mutate_if(is.numeric,~round(.x,digits = 3)) # A tibble: 1 × 12 r.squared adj.r.squared sigma statistic p.value df logLik AIC BIC 1 0.173 0.138 225. 5.01 0.035 1 -177. 359. 363. # ℹ 3 more variables: deviance , df.residual , nobs Monthly We have seen that there is a negative trend in annual HDD; what are the trends for individual months? Figure 3 shows timeseries of monthly HDD vs year for winter months, with linear regression lines plotted over them. Visually there appears to be a negative trend for some of the months. Codedd |> filter(month %in% c(11,12,1,2,3,4)) |> mutate(month_name = lubridate::month(date, label = TRUE)) |> ggplot(aes(year, HDD, group = month_name)) + geom_point(size = 3, alpha = 0.5) + geom_smooth(method = 'lm', formula = 'y ~ x') + facet_wrap('month_name', scales = 'free') + guides(x = guide_axis(angle = 45)) Figure 3: HDD vs year for winter months To better quantify these trends I want to fit a linear regression to the data for each month and examine the results. This could be done with a for loop, but I will take advantage of a nice nested workflow using the tidyr (Wickham, Vaughan, and Girlich 2023), *broom*(Robinson, Hayes, and Couch 2023), and purrr (Wickham and Henry 2023) packages. Codedd_fit_hdd group_by(month) |> nest() |> mutate(fit = map(data, ~ lm(HDD ~ year, data = .x) ), tidied = map(fit, broom::tidy), glanced = map(fit, broom::glance) ) %>% unnest(tidied) |> ungroup() dd_fit_hdd |> mutate_if(is.numeric,~round(.x,digits = 3)) |> DT::datatable(rownames = FALSE, options = list(pageLength = 5)) Now that the data and model fit results are in a tidy data, they can be easily filtered to identify significant fits using p-values. The months with significant trends are June, August, September, and October. These months and the linear regression lines are shown in Figure 4 Codedd_fit_hdd |> filter(term == 'year') |> filter(p.value mutate_if(is.numeric,~round(.x,digits = 3)) |> DT::datatable(rownames = FALSE) Codedd |> filter(month %in% c(6,8,9,10)) |> mutate(month_name = lubridate::month(date, label = TRUE)) |> ggplot(aes(year, HDD, group = month_name)) + geom_point(size = 4, alpha = 0.5) + geom_smooth(method = 'lm', formula = 'y ~ x') + facet_wrap('month_name', scales = 'free') Figure 4: HDD vs year for months with signficant trends Cooling Degree Days CDD Per Month Figure 5 shows the distribution of US heating degree days for each month. Not surprisingly CDD tends to be higher in summer months, although there is a decent amount of variability between years. Codedd |> mutate(month_name = lubridate::month(date, label = TRUE)) |> ggplot(aes(month_name, CDD, group = month_name)) + geom_boxplot() + labs(title = 'Monthly Cooling Degree Days for US', x = 'Month', y = "Cooling Degree Days") Figure 5: Boxplot of US cooling degree days for each month Trends in CDD Annual Is there a trend in CDD over time? I would expect that CDD might increase over time due to climate change and the increase in earth’s average temperature. Figure 6 shows a timeseries of the annual total heating degree days in the US, along with a linear regression line showing a positive trend. Codeg ggplot(aes(year, CDD)) + geom_point(size = 4, alpha = 0.5) + geom_smooth(method = 'lm', formula = 'y~x') + labs(title = "US Annual Cooling Degree Days") g #plotly::ggplotly(g) Figure 6: Timeseries of annual US CDD Looking at the fit metrics shows that the positive trend in CDD is indeed statistically significant: Codecdd_yearly_fit mutate_if(is.numeric,~round(.x,digits = 3)) # A tibble: 2 × 5 term estimate std.error statistic p.value 1 (Intercept) -23285. 4207. -5.54 0 2 year 12.3 2.09 5.86 0 Codebroom::glance(cdd_yearly_fit) |> mutate_if(is.numeric,~round(.x,digits = 3)) # A tibble: 1 × 12 r.squared adj.r.squared sigma statistic p.value df logLik AIC BIC 1 0.589 0.572 80.1 34.4 0 1 -150. 306. 309. # ℹ 3 more variables: deviance , df.residual , nobs Monthly Figure 7 shows timeseries of monthly CDD vs year for the 4 summer months with the highest CDD, with linear regression lines plotted over them. Visually there appears to be a positive trend for each month. Codedd |> filter(month %in% c(6,7,8,9)) |> mutate(month_name = lubridate::month(date, label = TRUE)) |> ggplot(aes(year, CDD, group = month_name)) + geom_point(size = 4, alpha = 0.5) + geom_smooth(method = 'lm', formula = 'y ~ x') + facet_wrap('month_name') Figure 7: CDD vs year for summer month Next i’ll apply a linear regression to each month using the same workflow used for HDD. Codedd_fit_cdd group_by(month) |> nest() |> mutate(fit = map(data, ~ lm(CDD ~ year, data = .x) ), tidied = map(fit, broom::tidy) ) %>% unnest(tidied) |> ungroup() dd_fit_cdd |> mutate_if(is.numeric,~round(.x,digits = 3)) |> DT::datatable(options = list(pageLength = 5), rownames = FALSE) I find that there are significant positive trends in CDD for July, August, September, October, and December. Figure 8 shows the data and fits for these months in detail. Codedd_fit_cdd |> filter(term == 'year') |> filter(p.value mutate_if(is.numeric,~round(.x,digits = 3)) |> DT::datatable(rownames = FALSE,options = list(pageLength = 5)) ?(caption) Codedd |> filter(month %in% c(7,8,9,10,12)) |> mutate(month_name = lubridate::month(date, label = TRUE)) |> ggplot(aes(year, CDD, group = month_name)) + geom_point(size = 4, alpha = 0.5) + geom_smooth(method = 'lm', formula = 'y ~ x') + facet_wrap('month_name', scales = 'free') + guides(x = guide_axis(angle = 45)) Figure 8: CDD vs year for Months with significant trends Summary Annual and monthly heating and cooling degree days for the US 1997-2022 were analyzed. A linear regression was applied to the annual data, and to each month, to determine if there was a trend. Model fits with a p-value less than 0.05 were considered significant. There are significant negative (positive) trends in annual HDD (CDD). There are significant negative trends in HDD for the months of June, August, September, and October. There are significant positive trends in CDD for the months of July, August, September, October, and December. SessionInfo CodesessionInfo() R version 4.3.1 (2023-06-16) Platform: x86_64-apple-darwin20 (64-bit) Running under: macOS Sonoma 14.1.2 Matrix products: default BLAS: /Library/Frameworks/R.framework/Versions/4.3-x86_64/Resources/lib/libRblas.0.dylib LAPACK: /Library/Frameworks/R.framework/Versions/4.3-x86_64/Resources/lib/libRlapack.dylib; LAPACK version 3.11.0 locale: [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8 time zone: America/Denver tzcode source: internal attached base packages: [1] stats graphics grDevices datasets utils methods base other attached packages: [1] plotly_4.10.3 DT_0.30 broom_1.0.5 janitor_2.2.0 [5] lubridate_1.9.3 forcats_1.0.0 stringr_1.5.0 dplyr_1.1.3 [9] purrr_1.0.2 readr_2.1.4 tidyr_1.3.0 tibble_3.2.1 [13] ggplot2_3.4.4 tidyverse_2.0.0 loaded via a namespace (and not attached): [1] gtable_0.3.4 xfun_0.40 bslib_0.5.1 htmlwidgets_1.6.2 [5] lattice_0.22-5 tzdb_0.4.0 vctrs_0.6.4 tools_4.3.1 [9] crosstalk_1.2.0 generics_0.1.3 parallel_4.3.1 fansi_1.0.5 [13] pkgconfig_2.0.3 Matrix_1.6-1.1 data.table_1.14.8 lifecycle_1.0.3 [17] farver_2.1.1 compiler_4.3.1 munsell_0.5.0 snakecase_0.11.1 [21] htmltools_0.5.6.1 sass_0.4.7 yaml_2.3.7 lazyeval_0.2.2 [25] pillar_1.9.0 crayon_1.5.2 jquerylib_0.1.4 ellipsis_0.3.2 [29] cachem_1.0.8 nlme_3.1-163 tidyselect_1.2.0 digest_0.6.33 [33] stringi_1.7.12 splines_4.3.1 labeling_0.4.3 fastmap_1.1.1 [37] grid_4.3.1 colorspace_2.1-0 cli_3.6.1 magrittr_2.0.3 [41] utf8_1.2.4 withr_2.5.1 scales_1.2.1 backports_1.4.1 [45] bit64_4.0.5 timechange_0.2.0 rmarkdown_2.25 httr_1.4.7 [49] bit_4.0.5 hms_1.1.3 evaluate_0.22 knitr_1.44 [53] viridisLite_0.4.2 mgcv_1.9-0 rlang_1.1.1 glue_1.6.2 [57] renv_1.0.3 rstudioapi_0.15.0 vroom_1.6.4 jsonlite_1.8.7 [61] R6_2.5.1 References Robinson, David, Alex Hayes, and Simon Couch. 2023. “Broom: Convert Statistical Objects into Tidy Tibbles.” https://CRAN.R-project.org/package=broom. Wickham, Hadley, and Lionel Henry. 2023. “Purrr: Functional Programming Tools.” https://CRAN.R-project.org/package=purrr. Wickham, Hadley, Davis Vaughan, and Maximilian Girlich. 2023. “Tidyr: Tidy Messy Data.” https://CRAN.R-project.org/package=tidyr. " />
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# Introduction

Degree days are useful as a measure of building heating and cooling demands. A degree day is calculated as the difference between the average temperature (the average of the high and low temperature for the day) and a reference temperature (in the US 65°F is used). For example, if the average temperature today is 40°F, that would be 25 heating degree days (HDD). A summer day with an average temperature of 85°F would have 20 cooling degree days (CDD). Degree days are usually well correlated with the amount of energy used to heat or cool a home.

I was interested in obtaining and analyzing degree day data; in particular I wanted to see if there were any noticeable trends over time. Given an overall increase in earth’s average temperature due to climate change, I would hypothesize that there might be an overall increase in CDD and a decrease in HDD.

Changes in heating or cooling degree days would have implications for the amount of energy needed in the future to heat and cool residential or commercial buildings, resulting changes in demand on the electric grid, and implications for related carbon emissions (either for the power grid or from burning fossil fuels to heat buildings).

# Data

I obtained heating and cooling degree day data from the U.S. Energy Information Administration for the US. Note these data are weighted by population, see details of how the EIA data are calculated here.

Code
```suppressPackageStartupMessages(library(tidyverse))
ggplot2::theme_set(theme_grey(base_size = 15))
suppressPackageStartupMessages(library(janitor))
library(broom)
library(DT)
suppressPackageStartupMessages(library(plotly))```

I’ll only use years we have complete data for (1997-2022).

Code
```region <- "u_s"

skip = 4,
show_col_types = FALSE) |>
janitor::clean_names() |>
rename(CDD = paste0('cooling_degree_days_',region,
'_cooling_degree_days_cooling_degree_days')) |>
rename(HDD = paste0('heating_degree_days_',region,
'_heating_degree_days_heating_degree_days')) |>
mutate(date = lubridate::my(month)) |>
select(-month) |>
mutate(month = lubridate::month(date)) |>
mutate(year = lubridate::year(date)) |>
filter(year > 1996, year < 2023) # keep only complete years

dd |>
DT::datatable(options = list(pageLength = 5), rownames = FALSE)```

I’ll also make a dataframe of the yearly totals:

Code
```dd_yearly <- dd |>
filter(year > 1996) |>
group_by(year) |>
summarise(HDD = sum(HDD, na.rm = TRUE),
CDD = sum(CDD, na.rm = TRUE)
)

dd |>
DT::datatable(options = list(pageLength = 5), rownames = FALSE)```

# Analysis

## Heating Degree Days

Figure 1 shows the distribution of US heating degree days for each month. Not surprisingly HDD tends to be higher in winter months, although there is a decent amount of variability between years.

### HDD Per Month

Code
```dd |>
mutate(month_name = lubridate::month(date, label = TRUE)) |>
ggplot(aes(month_name, HDD, group = month_name)) +
geom_boxplot() +
labs(title = 'Monthly Heating Degree Days for US (1997-2022)',
x = 'Month',
y = "Heating Degree Days")```

#### Annual

Figure 2 shows a timeseries of the annual total heating degree days in the US, along with a linear regression line that shows a negative trend.

Code
```g <- dd_yearly |>
ggplot(aes(year, HDD)) +
geom_point(size = 4, alpha = 0.5) +
geom_smooth(method = 'lm', formula = 'y~x') +
labs(title = "US Annual Heating Degree Days")

g
#plotly::ggplotly(g)```

There is a fair bit of variability, but looking at the fit metrics shows that the negative trend in HDD is statistically significant (p-value < 0.05):

Code
```hdd_yearly_fit <- lm(data = dd_yearly, formula = 'HDD ~ year')
broom::tidy(hdd_yearly_fit) |> mutate_if(is.numeric,~round(.x,digits = 3))```
```# A tibble: 2 × 5
term        estimate std.error statistic p.value
<chr>          <dbl>     <dbl>     <dbl>   <dbl>
1 (Intercept)  30788.   11849.        2.60   0.016
2 year           -13.2      5.90     -2.24   0.035```
Code
`broom::glance(hdd_yearly_fit) |> mutate_if(is.numeric,~round(.x,digits = 3))`
```# A tibble: 1 × 12
r.squared adj.r.squared sigma statistic p.value    df logLik   AIC   BIC
<dbl>         <dbl> <dbl>     <dbl>   <dbl> <dbl>  <dbl> <dbl> <dbl>
1     0.173         0.138  225.      5.01   0.035     1  -177.  359.  363.
# ℹ 3 more variables: deviance <dbl>, df.residual <dbl>, nobs <dbl>```

#### Monthly

We have seen that there is a negative trend in annual HDD; what are the trends for individual months? Figure 3 shows timeseries of monthly HDD vs year for winter months, with linear regression lines plotted over them. Visually there appears to be a negative trend for some of the months.

Code
```dd |>
filter(month %in% c(11,12,1,2,3,4)) |>
mutate(month_name = lubridate::month(date, label = TRUE)) |>
ggplot(aes(year, HDD, group = month_name)) +
geom_point(size = 3, alpha = 0.5) +
geom_smooth(method = 'lm', formula = 'y ~ x') +
facet_wrap('month_name', scales = 'free') +
guides(x =  guide_axis(angle = 45))```

To better quantify these trends I want to fit a linear regression to the data for each month and examine the results. This could be done with a for loop, but I will take advantage of a nice nested workflow using the tidyr (Wickham, Vaughan, and Girlich 2023), *broom*(Robinson, Hayes, and Couch 2023), and purrr (Wickham and Henry 2023) packages.

Code
```dd_fit_hdd <- dd |>
group_by(month) |>
nest() |>
mutate(fit = map(data, ~ lm(HDD ~ year, data = .x) ),
tidied = map(fit, broom::tidy),
glanced = map(fit, broom::glance)
) %>%
unnest(tidied) |>
ungroup()

dd_fit_hdd |>
mutate_if(is.numeric,~round(.x,digits = 3)) |>
DT::datatable(rownames = FALSE, options = list(pageLength = 5))```

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