Excess Heat and Cold Factors¶

The Excess Heat Factor (EXHF) and Excess Cold Factor (EXCF) are thermal indices that quantify the hazard of extreme heat and cold events.

Each index combines two components: a significance index that measures how much the current temperature exceeds a climatological threshold, and an acclimatisation index that measures how much the current temperature departs from the recent past. EXHF or EXCF indicate events that are both unusually hot or cold relative to climatology and to which the population has had little time to acclimatise, and are therefore associated with elevated health risk.

The indices and their reference definitions typically use a day defined from 9 am to 9 am local time, so that the daily maximum typically precedes the daily minimum. This accounts for the greater physiological significance of a hot night following a hot day compared to the other way around.

More information:

Nairn, J. & Fawcett, R. The Excess Heat Factor: A Metric for Heatwave Intensity and Its Use in Classifying Heatwave Severity. Int J Environ Res Public Health 12(1), 227–253 (2014). https://doi.org/10.3390/ijerph120100227
Nairn, J. Defining heatwaves: heatwave defined as a heat-impact event servicing all community and business sectors in Australia. CAWCR Technical Report No. 060 (2013). https://www.cawcr.gov.au/technical-reports/CTR_060.pdf
Nairn, J. Heatwave Severity. Int J Environ Res Public Health 15(11), 2494 (2018). https://doi.org/10.3390/ijerph15112494

How to use¶

Note

The functions defined here only implement the basic formulas of the indices, not the required aggregations of the input data. The intermediate aggregated quantities required by the pipeline — including running means of daily mean temperature and climatological percentile thresholds — can for example be computed with earthkit-transforms.

Daily mean temperature¶

The excess heat and cold factor computations are based on 2 m daily mean temperature. Nairn and Fawcett (2014) approximate the daily mean temperature with the average of the daily minimum and maximum temperatures, which are more readily available as inputs from long-running historical records.

from thermofeel.excess_heat import daily_mean_temperature

dmt = daily_mean_temperature(t2_min, t2_max)

Both inputs must be in the same unit (K or °C); the output is in the same unit.

Significance index¶

The significance index measures how far the 3-day running mean of daily mean temperature exceeds a climatological threshold. For heat events the threshold is typically the 95th percentile of daily mean temperature over a reference period; for cold events the 5th percentile is used instead.

from thermofeel.excess_heat import significance_index

# heat events: threshold = 95th-percentile climatology of dmt
ehi_sig_heat = significance_index(dmt_3day_mean, threshold_95th)

# cold events: threshold = 5th-percentile climatology of dmt
ehi_sig_cold = significance_index(dmt_3day_mean, threshold_5th)

The output unit matches the input unit.

Note

The use of a static climatological threshold in the significance index means that indicated hot and cold extremes will almost exclusively occur in the summer or winter seasons, respectively. A time-varying climatological threshold allows for the detection of warm and cold spells (relative anomalies) instead.

Acclimatisation index¶

The acclimatisation index measures how far the 3-day running mean of daily mean temperature (days i, i+1, i+2) exceeds the 30-day running mean of daily mean temperature in the preceding period (days i-30, ..., i-1).

from thermofeel.excess_heat import acclimatisation_index

ehi_accl = acclimatisation_index(dmt_3day_mean, dmt_30day_mean)

The output unit matches the input unit.

Excess heat factor¶

The excess heat factor combines the significance index and the acclimatisation index. Optionally, set clip=True to restrict the EXHF to non-negative values.

from thermofeel.excess_heat import excess_heat_factor

exhf = excess_heat_factor(ehi_sig_heat, ehi_accl)
exhf_clipped = excess_heat_factor(ehi_sig_heat, ehi_accl, clip=True)

This factor is also available at the top level as thermofeel.calculate_excess_heat_factor(ehi_sig, ehi_accl, clip=False).

The output unit is the input unit squared, e.g. K².

Heatwave severity¶

The heatwave severity index normalises the excess heat factor by a threshold to produce a dimensionless measure of event severity relative to a historical baseline. The 85th percentile of all positive EXHF values over a reference period is typically used as the threshold value.

from thermofeel.excess_heat import heatwave_severity

hsev = heatwave_severity(exhf, threshold_exhf_85th)

The severity index is nondimensional.

Excess cold factor¶

The excess cold factor uses the same formulation as the excess heat factor but is symmetric about zero to capture cold extremes. Use the significance index computed against the 5th-percentile threshold. Optionally set clip=True to restrict the result to cold events only.

from thermofeel.excess_heat import excess_cold_factor

excf = excess_cold_factor(ehi_sig_cold, ehi_accl)
excf_clipped = excess_cold_factor(ehi_sig_cold, ehi_accl, clip=True)

This factor is also available at the top level as thermofeel.calculate_excess_cold_factor(ehi_sig, ehi_accl, clip=False).

The output unit is the input unit squared, e.g. K².