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Annual Maximum JJA Heat Index at Boulder, CO and Chicago, IL (1990–2005)

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 1990–2005.

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

Requirement already satisfied: heatindex in /glade/u/home/harshah/.conda/envs/osdf/lib/python3.11/site-packages (0.0.2)
Requirement already satisfied: numpy in /glade/u/home/harshah/.conda/envs/osdf/lib/python3.11/site-packages (from heatindex) (2.4.6)
<donfig.config_obj.ConfigSet at 0x145832fee150>

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 OSDF catalog.

/glade/derecho/scratch/harshah

Step 2 - Set up cluster

  • Please set these two flags to False if you are not on NCAR’s HPC cluster or not using a dask gateway.

  • Setting these flags to False immediately selects a local cluster which can run on your personal device

2026-06-26 10:18:21,741 - tornado.application - ERROR - Uncaught exception GET /status/ws (127.0.0.1)
HTTPServerRequest(protocol='http', host='jupyterhub.hpc.ucar.edu', method='GET', uri='/status/ws', version='HTTP/1.1', remote_ip='127.0.0.1')
Traceback (most recent call last):
  File "/glade/u/home/harshah/.conda/envs/osdf/lib/python3.11/site-packages/tornado/websocket.py", line 965, in _accept_connection
    open_result = handler.open(*handler.open_args, **handler.open_kwargs)
                  ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/glade/u/home/harshah/.conda/envs/osdf/lib/python3.11/site-packages/tornado/web.py", line 3388, in wrapper
    return method(self, *args, **kwargs)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/glade/u/home/harshah/.conda/envs/osdf/lib/python3.11/site-packages/bokeh/server/views/ws.py", line 149, in open
    raise ProtocolError("Token is expired. Configure the app with a larger value for --session-token-expiration if necessary")
bokeh.protocol.exceptions.ProtocolError: Token is expired. Configure the app with a larger value for --session-token-expiration if necessary
2026-06-26 10:18:24,439 - tornado.application - ERROR - Uncaught exception GET /status/ws (127.0.0.1)
HTTPServerRequest(protocol='http', host='jupyterhub.hpc.ucar.edu', method='GET', uri='/status/ws', version='HTTP/1.1', remote_ip='127.0.0.1')
Traceback (most recent call last):
  File "/glade/u/home/harshah/.conda/envs/osdf/lib/python3.11/site-packages/tornado/websocket.py", line 965, in _accept_connection
    open_result = handler.open(*handler.open_args, **handler.open_kwargs)
                  ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/glade/u/home/harshah/.conda/envs/osdf/lib/python3.11/site-packages/tornado/web.py", line 3388, in wrapper
    return method(self, *args, **kwargs)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/glade/u/home/harshah/.conda/envs/osdf/lib/python3.11/site-packages/bokeh/server/views/ws.py", line 149, in open
    raise ProtocolError("Token is expired. Configure the app with a larger value for --session-token-expiration if necessary")
bokeh.protocol.exceptions.ProtocolError: Token is expired. Configure the app with a larger value for --session-token-expiration if necessary
2026-06-26 10:35:00,412 - tornado.application - ERROR - Uncaught exception GET /status/ws (127.0.0.1)
HTTPServerRequest(protocol='http', host='jupyterhub.hpc.ucar.edu', method='GET', uri='/status/ws', version='HTTP/1.1', remote_ip='127.0.0.1')
Traceback (most recent call last):
  File "/glade/u/home/harshah/.conda/envs/osdf/lib/python3.11/site-packages/tornado/websocket.py", line 965, in _accept_connection
    open_result = handler.open(*handler.open_args, **handler.open_kwargs)
                  ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/glade/u/home/harshah/.conda/envs/osdf/lib/python3.11/site-packages/tornado/web.py", line 3388, in wrapper
    return method(self, *args, **kwargs)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/glade/u/home/harshah/.conda/envs/osdf/lib/python3.11/site-packages/bokeh/server/views/ws.py", line 149, in open
    raise ProtocolError("Token is expired. Configure the app with a larger value for --session-token-expiration if necessary")
bokeh.protocol.exceptions.ProtocolError: Token is expired. Configure the app with a larger value for --session-token-expiration if necessary
2026-06-26 10:51:02,421 - tornado.application - ERROR - Uncaught exception GET /status/ws (127.0.0.1)
HTTPServerRequest(protocol='http', host='jupyterhub.hpc.ucar.edu', method='GET', uri='/status/ws', version='HTTP/1.1', remote_ip='127.0.0.1')
Traceback (most recent call last):
  File "/glade/u/home/harshah/.conda/envs/osdf/lib/python3.11/site-packages/tornado/websocket.py", line 965, in _accept_connection
    open_result = handler.open(*handler.open_args, **handler.open_kwargs)
                  ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/glade/u/home/harshah/.conda/envs/osdf/lib/python3.11/site-packages/tornado/web.py", line 3388, in wrapper
    return method(self, *args, **kwargs)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/glade/u/home/harshah/.conda/envs/osdf/lib/python3.11/site-packages/bokeh/server/views/ws.py", line 149, in open
    raise ProtocolError("Token is expired. Configure the app with a larger value for --session-token-expiration if necessary")
bokeh.protocol.exceptions.ProtocolError: Token is expired. Configure the app with a larger value for --session-token-expiration if necessary
2026-06-26 10:51:22,751 - tornado.application - ERROR - Uncaught exception GET /status/ws (127.0.0.1)
HTTPServerRequest(protocol='http', host='jupyterhub.hpc.ucar.edu', method='GET', uri='/status/ws', version='HTTP/1.1', remote_ip='127.0.0.1')
Traceback (most recent call last):
  File "/glade/u/home/harshah/.conda/envs/osdf/lib/python3.11/site-packages/tornado/websocket.py", line 965, in _accept_connection
    open_result = handler.open(*handler.open_args, **handler.open_kwargs)
                  ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/glade/u/home/harshah/.conda/envs/osdf/lib/python3.11/site-packages/tornado/web.py", line 3388, in wrapper
    return method(self, *args, **kwargs)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/glade/u/home/harshah/.conda/envs/osdf/lib/python3.11/site-packages/bokeh/server/views/ws.py", line 149, in open
    raise ProtocolError("Token is expired. Configure the app with a larger value for --session-token-expiration if necessary")
bokeh.protocol.exceptions.ProtocolError: Token is expired. Configure the app with a larger value for --session-token-expiration if necessary
Loading...

Open the catalog, find and load the variable of interest

CPU times: user 97.8 ms, sys: 13.2 ms, total: 111 ms
Wall time: 1.48 s
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
osdf:///ncar/gdex/d633000/e5.oper.an.sfc.zarr/e5.oper.an.sfc.2t.zarr
osdf:///ncar/gdex/d633000/e5.oper.an.sfc.zarr/e5.oper.an.sfc.2d.zarr
https://data.gdex.ucar.edu/d640000/kerchunk/anl_surf125-remote-osdf.parq
https://data.gdex.ucar.edu/d640000/kerchunk/anl_surf125-remote-osdf.parq
/glade/u/home/harshah/.conda/envs/osdf/lib/python3.11/site-packages/tqdm/auto.py:21: TqdmWarning: IProgress not found. Please update jupyter and ipywidgets. See https://ipywidgets.readthedocs.io/en/stable/user_install.html
  from .autonotebook import tqdm as notebook_tqdm
CPU times: user 2.74 s, sys: 370 ms, total: 3.11 s
Wall time: 9.47 s
Loading...
CPU times: user 451 ms, sys: 51.5 ms, total: 502 ms
Wall time: 2.12 s
Loading...

Extract data

  • Resample ERA5 data to 6hr frequency

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

Loading JRA-3Q / Boulder_CO into memory ...
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)
Loading JRA-3Q / Chicago_IL into memory ...
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)
  35,328 → 5,888 time steps retained (16.7%, expected ≈16.7%)
ERA5 / Boulder_CO: subsampling complete
  35,328 → 5,888 time steps retained (16.7%, expected ≈16.7%)
ERA5 / Chicago_IL: subsampling complete
Relative humidity prepared for all sites.

Data Analysis

Computing ERA5 / Boulder_CO ...
/glade/u/home/harshah/.conda/envs/osdf/lib/python3.11/site-packages/distributed/client.py:3363: UserWarning: Sending large graph of size 14.76 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: 1990–2005
Computing ERA5 / Chicago_IL ...
/glade/u/home/harshah/.conda/envs/osdf/lib/python3.11/site-packages/distributed/client.py:3363: UserWarning: Sending large graph of size 14.76 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: 1990–2005
ERA5 complete. Starting JRA-3Q ...
Computing JRA-3Q / Boulder_CO ...
  Done. Years: 1990–2005
Computing JRA-3Q / Chicago_IL ...
  Done. Years: 1990–2005
CPU times: user 36.5 s, sys: 1.82 s, total: 38.4 s
Wall time: 2min 32s
{'Boulder_CO': {'ERA5': <xarray.DataArray 'VAR_2T' (year: 16)> Size: 128B array([30.31437118, 29.37980066, 30.16152357, 28.83467811, 29.26095098, 29.52726534, 29.01216692, 28.71528863, 29.81360704, 28.70810495, 28.74855309, 28.44405876, 30.25122393, 30.32078968, 28.86774954, 31.27154208]) Coordinates: * year (year) int64 128B 1990 1991 1992 1993 ... 2002 2003 2004 2005 latitude float64 8B 40.0 longitude float64 8B 254.8 Attributes: units: K long_name: Heat Index (Lu and Romps, 2022), 'JRA-3Q': <xarray.DataArray 'tmp2m-hgt-an-ll125' (year: 16)> Size: 128B array([31.4855916 , 28.81282681, 30.29212844, 28.59815461, 32.24661062, 31.68685696, 30.37146765, 29.93243945, 31.29662387, 31.14809228, 30.77979553, 29.67094706, 32.12703736, 31.94868504, 30.1000814 , 31.80103818]) Coordinates: * year (year) int64 128B 1990 1991 1992 1993 1994 ... 2002 2003 2004 2005 lat float64 8B 40.0 lon float64 8B 255.0}, 'Chicago_IL': {'ERA5': <xarray.DataArray 'VAR_2T' (year: 16)> Size: 128B array([40.81386318, 37.23952255, 36.54530183, 37.43253038, 36.23931439, 47.78195681, 37.07372576, 43.51830227, 37.92607486, 42.95852188, 34.48469987, 38.67871986, 38.97232824, 37.93252271, 33.40900486, 41.54673062]) Coordinates: * year (year) int64 128B 1990 1991 1992 1993 ... 2002 2003 2004 2005 latitude float64 8B 42.0 longitude float64 8B 272.2 Attributes: units: K long_name: Heat Index (Lu and Romps, 2022), 'JRA-3Q': <xarray.DataArray 'tmp2m-hgt-an-ll125' (year: 16)> Size: 128B array([31.77173653, 32.13740182, 28.5423206 , 30.50860181, 27.81349282, 33.17215482, 30.23272175, 30.19124475, 30.94414974, 35.88272937, 29.87920044, 32.24332376, 32.28697817, 34.02234904, 27.73460363, 34.579493 ]) Coordinates: * year (year) int64 128B 1990 1991 1992 1993 1994 ... 2002 2003 2004 2005 lat float64 8B 42.5 lon float64 8B 272.5}}
<Figure size 1000x500 with 1 Axes>
CPU times: user 171 ms, sys: 16.3 ms, total: 187 ms
Wall time: 298 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