Introducing the Climate Thermometer

Many of us own a thermometer and check the outdoor temperature once or more per day. Wouldn’t it be interesting to know how that temperature compares to what is normal for your location, on that date, at that time of day?  The Climate Thermometer shows you the temperature right now, along with “what’s normal.” It has the average hourly temperature record for your location stored within it and tells you how the current temperature differs from that average. The Climate Thermometer’s  display includes:

• the outdoor temperature right now
• the normal temperature for this time/date/locale (based on a 50-year average)
• the difference between the two (called the “departure”)
• the average hourly departure since January 1 (or other set date)

 Perhaps you checked your Climate Thermometer at 8 a.m. on March 30, 2006 in Seattle, Washington. You might see a display that looks like this: 

 

These readings tell you that the current temperature of 42 º F is 2.5 degrees above the average for this time and location, and that the temperature at this location has been above average since the first of the year or for the last 2136 hours. Observing the changes in the Average Departure Window will give you a revealing look at how the climate is changing at your location. Maybe you are concerned about global warming, or maybe you doubt it is a reality. You can judge for yourself with the Climate Thermometer. Imagine being able to monitor temperature changes first hand, hour-by-hour, day-by-day, and be aware of what is happening with the climate where you live.

 A Climate Thermometer calibrated for your area will soon be available.  Let us know where you live and if you might be interested in obtaining one. If possible, also let us know the latitude, longitude and elevation of the location that your climate thermometer would be used, and whether it should be in Celsius or Fahrenheit units.

Derivation of mean hourly temperatures

A record of at least 50 years of hourly mean temperatures is required to calculate a statistically valid departure of the current temperature from an average or “normal” temperature   However, continuous records of hourly temperature observations for long historical periods are practically non-existent. Therefore, it is necessary to develop a technique that will simulate hourly means from observations of daily maximum and minimum temperature. Reliable records of daily maximum and minimum temperature observations have been collected in every country for many decades, with some continuous records exceeding 100 years.  Worldwide, the number of long-term weather stations collecting daily maximum and minimum temperatures likely exceeds 50,000.

Long-term weather-station temperature data are in the form of daily highs and lows, without note of the times of day they occurred. The Climate Thermometer makes instantaneous comparisons of the temperature it reads to the 1950-2005 base temperature, and therefore requires a continuous reference temperature at any time during the day. The first step in constructing the reference curve is to find the average high and average low for each day of the year from the 1950-2005 dataset. Next, although long-term temperature observations are usually just highs and lows, a few stations typically have shorter periods of hourly data. This limited record of temperature variations throughout each day yields typical times at which the highs and lows occur. Lows usually occur in early morning, and highs in the afternoon. The daily warming half-cycle between the low and the high lengthens in summer in response to longer daylight hours, and shortens in winter. The final step is to determine appropriate warming half-cycles to reach from lows to highs, and cooling half-cycles from highs to lows. The cooling half-cycle shape is approximately the first half of a cosine wave, as its value goes from 1 to -1 while the angle goes from 0 to 180 degrees. A warming half-cycle is approximately the negative cosine, running from -1 to +1, instead. Real warming and cooling half-cycles are a bit more complex, with slightly altered shapes. In the language of Fourier analysis, the real trends have components of shorter wavelengths, so instead of just cos(angle), they have components of cos(2 x angle), cos(3 x angle), and so on. The hourly data yield typical real warming and cooling cycles, which are decomposed in this way into their Fourier components, in what is known as a Fourier series. As is usually the case, a very good approximation to the real trends is obtained with the first few terms of this series. For an introduction to Fourier series, see  http://www.sosmath.com/fourier/fourier1/fourier1.html, which shows nicely the refined approximations with added terms. The Climate Thermometer’s reference temperature thus passes through the average highs and average lows for each day, as determined from the 1950-2005 data. They occur at typical times, as determined from the more limited hourly data. The warming half-cycles from lows to highs, or cooling half-cycles from highs to lows, are Fourier representations of typical cycles, again as revealed by the limited hourly dataset.

Comparison of observed and simulated hourly temperatures

 Comparisons of observed mean hourly temperatures with those simulated from the daily maximum and minimum are shown for January 1-7 (Figure 1a) and July 1-7 (Figure 1b).  At the SeaTac airport location, error of simulating hourly temperatures is highest during the winter months and lowest during the summer when there are few storms, fair weather is dominant and solar radiation is the main influence that determines temperature.

Figure 1a. Simulated and observed mean hourly temperatures at SeaTac Airport for January 1-8, averaged for the 1992-2005 period.

Figure 1b. Simulated and observed mean hourly temperatures at SeaTac Airport for July 1-8, averaged for the 1992-2005 period.

 The average hourly simulated and observed temperature for the 1992-2005 period (5110 days) is shown in Figure 1c.  The R-squared resulting from regressing these 24 pairs of average simulated versus observed hourly temperatures is 0.987 and the probable simulation error is 0.72 degrees F.  

Figure 1c. Simulated and observed mean hourly temperatures at SeaTac Airport averaged for the 1992-2005 period.

 Comparison of observed and simulated hourly temperatures at SeaTac for December 2005 is shown in Figure 2a, for January 2006 in Figure 2b, and for part of February 2006 in Figure 2c.  Observed daily mean temperatures from December 20 to mid-January were as high as 18 degrees F above the historical mean.

Figure 2a. Simulated and observed mean hourly temperatures at SeaTac Airport for December 2005. The hourly means are derived from the observed daily maximum and minimum temperatures averaged for the 1950-2005 period.

Figure 2b. Simulated and observed mean hourly temperatures at SeaTac Airport for January 2006. The hourly means are derived from the observed daily maximum and minimum temperatures averaged for the 1950-2005 period.

Figure 2c. Simulated and observed mean hourly temperatures at SeaTac Airport for February 2006. The hourly means are derived from the observed daily maximum and minimum temperatures averaged for the 1950-2005 period.

 On February 13, 2006, observed temperatures made a rapid transition from above to below normal in a few hours, marking the end of a long period of mostly positive departures that began in mid-December 2005.  Figure 3 shows both the hourly observed temperature and the departure from the 1950-2004 average on February 13. Similar graphs of observed temperatures and departures can be downloaded each day from the climate thermometer and available for publication in a daily newspaper.  

Figure 3. Observed hourly temperatures and departures at SeaTac Airport on February 13, 2006. The hourly departures are calculated from the observed temperatures subtracted from the hourly averages derived from daily maximum and minimum temperatures averaged for the 1950-2005 period.

Departure of SeaTac temperatures from a historical average

 The cumulative departure of SeaTac temperatures from the 1932-57 average is shown in Figure 4 for the 1958-2004 period along with annual average concentration of atmospheric carbon dioxide.  Note that both temperature departure and carbon dioxide are increasing exponentially during this 47-year period.  Although an unassailable cause and effect mechanism relating these positive temperature departures to increasing concentrations of carbon dioxide cannot be made, the similarity of the quadratic equations that define each time-series shown in Figure 4 is likely not a coincidence.

Figure 4.  The cumulative departure of SeaTac temperatures from the 1932-57 average for the 1958-2004 period along with the annual average concentration of atmospheric carbon dioxide.

Extrapolation of both curves shown in Figure 4 to the year 2100 implies a “business as usual” scenario throughout the 21^st century (Figure 5).  If current trends in both atmospheric carbon dioxide concentration and temperature departures are maintained,  the concentration will reach 665 PPM and cumulative departures 344 degrees F, which indicates an average annual temperature increase of 2.4 degrees F by 2100.

Figure 5.  The cumulative departure of SeaTac temperatures and atmospheric carbon dioxide extrapolated to the year 2100 by application of the quadratic equations shown in Figure 4.

 

Wendell Tangborn
HyMet, Inc
August 8, 2006
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