Climatological normals and indicators of Brazilian municipalities

Introduction

Climatological normals are averages of climate variables observed for a given time – usually months – in a 30-year range. The normals are usually used as comparison benchmarks against recent or current conditions, being useful to recognize anomalies and to characterize global warming impacts.

The normals are usually computed with surface meteorological stations data, maintained by government meteorological institutions, and its distribution over the territory may be scarce or uneven, like in Brazil. Thus, the availability of climatological normals to different regions and administrative divisions like municipalities is difficult to obtain.

I propose here a method to compute monthly climatological normals for the 1961–1990 and monthly aggregated climate indicators from 1991 to 2023 for Brazilian municipalities using a climate reanalysis dataset.

Tip

In a hurry? Jump to the download section ;-)

Methods

A climatological normal can be computed with data from different sources, including remote sensing sensors and “area averages or points in gridded datasets” (WMO 2017). Some gridded climatological datasets are available for the Brazilian territory, including the ERA5-Land from Copernicus (Muñoz-Sabater et al. 2021) and the BR-DWGD dataset (Xavier et al. 2022), offering several climatological indicators for a long time range, and continuously updates.

Some research methods demands that climate data must be aggregated in the same spatial and temporal units of other data to be used in statistical models, being a fairly common procedure in epidemiology and economy studies. In order to approach this issue, spatial gridded data can be aggregated using zonal statistics (Saldanha et al. 2024).

I used the same methodology from the study above to create zonal statistics of climate indicators from the BR-DWGD project (Xavier et al. 2022). This data is available here, presenting climatological indicators from 1961 to March 2024 for all Brazilian municipalities. I propose here to compute the climatological normals and other climate aggregated indicators from this dataset of zonal statistics.

In order to compute these indicators, I created an R package named {climindi}. The package provides helper functions to compute climatological normals and other aggregated indicators in a tidy way.

Normal indicators

The {climindi} package computes the average, 10th and 90th percentile as climatological normals.

Aggregated indicators

The {climindi} package present functions to compute the following statistics for time-aggregated data: count of data points, average, median, standard deviation, standard error, maximum and minimum values, the 10th, 25th, 75th and 90th percentiles, and indicator-specific indicators, listed bellow.

• Precipitation
  • Rain spells: count of rain spells occurrences, with 3 and 5 or more consecutive days with rain above the climatological normal average value
  • Count of days with precipitation above 1mm, 5mm, 10mm, 50mm, and 100mm
  • Count of sequences of 3 days, 5 days, 10 days, 15 days, 20 days, and 25 days or more without precipitation
• Maximum temperature
  • Heat waves: Count of heat waves occurrences, with 3 and 5 or more consecutive days with maximum temperature above the climatological normal value plus 5 Celsius degrees
  • Hot days: count of warm days, when the maximum temperature is above the normal 90th percentile
  • Count of days with temperatures above or equal to 25, 30, 35, and 40 Celsius degrees
• Minimum temperature
  • Cold spells: count of cold spells occurrences, with 3 and 5 or more consecutive days with minimum temperature bellow the climatological normal value minus 5 Celsius degrees
  • Cold days: count of cold days, when the minimum temperature is bellow the normal 10th percentile
  • Count of days with temperatures bellow or equal to 0, 5, 10, 15, and 20 Celsius degrees
• Relative humidity
  • Count of dry spells occurrences, with 3 and 5 or more consecutive days with relative humidity bellow the climatological normal value minus 10 percent
  • Count of wet spells occurrences, with 3 and 5 or more consecutive days with relative humidity above the climatological normal value plus 10 percent
  • Count of dry days, when the relative humidity is bellow the normal 10th percentile
  • Count of wet days, when the relative humidity is above the normal 90th percentile
  • Count of days with relative humidity between 21% and 30% (Attention level)
  • Count of days with relative humidity between 12% and 20% (Alert level)
  • Count of days with relative humidity bellow 12% (Emergence level)
• Wind speed
  • Count of sequences of 3 and 5 days or more with wind speed bellow the climatological average normal
  • Count of sequences of 3 and 5 days or more with wind speed above the climatological average normal
• Evapotranspirations
  • Count of sequences of 3 and 5 days or more with evapotranspirations bellow the climatological average normal
  • Count of sequences of 3 and 5 days or more with evapotranspirations above the climatological average normal
• Solar radiation
  • Count of sequences of 3 and 5 days or more with solar radiation bellow the climatological normal
  • Count of sequences of 3 and 5 days or more with solar radiation above the climatological normal

Data source

The zonal statistics for the Brazilian municipalities computed with the BR-DWGD project is described here. We can use the {zendown} package to download the data files directly from from Zenodo.

Packages

library(dplyr)
library(lubridate)
library(arrow)
library(readr)
library(climindi) # http://rfsaldanha.github.io/climindi/
library(zendown) # https://rfsaldanha.github.io/zendown/

Warning

To perform those computations, I needed to increase the envinroment variable R_MAX_VSIZE, as explained here.

Precipitation (mm)

Data

pr_data <- zen_file(13906834, "pr_3.2.3.parquet") |>
    open_dataset() |>
    filter(name == "pr_3.2.3_mean") |>
    filter(date >= as.Date("1961-01-01")) |>
    filter(date <= as.Date("2023-12-31")) |>
    select(-name) |>
    collect()

Normal

pr_normal <- pr_data |>
    # Identify month
    mutate(month = month(date)) |>
    # Group by id variable and month
    group_by(code_muni, month) |>
    # Compute normal
    summarise_normal(
        date_var = date, value_var = value, 
        year_start = 1961, year_end = 1990
    ) |>
    # Ungroup
    ungroup()

Indicators

pr_indi <- pr_data |>
    # Identify year
    mutate(year = year(date)) |>
    # Identify month
    mutate(month = month(date)) |>
    # Filter year
    filter(year >= 1991) |>
    # Group by id variable, year and month
    group_by(code_muni, year, month) |>
    # Compute precipitation indicators
    summarise_precipitation(
        value_var = value, 
        normals_df = pr_normal
    ) |>
    # Ungroup
    ungroup()

Export

write_parquet(x = pr_normal, sink = "pr_normal.parquet")
write_csv2(x = pr_normal, file = "pr_normal.csv")
write_parquet(x = pr_indi, sink = "pr_indi.parquet")
write_csv2(x = pr_indi, file = "pr_indi.csv")

Evapotranspiration (mm)

Data

eto_data <- zen_file(13906834, "ETo_3.2.3.parquet") |>
    open_dataset() |>
    filter(name == "ETo_3.2.3_mean") |>
    filter(date >= as.Date("1961-01-01")) |>
    filter(date <= as.Date("2023-12-31")) |>
    select(-name) |>
    collect()

Normal

eto_normal <- eto_data |>
    # Identify month
    mutate(month = month(date)) |>
    # Group by id variable and month
    group_by(code_muni, month) |>
    # Compute normal
    summarise_normal(
        date_var = date, value_var = value, 
        year_start = 1961, year_end = 1990
    ) |>
    # Ungroup
    ungroup()

Indicators

eto_indi <- eto_data |>
    # Identify year
    mutate(year = year(date)) |>
    # Identify month
    mutate(month = month(date)) |>
    # Filter year
    filter(year >= 1991) |>
    # Group by id variable, year and month
    group_by(code_muni, year, month) |>
    # Compute precipitation indicators
    summarise_evapotrapiration(
        value_var = value, 
        normals_df = eto_normal
    ) |>
    # Ungroup
    ungroup()

Export

write_parquet(x = eto_normal, sink = "eto_normal.parquet")
write_csv2(x = eto_normal, file = "eto_normal.csv")
write_parquet(x = eto_indi, sink = "eto_indi.parquet")
write_csv2(x = eto_indi, file = "eto_indi.csv")

Maximum temperature (°C)

Data

tmax_data <- zen_file(13906834, "Tmax_3.2.3.parquet") |>
    open_dataset() |>
    filter(name == "Tmax_3.2.3_mean") |>
    filter(date >= as.Date("1961-01-01")) |>
    filter(date <= as.Date("2023-12-31")) |>
    select(-name) |>
    collect()

Normal

tmax_normal <- tmax_data |>
    # Identify month
    mutate(month = month(date)) |>
    # Group by id variable and month
    group_by(code_muni, month) |>
    # Compute normal
    summarise_normal(
        date_var = date, value_var = value, 
        year_start = 1961, year_end = 1990
    ) |>
    # Ungroup
    ungroup()

Indicators

tmax_indi <- tmax_data |>
    # Identify year
    mutate(year = year(date)) |>
    # Identify month
    mutate(month = month(date)) |>
    # Filter year
    filter(year >= 1991) |>
    # Group by id variable, year and month
    group_by(code_muni, year, month) |>
    # Compute precipitation indicators
    summarise_temp_max(
        value_var = value, 
        normals_df = tmax_normal
    ) |>
    # Ungroup
    ungroup()

Export

write_parquet(x = tmax_normal, sink = "tmax_normal.parquet")
write_csv2(x = tmax_normal, file = "tmax_normal.csv")
write_parquet(x = tmax_indi, sink = "tmax_indi.parquet")
write_csv2(x = tmax_indi, file = "tmax_indi.csv")

Minimum temperature (°C)

Data

tmin_data <- zen_file(13906834, "Tmin_3.2.3.parquet") |>
    open_dataset() |>
    filter(name == "Tmin_3.2.3_mean") |>
    filter(date >= as.Date("1961-01-01")) |>
    filter(date <= as.Date("2023-12-31")) |>
    select(-name) |>
    collect()

Normal

tmin_normal <- tmin_data |>
    # Identify month
    mutate(month = month(date)) |>
    # Group by id variable and month
    group_by(code_muni, month) |>
    # Compute normal
    summarise_normal(
        date_var = date, value_var = value, 
        year_start = 1961, year_end = 1990
    ) |>
    # Ungroup
    ungroup()

Indicators

tmin_indi <- tmin_data |>
    # Identify year
    mutate(year = year(date)) |>
    # Identify month
    mutate(month = month(date)) |>
    # Filter year
    filter(year >= 1991) |>
    # Group by id variable, year and month
    group_by(code_muni, year, month) |>
    # Compute precipitation indicators
    summarise_temp_min(
        value_var = value, 
        normals_df = tmin_normal
    ) |>
    # Ungroup
    ungroup()

Export

write_parquet(x = tmin_normal, sink = "tmin_normal.parquet")
write_csv2(x = tmin_normal, file = "tmin_normal.csv")
write_parquet(x = tmin_indi, sink = "tmin_indi.parquet")
write_csv2(x = tmin_indi, file = "tmin_indi.csv")

Solar radiation (MJm-2)

Data

rs_data <- zen_file(13906834, "Rs_3.2.3.parquet") |>
    open_dataset() |>
    filter(name == "Rs_3.2.3_mean") |>
    filter(date >= as.Date("1961-01-01")) |>
    filter(date <= as.Date("2023-12-31")) |>
    select(-name) |>
    collect()

Normal

rs_normal <- rs_data |>
    # Identify month
    mutate(month = month(date)) |>
    # Group by id variable and month
    group_by(code_muni, month) |>
    # Compute normal
    summarise_normal(
        date_var = date, value_var = value, 
        year_start = 1961, year_end = 1990
    ) |>
    # Ungroup
    ungroup()

Indicators

rs_indi <- rs_data |>
    # Identify year
    mutate(year = year(date)) |>
    # Identify month
    mutate(month = month(date)) |>
    # Filter year
    filter(year >= 1991) |>
    # Group by id variable, year and month
    group_by(code_muni, year, month) |>
    # Compute precipitation indicators
    summarise_solar_radiation(
        value_var = value, 
        normals_df = rs_normal
    ) |>
    # Ungroup
    ungroup()

Export

write_parquet(x = rs_normal, sink = "rs_normal.parquet")
write_csv2(x = rs_normal, file = "rs_normal.csv")
write_parquet(x = rs_indi, sink = "rs_indi.parquet")
write_csv2(x = rs_indi, file = "rs_indi.csv")

Wind speed at 2m height (m/s)

Data

u2_data <- zen_file(13906834, "u2_3.2.3.parquet") |>
    open_dataset() |>
    filter(name == "u2_3.2.3_mean") |>
    filter(date >= as.Date("1961-01-01")) |>
    filter(date <= as.Date("2023-12-31")) |>
    select(-name) |>
    collect()

Normal

u2_normal <- u2_data |>
    # Identify month
    mutate(month = month(date)) |>
    # Group by id variable and month
    group_by(code_muni, month) |>
    # Compute normal
    summarise_normal(
        date_var = date, value_var = value, 
        year_start = 1961, year_end = 1990
    ) |>
    # Ungroup
    ungroup()

Indicators

u2_indi <- u2_data |>
    # Identify year
    mutate(year = year(date)) |>
    # Identify month
    mutate(month = month(date)) |>
    # Filter year
    filter(year >= 1991) |>
    # Group by id variable, year and month
    group_by(code_muni, year, month) |>
    # Compute precipitation indicators
    summarise_windspeed(
        value_var = value, 
        normals_df = u2_normal
    ) |>
    # Ungroup
    ungroup()

Export

write_parquet(x = u2_normal, sink = "u2_normal.parquet")
write_csv2(x = u2_normal, file = "u2_normal.csv")
write_parquet(x = u2_indi, sink = "u2_indi.parquet")
write_csv2(x = u2_indi, file = "u2_indi.csv")

Relative humidity (%)

Data

rh_data <- zen_file(13906834, "RH_3.2.3.parquet") |>
    open_dataset() |>
    filter(name == "RH_3.2.3_mean") |>
    filter(date >= as.Date("1961-01-01")) |>
    filter(date <= as.Date("2023-12-31")) |>
    select(-name) |>
    collect()

Normal

rh_normal <- rh_data |>
    # Identify month
    mutate(month = month(date)) |>
    # Group by id variable and month
    group_by(code_muni, month) |>
    # Compute normal
    summarise_normal(
        date_var = date, value_var = value, 
        year_start = 1961, year_end = 1990
    ) |>
    # Ungroup
    ungroup()

Indicators

rh_indi <- rh_data |>
    # Identify year
    mutate(year = year(date)) |>
    # Identify month
    mutate(month = month(date)) |>
    # Filter year
    filter(year >= 1991) |>
    # Group by id variable, year and month
    group_by(code_muni, year, month) |>
    # Compute precipitation indicators
    summarise_rel_humidity(
        value_var = value, 
        normals_df = rh_normal
    ) |>
    # Ungroup
    ungroup()

Export

write_parquet(x = rh_normal, sink = "rh_normal.parquet")
write_csv2(x = rh_normal, file = "rh_normal.csv")
write_parquet(x = rh_indi, sink = "rh_indi.parquet")
write_csv2(x = rh_indi, file = "rh_indi.csv")

Results and dataset download

The climatological normals and aggregated indicators of Brazilian municipalities can be downloaded from Zenodo on CSV and parquet formats. Click the link bellow to access and download the data.

You can also download the dataset directly from R, using the {zendown} package.

Let’s check some results.

Maximum temperature, Rio de Janeiro, RJ, 2023

Observed and normal

tmax_data <- zen_file(13906834, "Tmax_3.2.3.parquet") |>
    open_dataset() |>
    filter(name == "Tmax_3.2.3_mean") |>
    filter(code_muni == 3304557) |>
    filter(date >= as.Date("2023-01-01")) |>
    filter(date <= as.Date("2023-12-31")) |>
    select(-name) |>
    collect()

tmax_normal <- zen_file(13934888, "tmax_normal.parquet") |>
    open_dataset() |>
    filter(code_muni == 3304557) |>
    collect()

library(ggplot2)
library(tidyr)

tmax_normal_exp <- tmax_normal |>
    mutate(date = as_date(paste0("2023-",month,"-01"))) |>
    group_by(month) %>%
    expand(
        date = seq.Date(floor_date(date, unit = "month"), ceiling_date(date, unit="month")-days(1), by="day"), normal_mean, normal_p10, normal_p90
    ) |>
    pivot_longer(cols = starts_with("normal_")) |>
    mutate(name = substr(name, 8, 100))

ggplot() +
    geom_line(data = tmax_data, aes(x = date, y = value)) +
    geom_line(data = tmax_normal_exp, aes(x = date, y = value, color = name)) +
    theme_bw() +
    labs(
        title = "Maximum temperature and climatological normal", 
        subtitle = "Rio de Janeiro, RJ",
        color = "Normal (1961-1990)",
        x = "Date", y = "Celsius degrees"
    ) +
    theme(legend.position = "bottom", legend.direction = "horizontal")

Indicators

library(gt)

zen_file(13934888, "tmax_indi.parquet") |>
    open_dataset() |>
    filter(code_muni == 3304557) |>
    filter(year == 2023) |>
    select(-code_muni, -year) |>
    collect() |>
    gt() |>
    fmt_number(
        columns = where(is.double),
        decimals = 2,
        use_seps = FALSE
    )

month	count	normal_mean	normal_p10	normal_p90	mean	median	sd	se	max	min	p10	p25	p75	p90	heat_waves_3d	heat_waves_5d	hot_days	t_25	t_30	t_35	t_40
1.00	31	31.73	26.93	36.51	30.56	31.44	3.92	0.70	35.32	21.36	23.99	29.28	32.96	34.65	0	0	0	2	4	1	0
2.00	28	32.23	27.80	36.05	32.67	32.22	2.47	0.47	37.20	28.26	30.04	30.92	34.91	35.86	0	0	3	1	3	5	0
3.00	31	31.15	26.95	34.75	31.63	31.01	2.21	0.40	36.72	27.88	29.21	30.32	33.14	35.03	0	0	4	1	5	4	0
4.00	30	28.83	25.03	32.98	27.86	27.79	2.33	0.42	32.16	23.10	24.92	26.17	29.54	30.68	0	0	0	3	4	0	0
5.00	31	27.19	23.23	31.03	26.33	27.45	2.55	0.46	30.42	20.67	23.26	24.11	28.06	29.22	0	0	0	3	1	0	0
6.00	30	26.14	21.77	30.30	26.55	26.39	2.56	0.47	31.11	21.69	23.39	25.09	28.06	30.46	0	0	2	2	2	0	0
7.00	31	25.85	21.44	30.29	25.99	25.40	3.40	0.61	35.50	20.93	22.13	23.04	28.41	29.46	0	0	3	6	3	1	0
8.00	31	26.79	21.34	31.84	27.29	26.51	4.91	0.88	37.73	17.49	22.32	24.37	30.79	33.19	1	0	4	6	5	1	0
9.00	30	26.82	21.49	32.93	30.39	30.81	4.17	0.76	36.94	21.40	23.91	27.73	33.35	35.00	3	0	6	4	6	3	0
10.00	31	27.59	22.33	33.40	28.49	29.49	4.54	0.82	37.85	20.91	23.06	24.81	32.65	33.71	1	0	4	5	6	1	0
11.00	30	29.02	23.87	34.44	31.21	30.75	4.79	0.88	40.94	24.80	25.35	26.20	34.72	37.07	1	1	5	4	5	5	1
12.00	31	30.41	25.32	35.41	31.30	31.32	3.27	0.59	38.47	25.13	26.78	29.20	33.47	34.47	0	0	2	1	5	3	0

Session info

sessioninfo::session_info()

─ Session info ───────────────────────────────────────────────────────────────
 setting  value
 version  R version 4.3.2 (2023-10-31)
 os       macOS 15.0.1
 system   aarch64, darwin20
 ui       X11
 language (EN)
 collate  en_US.UTF-8
 ctype    en_US.UTF-8
 tz       Europe/Paris
 date     2024-10-16
 pandoc   3.2 @ /Applications/quarto/bin/tools/ (via rmarkdown)

─ Packages ───────────────────────────────────────────────────────────────────
 package     * version    date (UTC) lib source
 arrow       * 17.0.0.1   2024-08-21 [1] CRAN (R 4.3.3)
 assertthat    0.2.1      2019-03-21 [1] CRAN (R 4.3.0)
 backports     1.5.0      2024-05-23 [1] CRAN (R 4.3.3)
 bit           4.5.0      2024-09-20 [1] CRAN (R 4.3.3)
 bit64         4.5.2      2024-09-22 [1] CRAN (R 4.3.3)
 checkmate     2.3.2      2024-07-29 [1] CRAN (R 4.3.3)
 cli           3.6.3      2024-06-21 [1] CRAN (R 4.3.3)
 climindi    * 0.0.0.9000 2024-10-16 [1] local
 colorspace    2.1-1      2024-07-26 [1] CRAN (R 4.3.3)
 digest        0.6.37     2024-08-19 [1] CRAN (R 4.3.3)
 dplyr       * 1.1.4      2023-11-17 [1] CRAN (R 4.3.1)
 evaluate      1.0.1      2024-10-10 [1] CRAN (R 4.3.3)
 fansi         1.0.6      2023-12-08 [1] CRAN (R 4.3.1)
 farver        2.1.2      2024-05-13 [1] CRAN (R 4.3.3)
 fastmap       1.2.0      2024-05-15 [1] CRAN (R 4.3.3)
 fs            1.6.4      2024-04-25 [1] CRAN (R 4.3.1)
 generics      0.1.3      2022-07-05 [1] CRAN (R 4.3.0)
 ggplot2     * 3.5.1      2024-04-23 [1] CRAN (R 4.3.1)
 glue          1.8.0      2024-09-30 [1] CRAN (R 4.3.3)
 gt          * 0.11.1     2024-10-04 [1] CRAN (R 4.3.3)
 gtable        0.3.5      2024-04-22 [1] CRAN (R 4.3.1)
 hms           1.1.3      2023-03-21 [1] CRAN (R 4.3.0)
 htmltools     0.5.8.1    2024-04-04 [1] CRAN (R 4.3.1)
 htmlwidgets   1.6.4      2023-12-06 [1] CRAN (R 4.3.1)
 jsonlite      1.8.9      2024-09-20 [1] CRAN (R 4.3.3)
 knitr         1.48       2024-07-07 [1] CRAN (R 4.3.3)
 labeling      0.4.3      2023-08-29 [1] CRAN (R 4.3.0)
 lifecycle     1.0.4      2023-11-07 [1] CRAN (R 4.3.1)
 lubridate   * 1.9.3      2023-09-27 [1] CRAN (R 4.3.1)
 magrittr      2.0.3      2022-03-30 [1] CRAN (R 4.3.0)
 munsell       0.5.1      2024-04-01 [1] CRAN (R 4.3.1)
 pillar        1.9.0      2023-03-22 [1] CRAN (R 4.3.0)
 pkgconfig     2.0.3      2019-09-22 [1] CRAN (R 4.3.0)
 purrr         1.0.2      2023-08-10 [1] CRAN (R 4.3.0)
 R6            2.5.1      2021-08-19 [1] CRAN (R 4.3.0)
 readr       * 2.1.5      2024-01-10 [1] CRAN (R 4.3.1)
 rlang         1.1.4      2024-06-04 [1] CRAN (R 4.3.3)
 rmarkdown     2.28       2024-08-17 [1] CRAN (R 4.3.3)
 sass          0.4.9      2024-03-15 [1] CRAN (R 4.3.1)
 scales        1.3.0      2023-11-28 [1] CRAN (R 4.3.1)
 sessioninfo   1.2.2      2021-12-06 [1] CRAN (R 4.3.0)
 tibble        3.2.1      2023-03-20 [1] CRAN (R 4.3.0)
 tidyr       * 1.3.1      2024-01-24 [1] CRAN (R 4.3.1)
 tidyselect    1.2.1      2024-03-11 [1] CRAN (R 4.3.1)
 timechange    0.3.0      2024-01-18 [1] CRAN (R 4.3.1)
 tzdb          0.4.0      2023-05-12 [1] CRAN (R 4.3.0)
 utf8          1.2.4      2023-10-22 [1] CRAN (R 4.3.1)
 vctrs         0.6.5      2023-12-01 [1] CRAN (R 4.3.1)
 withr         3.0.1      2024-07-31 [1] CRAN (R 4.3.3)
 xfun          0.48       2024-10-03 [1] CRAN (R 4.3.3)
 xml2          1.3.6      2023-12-04 [1] CRAN (R 4.3.1)
 yaml          2.3.10     2024-07-26 [1] CRAN (R 4.3.3)
 zendown     * 0.1.0      2024-04-18 [1] Github (rfsaldanha/zendown@afbd73a)

 [1] /Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/library

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References

Muñoz-Sabater, Joaquín, Emanuel Dutra, Anna Agustí-Panareda, Clément Albergel, Gabriele Arduini, Gianpaolo Balsamo, Souhail Boussetta, et al. 2021. “ERA5-Land: A State-of-the-Art Global Reanalysis Dataset for Land Applications.” Earth System Science Data 13 (9): 4349–83. https://doi.org/10.5194/essd-13-4349-2021.

Saldanha, Raphael, Reza Akbarinia, Marcel Pedroso, Victor Ribeiro, Carlos Cardoso, Eduardo H. M. Pena, Patrick Valduriez, and Fabio Porto. 2024. “Zonal Statistics Datasets of Climate Indicators for Brazilian Municipalities.” Environmental Data Science 3: e2. https://doi.org/10.1017/eds.2024.3.

WMO. 2017. WMO Guidelines on the Calculation of Climate Normals. Geneva: WMO.

Xavier, Alexandre C., Bridget R. Scanlon, Carey W. King, and Aline I. Alves. 2022. “New Improved Brazilian Daily Weather Gridded Data (1961).” International Journal of Climatology, December. https://doi.org/10.1002/joc.7731.