In 2004, the following paper was published
Seidel, D. J., and J. R. Lanzante (2004), An assessment of three alternatives to linear trends for characterizing global atmospheric temperature changes, J. Geophys. Res., 109, D14108, doi:10.1029/2003JD004414.
The abstract reads [highlight added]
Historical changes in global atmospheric temperature are typically estimated using simple linear trends. This paper considers three alternative simple statistical models, each involving breakpoints (abrupt changes): a flat steps model, in which all changes occur abruptly; a piecewise linear model; and a sloped steps model, incorporating both abrupt changes and slopes during the periods between breakpoints. First- and second-order autoregressive models are used in combination with each of the above. Goodness of fit of the models is evaluated using the Schwarz Bayesian Information Criterion. These models are applied to the instrumental record of global monthly temperature anomalies at the surface and to the radiosonde and satellite records for the troposphere and stratosphere. The alternative models often provide a better fit to the observations than the simple linear model. Typically the two top-performing models have very close values of the Schwarz Bayesian Information Criterion. Usually the two models have the same basic form and the same net temperature change but with a different choice of autoregressive model. However, in some cases the best fits are from two different basic models, yielding different net temperature changes and suggesting different interpretations of the nature of those changes. For the surface data during 1900–2002 the sloped steps and piecewise linear models offer the best fits. Results for tropospheric data suggest that it is reasonable to consider most of the warming during 1958–2001 to have occurred at the time of the abrupt climate regime shift in 1977. Two fundamentally different, but equally valid, descriptions of stratospheric cooling were found: gradual linear change versus more abrupt ratcheting down of temperature concentrated in postvolcanic periods (∼2 years after eruption). Because models incorporating abrupt changes can be as explanatory as simple linear trends, we suggest consideration of these alternatives in climate change detection and attribution studies.
The significance of this paper seems to have been missed in the discussion of long term trends in climate metric trends, including the posts on Tamino by Grant Foster and Skeptical Science by dana1981. The assessment of shorter term abrupt changes was the intent of my post on trends in Arctic sea ice area.
As we wrote in
Rial, J., R.A. Pielke Sr., M. Beniston, M. Claussen, J. Canadell, P. Cox, H. Held, N. de Noblet-Ducoudre, R. Prinn, J. Reynolds, and J.D. Salas, 2004: Nonlinearities, feedbacks and critical thresholds within the Earth’s climate system. Climatic Change, 65, 11-38.
The Earth’s climate system is highly nonlinear: inputs and outputs are not proportional, change is often episodic and abrupt, rather than slow and gradual, and multiple equilibria are the norm.
I present below several other climate metrics which appear (using the eyecrometer) to have an abrupt [step] change in the trends. They also seem to be a long enough change such that they would be statistically significant, but will let others examine that. The Arctic sea area ice trend may be just a short deviation from a longer term decline, for example, or a significant abrupt step, but I now agree the time since a possible shift is too short to know which is correct.
For the fields with a longer record since an apparent shift:
1. The first field to show is the lower tropospheric temperature anomalies over time from the University of Alabama at Huntsville and from Remote Sensing Systems.
While a linear trend is plotted on the bottom figure, the eyecrometer indicates a change to a flatter trend (if there is any trend at all] after 1998. The lower tropospheric anomalies are clearly (even by eye) warmer than earlier in the record. But after about 12 years ago, there is no obvious slope.
2. The northern hemisphere anomaly plot from the Rutgers Snow Lab shows a similar abrupt change, but this time about 1988.
It does not require a quantitative statistical analysis to see that the snow cover anomalies are less than the values before 1988 but have been ~flat since then.
By month there are also abrupt appearing changes. For example, in Aprils from the Rutgers Snow Lab there is shift to mostly below average anomalies in 1988.
However, for Decembers from the Rutgers Snow Lab, there no such abrupt change, and indeed, there is less variation in the last two decades and as well as somewhat higher values.
3. The Antarctic sea ice from the Cryosphere Today seems to indicate a jump to higher values in about 1995 [although not as clearly as in the other figures above].
Each of this “steps” are seen visually but need quantitative statistical testing to see if they are real. [Note: the weblog Jonova also has a post on such “steps” in the data]
Climate Science: Roger Pielke Sr. 
