What are the main differences between the reference temperature and the average air temperature?

Question

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.

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:

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.