Wet bulb globe temps too high; games cancelled

The football game between Brea Olinda High School and Sonora High School in California was cancelled Friday due to excessive heat, Raina Kim reports in the student newspaper at Brea Olinda.

The article is running a correction as follows: “An earlier version of this story attributed the cancellations to a high Ultraviolet (UV) Index when, in fact, the cancellations were due to a high WetBulb Globe Temperature (WBGT).”

The Wet Bulb Globe Temperature

Let me break this down in two parts:

What Wet Bulb Globe Temperature (WBGT) Is

The Wet Bulb Globe Temperature is an index developed to measure heat stress in direct sunlight. The US National Weather Service (NWS) defines it as a composite temperature that incorporates:

• Air temperature (dry bulb)
• Humidity (via the wet bulb)
• Solar radiation (measured with a black globe thermometer)
• Wind speed (which affects evaporative cooling)

This makes it a more complete measure of environmental heat stress than simple air temperature or even the heat index.

By contrast, the heat index used in most US weather reports only combines air temperature and relative humidity. It assumes you’re in the shade with light wind. That makes it less representative of conditions during outdoor activity in direct sun.

Why WBGT is Often Preferred in Sports

For sports like football, soccer, track, or military training, where athletes are exerting themselves outdoors in full gear and often in the sun, WBGT is generally considered more useful than the heat index because:

• It accounts for solar load (direct sunlight on the body), which the heat index ignores.
• It considers wind, which can make a big difference in cooling.
• It provides safety thresholds: Many athletic associations (e.g., NCAA, military, OSHA guidelines) use WBGT cutoffs to recommend hydration breaks, equipment modifications, or even cancellation of practices.

For example, the NCAA Sports Medicine Handbook specifies activity modifications at WBGT levels starting around 82°F, with cancellation at 92°F or higher. These numbers are lower than equivalent “danger zones” in the heat index, because WBGT is more conservative and better tied to the actual risk of exertional heat illness.

So, while the heat index is easy to calculate and good for the general public, it assumes you’re in the shade and that the wind is light. The WBGT, while more complex, is more realistic for athletes, outdoor workers, and soldiers in the sun. For football and similar sports, WBGT is the safer and more practical metric. Many professional guidelines in sports medicine and occupational health recommend it over the heat index for activity planning.

How to Measure WGBT

There is a formula for WBGT, and in fact there are two versions depending on whether you are in direct sun (outdoors) or in shade (indoors).

(1) Outdoors with solar radiation (sunlight):

(2) Indoors or outdoors without sun:

Where:

The natural wet bulb temperature is measured with a thermometer wrapped in wet cloth, exposed to wind, no fan. The globe temperature is measured inside a matte black globe, usually 6 in. in diameter, capturing radiant heat from the sun and ground. And the dry bulb temperature is the the air temperature in the shade.

These are weighted averages, so the wet bulb (humidity + wind effects) is given the heaviest weight, since evaporative cooling is the body’s main defense. But as you read, to measure WBGT accurately, you need special instruments (a WBGT meter with a black globe and natural wet bulb sensor). The NWS calculator estimates WBGT by combining regular meteorological data (temp, humidity, wind, solar radiation) with a model, because most weather stations don’t have globe or natural wet bulb thermometers.

So: If you have the right equipment, use the formula. If you don’t have the equipment, you must rely on an estimator, like the NWS online calculator or commercial apps that approximate WBGT.

If You Have a Good Weather Station

Many high-quality and commercially available weather stations measure solar radiation in watts per square meter (W/m²). If you have this equipment, you can get an estimate of the WBGT. This uses an empirical estimate for the wet bulb temperature, which is typically accurate to within ±0.3°C. So it’s not perfect, but it is based on the calculation adopted by the NWS for their calculator.

To assist, I’ve written a Python script that will compute the WBGT estimate based on (1) the temperature in degrees Fahrenheit, (2) the relative humidity, and (3) the solar radiation in watts per square meter. You will read that it assumes a fairly low wind speed of 1 meter per second (about 2 mph). If you know the wind speed, convert it to m/s and plug it in as WIND_M_S to the compute_wbgt() function.

import math
from typing import Tuple

def compute_wbgt(temp_fahrenheit: float,
                 humidity_percent: float,
                 solar_radiation_W_m2: float) -> Tuple[float, float]:
    """
    Estimate outdoor (sun) Wet Bulb Globe Temperature (WBGT).

    Inputs
    ------
    temp_fahrenheit : Air (dry-bulb) temperature in °F
    humidity_percent: Relative humidity in %
    solar_radiation_W_m2 : Global solar radiation in W/m^2 (typical weather station)

    Returns
    -------
    (wbgt_c, wbgt_f) : WBGT in °C and °F

    Method
    ------
    1) Natural wet-bulb temperature T_wb via Stull (2011) approximation (°C).
       Reference: Stull, R. (2011), "Wet-Bulb Temperature from Relative Humidity and Air Temperature."
    2) Globe temperature T_g via simplified radiative balance for a 15 cm black globe (°C),
       using typical absorptivity/emissivity for matte black surfaces.
       Reference: Liljegren et al. (2008) modeling approach (simplified here).
    3) Outdoor WBGT = 0.7*T_wb + 0.2*T_g + 0.1*T_db  (all in °C).

    Notes
    -----
    - Assumes direct sun exposure and light wind (~1 m/s). With stronger winds,
      the true T_g tends to be a bit lower; with very low winds it can be higher.
    - For shaded/indoor conditions, a common alternative is: WBGT = 0.7*T_wb + 0.3*T_g (no T_db term).
    - This is an approximation. A calibrated WBGT meter is best for critical decisions.

    """

    # --- helpers ---
    def f_to_c(tf: float) -> float:
        return (tf - 32.0) * 5.0 / 9.0

    def c_to_f(tc: float) -> float:
        return tc * 9.0 / 5.0 + 32.0

    # Clamp inputs to reasonable ranges
    RH = max(1.0, min(100.0, float(humidity_percent)))
    S = max(0.0, float(solar_radiation_W_m2))
    Tdb_c = f_to_c(float(temp_fahrenheit))

    # --- 1) Natural wet-bulb temperature (Stull 2011, °C) ---
    # Empirical fit; accurate to ~±0.3 °C over common ranges.
    # T_wb = f(Tdb, RH)
    T = Tdb_c
    rh = RH
    Twb_c = (
        T * math.atan(0.151977 * (rh + 8.313659) ** 0.5)
        + math.atan(T + rh)
        - math.atan(rh - 1.676331)
        + 0.00391838 * rh ** 1.5 * math.atan(0.023101 * rh)
        - 4.686035
    )

    # --- 2) Globe temperature (simplified) ---
    # Radiative balance for a matte black globe.
    # Tg ≈ [ (absorbed solar term) / (4 ε σ) + (T_air_K)^4 ]^(1/4) - 273.15
    # Constants (typical)
    SIGMA = 5.670374419e-8       # Stefan–Boltzmann (W/m^2/K^4)
    EPS   = 0.95                 # emissivity of black globe
    ALPHA = 0.95                 # solar absorptivity
    D     = 0.15                 # globe diameter (m) – standard ~150 mm

    # A very simple treatment lumps geometry into an effective factor.
    # We also include a mild convective "dilution" assuming ~1 m/s wind.
    # If you know wind speed, you can refine this piece.
    WIND_M_S = 1.0
    convective_factor = 1.0 / (1.0 + 0.25 * max(0.0, WIND_M_S - 1.0))  # small reduction when wind >1 m/s

    Tair_K = Tdb_c + 273.15
    absorbed = (S * (1.0 - (1.0 - ALPHA)) * D) * convective_factor  # simplified effective absorption
    Tg_K = ((absorbed / (4.0 * EPS * SIGMA)) + Tair_K ** 4) ** 0.25
    Tg_c = Tg_K - 273.15

    # --- 3) Outdoor WBGT formula (°C) ---
    wbgt_c = 0.7 * Twb_c + 0.2 * Tg_c + 0.1 * Tdb_c
    wbgt_f = c_to_f(wbgt_c)

    return wbgt_c, wbgt_f


# Example:
if __name__ == "__main__":
    # 95°F air temp, 55% RH, 800 W/m^2 sun (bright midday) used here
    # Replace with your values.
    temp_fahrenheit = 95.0
    relative_humidity = 55.0
    solar_radiation_w_m2 = 800.0
    print(f"Using {temp_fahrenheit}°F air temp, {relative_humidity}% RH, {solar_radiation} W/m^2 sun ...")

    # calculate estimate for outdoor WBGT
    wbgt_c, wbgt_f = compute_wbgt(temp_fahrenheit, relative_humidity, solar_radiation_w_m2)
    print(f"WBGT ≈ {wbgt_c:.1f} °C  /  {wbgt_f:.1f} °F")

Make a Project Out of It

A computer science class could make a real contribution by building a simple web interface that wraps around the WBGT calculation function. The class could take the Python function above and connect it to a lightweight web framework. This would allow the function to be run on a school server or even a classroom laptop. Students could then design a basic HTML form where the athletic director (or any coach) enters three values (temperature, relative humidity, and solar radiation) from the school’s weather station. With a single button click, the form would send those values to the server, call the Python function, and return the calculated WBGT in both °C and °F.

On the front end, students could practice skills in HTML, CSS, and JavaScript by styling the page so it’s clear and easy to use. For example, the interface might highlight the WBGT result in green, yellow, orange, red, or black depending on which risk category it falls into. That kind of visual feedback would make the tool immediately useful to the athletic director, who wouldn’t need to memorize WBGT cutoffs. Students could also add input validation, so if the athletic director accidentally typed “950” instead of “95” the form would prompt for correction. These small touches make the difference between a prototype and something genuine.

I think the project could serve as a real practical learning experience. Students would see how software can directly support school safety and athletic programs, while applying skills they learn in class: handling user input, building a web form, processing data on the server, and returning a formatted result. The athletic department gains a user-friendly tool, while students gain a sense of purpose by writing code that protects their peers during hot weather practices. It’s the kind of partnership between athletics and academics that demonstrates the real-world value of computer science.