Universal Thermal Climate Index (UTCI)

Equivalent temperature representing the physiological response to the thermal environment. Based on a multi-node human thermoregulation model.

Reference: Bröde et al. (2012), Fiala et al. (2012)

Equation

UTCI is computed from a 6th-order polynomial approximation of the Fiala model:

UTCI = Ta + offset(Ta, Tmrt-Ta, va, Pa)

The offset is a complex polynomial function (~200 terms) of: - Ta = air temperature (°C) - ΔTmrt = Tmrt - Ta (°C) - va = wind speed at 10m (m/s) - Pa = water vapor pressure (kPa). Note: vapor pressure is converted from hPa to kPa (pa = ehPa / 10.0) before entering the polynomial.

Inputs

Input	Type	Description
Ta	float or 2D array (°C)	Air temperature
Tmrt	float or 2D array (°C)	Mean radiant temperature
va	float or 2D array (m/s)	Wind speed at 10m height
RH	float or 2D array (%)	Relative humidity

Outputs

Output	Type	Description
UTCI	float or 2D array (°C)	Universal Thermal Climate Index

Stress Categories

UTCI (°C)	Stress Category	Physiological Response
> 46	Extreme heat stress	Heat stroke risk
38 to 46	Very strong heat stress	Failure of thermoregulation
32 to 38	Strong heat stress	Strong sweating, dehydration
26 to 32	Moderate heat stress	Sweating, discomfort
9 to 26	No thermal stress	Comfort zone
0 to 9	Slight cold stress	Vasoconstriction
-13 to 0	Moderate cold stress	Shivering begins
-27 to -13	Strong cold stress	Risk of frostbite
-40 to -27	Very strong cold stress	Numbness, hypothermia risk
< -40	Extreme cold stress	Frostbite in minutes

Properties

Fundamental Properties

1. UTCI is an equivalent temperature
2. Units are °C
3. Represents how the environment "feels"

4. Reference: walking outdoors at 4 km/h

5. Valid input ranges (from UTCI specification)

6. Ta: -50°C to +50°C
7. Tmrt-Ta: -30°C to +70°C
8. va: 0.5 to 17 m/s (specification minimum; implementation enforces only va > 0)
9. RH: 5% to 100%
10. Note: These ranges are from the UTCI specification. The current implementation does NOT enforce these ranges at runtime — out-of-range inputs are computed without clamping or warnings, matching upstream UMEP behavior.

Radiation Properties

1. Higher Tmrt → higher UTCI
2. Radiation increases thermal stress

3. Sun to shade: ΔUTCI ≈ 5-20°C

4. UTCI ≈ Ta when Tmrt = Ta and low wind

5. No radiation difference, no wind chill
6. Neutral reference condition

Wind Properties

1. Wind reduces UTCI in heat
2. Convective cooling

3. Effect saturates at high wind speeds

4. Wind reduces UTCI in cold

5. Wind chill effect
6. Stronger effect in cold conditions

Humidity Properties

1. Humidity effect small in cold
2. Water vapor pressure low at cold temperatures

3. Main effect is in warm/hot conditions

4. High humidity increases UTCI in heat

5. Impairs evaporative cooling
6. Tropical conditions feel hotter

Comparison with Other Indices

Index	Accounts for	Limitations
UTCI	Ta, Tmrt, wind, humidity	Fixed clothing/activity
PET	Ta, Tmrt, wind, humidity, person	More parameters needed
Heat Index	Ta, humidity	No radiation or wind
Wind Chill	Ta, wind	Cold only, no radiation

Typical Values

Condition	Ta	Tmrt	Wind	UTCI	Category
Hot sunny	35	65	1	45	Very strong heat
Hot shaded	35	40	1	36	Strong heat
Comfortable	22	25	2	22	No stress
Cold windy	-5	-5	10	-15	Strong cold
Cold calm	-5	-5	1	-6	Moderate cold

Implementation Notes

1. Wind height adjustment
2. Input wind typically at 10m height

3. Model assumes standard reference height

4. Polynomial approximation

5. 210-coefficient polynomial (6th order in 4 variables)

6. Accurate within ±0.5°C of full Fiala model

7. Saturation Vapor Pressure

8. Computed via 8-coefficient polynomial (from UTCI_calculations.py / utci.rs)

9. Converted from hPa to kPa before entering the UTCI polynomial

10. Return values for invalid inputs

11. utci_single() returns -999.0 for invalid inputs (Ta or wind out of range)
12. utci_grid() returns NaN for invalid pixels

13. This inconsistency exists in the current implementation

14. Extrapolation warning

15. Results outside valid ranges may be unreliable
16. The implementation does not clamp or flag out-of-range inputs (matching upstream UMEP)

References

Primary UMEP Citation:

• Lindberg F, Grimmond CSB, Gabey A, Huang B, Kent CW, Sun T, Theeuwes N, Järvi L, Ward H, Capel-Timms I, Chang YY, Jonsson P, Krave N, Liu D, Meyer D, Olofson F, Tan JG, Wästberg D, Xue L, Zhang Z (2018) "Urban Multi-scale Environmental Predictor (UMEP) - An integrated tool for city-based climate services." Environmental Modelling and Software 99, 70-87. doi:10.1016/j.envsoft.2017.09.020

UTCI Model:

• Błażejczyk K, Jendritzky G, Bröde P, Fiala D, Havenith G, Epstein Y, Psikuta A, Kampmann B (2013) "An introduction to the Universal Thermal Climate Index (UTCI)." Geographia Polonica 86(1), 5-10.
• Bröde P, Fiala D, Błażejczyk K, Holmér I, Jendritzky G, Kampmann B, Tinz B, Havenith G (2012) "Deriving the operational procedure for the Universal Thermal Climate Index (UTCI)." International Journal of Biometeorology 56(3), 481-494.