The 1690's: a cold decade in Scotland

The 1690's: a cold decade in Scotland

The EOS article How the Cold Climate Shaped Scotland’s Political Climate presents the results of tree ring data analysis supporting historic accounts of anomalously cold weather during the 1690s.

For some context, I present some analysis of the Central England temperature data that consists of daily temperatures measured from 1659 until the present. The record reveals some unique aspects of the 1690s cold snap. The EOS article suggests this cold spell led to Scotland's failed attempt to colonize the Darien region of Panama and to its union with England. The article notes "The colony’s failure (to colonize the Darien region) left Scotland in an even worse economic situation and helped trigger the Acts of Union with England. The average annual temperatures (Figure 1) reveal this anomalous period of low temperatures in the late 1600s.

Figure 1: Smoothed July (red), average annual (green) and January (blue) temperature comparison

A magnified view of the average July and January temperatures (Figure 2) reveals that the last of the 1600s is unusual in that temperatures in both the summer and winter dropped during the 1690s. The EOS tree ring data reveals narrow growth rings during the 1690s. The temperature data reveals this is consistent with the colder summer temperatures. I don't have temperatures for Scotland during this period, but we can imagine that they may have been cooler than in central England to the south.

Figure 2: Comparison of smoothed July temperatures (red) and January temperatures (blue).

A plot of the residual July and January temperatures together (Figure3) emphasizes some of these differences through time. Note that the juxtaposition of colder summers and winters is unique to this time.

Figure 3: Residual smoothed temperatures for January (blue),July (pink) and average annual (green)

The paper "Complexity in crisis: The volcanic cold pulse of the 1690s and the consequences of Scotland's failure to cope" shows temperature reconstruction of July to August temperatures from 1200 to present for Scotland (Figure 4).

Figure 4: July to August temperature reconstruction. The blue dots note the colder summers. The yellow line is a 20 year low pass filtered version of temperature variations.

I would suggest that it is this combination of colder winters and summers that led to the hardships in Scotland during the late 1690s.

Thwaites - An unstable ice flow in the West Antarctic

Thwaites is an unstable ice flow in the West Antarctic along the Amundsen Sea. The melting of this large glacier is hidden, occurring at its base as shown in this figure from the EOS article that describes the US-UK initiative called the International Thwaites Glacier Collaboration (ITGC). (see - https://eos.org/features/diagnosing-thwaites?utm_source=eos&utm_medium=email&utm_campaign=EosBuzz020720)

Glacial undercutting is believed to be the result of warmer surface waters and to the global scale circumpolar deepwater current melting the underside of the glacier along the continental shelf. As the underside melts the glacier load becomes lighter and becomes less strongly anchored to the underlying bedrock. Additional melting and undercutting occurs making larger sections of the glacier unstable and prone to collapse. Retreat of the grounding zone can hasten the calving rate. Melting of the Thwaites could raise global seal level by 1/2 meter.

Glacial retreat: southern Alaska, Greenland and Norway

Abstract

The retreats of glaciers in glacial fields located at approximately 60^o north latitude along the margins of the major north Pacific and north Atlantic gyres are not clearly related to increased atmospheric CO₂ concentrations. The temporal records of glacial retreat are not long enough to draw a more certain conclusion. Temperature variations show variable periods of rise and fall over the span of observation with persistent temperature rise during the 150 year period of this study. In Alaska during this period, the temperature rose by about 1.6^oC; in Greenland, by 2 ^oC; and in Norway, by 1.62 ^oC.  Increased temperatures are significant and coincide with rising atmospheric CO₂ concentrations, but the temporal records of glacial retreat are too variable and not long enough to draw direct correlation. Solar intensity variations, historical radiative forcing and greenhouse gas totals increase over the span of observations, but again without any obvious correlation to the complex records of glacial retreat. In general a positive feedback between glacial retreat and increases in atmospheric CO₂ is very likely during the interval to time examined in this study: glacial retreat, atmospheric CO₂ and other greenhouse gas concentrations and radiative forcing were all on the rise during the period of observation.

Data

Glacial retreat data

I selected glacier fields along the northern border of the major Pacific and Atlantic Ocean gyres. The Alaskan area is located near the northeast margin of the Kuroshiro gyre, the Greenland field, near the northwest margin of the Gulf Stream (north Atlantic gyre) and, the Norwegian field near the northeast margin of the Gulf Stream. All glaciers are located at roughly the same latitude of ~60^oN. I obtained glacial retreat data from University of Chicago time series browser at http://climatemodels.uchicago.edu/timeseries/. I selected 14 glaciers near the Alaskan Kenai Peninsula (Figure 1A), 11 from southern Greenland (Figure 1B), and 13 from southern Norway (Figure 1C). Due to space limitations of the project, data are displayed in relatively small areas. Please adjust display size using your pdf display controls to see details you may wish to explore in detail.

Temperature data

I also compared glacial retreat patterns to recorded temperature variations obtained at several meteorological stations near each glacier field. The URL for temperature time series data from the Alaskan area is http://climatemodels.uchicago.edu/timeseries/#GuwBBKBBBBDGB. The URL for the Greenland meteorological station temperature time series is http://climatemodels.uchicago.edu/timeseries/#HvlBCF. The URL for meteorological stations used for the Norwegian area is http://climatemodels.uchicago.edu/timeseries/#JtuBFBBBCBD.

Forcing mechanisms

The fluxes associated with additional forcing mechanisms including solar intensity, historical radiative forcing and greenhouse gasses (total) are also considered. You can find these data in the Forcings/Records tab of http://climatemodels.uchicago.edu/timeseries/

Figure 1: A, B and C show the glacier retreat records from Alaska, Greenland and Norway, respectively. Locations of glaciers examined in this study are contained within the red circled areas of Alaska, Greenland and Norway D, E and F are plots of residual retreat from Alaska, Greenland and Norway, respectively.

Glacial Retreat Data

Glacial retreat in Alaska (Figure 1A) showed the most dramatic variations with retreats extending from around a kilometer to nearly 25kms. Glacial retreats in Greenland (Figure 1B) had the smallest range, varying from a couple hundred meters to 2.25kms. In Norway (Figure 1C), glacial retreat ranged from about 1/2km to 4.5kms. In Greenland and Norway, there is persistent retreat through the period of observation extending from 1850 to 2010. In Alaska, pronounced retreat begins roughly between 1900 and 1940; in Greenland, increased rates of retreat occur between 1940 and 1970; in Norway, initiation of glacial retreat is quite variable, however the retreat of some of the glaciers accelerate between 1940-1970. In general, glacial retreat appears to occur throughout the observation period in Norway. Generally in the early 1900s there is accelerated retreat in Alaska and Greenland. I calculated residuals (Figure 1D-1F) by subtracting a smoothed record of retreat obtained using an 11-point moving average from the raw retreat data. The residuals highlight periods of accelerated retreat. The residual signature of increased retreat is a peak-trough response in the residual. The trough identifies acceleration away from the average. There is considerable variability in times of accelerated retreat within each area as well as among areas (Figure 1D-1F). Alaskan glaciers show some significant acceleration around 1930, 1950 and in the 80s.  Greenland glacial retreat is relatively stable 1940 with notable periods of acceleration in 1960, early 70s and early 80s (Figure 1E). In Norway, accelerated retreat is spread throughout the period of observation (roughly 1880 to 2013) (Figure 1F). Any notion of similarity in the records of glacial retreat in the northeast corners of the two ocean gyres occupied by Alaska and Norway is ruled out immediately by inspection. The north Atlantic glacial fields have some general similarity in that the glaciers in these areas generally collapsed during the 1850-2017 observation period.

The relationship between increased concentration of atmospheric CO2 and glacial retreat?

In this analysis, we examine glacier retreat data for some similarities in the timing of retreat. We do this for glaciers bordering the north Atlantic in Greenland and Norway and between Alaska and Norway. The Alaskan and Norwegian glacier fields are located east of the major Pacific and Atlantic gyres, respectively. I inquire into whether there might be some similarity between Alaska and Norway retreat patterns. Preliminary analysis provide no support for this. 

I also look for any relationship between episodes of glacial retreat and variations in atmospheric CO₂ concentrations. I plotted CO₂ data over the past 2000 years (Figure 2A) and computed residuals (Figure 2B).  You can obtain these and other CO₂ data at https://www.co2.earth/historical-co2-datasets from the Institute for Atmospheric and Climate Studies in Zurich, Switzerland. CO₂ concentrations rise rapidly in the late 1800s. The residual concentrations show only minor excursions prior to 1800. From 1800 to present the residuals increase in magnitude with pronounced increase through the 1900s.

I did not find a clear relationship between glacial retreat and atmospheric CO2 concentrations. Glacial retreat during the 1850 to 2010 time period may be associated with the increased concentration of atmospheric CO₂ during that same period, but the lack of data preceding 1850 make this speculative. I examine this issue further in the following analysis.

Figure 2: Atmospheric CO₂ concentrations A) from 0 to 2014 and B) from 1880 to 2014.

Temperature variations: Alaska, Greenland and Norway

Alaska

Temperature records from 9 stations in the area surrounding the glaciers were selected to obtain a representative temperature trends (Figure 3). The temperature records are generally continuous following 1950. Some of the records preceding 1950 tend to be incomplete. The stations links can be loaded on the climate models timeseries site using the URL http://climatemodels.uchicago.edu/timeseries/#GuwBBKBBBBDGB

Figure 3: A) Stations in the vicinity of glaciers (small blue dots) examined in the Alaska are located on the Kenai Peninsula. B) Temperature variations of 9 stations in the vicinity of Alaskan glaciers examined in this study along with trendlines fit for over the 1917 to 2013 time frame.

Average decadal temperature trends are positive and vary between 0.04 and 0.36^oC. Some normalized trends are shown in Figure 4. Note that in the region there is a general rise in temperature between about 1918 and 1945, followed by a sudden drop of about 1.95 degrees from 1945-1950. Between 1950 and 1975 the temperature drop is roughly -0.18^oC. The decadal trends are at 0.51 and -0.0.7^oC, respectively. There are different ways to parse the data, but this rise and fall does coincide roughly with the episode of major retreat observed in the glaciers of this area during that time period Figure 1(A and D).

Figure 4: Normalized temperature changes for the Alaskan glaciers in the Kenai Peninsula with temperature trends between 1918-1945 and 1940-1975 identified and those from 1950 to 2016 shown individually.

It is difficult to fit a single line to the data over the entire duration of measurements. While there is an average decadal rise over the last 100 years of 0.16^oC/decade it is not uniform. The temperature trend between 1975 and 2006 is 0.36^oC/decade. However, if we start just 5 years earlier we get a rise of is 0.5^oC/decade. These linear fits must be made with an eye on parts of the data especially if comparisons are to be made.

The combined curve provides a good summary (Figure 5), but we don’t get a good sense for some of the discontinuity and limits in coverage observed in individual stations, particularly for more recent records (2006-2016). Compare figures 4 and 5. 

Figure 5: Composite temperature variations in the Kenai Peninsula area of Alaska.

The record of glacial retreat in the Kenai Peninsula region of Alaska reveals remarkably extensive retreat between 1900 and 1960 for some glaciers in the area. These retreats occur during that period where there was a rise in temperature of about 1^oC (1910-1945) followed by a drop of about 1^oC from 1940-1975. While variations are not uniformly increasing from the early 1900s into the 2000s, there is an average rise of ~1.6^oC through the 100year plus span of temperature measurements in the area.

Greenland

I undertook similar analysis of Greenland meteorological stations. Meteorological stations in the area are not too numerous (Figure 6). The URL for these stations is http://climatemodels.uchicago.edu/timeseries/#HvlBCF. The temperature changes in this area extend almost continuously from 1866 to 2016. The decadal temperature change over the 1.5 century time frame is 0.15^oC/decade with total change of 2^oC. The records of retreat shown in Figure 1B reveal a period of accelerated retreat during the early-mid 1900s. The decadal temperature increase during this 50 year period is 0.39 ^oC/decade and may begin a couple decades earlier. This provides a relatively clear association between prominent episodes of glacial retreat in the region with temperature increase.

Figure 6: A) Meteorological stations in southern Greenland near the glacier field examined in this study (circled blue dots); B) temperature records in the area with best fit lines plotted for the 1900-1950 time period.

Norway

In Norway, stations near glaciers used in this analysis can be located and plotted using the URL http://climatemodels.uchicago.edu/timeseries/#JtuBFBBBCBD. The blue dots in Figure 7A indicate glacier locations. Various colored larger dots indicate the locations of meteorological stations used in the study.Temperature trends over this 167-year period are all positive and vary between 0.08 and 0.18^oC/decade. There is a slight drop of temperature in the 1960s. On average from 1948 to 1965 there was a -0.22^oC/decade drop in temperature. In the following decade there was a 1.63^oC increase in temperature. During this same period (1950 to 1975) we saw an increase in the retreat rates for several of the glaciers in this area (Figure1C and 1F).  Overall, the Norwegian glacier set has been in continuous retreat over the last 167 years of recorded extents. On average, temperatures rose steadily during this period at about 0.12^oC/decade, while the increase along the best fit line totals about 1.62^oC. There appears to be a general association of glacial retreat with overall temperature rise.

Figure 7: Data from Norway include A) meteorological stations surrounding the glaciers used in the analysis and B) composite temperature variations measured at the meteorological stations in the area.

CO₂ Residuals: another approach

Figure 8: The power law fit to northern hemisphere CO₂ concentrations (blue line) is shown by the black line. The residual (CO₂ concentrations minus residual) is show in green.

My approach to residual calculation in Figure 1 employed removal of smoothed retreat from the raw records. I computed the smoothed version using a centered 11-point moving average. The smoothing was decadal and the residual reveals short-term variations from the underlying trend. As a follow up, I took another approach to fitting the data and calculating a residual. I started the CO₂ time series at 1800 (year 0) and calculated a power law fit to the CO₂ concentrations (Figure 8).

The power law fit yields a good representation of the overall exponential rise in CO₂ concentrations observed during the last 200 years. The residuals relative to this exponential fit show a period of increased CO₂ concentration spanning about a 75 year period from 1875 to 1950. The residual indicates that concentrations rose more rapidly introducing an additional 2-5 ppm CO₂ annually into the atmosphere. This gives rise to the question of whether this anomalous increase in the rate of CO₂ rise could initiate more extensive glacial retreat.

Greenhouse gasses, radiative forcing and solar intensity

The episodes of glacial retreat shown in Figure 1A-1C generally pick up in the last half of the 20^th century. This is also generally associated with increased forcing (Figure 9). Combined forcing steps up

Figure 9: Display of fluxes associated with solar intensity, historical radiative forcing and greenhouse gas totals. The sum of the forcing mechanisms is also plotted for reference.

Conclusions

I analyzed records of glacial retreat for glaciers in glacial fields located at approximately 60^o north latitude along the margins of the major north Pacific and north Atlantic gyres. These records covered a period of approximately 150 years beginning in 1850. The records of glacial retreat in these three areas are quite different immediately ruling out any association to their relative position in ocean gyres. Outgrowths of the study include the following:

·         A clear relationship between glacial retreat and increased atmospheric CO₂ concentrations cannot be definitively established since the rapid rise in contemporary atmospheric CO2 concentrations begins around 1850 and observations of behavior in the preceding century were not available. The glacial fields in Greenland and Norway were unstable and experienced significant retreat throughout this period of time. In Alaska significant retreat did not begin until about 1900. However, the Alaskan retreats were 3 to 5 times as extensive as those in Norway and as much as 10 times more extensive than those in Greenland. Maximum glacial retreat for the McCarty glacier reached just over 24km.

·         Records of temperature during the 1850 to 2017 year period were not as extensive as the glacial retreat records. Temperature records in Alaska were available from about 1900 on; those from Greenland, about 1870 on and those from Norway spanned the 1850 to recent period. Temperature rise was observed in all three areas. In Alaska the temperature rose by about 1.6^oC; in Greenland, by 2 ^oC; and in Norway, by 1.62 ^oC. Increased temperatures are significant and coincide with rising atmospheric CO₂ concentrations, but, again, the temporal records of glacial retreat are not long enough to establish a direct relationship.

·         Residual CO₂ concentrations in the last 200 years reveal a more rapid rise in atmospheric CO₂ concentration by about 2-5ppm above the background trend during the 1874 to 1950 time period. While this anomalous increase in the rate of CO₂ rise cannot be associated with a distinct onset time of extensive glacial retreat we do see accelerated glacial retreat around the 1950s. This is also a time when we see CO2 concentrations increase at a more dramatic pace.

·         Solar intensity variations, historical radiative forcing and greenhouse gas totals all increase over the span of observations. However, once again the limited span of glacial retreat data limits more definitive conclusions from the analysis.

·         The relationship of any individual glacier’s retreat or of the general behavior of individual glacier fields to rising CO₂ concentration, temperature or various forcing mechanisms cannot be definitively established. However, in general, the analysis provides some evidence that positive feedback between glacial retreat and increases in atmospheric CO₂, other greenhouse gasses and radiative forcing is very likely during the interval of time examined in this study. While glacial retreat may have served the role of the canary in the mine if records from the 1700s were available, they certainly provide dramatic evidence for the long term impacts of global warming.

References

Glacial retreat data from University of Chicago time series browser at http://climatemodels.uchicago.edu/timeseries/.

Temperature time series data from the Alaskan area is http://climatemodels.uchicago.edu/timeseries/#GuwBBKBBBBDGB.

Temperature time series data for Greenland is located at  http://climatemodels.uchicago.edu/timeseries/#HvlBCF.

The URL for meteorological stations used for the Norwegian area is http://climatemodels.uchicago.edu/timeseries/#JtuBFBBBCBD.

Forcings/Records are located at http://climatemodels.uchicago.edu/timeseries/

Spectral Analysis Clairemorris, Ireland Wind Speeds

Clairemorris, Ireland Wind Speed data (1970.7 - 1973.7)

As part of the Future Learn Environmental Modeling class we are given some data from Clairemorris Ireland. Clairemorris is located in the west of Ireland about 30 miles north of Galway. The wind speed data (Figure 1) reveals some long period (roughly annual) oscillations in speed along with seasonal changes in the wind speed variation.

Figure 1: Wind speed measurements from 1970.7 to 1973.7. Speed is in knots.

The amplitude spectrum of wind speed is characterized by a general decay of amplitudes with frequency(Figure 2). Low frequency (long period) amplitudes are greater than the higher frequency (short period) variations.

Figure 2: Amplitude spectrum of wind speed observations at Clairemorris. 

A frequency of 0.1 corresponds to a period of 10 days and 0.5 to 2 days.

A closeup view of the spectrum from 0 to 0.1 cycles/day (Figure 3) reveals that the highest amplitude components of the wind speed variation occur with annual and semiannual period. There are some additional relatively high amplitude peaks in the data around 26 and 14 day periods. A low pass filter is designed to extract the annual, semi annual variations and longer period variations in the data. A cutoff frequency of 0.01 cycles/day (100 day periods) is used. 

Figure 3: Closeup view of wind speed spectrum out to 0.1cycles/day.

The low pass filtered output provides a more seasonal view of the average fluctuations through the period of observation. The scatter in observations about the long period response highlights changes in the standard deviation through time. The plot reveals peak winds in the fall-early winter of 1970 and 1973. There is also a period of high winds mid year 1972. The period of observations is not long enough to reveal consistent annual wind patterns.

Figure 4: The low pass filtered output (red) shows the longer period oscillations 

extracted by low pass filtering.

The  

 Figure 5: Change points identified in the wind speed differences (bottom) are

projected onto the input data (top)

 Figure 6: The derivative or difference is easily calculate in the frequency domain 

through multiplication of the spectrum by i x angular frequency.

 Figure 7: Wind speed standard deviations.

Analysis of Mauna Loa CO2 data

 Basic Data Analysis

CO2 data provided through the Future Learn Course  "Data Science for Environmental Modelling and Renewables",  University of Glasgow lead by Professor Marian Scott. Atmospheric concentrations of CO2 measured on the summit of Mauna Loa on the Big Island of Hawaii show annual oscillations superimposed on a long term rise (Figure 1). The best fit quadratic (Figure 1) provides 0.997 correlation to the long term CO2 trend.

 

Figure 1: Atmospheric CO2 Concentrations 1952-2018 - Mauna Loa, Hawaii.

Some shorter period annual oscillations about the best fit line can be observed (Figure 1). A plot of the residual (Figure 2) emphasizes these variations. The annual variations about the best fit quadratic are on the order of 6 ppm.

 

Figure 2: Residual atmospheric CO2 concentrations. The annual cycles are pronounced.

I take a spectral filtering approach to remove the annual cyclical rise and fall of CO2 from the data. The spectrum of the residual reveals some pronounced peaks associated with the annual variation and its harmonics (Figure 3). Ideally we would like to eliminate the annual cycles and harmonics. This is easily done using a low pass filter. The region of interest is shown in the lower frequency end of the spectrum (Figure 3).

 

Figure 3: Amplitude spectrum of residual Mauna Loa CO2 concentrations.

I applied a low pass filter with a 0.06 cycle/month (cpm) cutoff frequency to eliminate the annual variations. The low pass filtered output (Figure 4) matches the unfiltered spectra at low frequency and is 0 for frequencies greater than 0.06cpm.

 

 Figure 4: Low pass filtered output spectrum (red) shown 

along with the unfiltered residual spectrum.

A close up view of the spectrum from 0 to 0.1 cpm highlights the effect of filtering (Figure 5). The large annual peak (black) present in the unfiltered residual has been removed in the filtered output (red). The filtered residual contains some long period (low frequency) peaks that are further enhanced when plotted separately (Figure 6).

 Figure 5: Filtered (red) and unfiltered (black) CO2 residual spectra.

In the closeup view the low frequency response in the residual is enhanced (Figure 6). We see peaks at approximately 30 and 15 year cycles.

Figure 6:  Low pass filtered residual CO2 concentration spectrum. 

Period in years of some peaks are labeled.

Peaks that might be associated with solar intensity (sunspot cycle) variation are noted around 9 cpm.  An additional peak with a period of about about 4 years is also present in the data. The largest amplitude oscillations in the residual have a period of about 30 years. One wonders how local volcanic emissions from the East Rift zone may have contributed to some of these local variations.

The filtered and unfiltered output are shown for reference (Figure 7). Low pass filtered output suggests reveals the form of the subtle long and short period variations superimposed on the overall quadratic rise in CO2 concentration since 1959.

 Figure 7: Low pass filtered and unfiltered residual CO2 concentrations.

Is there a relationship between solar energy output to some of the fluctuations we see in the residual? Does increased solar radiation enhance plant growth O2 production and CO2 depletion? The comparison of long period residual CO2 oscillations with solar intensity variations (Figure 8) indicates there is little case to be made for any influence of 11 year sunspot/solar intensity variations on  CO2 fluctuations. However, a relationship could lie in the amplitude of the annual CO2 cycles.

 

Figure 8: Comparison of low pass filtered residual CO2 concentrations 

with solar intensity variations.

Comments

• The 59 year record of CO2 variations on the summit of Mauna Loa, Hawaii increase from about 316 ppm to 407 (mid 2017).
• The rising CO2 concentrations are accurately modeled using a quadratic relationship with correlation coefficient of 0.997. This is only slightly better than an exponential fit that yields a correlation of 0.992.

Spectral analysis and filtering have been used to evaluate the Mauna Loa CO2 data.

• The amplitude spectrum shows a pronounced peak for the annual frequency. Tree harmonics are also present.
• The filtered spectrum reveals a complex frequency response in the CO2 variations over the 59 year record of observation.
• We observe prominent cycles with periods of approximately 30, 15 9 and 4 years.
• These variations are subtle and of the order of +- 1ppm.
• The CO2 rise observed on Mauna Loa without annual variations is shown in the low pass filtered output (Figure 9).

 

Figure 9: Long term variations in atmospheric CO2 concentrations.

Annual cycles removed. 

As discussed in the class module 2.7 Trend and Seasonal Effects the trend in this data is quadratic although some would be on firm ground to argue exponential. The seasonal effect is easily recognized in the data as annual sinusoidal. The unexplained variations (eg. Figure 8) does not appear random. Understanding the significance of these variations would require some additional study, perhaps of local volcanic emissions. The annual effect was not extracted as a separate time series but could have been using a bandpass filter. We could then reconstruct the original data using an additive model approach with CO2 variations = sum of long term quadratic trend + unexplained variation + seasonal.

Central England Temperature Data Analysis

 Basic Data

Central England temperature data provided through the Future Learn Course  "Data Science for Environmental Modelling and Renewables",  University of Glasgow lead by Professor Marian Scott. Temperature measurements from central England reveal a gradual rise in temperature from 1659 to 2015 (Figure 1). Temperatures measured in the month of January rise more in the last 100-200 years than do the temperatures observed in the month of July. The parameters for the best fit quadratics are shown in Figure 1.The quadratic appears to do be a good approximation of the general temperature trend over the 357 year observation period. The residuals sum to 0.

                            a)

 

                           b)

Figure 1: a) Daily average temperatures in January; b) daily average temperatures in July. 

Best fit lines are quadratics.

Smoothed temperatures in July and January are plotted separately for reference (Figure 2). The winter temperatures have a range of about 3 degrees C, while the summer temperatures range is approximately 1.5 degrees C. Both exhibit a rising trend in recent years, but that rise is more pronounced and persistent in the January temperatures. January temperatures have increased persistently since the early 1800s.

Figure 2: Comparison of smoothed July temperatures (red) and January temperatures (blue).

 The three data sets along with best fit quadratics are presented for general comparison (Figure 3)

Figure 3: Smoothed July (pink), average annual (green) and January (blue) temperature comparison

The smoothed residual temperatures for July, annual and January (Figure 4) reveal some interesting interrelationships. The comparison reveals multiyear periods of warmer summer temperatures are sometimes accompanied by cooler winters, with the opposite also being true. This dampens the smoothed average annual response during those years. We also see periods of time when both the summers and winters were warmer along with periods when both were cooler.

 

Figure 4: Residual smoothed temperatures for January (blue),July (pink) and average annual (green)

The amplitude spectrum of the smoothed residuals reveals the presence of prominent longer period features in the temperature series (Figure 5). Temperature variations with periods less than 10 years appear to be largely random.

 

Figure 5: Amplitude spectrum of January, average annual and July temperatures from 1659-2015.

The expanded view of periods longer than 10 years provides some evidence for cyclical temperature change superimposed on the 356 period of measurement (Figure 6). 

 Figure 6: Long period peaks in the spectra of smoothed temperatures.

The periods visible in figures 2-4 are most pronounced in the winter temperature variations. Winter temperatures show some cyclicity with approximately 177 and 90-60 year period.   These peaks are less pronounced but also present in the summer and annual temperature variations. Summer and winter variations also appear to contain a 40-24 year component. One wonders if the small peak observed between 0.075 and 0.9 cycles per year might be associated with sunspot cycles and accompanying variations of solar intensity.

Comments

• We see evidence of increasing temperature in the July, average annual and January trends. This increase is most pronounced in the January temperatures. Winters see nearly twice the warming with winter temperatures increasing by more than a degree (quadratic fit in Figure 1a) with summer temperatures increasing by approximately a half degree.
• The comparisons reveal periods of time during which hotter summers are accompanied by cooler winters, periods when both summers and winters are hotter or cooler and periods with cooler summers accompanied by warmer winters. 
• Cyclical temperature variations are most pronounced in winter temperatures. Temperature variations occur with pronounced periods of approximately 177 years and 90-60 years. Smaller amplitude variations are also observed with 40 to 24 year periods. A speculative observation of potential sunspot cycle periodicity in the temperature data is made.