Just Chill with the Wind Chill

One of the major drivers in electricity forecasting models is the weather. In its simplest form, temperature is typically transformed into Heating and Cooling Degree Days (HDD and CDD) to capture the positive relationship between load and weather when temperatures are high, and the negative relationship when temperatures are low:

Where:
    DB = Drybulb Temperature
    65 = Breakpoint above which CDDs are positive and non-zero
    55 = Breakpoint below which HDDs are positive and non-zero

Of course, these breakpoints may not be the breakpoints you would use for your data and there is also the potential for using multiple breakpoints. But we are keeping this brief for simplicity’s sake.

While DryBulb temperature is widely used, there are many alternatives:

1. Wet bulb temperature (WB)
2. Australian Apparent Temperature (AAT)
3. Temperature Humidity Index (THI)
4. Wind chill

The first three account for humidity to address its impact on the human body. Similarly, wind chill is designed to incorporate the impact of wind speed, which makes the temperature feel colder. 

Formally, wind chill is defined as follows:

Where:
    C = Wind chill
    T = Temperature (Deg F)
    V = Wind speed (or velocity in mph)

Here are a few things to keep in mind:

1. The equation is nonlinear insofar as velocity is raised to an exponent. 
2. The equation is interactive: temperature and wind speed are multiplied together.
3. Wind chill is only defined for temperatures below 50 degrees F and wind speeds above 3.0 mph.
4. The constants in the equation are different when using temperature in Celsius and wind speed in kilometers per hour.  You can read more here.

It is not too much of an extension to imagine using wind chill as the basis for the HDD variable:

The first scatter plot below depicts load vs. temperature, while the second scatter plot shows load vs. wind chill. Each point in the figures represents the 12:00 AM KW value and the corresponding temperature or wind chill from a particular day.

The horizontal scales are purposely identical to allow for easy comparison. The most salient feature is that the curve is extended further to the left with wind chill. From a modeling perspective, this is a useful attribute as it may clarify the relationship and provide additional information.

That seems great. Should we now jump in with both feet and commit to using wind chill as the basis for HDD variables in our models? 

Wait — there’s more!

Each of the following two figures shows hourly DryBulb temperature and wind chill for one week. The most striking feature is that the wind chill is particularly volatile. More to the point, the wind chill is spiky, while the Drybulb temperature in these examples is smooth. The obvious explanation for the volatility in the wind chill is the variability in the wind speed itself. 

Here is another thought to consider. Even if the historical observations of wind speed are smooth and well behaved, we are still using it in forecast models, which means we are dependent upon the wind speed forecast. Wind speed is infamously difficult to forecast well, especially as the forecast horizon extends further into the future (i.e., tomorrow is harder to forecast than today). This is not to denigrate the hard-working and skilled meteorologists who do this work; they are faced with the thankless task of forecasting a fundamentally chaotic series.

If you are using wind chill in hourly or sub-hourly models directly or indirectly as an HDD or Heating Degree Hour variable, your model and the resulting forecasts have the potential for volatility. This may manifest in interval-to-interval variability during a single forecast run. It may also manifest as instability from forecast iteration to forecast iteration, when comparing the forecast generated at 1:00 PM to the one generated at 2:00 PM, for instance.

These troubles may be ameliorated by using variables that aggregate across the day or groups of hours. Still, this is certainly something to consider when developing forecast models that incorporate wind chill as a driver variable. Most importantly, you should just chill.