What is the maximum acceptable air temperature error in meteorology and climate monitoring?

Why is air temperature accuracy important?

The below table demonstrates how error (uncertainty in technical terms) in air temperature measurement translates into error in energy of the air in our atmosphere as used in thunderstorm and rain prediction. Energy in the atmosphere is the dominant force driving natural disasters like tornadoes, hurricanes, cyclones, typhoons, torrential downpours and extremes of air tempearures which have been prevalent in the last few years due to global warming.

Natural disasters feed on energy of air

Natural disasters are atmospheric moisture phenomenon that feed on the energy of warm and moist air masses. The interaction of air masses at different temperatures and moisture levels leads to strong gradients in energy in the atmosphere. Air masses mix to naturally equalize this energy difference and in the process create severe weather that is highly localized at their intersection. The bigger the energy difference, the more localized is the energy exchange and leads to very severe winds and rain on the scale of summer storms, tornadoes, twisters and winter blizzards.

If the air masses are large enough and the energy difference is also large, then hurricanes, typhoons, and cyclones form. This same effect also happens in winter where winter blizzards feed on the energy of moist air coming off large bodies of water and meet with cold dry air over large land masses.

Air temperature sensor can only be as accurate as the air conditions inside a solar radiation shield.
— Jan Barani, CTO of BARANI DESIGN Technologies

What dominates air temperature measurement error?

Since air temperature sensor can only measure the air conditions inside a solar radiation shield, the primary source or atmospheric air temperature measurement error is the radiation shield and only then can the air temperature sensor error be considered. Thus having a high-precision air temperature sensor only makes sense if the solar radiation shield on your weather station is in the same accuracy class as your sensor.

Error in Atmospheric Energy due to Air Temperature Sensor Error
  ±0.2 °C Sensor
Measurement Error
±0.5 °C Sensor
Measurement Error
±1 °C Sensor
Measurement Error
±2 °C Sensor
Measurement Error
±3 °C Sensor
Measurement Error
ATMOSPHERIC AIR TEMPERATURE Error kJ/kg Error % Error kJ/kg Error % Error kJ/kg Error % Error kJ/kg Error % Error kJ/kg Error %
50 °C 5.32 kJ/kg 2.0% 13.29 kJ/kg 5.1% 26.60 kJ/kg 11% 53.28 kJ/kg 22% 80.13 kJ/kg 35%
40 °C 3.22 kJ/kg 2.0% 8.06 kJ/kg 5.1% 16.12 kJ/kg 10% 32.29 kJ/kg 22% 48.55 kJ/kg 35%
30 °C 2.03 kJ/kg 2.1% 5.08 kJ/kg 5.4% 10.15 kJ/kg 11% 20.31 kJ/kg 23% 30.54 kJ/kg 37%
20 °C 1.33 kJ/kg 2.4% 3.32 kJ/kg 6.1% 6.63 kJ/kg 13% 13.28 kJ/kg 27% 19.95 kJ/kg 43%
10 °C 0.91 kJ/kg 3.2% 2.28 kJ/kg 8.3% 4.56 kJ/kg 17% 9.12 kJ/kg 38% 13.71 kJ/kg 62%
0 °C 0.69 kJ/kg 7.9% 1.73 kJ/kg 21.0% 3.44 kJ/kg 47% 6.87 kJ/kg 121% 10.31 kJ/kg 254%
-10 °C 0.54 kJ/kg -8.3% 1.35 kJ/kg -19.6% 2.70 kJ/kg -36% 5.40 kJ/kg -61% 8.12 kJ/kg -80%
-20 °C 0.46 kJ/kg -2.4% 1.15 kJ/kg -6.0% 2.31 kJ/kg -12% 4.61 kJ/kg -22% 6.92 kJ/kg -31%
-30 °C 0.43 kJ/kg -1.4% 1.07 kJ/kg -3.5% 2.13 kJ/kg -7% 4.25 kJ/kg -13% 6.38 kJ/kg -19%
-40 °C 0.41 kJ/kg -1.0% 1.02 kJ/kg -2.5% 2.06 kJ/kg -5% 4.92 kJ/kg -11% 6.16 kJ/kg -14%
-50 °C 0.41 kJ/kg -0.8% 1.01 kJ/kg -2.0% 2.03 kJ/kg -4% 4.05 kJ/kg -8% 6.08 kJ/kg -11%

Error in kJ/kg of air is the difference between the negative and positive sensor measurement errors given as ± values around the mean Atmospheric Air temperature of the 1st column.

Air Enthalpy (Energy) values in the table are calculated at 95% RH Relative Humidity since natural disasters are atmospheric moisture phenomenon and feed on the energy of warm moist air masses. Winter natural disasters also feed on the energy of moist air.

Zero degrees Celsius of dry air was used as the reference point for Zero Specific Enthalpy in the above table. This leads to positive numbers of specific enthalpy of 95% RH moist air at zero degrees Celsius.

Data was calculated using the free version of a Psychrometric Calculator from https://www.psychrometric-calculator.com/humidairweb.aspx and https://www.remak.eu/en/calculation-moist-air-properties