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TEMPERATURE DEPENDENCE OF ATMOSPHERIC CO2 BUILD UP AND GLACIER MELT By Larry L. Olson, PhD, PE INTRODUCTION: In article 4 at this web site, (Delineating Movement In The Atmosphere and Absorption of Carbon Dioxide By Our Oceans, Using Data That Has Been “Hiding-In-Plain-Sight”) there was considerable discussion about the breaks in the carbon dioxide curves for all of the sampling stations at the same time. If you have not read that article, it is suggested that you do so now. This article will rely heavily on the data in that study. The very interesting thing about these breaks is that they all occurred at the same time, namely l965, 1976, and 1994. But most interesting was the fact that there was no correlation between the emissions of carbon dioxide into the atmosphere by man and those breaks. A possible explanation for those breaks was advanced, but based on the results of this study, it appears that that explanation is not correct. That CO2 data is presented in Figure 1 below with the three straight lines that delineate these breaks drawn on the data. The data are for Mauna Loa, but similar plots were obtained for all those stations that had adequate data coverage to include the appropriate time frames. This is the same figure as Figure 4 in article 4 of this web site. These data are from (reference 1). While preparing this study, I came across curves for the melt of glaciers, world wide, and the melt rate for glaciers exhibited the same breaks in their curves and at roughly the same times. Those curves are usually presented as decreasing curves to illustrate the diminution of the glacier mass, but to keep the curve similar to the CO2 data in Figure 1, I repotted the glacier melt data to show that amount of glacier melt as per Figure 2 below. These data are from (reference 2). I reviewed a lot of glacier melt data before I settled on these data. The data field only went to 2004 and I looked for data after that date, but was not successful---I know that it exists, I just grew tired of trying to find it. Similar data from other sources indicates that the trend established from 1994 to 2004 continues on until at least 2008. So, there are two environmental phenomena that exhibit similar trends with breaks at the same times in recent history. Lots of other authors have tied atmospheric carbon dioxide and ice melt together but I could not find anyone who has noticed what is presented in the above two paragraphs. I spent a lot of time investigating whether the CO2 increase could come from gaseous release when the glaciers melted, but could never account for more than 10% of the CO2 increase. However, I learned a lot about glaciology. The only environmental factor that seemed reasonable to me that might account for these breaks would be temperature. That is obvious for glacier melt, but not so obvious for CO2. Hence, this article is a report of my investigation into the relationship between temperature and glacier melt and CO2 increase. VARIATION OF CO2 SOLUBILITY WITH TEMPERATURE: If I was going to associate atmospheric CO2 with temperature, it would be a good idea to present justification for the concept that if temperature increases then CO2 solubility in water must either increase or decrease by a certain amount. For those of you who believe that the solubility of CO2 in water is inversely proportional to temperature, skip this section. For the rest of you, the reasoning goes as follows. One of the most accepted equations to define the variation of the Henry’s law constant with temperature in sea water is by Weiss (reference 3) is : Ln Kh = 9345.17/T - 60.2409 + 23.3585(T/100) + S(0.023517 - 0.00023656T + .00047036((T/100)**2) Where Kh = Henry’s law constant, moles/Kg-atmospheres T = Temperature, degrees Kelvin ( Kelvin = centigrade + 273.15) S= Salinity, parts per thousand by mass Ln= Natural logarithm The Henry’s law constant that corresponds to the above equation is P = c/Kh where P is the partial pressure of carbon dioxide, c is the solute concentration and Kh is the corresponding Henry’s law constant. (Note: Henry’s law can be written in several different ways and the constant that corresponds to each equation are all different) This form of the Henry’s law means that if the Henry’s law constant increases with increasing temperature and the solute concentration remains nearly constant, then the partial pressure of CO2 will go down. If the constant decreases with increasing temperature, than the partial pressure of CO2 will increase. Remember, the partial pressure is just the atmospheric concentration of CO2, corrected for the ratio between the ppmv and partial pressure. I solved the above equation for temperatures from 25 degrees centigrade to 26 degrees centigrade for each 0.2 degrees with an assumed salinity of 35 ppt. The results of those solutions are shown in Figure 3. It is obvious that the Henry’s law constant decreases with increasing temperature in a linear fashion. This means that if the ocean water temperature increases, and the amount of CO2 in the ocean remains nearly constant, then we would expect the CO2 in the atmosphere to increase and that this increase would be linearly dependent on the temperature. The above equation is an equilibrium equation and does not say whether the CO2 will come out of solution or whether it will just not go into solution as fast. However, it gives us a quantitative handle on which way the CO2 will tend to go. It also show us that for the temperature range that we are interested in, the variation of the Henry’s law constant with temperature appears to be a first order function. I would not have expected that because the above equation is an exponential of a quadratic equation. Now on to see if we can observe this type of first order function. QUANTIFYING THE SLOPES FOR THE CO2 BUILD UP AND GLACIER MELT FOR 3 TIME FRAMES: The slopes for the three time frames represented in Figures 1 and 2 were determined by drawing lines of best fit visually. For the CO2 data, slopes were determined for the South Pole data and for Point Barrow also. Point Barrow did not have adequate data to determine the slope for the time frame 1965 - 1994. Generally, the slopes were about the same, so it was decided to use only the Mauna Loa data. The slopes for both the CO2 and glacier melt are shown in Table 1. Below. Table 1. Slopes for CO2 and Glacier Melt For The Three Time Frames We will use these data later to compare to two temperature measures. TEMPERATURES: It was determined that only two temperature measures would be used. Those are world wide air temperatures and world wide sea surface temperatures. The data were obtained from NCDC,NOAA (reference 4) and the Hadley Centre records (reference 5). At first the annual averages were used, but the data were deemed too insensitive to characterization for the time frames involved. Consequently, the monthly averages were used. It was also determined that running averages tended to smooth over the data too much, so it was decided that all of the temperature data would be evaluated using least squares analysis for the time period in question. AIR TEMPERATURES: The air temperature data are shown in Figure 4. I have drawn the best fit line for each of the time frames according to least squares analysis. The corresponding slopes are shown below in the next section in Table 2. It is interesting to note that the three lines are connected. That is not so for the sea surface temperatures. SEA SURFACE TEMPERATURES; The sea surface temperature(SST) data are shown in Figure 5. Once again, I have drawn in the three lines of best fit associated with the three temperature ranges. Table 2. Air and Sea Surface Temperature Changes for the Three Time Frames Slope Time Frame AirTemperature SeaSurfaceTemperature Designation Years Degrees C/Year Degrees C/Year ----------------------------------------------------------------------------------------------------------------------------------- S1 1994 - 2009 0.026335 0.0099562 S2 1976 -1994 0.023753 0.0079756 S3 1965 - 1994 0.008287 -0.0119616 The importance of that figure is that whatever occurred in 1994 to 1998, the range where we see a break in the CO2 and glacier melt curves also caused a break in the ocean temperature curve. However, the ocean temperatures illustrate a much declined increase rate whereas the temperatures increase rates in Table 2 above grew larger for the 1994 - 2009 time frame. Interesting. COMPARING CO2 & GLACIER MELT RATES WITH TEMPERATURE INCREASE RATES: Comparing the rates and their effect on each other is best accomplished in a table. The table compares both CO2 and glacier melt to both SST and air temperatures. This is not logical because you would not expect the glacier melt rate to be influenced much by SST and you would not expect the CO2 rate to be much influenced by air temperatures. However, the calculated values are presented in Table 3. Table 3. Dividing CO2 and Glacier Melt Rates by The Two Temperature Rates. The most striking trend to be noticed from this table is shown in column 3. For time frames S1 & S2, the CO2 rise per degree is almost identical at about 184 ppmv/degree and almost exactly twice that of S3 although the sign is opposite. Looking at column 4, the rate for S1 & S2 are almost equal, but the rate for S3 is twice the other two rates. This does not make any sense, and just as was stated in the above paragraph, we would not expect to see a readily definable relationship between air temperatures and CO2. Lets just ignore column 4, but I will get back to the data in column 3 in much more detail later. The trend in column 5 shows an increasing trend from S3 to S1 and of course, we did not expect to see a correlation of glacier melt with SST. For column 6, there appears to be somewhat of a trend, but not as much as I had hoped for. The data are all in the same order of magnitude but a glacier melt range from 6880 to 14,815 cubic kilometers per degree is a large variation. The average is 10,539 cubic kilometers per degree centigrade of air temperature. This range might not be unexpected when you look at all that is involved in ice melt, such as surface area, wind speed, wind direction, sunny days versus cloudy days, heat content with respect to the latent heat of melting, and changing aerial extent of the glaciers. The list is much longer than that but, you get the idea. I do not plan to do anything more with the glacier melt data, but I will spend a lot more time and effort on the CO2 data. The data from column 3 of Table 3 is most interesting, but cannot be taken at face value. The reason for that statement is that the increase of CO2 per year is positive 1.111 ppmv/year. However, the temperature for the sea surface is in a cooling trend with a slope of -0.0119616 degrees centigrade per year as per Table 2 above. If there is a temperature component of the S3 time frame which is negative, then there must be a temperature independent component that is larger than the 1.111 ppmv/year. In simple terms, if I am going to subtract a temperature dependent component from something to get 1.111 then that something has to be larger. The other reason for not taking the 184 ppmv/degree at face value is that this is many times larger than the relationship between temperature and CO2 from the Vostok ice core samples. Some sources put that number at 8 ppmv/degree centigrade(reference 6), but my review of the Antarctic Ice data as presented by (reference 7), leads me to a number closer to 10 ppmv per degree, but a difference not worth arguing about. So another way to get at the correct CO2 rise per degree is to look once again at the data for S1 time frame. Before we begin the calculations, let’s designate the unknown CO2 rise rate that is not dependent on temperature as BR. We know that this base rate, BR, is something larger than 1.111 ppmv/year. Lets further assume that this base rate is constant from 1965 to 2009. We may revisit that assumption later, but it is necessary to get the calculations moving. We need one further assumption and that is that because the CO2 rate shown in column 3 of Table 3 is the same for S1 and S2, we need to assume that the temperature dependent rate for these two time frames are the same. This might be the weakest part of the analysis, but it basically says that whatever altered the buildup rate of CO2 in 1976 was still operational and unvaried after 1994 as well. With all of these assumptions, lets do the calculations and then reflect on the results. The CO2 buildup rates for the time frames S1 and S2 are 1.825 and 1.469 ppmv/year, see Table 1. The difference between these two rates is 0.356 ppmv/year. The SST increase rate for the S1 time frame is 0.0099562 degrees/year, see Table 2. Dividing the 0.356 ppmv/year by the0.0099562 degrees/year yields 35.76 ppmv/degree. Now, multiplying this figure by the SST rate for the S2 time frame of 0.0.0079756 degrees/year yields a value of 0.2852 ppmv/year. This is the temperature dependent portion of the CO2 rate for the S2 time frame. So, if we subtract that from the CO2 buildup rate for the S2 time frame, we should get the temperature independent rate, BR. So, 1.469 minus 0.285 = 1.184 ppmv/year. This fits, because it is larger than the 1.111 ppmv/year associated with the S3 time frame. Now, we can look at the temperature dependent portion of the S3 time frame. Subtracting 1.11 from 1.184 = 0.073 ppmv/year. Dividing this by the SST rise for the same time frame, 0.073/0.0119616 = 6.10 ppmv/degree. This is smaller than the 8 to 10 ppmv/degree shown from the Vostok ice cores, but nicely in the same range. Another check on these calculations would be to refer back to the predicted change in the partial pressure from Figure 3. These data show a slope of the Henry’s law constant of 0.004294 moles per kilogram atmospheres per degree centigrade. Using the appropriate Henry’s law equation and the simplifying assumption that the solute concentration does not change significantly, this equates to 42.94 ppmv/degree. This is in very good agreement with the 35.76 derived above. Because of this good agreement and the good agreement between the pre-1976 temperature dependent rate of 6.1 ppmv/degree with the Vostok ice data of 8 to 10 ppmv/degree, no further review of the assumptions used in the calculations will be performed. Before I wrap this article up, I want to pull one data plot and the corresponding data analysis technique into this article from article 4. That will be the last section. CO2 DROP/INCREASE AND SEA SURFACE TEMPERATURES: In article 4 of this web site, I presented a new technique for looking at CO2 absorption in the oceans. It is an old technique from chemistry, but has not been used before when considering atmospheric CO2. If you want to go back to that article, review Figures 16 through 18. If you do not want to go back, I present that Figure 17 as Figure 7 below. The data in that figure are derived by subtracting the lowest monthly average for a single year from the highest monthly average for the same year. In that article, this was defined as the drop in CO2. It is also possible to term this as the increase from that year’s lowest value, which is what it will be called in this article. Technically, for it to truly be called the increase, the value should be the difference between the lowest value this year and the highest value next year. Because the CO2 concentration is increasing every year, that would yield a slightly larger number. Because I am only looking for trends from this data, I accepted the same data as the CO2 drop and am calling it the CO2 increase. I could not find any correlatable trends for these data in the previous article, but I am going to plot them with the SST data and point out some trends in this article. Consequently, I present the data from Figure 6 and the annual averages for the SST in the same figure and label it Figure 8. I have multiplied the SST by 10 to get the data in nearly the same range. If you look carefully at Figure 7, you will see that the peaks and valleys from 1965 to 1970 occur at about the same time on the two plots. From 1970 to 1980, the time frame that includes 1976, the peaks and valleys get seriously out of sync. After 1976, the peaks and valleys get back into sync for the most part, but the SST peaks and valleys occur 1 to 3 years before the same for the CO2. This takes some imagination, and I have aided your view of that relationship by drawing dotted lines from the top to the bottom to give you my interpretation. However, I wanted to make it clearer without smoothing the data too much, so I normalized the SST data, which involved taking out the gradually rising average temperature and then modifying the spacing. To make the data even clearer, I did a 3 year running average on both sets of data and that is what is plotted in Figure 9. Once again, I have dotted in lines that I think connect peaks and valleys. Notice that all of the peaks and valleys do not correspond, but most of them do. I have not attempted to connect any peaks of valleys prior to 1970. If you will accept my connecting the peaks and valleys in this way ,then Figure 8 illustrates that the temperature peaks occur 1 to 3 years before the CO2 peaks. I have tried my best and I cannot see that the CO2 leads the temperature. It is also interesting to note the general trends involved in the CO2 increase data (that shown in the top of Figure 8). Generally, the data show an increase up until 1992 and then a drop till 2010. The only significance that I can discern from this observation is that the 1992 break is very close to the 1994 break reported for CO2 and glacier melt. The other important trend is that the CO2 increase starts slowing down after 1992, much like the ocean temperatures. I don’t know what that means, but it is interesting. Thus ends my presentation in this article. It is time for discussions and conclusions. DISCUSSION: Most of the discussion of the techniques and the results are contained in the previous sections and will not be repeated here. The discussions that I think are relevant are related to what this all means with respect to our overall understanding of the “CO2 problem”. A lot of people have spent a lot of time to prove that the increase in CO2 in the atmosphere is solely caused by the burning of fossil fuels. Perhaps the best comprehensive discussion of that topic is found in (reference 6). The evidence is almost overwhelming and yet the trends in both CO2 and glacier melt that are pointed out in this article have been completely overlooked. I do not think that makes the conclusions about the source of the CO2 any less viable, but the results of this study will allow us to take into account the temperature dependence of the CO2 rise. Since 1965, the air temperatures world wide have risen about 1.2 degrees centigrade, see Figure 6 above, and the sea surface temperatures have risen about 0.4 degrees, see Figure 5 above. The CO2 level at Mauna Loa, and for the most of the rest of the world, have risen from 320 ppmv in 1965 to the present level of about 390 ppmv in 2010, which is a 70 ppmv rise. That CO2 rise should nearly equal the rise from all of the various time frames and from the temperature independent rise rate: Base Rate = 1.184 ppmv/year X 45 years = 53.28 ppmv 1965 - 1976 = -(1.184 - 1.111) X 11 years = -0.69 ppmv 1976 - 1994 = (1.469 - 1.184) X 18 years = 5.13 ppmv 1994 - 2010 = (1.825 - 1.469) X 16 years = 5.70 ppmv ----------------------------------------------------------------------- Total = 63.4 ppmv This compares favorably with 70 ppmv. Now, doing the same calculations, but using the temperature changes and the temperature dependent rates: Base Rate = 1.184 ppmv/year X 45 years = 53.28 ppmv 1965 - 1976 = -0.01434 degrees X 6.10 ppmv/degree = -0.087 ppmv 1994 - 2010 = 0.400 degrees X 35.76 ppmv/degree = 14.30 ppmv ------------------------------------------------------------------------------------ Total = 67.49 ppmv This compares even more favorably with 70 ppmv. The difference is just in the mathematics and rounding errors. The general numbers give good agreement and that was the goal of this exercise. So, where does that leave us with respect to the commonly accepted values for amount of CO2 added to the atmosphere and the amount that stays in the atmosphere. Not well at all. The data in this study illustrates that the base rate of CO2 rise (BR) has not changed since 1965 and is constant at about 1.184 ppmv per year. All of the increases in the rate of CO2 rise can be properly attributed to increase in temperatures. Of course, the major inference from that conclusion is that the variations in carbon emissions over that 45 year time period have had no effect on the rate of the CO2 increase in the atmosphere. And the follow on to that inference is that the effect of CO2 as a green house gas is nil. This leads us to many other questions. Question 1. What caused the breaks in the CO2 curve at 1976 and 1994? Bob Tisdale has lots of information on temperature variations the El Nino Southern Oscillation (ENSO) (reference 8), at least for the 1976 temperature jumps. He makes a very good case for this as the cause, but of course, the ENSO is only an indicator and not the cause of anything. However, the ENSO could be an indicator of the fashion in which the oceans of the world are getting rid of their heat which was acquired during the heat rise prior to that time. That was a very large amount of heat. Question 2. Where is all of the CO2 going from all of our emissions? My answer to that it is going into the biota in the oceans and on the land and of course, it is being absorbed by the Artic Ocean. The remainder is going into the atmosphere as evidenced by the isotopic data for both carbon and oxygen, again referring to reference 6. Question 3. Is the temperature dependent portion of the CO2 build up caused by release from the oceans or rather the oceans not being able to absorb as much as before the temperature rise? This is the same question that the people who study ice cores are dealing with. In their case, the exact age of the samples are somewhat in doubt so they have not been able to determine which came first, the CO2 or the temperature. That is the reason that the last section is included in this study. We have good time data on both the CO2 and the SST so that is not a problem. What is in doubt is which peak to associate with which other peak in Figures 7 & 8. I have made what I think is the correct choice of what leads what, but it is only my choice. The curves are dissimilar enough that can not argue with any authority that the temperature was the cause and the CO2 was the effect. To me, it is logical but I hope that someone else can come up with a better argument than I have. Question 4. Why does the base rate of CO2 build up not change? I have given this question a lot of thought and it was all for naught. I have no idea. If anyone else has any ideas and logical explanations, I look forward to hearing from you.
CONCLUSIONS: I will try to keep the conclusion focused on the study and not the implications of the results of the study. -1- The breaks observed in the CO2 versus time curve that occurred about 1965, 1976, and 1994 were also evident in the glacier melt curves. -2- Correlating glacier melt with air temperatures gave the most logical results and yielded a temperature dependence of between 6880 and 14,815 cubic kilometers of melt per degree centigrade with an average melt rate of 10,539 cubic kilometers per degree centigrade.. -3- Correlating CO2 build up in the atmosphere with sea surface temperatures gave the most logical results. Because of the character of the results, a mathematical technique was employed to delineate the trends. -4- It was found that there is a temperature independent portion of the CO2 build up over that last 45 years, called the base rate (BR). This base rate was found to be 1.184 ppmv/year. -5- The temperature dependent portion of the CO2 build up curve was found to be 6.10 ppmv/degree centigrade for the SST for the time frame 1965 to 1976. -6- The temperature dependent portion of the CO2 curve was found to be 35.76 ppmv/degree centigrade for the SST for the time period 1976 to 2010. -7- The numerical values were derived assuming that the temperature independent rise, or BR, was constant over the 45 year time frame and that the temperature dependent portion was the same for the two time periods encompassing the 1976 to 2010. The results seemed to justify these two assumptions. -8- The temperature dependent build up rates were found to be consistent with ice core data (8 to 10 ppmv/degree) and with the temperature dependence of the Henry’s law constant (42.94 ppmv/degree). The discussions dealt heavily with the implications of the derived temperature dependent build up rates for the CO2. The implications of the temperature independent build up rates for CO2 are myriad, but no explanations were advanced.
REFERENCES: 1.http://cdiac.ornl.gov/trends/co2/cmdl-flask/alt.html NOAA/CMDL ATMOSPHERIC CO2 RECORDS. Pieter P. Tans and Thomas J. Conway NOAA Climate Monitoring and Diagnostic Laboratory, Boulder, Colorado 80305 2.http://nsidc.org/data/collections.html "Glaciers and the Changing Earth System: A 2004 Snapshot" by Mark B. Dyargerov and Mark F./ Meier, INSTAAR, University of Colorado at Boulder 3. Journal of Geophysical Research, Vol 110, D07302 (2005), pp14, by Mark Z. Jacobson. Also from chapter 5, pp 39 of Chemical Oceanography, by Emerson and Hodges. 4. Monthly average land temperatures, 1887 - 2009, www.ncdc.noaa.gov/oa/climate/research/anomalies/indes.html 5. Global Sea Surface Temperature Trends (1850 - 2009) htrp://www.cru.uea.ac.uk/cru/data/temperature/hadsst2gl.txt 6.http://www.ferdinand-englbeen.be/klimaat/coe_measurements.html 7.http://www.daviesand.com/Choicess/Precautionary_Planning/closer_Look/index.html 8.http://bobtisdale.blogspot.com/2008/10/1976-pacific-climate-shift.html |
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