My View Of The Terminolgy “Heating In The Pipeline”

Len Ornstein presented a thoughtful guest post yesterday on ocean heat content (see), in which he and I disagree on the meaning of the phrase “heating in the pipeline. Len provided an effective succinct summary of this issue in his post.

The basic issue is whether the term “heating in the pipeline” refers to heat that is sequestered for a period of time deeper in the ocean only to reappear later in the atmosphere, or if it refers to a continuing assumed radiative imbalance until the atmosphere warms.

I do not conclude that the first perspective is an error in the physics, but it is not, in my view, what is meant by the terminology “heat in the pipeline”.

To illustrate my perspective, lets write the Earth’s energy budget in two ways:

1.   The National Research Council report[http://www.nap.edu/openbook/0309095069/html/] on pages 19 and 21 has the text

“According to the radiative-convective equilibrium concept, the equation for determining global average surface temperature of the planet is

dH/dt = f – T´/λ  (1-1)

where

 

is the heat content of the land-ocean-atmosphere system with ρ the density, C_p the specific heat, T the temperature, and z_b the depth to which the heating penetrates. Equation 1-1 describes the change in the heat content where f is the radiative forcing at the tropopause, T′ is the change in surface temperature in response to a change in heat content, and λ is the climate feedback parameter (Schneider and Dickinson, 1974), also known as the climate sensitivity parameter  [which more accurately should be called the “temperature feedback parameter”], which denotes the rate at which the climate system returns the added forcing to space as infrared radiation or as reflected solar radiation (by changes in clouds, ice and snow, etc.). In essence, λ accounts for how feedbacks modify the surface temperature response to the forcing.”. 

In this context, the “heating in the pipeline”  is that, with a continued radiative forcing [e.g. the o.85 Watts per meter squared that Hansen et al concluded was the imbalance at the end of the 1990s],  T′ continues to increase until the imbalance ends. It is this added value of T′ into the future that is referred to (in my view) as “heating in the pipeline”.

2. We can also write the energy budget of the climate system, from Pielke (2003), using some of the notation from the NRC report,  as

∫∫R dAdt = f = ∫∫Q[atmos]dVdt +  ∫∫Q [ocean]dVdt +  other reservoirs of heat 

where R is the  mean nonequilibrium radiative forcing, f is the resulting global average radiative forcing at the tropopause (as in #1), A is the area of the earth, Q is the heating rate, V[atmos] is the volume of the atmosphere, and V[ocean] is the volume of the ocean. By accurately measuring Q [ocean], a good estimate of f can be achieved over the time period of the integration (e.g. see). Len and I disagree on the ability to accurately sample Q [ocean] but  Josh Willis (e.g. see)  and others (see) have concluded the data is quite accurate for this purpose, particularly since 2005.

With this viewpoint, there is no heat in the pipeline as all of the Joules in the atmosphere, oceans and other reservoirs of the climate system are accounted for.

Len is correct, however, that if heat is not sampled deeper in the ocean, but the upper ocean is used to diagnose f (as proposed in Pielke, 2003), the value of f would be incorrect (and too small).  But unless observations document that significant heat is accumulating deeper in the ocean, there are no major amounts of unaccounted for Joules in the climate system. There is therefore no “unrealized heat” and, thus, no “heating in the pipeline”.

 However, if Len is correct and there is significant heat at depth in the oceans,  this heat would need to later reemerge into the atmosphere (having first passed through the upper ocean which is, however, well sampled).  But this heat, if it is even present, may not reemerge for centuries, and, if it did, is likely to be a slow process as differential advection by currents and turbulent diffusion would smear heat over large volumes. 

The phrase “heating in the pipeline”, therefore,  does not accurately capture this concept.  However, Len raises an important issue as to whether the deeper ocean’s heat content is well sampled or not. This is a challenge to the ocean science community.