Seasonal and Diurnal CO2 Patterns at Diekirch, LU

2003 - 2005

Francis Massen 1, Antoine Kies 2, Nico Harpes 3 and a group of students of the LCD                                                                                                                                                   

1 Physics Lab and meteoLCD, Lycée Classique de Diekirch, francis., 
2 LPR, Laboratoire de la Physique des Radiations, University of Luxembourg,
3 Radiation Protection Office,

      pdf version 1.02

file: co2_patterns.html  

History: version      1.0      02 Feb 2007
                             1.01    11 Feb 2007  correction of some spelling faults and typing errors  
                             1.02    24 Mar 2007  added addendum 7


The seasonal and diurnal variations of the CO2 mixing ratio measured at meteoLCD, Diekirch, LU from 2003 to 2005 are analysed for typical variation patterns and relationships with environmental parameters. For seasonal and long term mean CO2 levels, it can be shown that sunshine (duration and energy) plays a variable and minor role, whereas the daily amplitude of air temperature and CO2 variations correlate positively over the whole year as well for winter and summer months. Increased wind velocities always lower CO2 levels, whatever the wind direction may be. Storm "Franz" passing over Diekirch the 11th Jan.07 allowed to quantify this relationship by a simple mathematical model, which might be used to compute an asymptotic CO2 level close to the global mixing ratio. Diurnal variability (exceeding 100 ppm) shows up in 3 characteristic pattern due to different atmospheric mixing caused by wind speed disrupting ABL inversions.


1. How is CO2 measured at meteoLCD?
2. Geographic location of meteoLCD
3. Seasonal variations of the CO2 mixing ratio:
3.1. mean and extreme levels
3.2. Relationship between CO2 mixing ratios, temperature and sunshine duration according to season
3.3. Relationship between mean CO2 parameters and mean wind velocity and direction
4. Diurnal variations:
4.1. The dual peak diurnal CO2 pattern
4.2. The single peak diurnal CO2 pattern
4.3. No peak days and average pattern
4.4. Can day-time biological fixing be detected?
5, Conclusion
6. References
7.  Addendum A: A revised model for the relationship between CO2 and windspeed

How is CO2 measured at meteoLCD?


Starting 28 Feb. 2002, the MIR 9000 from Environment SA,  an EPA compliant professional NDIR instrument  is used for CO2 measurements. The specifications are:

range used:    0-500 ppmV

span and zero drift: +/- 2% of full scale in 30 days
resolution 0.1 ppmV
sampling 1 minute, 30min. avg. stored

The instrument is recalibrated about every 3 weeks using span and zero gas (or CO2-free dry air), a general overhaul done by Envitec SA four times a year. The span gas used is from Praxair: bottle concentration is 496 ppmV +/- 2%.  The same bottle has been in use since 30 June 2003.

Zero drift has been found to be practically inexistant and is in fact not a problem as the sensor is built to make regular zero autocalibrations at night-time. The span-factor varies from check to check and is changed as needed.

Besides CO2 many other meteorological parameters and gases are measured at meteoLCD; see for details.

In this paper, all major calculations are done using DADiSP and Statistica 7; missing data are not interpolated except for very few ones in a row. Impossible low CO2 levels (<330 ppm) are treated as missing data. There remain 52245 valid CO2 measurements for the 3 year period, which represents a fair data availability of 99.3%


Geographic location of meteoLCD

The small town of Diekirch (population ~5600) is located in a valley orientated South-West to North-East, at an altitude of about 200m asl. The dominant wind direction is that of the valley, South-West, and more rarely the opposite. It is a semi-rural town with few industries upwind: a brewery 
at a distance of 100-200m, a small industrial zone without much heavy machinery. A similar town (Ettelbruck) is situated upwind at a distance of 3 km. 
The only major industry is a Good-Year tire plant ensemble located upwind at about 8 km:

Seasonal variations of the CO2 mixing ratio

Seasonal variation, mean and extreme levels.


CO2 measurements made at locations undisturbed from industrial and traffic emissions show a clear seasonal pattern with winter-time levels usually several ppm higher than summertime ones: for instance the typical Mauna Loa seasonal amplitude is 8 ppm, the lower values corresponding to late summer or start of fall [1]:











fig. 1 Mauna Loa mean monthly CO2 mixing ratios

The situation is usually quite different in urban areas where patterns are heavily influenced by anthropogenic emissions which often cause strong short-time variations, but less visible seasonal patterns over the year. Nasralla et al [2] found an annual amplitude in Kuwait City less than 1.5 ppm from the mean monthly concentrations, whereas Idso et al [4] report almost constant daily minima but strong seasonal variations for the daily maxima over one year.

We will report the CO2 measurements from 2003 to 2005 taken at the meteoLCD site. All measurements have been made by the same instrument, 
using the same calibration bottle with 496 pm span gas, at a frequency of one per minute. The 30 minutes means are stored in the data file that holds about  58600 data points for the 2003-2005 time span.

Many natural factors influence CO2 mixing ratios: some parameters as wind direction, night or early morning inversions and daily changes in atmosperic boundary layer (ABL) mixing have a typical short time influence; others like mean air temperature, overall sunshine duration and vegetation activity show up as seasonal factors.

Fig.2 and fig.3 show the 2003 to 2005 sequence of monthly CO2 means, minima, maxima and the global monthly averages over the 3 years: the average for the 3 years is 405.6 ppm with a standard deviation of 8.9 ppm.

  monthly max. = 511.7 +/- 30.6
left axis from 300 to 600 ppm
  monthly min. = 355.7 +/- 14.6
left axis from 300 to 600 ppm

fig.2 Monthly mean CO2 levels; global mean is 405.6 +/- 8.9 ppm; left axis scale: 360 to 440 ppm













fig.3: Averages of the 2003 to 2005 monthly mean CO2 levels

Fig. 2 shows that the yearly variations do not repeat in an identical manner even if the periods of low and high mixing rations usually extend over 
Jun-Sep and Nov-Feb; the mean of the 3 years shows a visible summer low and winter high. The exceptional high Nov. and Dec 2004 values are somewhat misleading: omitting 2004 the lowest means are in July, the highest in February (to be compared to Sept/Feb in Kuwait-City, and May/Sep 
at Mauna Loa).
The difference of about 21 ppm between December and July mean levels is much higher than that found in Kuwait-City [2], pratically equal to Essen, Germany [8], but about only half of that given by Idso et al [4]; this same paper reports a surprisingly low standard deviation of 0.2 ppm for the daily minima over one year. The analogue monthly minima at Diekirch show a much greater variation with a standard deviation of about 15 ppm; the standard deviation of the monthly maxima is about 31 ppm; the daily minima. and maxima at Diekirch have standard deviations of 15.7 and 33.8, similar to the monthly values (all calculations over 3 years).

An autocorrelation computed on the daily means  over the 3 years gives maxima peaks at 45, 91, 179 and 352 days, i.e. roughly 1.5, 3, 6 months and full year periods; whereas the full year cycle has to be expected, the other periods remain unexplained.















fig 4. Autocorrelation confirms long-time periodicities in daily mean CO2 pattern



Relationship between CO2 mixing ratios, temperature and sunshine duration according to season


We will now look for a relationship between the following parameters: daily mean CO2, daily mean CO2 amplitude, daily mean air temperature, daily mean temperature amplitude and daily sunshine hours. A total solar irradiance greater than 120 W/m2 measured by the pyranometer will be taken as a sunshine condition. This convention differs from that of the WMO, where 120 W/m2 corresponds to the irradiance of the direct sunbeam on a perpendicular surface; our convention (including direct and diffuse radiation) gives sunshine hours well in excess: for instance, applying the much more complex Olivieri method [3] amounts to 1768 hours for 2005, wheres the above criterion gives 2646 hours. So it should be remembered that in this paper a sunshine hour means a situation where the total (direct and diffuse) iradiance measured by the horizontal pyranometer is equal or greater than 
120 W/m2. Sunshine and air temperature are of course dependant parameters (for 2005 the correlations are 0.64 between sunshine and daily mean temperature resp. 0.69 between sunshine and daily mean temperature amplitude, both significant at p <0.05). The following analysis searches the parameter having the best correlation with the mean daily CO2 levels.

To distinguish between the vegetation growing season and winter months we will take the months January and February (JF) as representive for winter and July-August (JA) as representative for summer. This differs from the ususal convention of DJF for winter and JJA for summer, but has the advantage to allow working on full year original data files. Outliers for CO2 (usually caused by calibration work) have been interpolated when possible, else replaced by a missing data (NA = not available) placeholder.

Table 1 shows the relevant correlations for the full year, the JF and JA months, the red ones being significative at p<0.05

year AirT_dailymean AirT_dailyamp Sunshine hours
CO2_dailymean 2003
JF JA -0.12

CO2_dailyamp 2003
JF JA 0.46

table 1

For the full year comparison the highest positive correlation exists between daily CO2 amplitude ( amplitude = maximum - minimum readings) and the corresponding daily temperature amplitude: regardless of season all coefficients are positive and significant at p<0.05; the correlations are better during the summer season.

The next figure 5 gives the corresponding graphs:
















fig.5: Daily CO2 amplitude versus daily temperature amplitude: slope of linear fit always positive.

One would expect that mean CO2 concentrations and mean daily temperature vary in opposite sense as higher (summer) temperatures usually happen  during days with maximum photosynthesis which lowers the CO2 mixing ratios: actually the data show a clear negative correlation for the winter months and surprisingly a clear high positive correlation for the summer season. A computation of 18 linear regression slopes for every couple of months gives essentially negative slopes for the months of November to February and positive slopes for the remaining months (with only 2 exceptions): fig 6 gives 
the graphs for Jan-Feb and July-Aug 2003:

fig.6: Daily mean CO2 versus daily mean temperature: slope of linear fit negative in winter, positive in summer.

Idso et al. [4] report a negative slope for the regression between maximum daily CO2 and minimum daily air temperature; the Diekirch data do 
not confirm this: CO2 and temperature antiregress during the winter months of Nov-Feb, but the regression line slope is positive for all other months 
over 2003 to 2005. 

Table 2 gives a mixed picture for the correlations between CO2 and sunshine: the full year correlations are slightly negative, the winter JF and summer 
JA months all have a positive correlation. A similar result is obtained when computing the linear regressions between the daily CO2 patterns and daily solar energy ( in kW/m2 on a horizontal surface) for the full 3 year measurement series:

slope and offset of linear regression of daily mean CO2 versus daily solar energy whole 3 year 2003-2005 period mean of Jan-Feb  mean of Jul-Aug 
dailymean CO2   -0.256
dailymin CO2   -2.791
dailymax CO2   +3.913
dailyamp CO2   +6.704

table 2

Even if the daily mean CO2 and daily solar energy antiregress for the full 3 year period they do not, contrary to what one would expect, antiregress 
for the summer months having the greatest solar energy. Over the 3 years high daily solar energy slightly lowers daily mean and noticably lowers daily minima CO2 levels and increases daily maxima. As a consequence the slope for the daily CO2 amplitude versus solar energy greatly increases for the months with higher solar input. The maximum solar energy per day is about 8 kWh/m2 on a horizontal surface in summer and 1 kWh/m2 in winter, 
which would increase the daily CO2 amplitude by about 7*6.7 = 47 ppm from winter to summer ( the measured mean winter and summer daily CO2 amplitudes are 39.3 ppm and 76.1 ppm) 



Relationship between mean CO2 parameters and mean wind velocity and direction


Windspeed and wind direction are measured at meteoLCD by an ultrasonic anonemeter (accuracy = 0.1 m/s) mounted on a mast 3 m above the 
terrasse holding the other instruments, and about 21m above groundlevel; the . The main wind directions over the whole period are SSW and NEE
as shown by figure 7:















fig. 7:  Histogram of wind direction; total sample size is 51516 (windspeed > 0).


Let us limit the main directions to the ranges [50°-120°] and [200°-270°] for the easterly and westerly winds; the statistics are the following:

  Easterly Wind Westerly Wind
data points with wind speed >0 17428 16111
mean wind speed of these points [m/s] 1.30 2.64
mean CO2 level [ppm] 403.1 395.0

table 3

The table shows that the higher the wind speed, the lower the CO2 level. Actually, the highest wind speeds correpond to a maximum mixing of the atmospheric boundary layer, and should be close to the global baseline CO2 mixing ratio.  Fig. 8 gives the plot of CO2 versus wind speed, and points 
to a background of approx. 380 ppm:









fig.8 : Baseline CO2 mixing ratio corresponding to maximum windspeed

Storm "Franz" passing over Luxembourg on  Jan.11th 07 gave an opportunity to test the relationship on a much smaller data set. This storm had wind speeds reaching 30 m/s over open country and up to 11 m/s at the meteoLCD site. There was no sunshine, air temperatures changed between 5°C and 9.5°C and the wind blew constantly from a [200° - 270°] direction . Fig. 9 shows CO2 concentrations and wind speeds varied during 48 hours; a 
simple model 

CO2 = a + b*windspeed/(c+windspeed)
      [eq. 1]

gives a correlation R = 0.76. This suggests an asymptotic baseline CO2 level of ~385 ppm for infinite wind speeds, i.e. for a maximum mixed-up atmospheric boundary layer. It should be noted that this asymptotic level is close to the Mauna Loa level of 382 ppm measured in December 2006.















fig. 9: CO2 and wind speed during storm "Franz"


















fig. 10: Simple model CO2 versus wind speed

The same model applied to the complete 2003-2005 data points gives a bad fit (R=0.22). The  modified model 

CO2 = a + b*(windspeed +c)/(d + windspeed)       [eq. 2]

(see also chapter 4.3) gives 362 ppm as baseline CO2 (R = 0.59). This is much too low; the line drawn by visual inspection in fig. 8 seems more adequate.

There are virtually no industries in the easterly direction, whereas the main potential emitters are located upwind to the west: nevertheless the corresponding mean CO2 levels are lower. This suggests that the higher levels especially noticeable during  calm wind conditions are not caused by CO2 plumes from industrial emitters, but by slower wind speeds which do not mix up the boundary layer as well as the higher westerly winds do. When wind speeds are higher than 2 m/s the CO2 levels are similar, regardless the wind direction (with and without upwind factories); this confirms the hypothesis:


wind speed < 2 m/s

wind speed > 2 m/s

  all directions ~WSW ~ENE all directions ~WSW ~ENE
mean CO2 mixing ratio


405.6 413.6 387.2 387.6 388.5

As a reminder: the overal mean CO2 level computed from the 52445 measurements is 405.1 +/- 28.7 ppm for the period 2003-2005; Mauna Loa's average mixing ratio is 376 ppm for the same period.



Diurnal variations of CO2 mixing ratio


Simple inspection shows that throughout the year, there is a periodic daily variation for most of the time; the autocorrelation computed on the 56000 
data gives a clear indication of a 24h period.

fig.11: Autocorrelation computed over all 56000 data points shows yearly and daily periods

Despite great variabilty in day to day CO2 levels, a few typical diurnal patterns can be found. As shown in the preceeding chapter, wind speed is a dominant cause in lowering CO2, and a stable atmosphere (often found at night and during morning hours) is an efficient trap of natural and anthropogenic CO2 emissions, .

Three typical diurnal CO2 patterns can be found: dual peak, single peak and no peak


The dual peak diurnal CO2 pattern

Fair weather conditions with little cloud cover and low wind favor two stable atmospheric inversions per day [7]: one close to midnight (due to nighttime radiation cooling) and the other around 6 hour in the morning, due to the cooling of air layers in contact with the soil, the upper regions beginning to be heated by the rising sun (all times are UTC). This second inversion coincides with one of the 2 heavier traffic periods (7-9 and 17-18 local time) where many commuters pass through Diekirch (or pass through Ettelbruck 3km west, going southwards to Luxembourg-City). All roads around Diekirch are smaller roads, the nearest highway starts at Colmar-Berg, 8km from Diekirch. Wind is the enemy of inversions, so we should expect this dual peak situations only during hours of low wind.

Lets us first show in detail the situation from Saturday 8th toTuesday 11th July 2006.

These 4 days are dry,  with only one small rain-fall of 1.8mm during 30 minutes at Tuesday; the night wind speeds are low ( <0.5 m/s), but have daily maxima  from 3 to 7 m/s; Monday is a blue sky day, all the others have intermittent moderate or heavy (Sunday) cloud cover, as shown by the variablitiy of the UVB and solar irradiance. All 3 nights display 2 peaks, the first at 00:00 and the second at 06:00 UTC; there is far less morning traffic during Sunday compared to Monday and Tuesday: NO peaks at 50 ug/m3 on Sunday and 60 ug/m3 on Monday.


















fig.12: CO2, air temperature, NOx and ozone from 8 to 11 July 2006

















fig.13: CO2, wind speed and solar irradiance from 8 to 11 July 2006

The same pattern can sometimes be found when temperatures are colder or freezing, as shown by fig. 14 for the 10th to 12th Dec. 2005 period; a double peak can be seen Saturday to Sunday night, and a much more preeminent one from Sunday to Monday. The last peak coincides with a NO maximum, sign of the Monday morning commuter traffic; the Monday CO2 peak exceeds the Sunday peak by about 40 ppm. As soon as the air 
warms and wind speeds are higher than 0.5 to 1 m/s the boundary layer starts rapidly to be better mixed up and CO2 levels fall to the daily minimum.


















fig. 14: Double peak situation during cold winter days (SAT & SUN: blue sky, MON: cloudy)



The single peak diurnal CO2 pattern

An interesting situation with single peak days alternating with dual peak ones happened  from 8th to11th July 2005:

















fig. 15: Alternating dual and single peak days 10 to 14 July 2005

Inspection shows that the double peak coincides with a small nocturnal dip in air temperature; if we magnify the graph of CO2 and wind velocity, it becomes clear that wind speed is the driver of the dual peak (and causes the small air temperature drop): a small rise of wind around midnight pushes down CO2 levels by disrupting the inversioon layer; low wind nights do not show this.












fig. 16: midnight wind causes double peak


No peak days
and average pattern  


From the preceeding chapters one should expect rather flat diurnal CO2 levels when wind speed exceeds a certain threshold. This is indeed the case, as shown by fig.17 which represents a windy 4 days period from 3rd to 6th Feb. 2005. Wind speeds over approx. 1 m/s are probably strong enough to disable most night and morning inversions and the corresponding CO2 peaks.











fig. 17:  Four days flat CO2 levels

Diurnal CO2 variations are wind driven and as periods of low nighttime and higher daytime wind speeds are the norm, the mean overal diurnal pattern is more or less sinusoidal (R=0.97), whereas the mean diurnal wind speed can be modeled (R = 0.99) by a Gaussian bell curve:














fig. 18: mean hourly CO2 level and windspeed (2003-2005)

A plot of these mean hourly CO2 levels versus wind speed suggests, similar to figure 8, a baseline CO2 level of about 376 ppm: the applied model  
[eq. 2] gives an excellent correlation R=0.988:

                                       CO2 = a + b*(windspeed + c)/(d + windspeed)       [eq.3]

The Mauna Loa measured mean CO2 mixing ratio for 2003-2005 is 377.6 ppm, very close to this baseline.

fig. 19: 2003-2005 mean hourly CO2 versus wind speed, with asymptotic baseline level 



Can day-time biological fixing be detected?


The principal cause of the antiregression with air temperature seems to be temperature driven changes in night and day wind speeds; actually enhanced biological activity as daytime CO2 fixation should give lower day levels during the greening period. This can be shown for instance using the 2003 daytime means for CO2 levels and wind speed:

  Jan-Feb 2003 Jul-Aug 2003
mean of (mean daytime 06:00-18:00) CO2 levels 406.2 +/- 19.1 400.9 +/- 18.2
mean of (mean daytime 06:00-18:00) windspeed 1.27 +/- 0.98 0.86 +/- 0.50

Even if the summer daytime wind speeds are lower, the corresponding CO2 levels are not higher, but also lower: this could be seen as a fingerprint of photosynthetic CO2 fixation. But the difference in winter/summer levels could also be caused by higher anthropogenic winter emissions from increased heating. As a consequence, it is difficult or impossible to detect a photosynthesis fingerprint unambiguously in the daytime CO2 signal.


Table 5 resumes some of the influences of environmental factors on CO2 pattern:

Environmental Parameter Influence on CO2 maxima Influence on CO2 minima Influence on double peak Influence on no peak
Wind speed lowest night windspeeds often coincide with CO2 peak (inversion) higher wind speeds during daytime give lower CO2 minima; lower windspeeds at night give higher CO2 minima higher midnight wind speeds (> 1m/s) cause double peak continous high wind (> 1 m/s) give flat daily CO2 pattern
Solar irradiance   CO2 daylight minima practically independent of solar irradiance  
Cloud cover CO2 daylight minima practically independent of cloud cover
Traffic visible influence of morning traffic on CO2 peak during inversions: Monday high traffic morning hour has peak 20-40 ppm higher then same Sunday hour (lower traffic confirmed by lower NO and NO2 concentrations)    
Ozone   CO2 daylight minima practically independent of ozone concentration  

table 5


5. Conclusion


Our report confirms some findings of other papers: CO2 peaks during inversion hours, and we often find the same dual maximum situation as in [4]. On the contrary, we can not confirm an antiregression with air temperature as being the general rule. Biological periodic activity ( which causes a mean  drop of about 21 ppm) can only be seen in autocorrelations and overall monthly averages. It is not easily detectable from the hourly measurement series. Diurnal variability is important and depends essential on atmospheric stability [5][6]: when there exist night or morning inversions, CO2 peaks may exceed the daily minimum by well over 100 ppm. The influence of morning traffic (detected by NO and NO2 variations) shows up in an increase of 20-40 ppm of the peak level. Overall traffic and anthropogenic emissions are too low to cause an urban CO2 dome.Ozone concentrations do not seem related to CO2 levels. Periods of very high wind speeds allow to find by inspection an asymptotical level close to the global mixing ratio measured at isolated reference stations like Mauna Loa; this same level can be found by applying a simple mathematical model which expresses the mean hourly CO2 levels as a function of wind speed. The mean hourly levels per day computed over the 3 years period can be modelled by a sinus function.


6. References:



NOAA, Earth Systems Research Laboratory, Global Monitoring Division:
[2] Nasrallah et al: Temporal Variations in Atmospheric CO2 Concentrations in Kuwat City. Elsevier, Environment Pollution, 2003, Vol 121
[3] meteoLCD data archive, 2005 data file (
[4] Idso et al: Seasonal and diurnal variations of near-surface atmospheric CO2 concentration within a residential sector of the urban CO2 dome of Phoenix, AZ, USA. Pergamon, Atmospheric Environment, 36 (2002) p.1655-1660
[5] Burns S.P et al: Measurements of the Diurnal Cycle of Temperature, Humidity, Wind, and Carbon Dioxide in a Subalpine Forest during the Carbon in the Mountain Experiment (CME04); NCAR, Boulder, CO
[6] Parazoo N.: Sources of Synoptic CO2 Variability in North America; Powerpoint presentation, Colorado State University, ChEAS June 5, 2006
[7] Ahrens, C.D.:Meteorology Today. 8th edition.Thomson, Brooks/Cole, 2007
[8] Henninger S. et al: Mobile Measurements of Carbon Dioxide wihin the Urban Canopy Layer of Essen, Germany.

All data files are available in the data archive of meteoLCD at

+ The following LCD students from the optional (baccalaureat year) course "CLIMATE" helped in preparing the preliminary research and calculations:
Dirkse Anne, Fischer Eric, Glaesener Laurent, Gleis Paul, Kobs Daniel, Lavandier Philippe, Meyer Julien, Miny Christian, Schmit Jonathan

(C) copyright meteoLCD

7. Addendum A

A revised relationship between CO2 and windspeed
The rational function  used in chapters 3.3 and 4.3 for fitting CO2 mixing ratios to wind speed may give a good asymptotical base level, but it lacks a clear physical base and represents nothing more than a mathematical trick. Using a physical sensible exponential function of the type

CO2 = a +b*exp(-c*windspeed)    [eq. 4]

resolves this problem. The horizontal asymptote for infinite windspeeds is the parameter a.

Here are the results of applying this model to different data sets; all parameters are significant at the 0.05 level

data set
and time period
of datapoints
anemometer asymptotic base level
Mauna Loa level
goodness of fit R
storm FRANZ
11/01/07 00:00 to
12/01/07 13:00
74 cup 386.3
382.0 (Dec. 2006)
2003 to 2005 52608 ultrasonic 381.3
2003 to 2005 52608 cup 375.9

The cup anemometer has the best goodness of fit R: this might not be surprinsing if one considers the different mounting heights of the air inlet, cup- and ultrasonic anemometers: the cup anemometer is mounted 1.10m, the ultrasonic 2.05m above the air inlet (see fig.20). The higher mountings show up in different mean windspeeds over 2003-2005: 1.58 m/s (cup, lower) and 1.77 m/s (ultrasonic, higher).