 0
#> $ Delta_E_dot_s_bar <dbl> 1374.5706729, 0.0269029, 1329.6928386
#> $ Delta_E_dot_emb_bar <dbl> 0, 0, 0
#> $ Delta_C_dot_s_bar <dbl> 23.991171074, 0.001012595, 23.207892469
#> $ Delta_C_dot_cap_bar <dbl> 0, 0, 0
#> $ Delta_R_alpha_C_dot_cap_bar <dbl> 0, 0, 0
#> $ Delta_C_dot_om_bar <dbl> 0, 0, 0
#> $ Delta_C_d_bar <dbl> 0, 0, 0
#> $ Delta_C_dot_d_bar <dbl> 0, 0, 0
#> $ Delta_R_omega_C_dot_d_bar <dbl> 0, 0, 0
#> $ Delta_C_dot_omd_bar <dbl> 0, 0, 0
#> $ Delta_C_dot_o_bar <dbl> 643.35287, 11.84977, 634.19400
#> $ Delta_N_dot_bar <dbl> -667.34404, -11.85078, -657.40189
#> $ Delta_M_dot_bar <dbl> 0, 0, 0
#> $ Delta_t_life_tilde <dbl> 0, 0, 0
#> $ Delta_R_alpha_tilde <dbl> 0, 0, 0
#> $ Delta_R_omega_tilde <dbl> 0, 0, 0
#> $ Delta_eta_engr_units_tilde <dbl> 0, 0, 0
#> $ Delta_eta_tilde <dbl> 0, 0, 0
#> $ Delta_p_s_tilde <dbl> 0, 0, 0
#> $ Delta_q_dot_s_tilde <dbl> 0, 0, 0
#> $ Delta_p_E_tilde <dbl> 0, 0, 0
#> $ Delta_E_dot_s_tilde <dbl> 0, 0, 0
#> $ Delta_E_dot_emb_tilde <dbl> 0, 0, 0
#> $ Delta_C_dot_s_tilde <dbl> 0, 0, 0
#> $ Delta_C_dot_cap_tilde <dbl> 0, 0, 0
#> $ Delta_R_alpha_C_dot_cap_tilde <dbl> 0, 0, 0
#> $ Delta_C_dot_om_tilde <dbl> 0, 0, 0
#> $ Delta_C_d_tilde <dbl> 0, 0, 0
#> $ Delta_C_dot_d_tilde <dbl> 0, 0, 0
#> $ Delta_R_omega_C_dot_d_tilde <dbl> 0, 0, 0
#> $ Delta_C_dot_omd_tilde <dbl> 0, 0, 0
#> $ Delta_C_dot_o_tilde <dbl> 0, 0, 0
#> $ Delta_N_dot_tilde <dbl> 0, 0, 0
#> $ Delta_M_dot_tilde <dbl> 0, 0, 0
#> $ Re_dempl <dbl> 0, 0, 0
#> $ Re_emb <dbl> 0.014492385, -0.002712225, 0.014492385
#> $ Re_cap <dbl> -0.095530088, -0.008434532, -0.079392022
#> $ Re_om <dbl> -0.009910093, 0.000000000, -0.009910093
#> $ Re_d <dbl> 6.512471e-06, 0.000000e+00, 8.186601e-06
#> $ Re_omd <dbl> -0.009903580, 0.000000000, -0.009901906
#> $ Re_empl <dbl> 0.004588805, -0.002712225, 0.004590479
#> $ Re_isub <dbl> -0.002558182, -0.070197801, -0.002621463
#> $ Re_dsub <dbl> 0.03305673, 0.17364943, 0.03387460
#> $ Re_sub <dbl> 0.03049855, 0.10345163, 0.03125314
#> $ Re_dinc <dbl> 0.0464818848, 0.0001275146, 0.0449643154
#> $ Re_iinc <dbl> 0.07373623, 0.19036445, 0.07268651
#> $ Re_inc <dbl> 0.1202181, 0.1904920, 0.1176508
#> $ Re_micro <dbl> 0.1553055, 0.2912314, 0.1534944
#> $ Re_macro <dbl> 0.07588324, 0.14233554, 0.07472885
#> $ Re_dir <dbl> 0.07953862, 0.17377694, 0.07883892
#> $ Re_indir <dbl> 0.1516501, 0.2597900, 0.1493844
#> $ Re_tot <dbl> 0.2311887, 0.4335669, 0.2282233Note that rebound_analysis() is a convenience function
that calls several helper functions in turn. Each helper function
calculates rebound parameters after one of the rebound effects.
simple <- rebound_analysis(eeu_data)
complicated <- eeu_data %>%
calc_orig() %>% # Calculate all parameters before the emplacement effect
calc_star() %>% # Calculate all parameters after the emplacement effect
calc_hat() %>% # Calculate all parameters after the substitution effect
calc_bar() %>% # Calculate all parameters after the income effect
calc_tilde() %>% # Calculate all parameters after the macro effect
calc_Deltas() %>% # Calculate all differences between stages
calc_rebound() # Calculate all rebound terms
all(simple == complicated)
#> [1] TRUERebound tables
ReboundTools contains two functions to create tables:
stages_table() and
rebound_results_table().
Stages table
After a rebound analysis has been performed, the results can be displayed in a stages table, which has rebound parameters in rows and rebound stages in columns.
digs <- matrix(c(rep(1, 7), # t_life
rep(1, 7), # R_alpha
rep(1, 7), # R_omega
rep(1, 7), # eta_engr_units
rep(3, 7), # eta
rep(3, 7), # p_s
rep(0, 7), # q_dot_s
rep(4, 7), # p_E
rep(0, 7), # E_dot_s
rep(0, 7), # E_dot_emb
rep(0, 7), # C_dot_s
rep(0, 7), # C_dot_cap
rep(0, 7), # R_alpha_C_dot_cap
rep(0, 7), # C_dot_om
rep(1, 7), # C_d
rep(2, 7), # C_dot_d
rep(2, 7), # R_omega_D_dot_d
rep(0, 7), # C_dot_omd
rep(0, 7), # C_dot_o
rep(0, 7), # N_dot
rep(0, 7)), # M_dot
nrow = 21, ncol = 7, byrow = TRUE)
load_eeu_data() %>%
dplyr::filter(.data[[ReboundTools::eeu_base_params$case]] == "Car") %>%
dplyr::mutate(
Case = NULL
) %>%
rebound_analysis() %>%
stages_table(digits = digs,
align = "lrrrrrr") %>%
print(type = "html",
include.rownames = FALSE,
booktabs = TRUE,
caption.placement = "top",
sanitize.text.function = function(x) {x},
format.args = list(big.mark = ","))| Original (\(\circ\)) | After empl (\(*\)) | After sub (\(\wedge\)) | After inc (\(-\)) | After macro (\(\sim\)) | |
|---|---|---|---|---|---|
| \(t_{li\!f\!e}\) [yr] | 14.0 | 14.0 | 14.0 | 14.0 | 14.0 |
| \(R_\alpha\) [–] | 1.2 | 1.2 | 1.2 | 1.2 | 1.2 |
| \(R_\omega\) [–] | 0.8 | 0.8 | 0.8 | 0.8 | 0.8 |
| \(\eta\) [mile/gal] | 25.0 | 42.0 | 42.0 | 42.0 | 42.0 |
| \(\eta\) [mile/MJ] | 0.197 | 0.332 | 0.332 | 0.332 | 0.332 |
| \(p_s\) [$/mile] | 0.088 | 0.053 | 0.053 | 0.053 | 0.053 |
| \(\dot{q}_s\) [mile/yr] | 14,425 | 14,425 | 14,749 | 15,205 | 15,205 |
| \(p_E\) [$/MJ] | 0.0175 | 0.0175 | 0.0175 | 0.0175 | 0.0175 |
| \(\dot{E}_s\) [MJ/yr] | 73,061 | 43,489 | 44,466 | 45,841 | 45,841 |
| \(\dot{E}_{emb}\) [MJ/yr] | 2,429 | 2,857 | 2,857 | 2,857 | 2,857 |
| \(\dot{C}_s\) [$/yr] | 1,275 | 759 | 776 | 800 | 800 |
| \(\dot{C}_{cap}\) [$/yr] | 2,015 | 1,966 | 1,966 | 1,966 | 1,966 |
| \(R_{\alpha}\dot{C}_{cap}\) [$/yr] | 2,425 | 2,366 | 2,366 | 2,366 | 2,366 |
| \(\dot{C}_{O\!M}\) [$/yr] | 2,861 | 2,775 | 2,775 | 2,775 | 2,775 |
| \(C_d\) [$] | 100.0 | 101.0 | 101.0 | 101.0 | 101.0 |
| \(\dot{C}_d\) [$/yr] | 7.14 | 7.21 | 7.21 | 7.21 | 7.21 |
| \(R_{\omega}\dot{C}_d\) [$/yr] | 5.68 | 5.74 | 5.74 | 5.74 | 5.74 |
| \(\dot{C}_{O\!M\!d}\) [$/yr] | 2,867 | 2,780 | 2,780 | 2,780 | 2,780 |
| \(\dot{C}_o\) [$/yr] | 20,834 | 20,834 | 20,812 | 21,455 | 21,455 |
| \(\dot{N}\) [$/yr] | 0 | 662 | 667 | 0 | 0 |
| \(\dot{M}\) [$/yr] | 27,401 | 27,401 | 27,401 | 27,401 | 27,401 |
Rebound results table
Rebound analysis results can also be displayed in a rebound results table. A rebound results table shows rebound terms and values.
load_eeu_data() %>%
dplyr::filter(Case == "Car") %>%
rebound_analysis() %>%
dplyr::mutate(
Case = NULL
) %>%
ReboundTools::rebound_results_table(include_subtotals = FALSE,
label = "tab:car_results",
digits = 1,
align = "rrr") %>%
print(type = "html",
include.rownames = FALSE,
booktabs = TRUE,
caption.placement = "top",
hline.after = c(-1, 0, nrow(.)-1, nrow(.)),
sanitize.text.function = function(x) {x},
format.args = list(big.mark = ","))| Rebound term | Value [%] |
|---|---|
| \(Re_{dempl}\) | 0.0 |
| \(Re_{emb}\) | 1.4 |
| \(Re_{cap}\) | -9.6 |
| \(Re_{O\!M\!d}\) | -1.0 |
| \(Re_{dsub}\) | 3.3 |
| \(Re_{isub}\) | -0.3 |
| \(Re_{dinc}\) | 4.6 |
| \(Re_{iinc}\) | 7.4 |
| \(Re_{macro}\) | 7.6 |
| \(Re_{tot}\) | 23.1 |
Conclusion
The ReboundTools package assists with analyzing rebound
effects and displaying the results. In particular,
- the
rebound_analysis()function performs rebound analysis on energy efficiency upgrades and - the
stages_table()function returns anxtableobject suitable for inclusion in papers and reports,
Taken together, these functions provide important capabilities to analyze rebound effects for energy efficiency upgrades.