Thongchai Thailand

Seasonal and Diurnal Cycles

Posted on: April 17, 2019

In the climate change debate, critics of AGW often present a chart of absolute temperature measurements that appear to contain no visible evidence of a long term trend as shown in the chart below. The chart is used to imply that the warming trend claimed by AGW theorists is fake and misleading because it is not seen in the data.



This line of reasoning as a challenge to AGW theory contains a fatal statistical flaw.

Temperature data taken at weather stations contain a diurnal cycle, a seasonal cycle, and random natural variations. Along with these they may also contain a long term trend over a period of many years. Typically, the diurnal and seasonal cycles represent more than 80-90% of the total variance in the actual temperature measurements. The remaining 10-20% or so consists mostly of unexplained random variations.

In cases where a statistically significant trend is found with OLS linear regression, no more than a small portion of the variance, around 3%-5% or so, can be ascribed to a long term warming or cooling trend. It is for these reasons that in the study of long term temperature trends over many decades, regression coefficients for long term trends are relatively a very weak feature of the time series that must be teased out of the data net of the greater diurnal, seasonal, and random variations.

The study of long term temperature trends must therefore be carried out after the diurnal cycle and the seasonal cycle are removed from the data. The diurnal cycle may be removed by taking daily means or by studying either the daily maximum or daily minimum temperatures as shown in a related post [LINK] . The seasonal cycle can be removed by studying one calendar month at a time [LINK] or by computing a de-seasonalized annual mean either with dummy variables to represent calendar months; or by subtracting temperatures in a reference period to compute what is referred to as “temperature anomalies”. A related post presents a critical evaluation of the temperature anomaly procedure [LINK] .


It is only in the absence of the much larger diurnal and seasonal cycles that a trend, if any, can become visible to the naked eye as shown in the chart below. Although the trend represents a small portion of the total variance, its persistence over a long period of many years can have significant effects as seen in the Little Ice Age (LIA) described in a related post [LINK] . The LIA was a period of great hardship for Europeans. Canals and rivers were frozen, growth of sea ice around Iceland closed down harbors and shipping, hailstorms and snowstorms were heavy and frequent, and road and water transport was made difficult or impossible. Agricultural failure and consequent starvation and death devastated Europe. The Scandinavian colonies in Greenland starved to death and disappeared. And yet it was the creation of a long term cooling trend that explained about 3% of the total variance and that could not have been visible to the naked eye in a plot of temperature measurements that contained the diurnal and seasonal cycles.














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