August 9, 2004

Non-linear Climate Change

Climate models generally depict global temperatures changes as smooth, nearly linear increases, in accordance with the relatively smooth increase in climate forcing agents. But real world observations show that climate change is not quite that well-behaved.

Prominently displayed at the top of page 4 of the “Summary for Policymakers” section of the Intergovernmental Panel on Climate Change’s (IPCC’s) 2001 Third Assessment Report is the following (misleading) statement:

Since the late 1950s (the period of adequate observations from weather balloons), the overall global temperature increases in the lowest 8 kilometers of the atmosphere and in surface temperatures have been similar at 0.1°C per decade.

The implication is clearly that the near-surface and lower atmospheric temperatures are behaving in a similar fashion. The IPCC sees this as an important concept because it is how climate models predict that things should be. If things didn’t act the way climate models indicate they should, then that would mean there was some fundamental problem with the models—not a concept that the IPCC warms up to.

Furthermore, climate models project not only that the surface and lower troposphere should be warming up in tandem, but also that the warm-up ought to be proceeding in a rather smooth, linear sort of way—after all, the buildup of climate forcing agents (e.g., greenhouse gases, aerosols) is proceeding rather smoothly.

A simple examination of global average annual surface temperatures since 1900 indicates that indeed, the planet has been warming (Figure 1). But has the warming actually been linear? A straight line fit through the data doesn’t do a great job of handling the cooling decades in the mid-20th century. Lower atmospheric temperatures as measured by weather balloons also show less than “model” behavior (Figure 2). Almost all the warming over the record occurred in a remarkable short-term jump in 1977. Once again, a linear fit doesn’t provide a very good guess at the underlying behavior of this temperature record.

IPCC Temperatures

Figure 1. Global annual average surface temperature departure (ºC), 1900-2002. Notice that there are three distinct periods of behavior.

Tropospheric Temperatures

Figure 2. Global annual average lower atmospheric temperature departure (ºC), 1958-2002. Notice that basically all the temperature rise occurred during a single jump from 1976 to 1977.

The basic problem here is that climatic reality is immune to climate model forecasts. Given these gradually changing inputs, climate models have a hard time reproducing temperature records like those shown in Figures 1 and 2.

A new paper that just appeared in the Journal of Geophysical Research by NOAA scientists Dian Seidel and John Lanzante decided to examine the nature of the observed temperature trends in a bit more detail. Specifically, in addition to the simple, linear fit, they tried to fit observed temperature patterns with statistical models that allow for discontinuities, or step changes (Figure 3). Their alternatives included “flat steps,” in which all of the temperature change is concentrated at the discontinuities, “piecewise linear,” in which different linear fits are used before and after break points, and “sloped steps,” or a combination of the flat steps and piecewise linear methods. To allow for a fair comparison between these different models, they used a statistic that chose the best fit while penalizing the more complex statistical models that used more parameters.

Model Fit

Figure 3. Example of the types of statistical models used by Seidel and Lanzante to best fit the observed temperature histories (source: Seidel and Lanzante, 2004)

Here is a summary of their results identifying the best model for each data set:

Surface temperature (1900-2002): a “sloped steps” model with break points in 1945 and 1977, and a net warming of 0.87°C (compared with a linear warming of 0.66°C).

Troposphere temperatures measured from weather balloons (1958-2001): a “sloped steps” solution, a net warming of 0.32°C, and an increase of 0.35°C at the 1977 breakpoint. In other words, virtually all of the warming took place around 1977.

MSU Satellite tropospheric temperatures (1979-2001): essentially a tie between a flat steps model with zero slope and no break points and a very weak linear trend of 0.053°C per decade with no break points.

Stratospheric temperatures (1979-2001): a sloped steps model with a net cooling of 0.88°C, a cooling rate that is 22% less than the linear model. The two major volcanic eruptions (El Chichon and Mt. Pinatubo) account for 94% of the total cooling. But a significant cooling trend is still evident if the eruption periods are removed from the data sets.

In summary, in a majority of cases examined, a simple linear model did not provide the best fit. Most of the tropospheric warming between 1958 and 2001 was concentrated at the time of the big “climate regime shift” around 1977. There is little evidence of warming in the satellite record of tropospheric temperatures.

According to the authors, “our best fit models yield more surface warming, less tropospheric warming, and generally less stratospheric cooling than simple linear fits.” Recall that tropospheric warming at the same rate as surface warming and stratospheric cooling is considered to be the human greenhouse gas imprint in the temperature record. So this means that the climate models’ proclivity for producing linear temperature trends, in general, overestimates the extent to which greenhouse gas increases have impacted the temperature record.

When a climate forcing factor, like greenhouse gas levels, increases gradually, it’s logical to look for a similar gradual increase in what is being forced—in this case, global temperatures. But it is also plausible that the climate can change abruptly in response to a gradual forcing. Could the “great climate shift” of 1977 been caused by greenhouse gases? We may never know the answer, but we do know that in 1977 sea-surface temperature patterns rapidly shifted in the Pacific Ocean. This feature, called the “Pacific Decadal Oscillation” or PDO, is linked fairly closely to surface temperatures. In 1977, the PDO index abruptly switched from its negative, cool phase to a positive, warm phase (Figure 4). As implied by the name, the PDO tends to switch from positive to negative with some regularity on the multi-decadal time scale. So a careful look back at the PDO and surface temperature record also indicates a shift in the late 1940s (a break point also identified by Seidel and Lanzante) and another possible break point in the 1920s. Since it’s highly unlikely that these early 20th century climate shifts were related to greenhouse gas levels, it appears that the PDO swings naturally from its warm and cool phases and thus climate “steps” without anthropogenic interference.


Figure 4. Annual values of the Pacific Decadal Oscillation (PDO) Index, 1900-2003. Notice the swings in the PDO occurring every two to three decades.

Most of the “evidence” for a major, human-induced warming in the 21st century is derived from climate models that have great difficulty accurately reproducing our planet’s temperature history. Until the climate models can reproduce the complexities that we observe, such as trends with varying slopes and step changes, then some key model physics must be wrong. So why, again, should we trust these model forecasts at all, or for that matter the IPCC authors who are pushing them?


Intergovernmental Panel on Climate Change, 2001. Climate Change 2001: The Scientific Basis. Cambridge University Press, Cambridge, UK. 881 pp.

Seidel, D.J., Lanzante, J.R., 2004. An assessment of three alternatives to linear trends for characterizing global atmospheric temperature changes. Journal of Geophysical Research, 109, D14108.

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