Mar 17th 2010

Future low solar activity periods may cause extremely cold winters in North America, Europe and Russia

by Jarl R. Ahlbeck

The writer is D.Sc. and lecturer at Abo Akademi University, Finland

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

NOAA, 2010: AO-data on:
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


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