Are land + sea averages meaningful ?

Introduction

Several of the major datasets that claim to represent “global average surface temperature” are directly or effectively averaging land air temperatures with sea surface temperatures. These are typically derived by weighting a global land average and global SST average according to the 30:70 land-sea geographical surface area ratio. However, there is very little consideration of whether such a result has any physical meaning and what, if anything, it means.

One thing it does not represent is a metric of global surface heat content. However, this is ( often implicitly ) one of the most common uses for such data.

Temperatures don’t add !

In technical terms, temperature is not an extensive quantity. That is illustrated by the fact that if you have one bucket of water at 30 degrees Celsius and you add another bucket of water at 30 degrees Celsius, you do not end up with water at 60 deg. C.

Energy is an extensive property: if you have a volume of water with a thermal energy of 4000 megajoules and you add a second similar volume you will have twice the thermal energy. The average energy per unit area can be compared to the radiative energy budget per unit area.

The ratio of temperature to thermal energy is not the same for all materials, it varies greatly depending on the physical properties of the substance. It also depends on the amount of a substance present, ie the mass. In physics and materials science, it is often most convenient to study “specific heat capacity”, that is the change in energy content per unit mass, per degree change in temperature. It is thus a property of each type of material, independent of any particular object.

In S.I. ( Système Internationale ) units this is measured in joule / kilogram / kelvin or J/kg/K . The kelvin is the same size as one degree C. and is interchangeable in this context. Some examples for common materials :

Material S.H.C.
Fresh Water 4.19
Sea Water ( 2 deg. C ) 3.93
Mercury 0.14
Dry Air 1.01
Stone 0.84
Dry Earth 1.26
Clay 0.92
Tar 1.47
Concrete 0.75

Table 1. Specific heat capacity of various materials in J/kg/K

So one could consider temperature change as a “proxy” for change in thermal energy for equivalent VOLUMES of the SAME material. In this context one could calculate an ‘average change in temperature’ for that medium and use it infer a change in thermal energy, which can be related to incoming and outgoing radiation, for example. If this is a surface temperature ( eg SST ) this implies assuming that the surface represents the temperature of a certain depth of water and that this representative depth remains about the same over regions that are being averaged, in order to respect the “volume” condition above. That is somewhat questionable for the ocean ‘mixed layer’ but may provide a crude energy proxy.

However, it is immediately clear that one cannot start adding or averaging air and SST, or land and sea temperatures. They are not compatible media. It is like asking what is the average of an apple and an orange: it has no physical meaning. It certainly can not be the basis of an energy budget calculation, since it is no longer a measure of the change in thermal energy.

As seen from the above figures: air, stone and earth will change temperature about four times as much as water in response to the same energy input.

No one would think of trying average temperature records in deg. Fahrenheit with records in deg. C, yet, for some reason, mixing land and sea data does not seem to raise any eyebrows.

Rate of change in global temperature datasets


Figure 1. Comparing the rate of change of temperature in land and sea datasets ( 30 month low-pass gaussian filter ).

Figure 1 shows the rate of change in two SST datasets and the BEST land dataset scaled down by a factor of two. They are all reasonably close with this scaling factor. The large peak in ICOADS data is a recognised sampling issue due to changes in shipping routes and sampling methods during and after WWII. The UK Met Office processed HadISST dataset aims to remove this bias.

The rate of change of near surface land air temperature as estimated in the Berkeley “BEST” dataset is very similar to the rate of change in the sea surface temperature record, except that it shows twice the rate of change.

Sea water has a specific heat capacity about 4 times that of rock. This means that rock will change in temperature four times more than water for the same change in thermal energy, for example from incoming solar radiation.

Since soil, in general, is a mix of fine particles of rock and organic material with a significant water content. The two temperatures records are consistent with the notion of considering land as ‘moist rock’. This also partly explains the much larger temperature swings in desert regions: the temperature of dry sand will change four times faster than ocean water and be twice as volatile as non-desert land regions.

This also underlines why is it inappropriate to average land and sea temperatures as is done in several recognised global temperature records such as HadCRUT4 ( a bastard mix of HadSST3 and CRUTem4 ) as well as GISS-LOTI and the new BEST land and sea averages.

It is a classic case of ‘apples and oranges’. If you take the average of an apple and an orange, the answer is a fruit salad. It is not a useful quantity for physics based calculations such as earth energy budget and the impact of a radiative “forcings”.

The difference in heat capacity will skew the data in favour of the land air temperatures which vary more rapidly and will thus give an erroneous basis for making energy based calculations. In addition land air temperatures are also compromised by urban heat island and other biases, so these will be effectively doubled before contaminating the global land + sea record.

In this sense the satellite data provide a more physically consistent global average because they are measuring a more consistent medium. If the aim is to do radiation based energy calculations it is probably more meaningful to use SST as the calorimeter.

Climate sensitivity is defined as the ∆rad , ∆T ratio, usually in the context of a linear approximation to the Planck feedback which is valid over relatively small deviations in the circa 300K temperature range. Other feedbacks are seen a perturbations that either add or subtract from the dominant Planck radiative feedback. All this and even the far more complex general circulation climate models are basically energy balance calculations. The conservation of energy is one of the defining axioms of physics. A fundamental test of any theory or equation is whether it respects the conservation of energy.

Horizontal heat transfer ensures that land temperature is constrained by ocean heat capacity: the thermal anchor of the climate system. It is well known that temperatures in coastal regions are stabilised by the proximity of sea/ocean and the centre of continents show greater extremes of diurnal and annual variation. However, land near-surface temperature remains more volatile than SST and analysis of climate models shows that they display greater climate sensitivity over land, and produce a different lapse rate.[1] IF that can be taken as being reliable.

In this context, temperature rise is the final result of all inputs, “forcings” and feedbacks many of which may be different over land. Heat capacity and available moisture both play an important role. Obviously these two factors are related. Using a non-thermodynamically relevant “average” temperature from two different ecologies with different climate sensitivities and lapse rates to produce an ‘average’ CS also seems open to bias.

Conclusion

Temperatures are not abstract statistics, their physical meaning needs to be considered when choosing how to process them. Using land + sea global average temperature datasets, biased by giving undue weight to the more volatile land-based temperatures, will produce physically incorrect results.

Most climate data are not just dimensionless numbers. Any processing should be considered in the context of the physical quantities that they represent. If temperature or temperature anomaly is being considered as an energy proxy for energy based calculations this should be explicitly stated and any biases that this may introduce should be discussed.

The physical significance, validity and limitations of “average” land + sea temperatures should be considered where they are used. This is rarely, if ever, done.

UPDATE

A typical equation for the definition of the settled change in temperature in response to a change in radiative ‘forcing’ F has the form:

∆F = λ * ∆T + ∆N ; where ∆N is the change in top-of-atmosphere radiation.

λ is the reciprocal of climate sensitivity ( CS ) . A more realistic model to asses the effect of differing responses would be :

∆F = α * λland * ∆Tland + (1 – α) * λsea * ∆Tsea + ∆N

Here alpha represents the geographic proportion of land area and is what is usually taken to weight the land and sea mean temperatures into a single “mean temperature”. Land temperatures will change by a greater magnitude due to the larger CS as indicated in the model runs in Geoffroy at al [1]

Due to it’s lesser heat capacity, land will equilibrate faster than the oceans. In this intermediate period there will be horizontal heat transfer from land to sea to redress the imbalance. This extra heat flux will somewhat increase the ocean temperature response thus increasing the effective transient climate sensitivity ( TCS ). The opposite will apply to land.

After hundreds of years, a dynamic equilibrium will establish where the horizontal flux balances the different responses of the two media. Land will heat more but is constrained by the ocean response.

The details of how this will level out is not trivial and will depend on arguments of heat capacity, lapse rate, moisture content and the mechanics of the horizontal heat transfer.

It is the λ * ∆T product ( a heat flux term ) that is being averaged, not temperature itself. That is as it should be to retain a physically meaningful calculation, so if temperatures are to be added ( or averaged ) they should be weighted not only by the land area but by the ratio λland / λsea. This respects the scientific requirement to be working in extensive properties, not an intensive one and restores the physical meaning to the resulting “global mean temperature”. It does not mean abandoning the GMST index, simply applying a correct weighting to account for the different media in a similar way to what is already done to account for land area.

According to the model runs this lies between 1.4 and 1.9 . Not dissimilar to the crude factor of 2 scaling of BEST land and SST shown in figure 1.

This implies that the classic 30/70% weighting of land and sea averages should probably be more like 15/85% or 20/80%.

DATA:

The data used in figure 1 can be obtained from KNMI climate explorer:
http://climexp.knmi.nl/start.cgi?id=someone@somewhere

The values of specific heat capacity shown in table 1 are provided by the Engineering Toolbox:
http://www.engineeringtoolbox.com/specific-heat-fluids-d_151.html

The 3-sigma gaussian filter is a standard filter available on most data processing packages. A description and graph of the frequency response is provided accompanied by a script to apply this filter at the following link:
https://climategrog.wordpress.com/2013/12/08/gaussian-low-pass-script/


Geoffroy et al 2015 : “Land-sea warming contrast: the role of the horizontal energy transport” [ paywalled ]
http://link.springer.com/article/10.1007/s00382-015-2552-y

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