Last week when I was dealing with the North American Multi-Model Ensemble (NMME) seasonal forecasting system, a variable named “tref,” or Reference Temperature, caught my attention.
I read some articles that used reference temperature but couldn’t understand this variable. My main question is, what is the definition of the reference temperature? And what is the difference between it and average air temperature?
Thank you all.

  • 1
    $\begingroup$ Thank you @gansub $\endgroup$
    – Behzad
    Nov 10, 2022 at 2:41

1 Answer 1


I have the same question and found a satisfying answer recently.

The reference state, including wind, temperature and pressure, is a dynamically-steady state to the equation of motion of the atmosphere. It is a steady-state solution only when the flow is adiabatic and inviscid (no external forcings). More specifically, the reference state is:

  • zonally uniform,
  • vertically in hydrostatic balance, and
  • meridionally in gradient-wind balance

everywhere in the domain.

Although scientists knew there exists such state, only Nakamura and Zhu (2010) and Methven and Berrisford (2015) provided numerical methods to calculate such reference state, given any instantaneous atmospheric state. This is equivalent to a conservative rearrangement, schematically shown below:

conservative rearrangement

This rearrangement conserve mass between any two isentrops and circulation along each PV contour, which can be called conservative zonalization.

Before these numerical algorithms were proposed, most people use Eulerian average of atmospheric state, like long-term time mean or zonal mean, to give a diffuse estimate of this reference state. As a result, the jet and temperature front in the averaged state are usually weaker than those in the reference state.

Another reference state, motionless and horizontally flat pressure surface in hydrostatic balance, is also a steady-state solution to the (adiabatic and inviscid) equation of motion. However, it is a trivial resting state that does not have circulation at all. Therefore, we may not be interested in this resting reference state.

  • $\begingroup$ You suggest this is what the NMME plots then? Any insight on why it would be an output (something to do with how things are setup in the model? Or it has a common use?) Or maybe there are multiple definitions for the term (yuck) (gansub's comment suggesting it is a historic time average seems reasonable, what I might have guessed) $\endgroup$ Nov 13, 2022 at 6:26
  • $\begingroup$ @JeopardyTempest This is not a NMME plots. Just a schematic plot showing how to get the reference state (right) corresponding to an instantaneous eddying atmospheric state (left). $\endgroup$
    – MiniUFO
    Nov 13, 2022 at 12:31
  • $\begingroup$ right, sorry, wasn't suggesting your plot was from NMME... but wondering if the reference temperature in it that Behzad is asking about is different from what you suggest $\endgroup$ Nov 19, 2022 at 4:53

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