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The minimal amount of weather data is not clearly listed. You will find clues in this section of the Auxiliary Programs Document. This table indicates what variables are used by EnergyPlus.

The more original data you have, the better, but the weather processor can create some data based on other available data (e.g. solar), or EnergyPlus will simply not take into account some data if it's missing (e.g. rain and snow). As you read further down this documentation, there are discussions of what the weather processor will do with alternate or missing data. For example, EnergyPlus reads dewpoint and RH (why both? not sure) but you could provide humidity ratio or wet-bulb to the weather processor and it will convert to DP and RH.

I will make an attempt here to make a list of what I think is the minimal set, but I can't say that I have actually tried this.

Required Data

1. Dry-bulb temperature
2. Some measure of humidity - dew-point temperature, relative humidity, humidity ratio, or wet-bulb temperature
3. Solar data - separate direct and diffuse data is best (direct normal or direct horizontal plus diffuse horizontal or global horizontal), next best is just global horizontal, or if you have none the weather processor will create it if you have sky cover data (this is the least accurate)
4. Wind speed and direction (but you could get away without direction if not using a directional convection model or airflownetwork)

Recommended Data

1. Horizontal Infrared Radiation Intensity or Opaque Sky Cover
2. Present Weather Observation with Present Weather Codes (useful to determine if it's raining)
3. Snow Depth (used to determine if snow is on the ground, used for ground reflected solar)