# What Does A Global Average 2 Degrees C Increase Mean With Respect To Upper Ocean Heat Content Change? Part I

In the media, there is considerable discussion as to the serious consequences to the environment and society, if the global average surface temperature increases to and beyond 2C from its pre-industrial value; for example, see Times Online on July 9 2009 where they wrote

“For the first time, America and the other seven richest economies agreed to the goal of keeping the world’s average temperature from rising more than 2C (3.6F).”

This temperature, however, is not one that can be directly measured as a single value. Rather, as discussed on page 21 in NRC (2005),  it is a derived temperature from the relationship between the global average radiative imbalance and is defined by the equation

dH/dt = f – T’/λ     (1)

where H is the heat content in Joules of the climate system, f is the radiative forcing at the top of the tropopause, T’ is the change in surface temperature in response to a change in heat content, and λ is the climate feedback parameter [which more accurately should be called the “temperature feedback parameter” since climate is much more than what is represented by this one equation]. Equation (1) above as a thermodynamic proxy for the thermodynamic state of the Earth system, as we wrote in our 2007 JGR paper.

The concept of a 2C threshold is based on equation (1).

However, how is T’ obtained? The approach is discussed in CCSP (2006) where land and ocean surface temperature anomalies are collected and the long term trend of the interpolated global average anomaly are used to obtain a value for T’. This involves ship and bouy measurements, and sea surface temperature observations from satellite, over the ocean, and surface weather stations over land. The land observations use the mean of the maximum and minimum temperatures to contruct the anomalies.

However, to compute dH/dt [which is the actual global warming], one needs to know the magnitude of the “temperature feedback parameter” and the radiative forcing in addition to  T’.

As documented in detail, this approach has major flaws which we reported in

Pielke Sr., R.A., C. Davey, D. Niyogi, S. Fall, J. Steinweg-Woods, K. Hubbard, X. Lin, M. Cai, Y.-K. Lim, H. Li, J. Nielsen-Gammon, K. Gallo, R. Hale, R. Mahmood, S. Foster, R.T. McNider, and P. Blanken, 2007: Unresolved issues with the assessment of multi-decadal global land surface temperature trends. J. Geophys. Res., 112, D24S08, doi:10.1029/2006JD008229.

In our paper we wrote

“This paper documents various unresolved issues in using surface temperature trends as a metric for assessing global and regional climate change. A series of examples ranging from errors caused by temperature measurements at a monitoring station to the undocumented biases in the regionally and globally averaged time series are provided. The issues are poorly understood or documented and relate to micrometeorological impacts due to warm bias in nighttime minimum temperatures, poor siting of the instrumentation, effect of winds as well as surface atmospheric water vapor content on temperature trends, the quantification of uncertainties in the homogenization of surface temperature data, and the influence of land use/land cover (LULC) change on surface temperature trends.”

We concluded that

” As reported by Pielke [2003], the assessment of climate heat system changes should be performed using the more robust metric of ocean heat content changes rather than surface temperature trends…….This paper presents reasons why the surface temperature is inadequate to determine changes in the heat content of the Earth’s climate system.”

The assessment of changes in heat content directly [H in equation (1)]  removes the need to compute a “temperature feedback parameter” (λ) and T’. The changes in H can be used to diagnose the radiative imbalance (the sum of the radiative forcings and feedbacks) as discussed in

Pielke Sr., R.A., 2003: Heat storage within the Earth system. Bull. Amer. Meteor. Soc., 84, 331-335.

Clearly. the use of T’ as a diagnostic climate metric for global warmng and cooling is a convuluted way to obtain the heating of the climate system (i.e. “dH/dt”). The quantity “dH/dt” is the proper metric of global heat change in the units of heat added or removed (which is in units of Joules). However, scientists and policymakers insist on using T’ as the metric to discuss global warming.

Thus, if there is an insistence to limit global warming to a 2C increase, what does this translate to in terms of an increase in Joules of heat content in the ocean?

I will discuss this in Part II.

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