Future low solar activity periods may cause extremely cold winters in North America, Europe and Russia
Summary.
The observed winter temperatures for Turku, Finland (and also generally for North America, Europe and Russia) for the past 60 winters have been strongly dependent on the Arctic Oscillation index (AO). When the Arctic Oscillation index is in "positive phase", high atmospheric pressure persists south of the North Pole, and lower pressures on the North Pole. In the positive phase, very cold winter air does not extend as far south into the middle of North America as it would during the negative phase. The AO positive phase is often called the "Warm" phase in North America. In this report I analyzed the statistical relation between the Quasi-Biennial Oscillation index (QBO is a measure of the direction and strength of the stratospheric wind in the Tropics), the solar activity, and the Arctic Oscillation index and obtained a statistically significant regression equation. According to this equation, during negative (easterly) values of the QBO, low solar activity causes a negative Arctic Oscillation index and cold winters in North America, Europe and Russia, but during positive (westerly) values of the QBO the relation reverses. However, the influence of the combination of an easterly value of the QBO and low solar activity on the AO is stronger and this combination is much more probable than the opposite. Therefore, prolonged low solar activity periods in the future may cause the domination of a strongly negative AO and extremely cold winters in North America, Europe and Russia.
Arctic oscillation index and Turku winter temperature.
Turku is located in the SW corner of Finland where the Arctic Oscillation Index for December-February almost completely controls the winter temperature for these months. See Figures 1 and 2.
Figure 1. Turku Winter temperature December-February 1951-2010 and corresponding Arctic Oscillation index, data from NOAA (2010).
Figure 2. Same as Figure 1., but the Arctic Oscillation index is by means of regression analysis converted to the same scale as the Turku winter temperature.
In January and February 1989 the Arctic Oscillation index jumped up to a very high level causing a warm winter. The index stayed at a higher level, but collapsed back to a record low level in December 2009 - February 2010. This kind of behavior of a time series is very typical for 1-lag and 2-lag random walk mechanisms.
The data for the Arctic Oscillation index (AO) December-February 1951-2010 (NOAA 2010) are presented in Appendix 1., and the probability density diagram in Figure 3.
Figure 3. Probability density diagram for the Arctic Oscillation index for December-February 1951-2010.
The Arctic Oscillation index for the winter months 1951-2010 follows a Gaussian distribution with an arithmetic mean value of -0.375.
The random walk behavior of the Arctic Oscillation index points towards a mechanism whereby the index consists of white noise that is driven by two or more harmonic oscillations. Most probable candidates for these oscillations are the Quasi-Biennial Oscillation with a period length of about 28 months, and the solar activity cycle with a period length of about 138 months.
A clear influence of the solar activity and the Quasi-Biennial Oscillation index on the Arctic Oscillation index has been discovered by Labitzke (2005) and will here be verified by means of statistical methods.
Quasi-Biennial Oscillation index.
The Quasi-Biennial Oscillation index is a measure of the strength and direction of tropical stratospheric wind. A negative value corresponds to easterly wind, and a positive value to westerly wind. The data for the Quasi-Biennial oscillation index (QBO) December-February 1951-2010 (NOAA 2010) are presented in Appendix 1. and the probability density diagram in Figure 4.
Figure 4. Probability density diagram for the Quasi-Biennial Oscillation index for December-February 1951-2010.
For the winter months 1951-2010 the distribution is almost rectangular with an arithmetic mean value of -2.9. Thus, negative or easterly values of the QBOhave been predominant during the winter months.
The solar activity.
Labitzke (2005) used the 10.7 cm solar flux as a measure of solar activity. As the correlation coefficient between this measure and the sunspot number is 0.98, we may as well use the sunspot number directly.
The data for sunspot number (SUN) December-February 1951-2010 (NOAA 2010) is presented in Appendix 1. and the probability density diagram in Figure 5.
Figure 5. Probability density diagram for the sunspot numbers for December-February 1951-2010.
As the sunspot number can never be negative, a log-Gauss curve fit can describe the observations. We can see that low solar activity has been more common than high solar activity. Taken together with theQBO, the combination low QBO- low SUNhas been much more common during the winters than the combination high QBO- high SUN.
AOas a function of QBOand SUN.
By means of multiple regression analysis, the following equation was tested:
AO = b0+ b1*QBO+b2*SUN+b3*QBO*SUN+b4*QBO2+b5*SUN2(1)
where b0- b5are regression coefficients. The result is shown in Appendix 1. b2, b4, and b5were eliminated as statistically insignificant.
The final statistically significant regression equation (p < 0.05) is:
AO = -0.2779 + 0.06096*QBO- 0.0005149*QBO*SUN (2)
Graphical presentation of the regression equation.
On order to obtain a picture of the Equation (2), AO was plotted as a function of SUN for two values of QBO in Figure 6. These values were chosen as minimum and maximum values from the rectangular probability density in Figure 4.
Figure 6. Statistically significant (p< 0.05) regression model for the Arctic Oscillation index as a function of Sunspot Number plotted for minimum (east), neutral, and maximum (west) values of the Quasi-Biennial Oscillation index.
It is very obvious that a predominantly low sunspot solar activity at negative (easterly) Quasi-Biennial oscillation index is able to decrease the Arctic Oscillation index much more than the other combinations are able to change the Arctic Oscillation index.
At high solar activity, the Arctic Oscillation index has not been very sensitive to the Quasi-Biennial oscillation.
Turku winter temperature.
The fact that the solar activity and the Quasi-Biennial Oscillation together with stochastic noise control the Arctic Oscillation means that the Turku winter temperature too is dependent on these two oscillating parameters.
Equation (2) together with the connection obtained from Figure 2. give the result shown in Figure 7. Despite considerably high variations between different winters, the combination low QBO-low SUN is more likely to correspond to colder winter temperatures in Turku than all other combinations.
Figure 7. Turku winter temperature as a function of solar activity and Quasi-Biennial oscillation.
Conclusion.
Historically, low solar activity has been connected to cold winters in Europe. A definitive physical mechanism for this fact has not yet been presented. This analysis however shows that the influence of solar activity together with stratospheric mechanisms acting on the Arctic Oscillation is statistically significant. It also explains why the Arctic Oscillation seems to behave according to a random walk mechanism. If the solar activity in the future goes into a new Dalton or Maunder Minimum, the winters inNorth America, Europe and Russia may become very cold.
REFERENCES
Labitzke, K., 2005: On The Solar Cycle-QBO relationship, a summary. J. Atm. Sol-Terr. Phys., 67, 45-54
Update on:
http://strat-www.met.fu-berlin.de/labitzke/moreqbo/MZ-Labitzke-et-al-2006.pdf
http://www.cpc.ncep.noaa.gov/products/precip/CWlink/daily_ao_index/monthly.ao.index.b50.current.ascii
NOAA, 2010: QBO-data on:
http://www.esrl.noaa.gov/psd/data/climateindices/
NOAA, 2010: Sunspot data on:
ftp://ftp.ngdc.noaa.gov/STP/SOLAR_DATA/SUNSPOT_NUMBERS/MONTHLY
APPENDIX 1.
Data matrix1951-2010 Dec-Feb QBO-index, SUNspot Number, and AO-index
QBO SUN QBO*SUN sq(QBO) sq(SUN) AO-index (dependent)
1951 -4.8800 59.700 -291.34 23.814 3564.1 -.80400 -6.1600 34.400 -211.90 37.946 1183.4 .20300 -2.4200 21.400 -51.788 5.8564 457.96 -1.0370 -4.7000 .70000 -3.2900 22.090 .49000 .82100E-01 -8.4600 17.900 -151.43 71.572 320.41 -.71700 -.14000 80.400 -11.256 .19600E-01 6464.2 -1.2250 -13.320 132.00 -1758.2 177.42 17424. .18600 5.5700 189.70 1056.6 31.025 35986. -.94600 -18.750 163.60 -3067.5 351.56 26765. -.38500
1960 5.4900 126.40 693.94 30.140 15977. -1.5790 -5.8200 52.500 -305.55 33.872 2756.3 -.40900 4.2400 35.000 148.40 17.978 1225.0 -.13100 -16.390 17.100 -280.27 268.63 292.41 -1.9140 4.8900 11.400 55.746 23.912 129.96 -.45600 -1.0800 14.100 -15.228 1.1664 198.81 -1.1250 -20.100 19.300 -387.93 404.01 372.49 -1.5020 11.590 83.800 971.24 134.33 7022.4 -.26600 -8.6200 46.600 -401.69 74.304 2171.6 -.97000 -8.1200 106.40 -863.97 65.934 11321. -2.2880
1970 1.3000 117.50 152.75 1.6900 13806. -1.8670 -10.580 86.300 -913.05 111.94 7447.7 -.49500 8.4200 76.700 645.81 70.896 5882.9 .26500 -7.0300 40.500 -284.71 49.421 1640.3 1.0850 .30000E-01 24.400 .73200 .90000E-03 595.36 -.14600 -18.220 15.500 -282.41 331.97 240.25 .78200 9.8900 6.2000 61.318 97.812 38.440 .99300 -13.640 18.000 -245.52 186.05 324.00 -2.6170 3.9300 60.800 238.94 15.445 3696.6 -1.2000 2.5100 140.70 353.16 6.3001 19797. -1.3030
1980 -10.920 145.10 -1584.5 119.25 21054. -.56800 8.3200 142.00 1181.4 69.222 20164. -.16800 -13.180 138.80 -1829.4 173.71 19265. -.37500 10.870 86.000 934.82 118.16 7396.0 .17300 -11.140 56.100 -624.95 124.10 3147.2 .26300 -1.4400 15.900 -22.896 2.0736 252.81 -1.2670 9.4700 12.100 114.59 89.681 146.41 -1.8060 -10.600 5.8000 -61.480 112.36 33.640 -.85400 7.4600 40.900 305.11 55.652 1672.8 -.44700 -2.9500 167.40 -493.83 8.7025 28023. 2.6880
1990 -9.6700 157.90 -1526.9 93.509 24932. 1.2530 9.2500 152.80 1413.4 85.563 23348. .37500 -13.660 147.70 -2017.6 186.60 21815. 1.0950 9.5400 78.900 752.71 91.012 6225.2 1.1790 -7.8300 50.700 -396.98 61.309 2570.5 -.41800 7.4400 26.900 200.14 55.354 723.61 .72300 -5.7500 8.9000 -51.175 33.063 79.210 -1.0550 -3.8300 8.5000 -32.555 14.669 72.250 -.96000E-01 -1.0100 34.900 -35.249 1.0201 1218.0 -.77800 1.6600 71.000 117.86 2.7556 5041.0 .64900
2000 5.1600 98.000 505.68 26.626 9604.0 1.1300 -15.260 97.100 -1481.8 232.87 9428.4 -1.3120 4.7100 128.50 605.23 22.184 16512. .45400 -1.1000 74.800 -82.280 1.2100 5595.0 -.64500 -1.2000 45.700 -54.840 1.4400 2088.5 -.94300 .31000 25.930 8.0383 .96100E-01 672.36 .10500 -18.370 22.800 -418.84 337.46 519.84 -.81000 3.7500 14.600 54.750 14.063 213.16 1.0030 -12.200 4.8000 -58.560 148.84 23.040 .85900 11.170 .80000 8.9360 124.77 .64000 .25800
2010 -15.000 4.5000 -67.500 225.00 20.250 -3.4220
Mean of Var.( 1) = -2.9428 stdev. = 8.98
Mean of Var.( 2) = 64.414 stdev. = 53.7
Mean of Var.( 3) = -163.12 stdev. = 798.
Mean of Var.( 4) = 87.990 stdev. = 98.1
Mean of Var.( 5) = 6982.6 stdev. = .908E+04
Mean of Var.( 6) = -.37535 stdev. = 1.08
Backward Elimination Multiple Regression Analysis:
Number 4 is insignificant and eliminated (square of QBO insignificant)
Number 2 is insignificant and eliminated (linear SUN insignificant)
Number 5 is insignificant and eliminated (square of SUN insignificant)
Statistically significant regression coefficients at 0.05 significance level:
b 0 ... -.27994110 Intercept
b 1 ... .60961730E-01 stdev. ... .220E-01 Linear coefficient for QBO
b 3 ... -.51492850E-03 stdev. ... .247E-03 Coefficient for QBO*SUN
F( 1) = ........ 7.68
F( 3) = ........ 4.33