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Annual Maximum JJA Heat Index at Boulder, CO and Chicago, IL (1990–2025)

ERA5 and JRA-3Q Reanalyses from NCAR GDEX

Scientific motivation

This notebook computes the annual maximum June–July–August (JJA) heat index at two mid-latitude United States cities — Boulder, Colorado (semi-arid, elevation 1655 m) and Chicago, Illinois (humid continental, Lake Michigan influence) — using two independent global reanalyses spanning 1990–2025.

The analysis follows the methodology of Romps (2024), who demonstrated using ERA5 that the annual maximum summer heat index in Texas has increased at a rate several times larger than the contemporaneous increase in dry-bulb temperature. The physical basis for this amplification lies in the nonlinearity of the heat index with respect to temperature and humidity: at near-saturated conditions, the Clausius–Clapeyron relation implies that a given increment of warming produces a disproportionately large increase in physiological heat stress. Chicago, situated in a persistently humid air mass, is expected to exhibit stronger amplification than semi-arid Boulder, where the heat index remains close to the dry-bulb temperature throughout the summer.

Datasets

ProductGDEX identifierTemporal resolutionQuantity archivedAccess format
ERA5 surface analysisd633000Hourly instantaneousVAR_2T, VAR_2DNative Zarr
JRA-3Q surface analysis (anl_surf125)d6400006-hourly instantaneousTMP_GDS0_HTGL, RH_GDS0_HTGLkerchunk reference

Because ERA5 provides 24 candidate values per day versus 4 for JRA-3Q, computing the JJA season maximum from the full hourly ERA5 stream would systematically inflate ERA5 relative to JRA-3Q through a sample-size effect alone. To remove this artifact, ERA5 is subsampled to one randomly selected observation per 6-hour window prior to computing the annual maximum, matching the JRA-3Q cadence. A random draw, rather than a fixed synoptic hour, is used to avoid introducing a systematic diurnal-phase bias into the sampled ERA5 distribution. We re-sample instead of taking a mean over a 6-hour window because the average might miss an extreme heat index value in this window.

Heat index formulation

The heat index is computed using the heatindex Python package of Lu & Romps (2025), which implements the extended formulation of Lu & Romps (2022) in python. The function takes air temperature in Kelvin and relative humidity on the interval [0, 1][0,\,1] and returns the heat index in Kelvin:

hi.heatindex(T_K, rh)  →  HI_K

ERA5 does not archive near-surface relative humidity directly. It is derived from the 2-m temperature (VAR_2T) and 2-m dew-point temperature (VAR_2D) via the August–Roche–Magnus approximation, consistent with the ECMWF IFS documentation. JRA-3Q provides relative humidity in percent as RH_GDS0_HTGL in the surface analysis product.

Required Packages

Please make sure to install the packages before moving forward

  • intake

  • intake-esm >= 2025.12.12

  • xarray

  • dask

  • zarr

  • kerchunk

  • numpy

  • pandas

  • matplotlib

  • heatindex >= 0.0.2

Defaulting to user installation because normal site-packages is not writeable
Requirement already satisfied: heatindex in /glade/u/home/harshah/.local/lib/python3.10/site-packages (0.0.2)
Requirement already satisfied: numpy in /glade/u/home/harshah/.local/lib/python3.10/site-packages (from heatindex) (1.26.4)

[notice] A new release of pip is available: 25.3 -> 26.0.1
[notice] To update, run: pip install --upgrade pip

Step 1 - Locate the Dataset

On the NCAR GDEX portal, go to the Data Access tab for the ERA5/ JRA-3Q dataset to find the intake-ESM catalogs needed to access data. In this notebook we will use GDEX POSIX catalog.

Step 2 - Set up cluster

/glade/derecho/scratch/harshah

Step 3 - Open the catalog, find and load the variable of interest

CPU times: user 9.97 ms, sys: 301 μs, total: 10.3 ms
Wall time: 9.73 ms
Loading...
  • Search for humidity and temperature variables in the catalog using the long_name and/or short_name columns. We only show the JRA-3Q example in the code below

Loading...
ERA5 matched: 2 entries
JRA-3Q matched: 2 entries
  • Now that we have figured out the correct variable names, let us load the data using xarray

CPU times: user 383 ms, sys: 113 ms, total: 497 ms
Wall time: 542 ms
Loading...
Loading...

Extract data

  • Resample ERA5 data to 6hr frequency

  • Subset the data in space (Colorado and Chicago) and time

ERA5   / Boulder_CO: requested (40.01°N, 254.73°E) → nearest (40.000°N, 254.750°E)
JRA-3Q / Boulder_CO: requested (40.01°N, 254.73°E) → nearest (40.000°N, 255.000°E)
ERA5   / Chicago_IL: requested (41.88°N, 272.37°E) → nearest (42.000°N, 272.250°E)
JRA-3Q / Chicago_IL: requested (41.88°N, 272.37°E) → nearest (42.500°N, 272.500°E)
  78,000 → 13,000 time steps retained (16.7%, expected ≈16.7%)
ERA5 / Boulder_CO: subsampling complete
  78,000 → 13,000 time steps retained (16.7%, expected ≈16.7%)
ERA5 / Chicago_IL: subsampling complete
Relative humidity prepared for all sites.

Step 4 - Data Analysis

Computing ERA5 / Boulder_CO ...
  Done. Years: 1990–2025
Computing JRA-3Q / Boulder_CO ...
/glade/u/home/harshah/venvs/mdm/lib/python3.10/site-packages/distributed/client.py:3383: UserWarning: Sending large graph of size 28.14 MiB.
This may cause some slowdown.
Consider loading the data with Dask directly
 or using futures or delayed objects to embed the data into the graph without repetition.
See also https://docs.dask.org/en/stable/best-practices.html#load-data-with-dask for more information.
  warnings.warn(
  Done. Years: 1990–2025
Computing ERA5 / Chicago_IL ...
  Done. Years: 1990–2025
Computing JRA-3Q / Chicago_IL ...
/glade/u/home/harshah/venvs/mdm/lib/python3.10/site-packages/distributed/client.py:3383: UserWarning: Sending large graph of size 28.24 MiB.
This may cause some slowdown.
Consider loading the data with Dask directly
 or using futures or delayed objects to embed the data into the graph without repetition.
See also https://docs.dask.org/en/stable/best-practices.html#load-data-with-dask for more information.
  warnings.warn(
  Done. Years: 1990–2025
Results written to: /glade/derecho/scratch/harshah/max_jja_ehi_boulder_chicago.zarr
<xarray.Dataset> Size: 1kB
Dimensions:                      (year: 36)
Coordinates:
  * year                         (year) int64 288B 1990 1991 1992 ... 2024 2025
Data variables:
    era5_boulder_co_hi_max_jja   (year) float64 288B dask.array<chunksize=(36,), meta=np.ndarray>
    era5_chicago_il_hi_max_jja   (year) float64 288B dask.array<chunksize=(36,), meta=np.ndarray>
    jra3q_boulder_co_hi_max_jja  (year) float64 288B dask.array<chunksize=(36,), meta=np.ndarray>
    jra3q_chicago_il_hi_max_jja  (year) float64 288B dask.array<chunksize=(36,), meta=np.ndarray>
<Figure size 1000x500 with 1 Axes>
CPU times: user 184 ms, sys: 47.1 ms, total: 231 ms
Wall time: 258 ms
  • The plot confirms our intuition: Chicago, a more humid place, has a higher JJA maximum heat index than Boulder

  • We see the infamous 1995 Chicago Heat Wave in the plot, but it is not captured by JRA-3Q!

  • For both Chicago and Boulder, the predictions from both the ERA5 and JRA-3Q reanalyses seem to broadly agree!

References

  • Romps, D.M., 2024. Heat index extremes increasing several times faster than the air temperature, ERL, 2024 Environmental Research Letters

  • Lu, Y.-C. and Romps, D.M., 2022. Extending the heat index. Journal of Applied Meteorology and Climatology, 61(10), 1367–1383. DOI: Lu & Romps (2022)

  • Lu, Y.-C. and Romps, D.M., 2025. heatindex: Tools for Calculating Heat Stress, version 0.0.2. https://heatindex.org

  • Hersbach, H., et al., 2020. The ERA5 global reanalysis. Quarterly Journal of the Royal Meteorological Society, 146(730), 1999–2049. DOI: Hersbach et al. (2020)

  • Kosaka, Y., et al., 2024. The JRA-3Q Reanalysis. Journal of the Meteorological Society of Japan, 102, 49–109. DOI: KOSAKA et al. (2024)

References
  1. Lu, Y.-C., & Romps, D. M. (2022). Extending the Heat Index. Journal of Applied Meteorology and Climatology, 61(10), 1367–1383. 10.1175/jamc-d-22-0021.1
  2. Hersbach, H., Bell, B., Berrisford, P., Hirahara, S., Horányi, A., Muñoz‐Sabater, J., Nicolas, J., Peubey, C., Radu, R., Schepers, D., Simmons, A., Soci, C., Abdalla, S., Abellan, X., Balsamo, G., Bechtold, P., Biavati, G., Bidlot, J., Bonavita, M., … Thépaut, J. (2020). The ERA5 global reanalysis. Quarterly Journal of the Royal Meteorological Society, 146(730), 1999–2049. 10.1002/qj.3803
  3. KOSAKA, Y., KOBAYASHI, S., HARADA, Y., KOBAYASHI, C., NAOE, H., YOSHIMOTO, K., HARADA, M., GOTO, N., CHIBA, J., MIYAOKA, K., SEKIGUCHI, R., DEUSHI, M., KAMAHORI, H., NAKAEGAWA, T., TANAKA, T. Y., TOKUHIRO, T., SATO, Y., MATSUSHITA, Y., & ONOGI, K. (2024). The JRA-3Q Reanalysis. Journal of the Meteorological Society of Japan. Ser. II, 102(1), 49–109. 10.2151/jmsj.2024-004