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The long temperature series at Svalbard (Longyearbyen) show large variations and a positive trend since its start in 1912. During this period solar activity has increased, as indicated by shorter solar cycles. The temperature at Svalbard is negatively correlated with the length of the solar cycle. The strongest negative correlation is found with lags 10–12 years. The relations between the length of a solar cycle and the mean temperature in the following cycle are used to model Svalbard annual mean temperature and seasonal temperature variations. Residuals from the annual and winter models show no autocorrelations on the 5 per cent level, which indicates that no additional parameters are needed to explain the temperature variations with 95 per cent significance. These models show that 60 per cent of the annual and winter temperature variations are explained by solar activity. For the spring, summer, and fall temperatures autocorrelations in the residuals exist, and additional variables may contribute to the variations. These models can be applied as forecasting models. We predict an annual mean temperature decrease for Svalbard of

The question of a possible connection between solar activity and the Earth’s climate has received considerable attention in the last 200 years [

One of the longest Arctic temperature series is from Svalbard. It started in 1912 and is discussed and analysed by Humlum et al. [^{−1}, in addition to cyclic variations. The strongest cyclic variations have periods 62–68, 26, and 15–17 years. HSS12 also finds lower amplitude variations with periods 11–12 years, which may be related to the solar activity cycle.

Solar activity can be described by the following proxies described by Gray et al. [^{10}Be isotope. Most attention has been paid to the number of sunspots, which varies with a period of 9–13 years. Also the length of the sunspot cycle is known to vary with the solar activity, in the sense that high activity is related to short cycles and low activity to long cycles. The length is shown to vary in a systematic way in a cycle of length of 80–90 years, named after Gleissberg [

The length of a solar cycle can be determined from the appearance of the first spot in a cycle at high solar latitude, to the disappearance of the last spot in the cycle near solar equator. However, before the last spot in a cycle disappears, the first spot in the next cycle appears at high latitude, and there is normally a two-year overlap [

It was for a long time thought that the appearance of a solar cycle was a random event, that is, each cycle′s length and amplitude were independent of the previous. However, Dicke [

Comparing sunspot numbers with the Northern Hemisphere land temperature anomaly, Friis-Christensen and Lassen [

However, at the turn of the millennium, inconsistency with this relation was found [

Length of solar cycles (inverted scale) since 1900. The black dots are the midtime for each cycle.

Solanki and Krivova [

Butler [

A systematic study by Solheim et al. [

In Figure

Correlation

In the following we will discuss the Svalbard temperature series in more detail and investigate how this correlation is related to seasons. We will also investigate how other variables may contribute to temperature variations at Svalbard.

The modern official Svalbard meteorological station is located near the main settlement in Svalbard, Longyearbyen (78° 13′N, 15° 33′E, about 2000 inhabitants), in central Spitsbergen. The station is located at the Svalbard Airport (24 m asl.), about 3 km NW of Longyearbyen, near the shore of the large fjord Isfjorden. Monthly temperature data were obtained from the

The Svalbard meteorological record is a composite record, representing homogenized observations originally made at 4 different stations, located along the shore of the fjord Isfjord, extending from the west coast to the interior of the main island Spitsbergen. A survey of meteorological statistics for the Norwegian Arctic is described by Førland et al. [

The mean yearly (MAAT) temperatures at Svalbard (Spitzbergen)—for the year and the four seasons. The red circles are the mean temperatures in sunspot cycles with standard error bars, also used for the correlation analysis. The red thick lines are weighted linear least square fits to the solar cycle mean temperatures, with the trends for the period 1914–2008 (

Comparing the Svalbard MAAT record with average Arctic temperature development since 1912 [

The Svalbard temperature series starts in 1912. The starting dates (in decimal years) and the length of solar cycles after 1900 are given in Table

Svalbard: Mean temperatures in sunspot cycles.

Cycle | Minimum | Length | Years temp. | Year MAAT | Winter DJF | Spring MAM | Summer JJA | Fall SON | |

no. | yr | no. | yr | °C | °C | °C | °C | °C | |

14 | 1901.7 | 64.2 | 11.9 | ||||||

15 | 1913.6 | 105 | 10.0 | 1914–23 | −7.80 | −17.01 | −12.70 | 4.32 | −5.90 |

16 | 1923.6 | 78.1 | 10.2 | 1924–33 | −5.89 | −11.70 | −11.51 | 4.40 | −4.77 |

17 | 1933.8 | 119 | 10.4 | 1924–43 | −5.32 | −11.61 | −10.44 | 4.39 | −3.53 |

18 | 1944.2 | 152 | 10.1 | 1944–53 | −5.86 | −13.06 | −10.47 | 4.19 | −4.30 |

19 | 1954.3 | 201 | 10.6 | 1954–64 | −5.77 | −13.73 | −9.72 | 4.07 | −3.62 |

20 | 1964.9 | 111 | 11.6 | 1965–76 | −6.70 | −14.51 | −10.72 | 4.20 | −5.73 |

21 | 1976.5 | 165 | 10.3 | 1977–86 | −6.45 | −14.70 | −10.53 | 4.29 | −4.78 |

22 | 1986.8 | 159 | 10.0 | 1987–96 | −5.96 | −14.24 | −8.85 | 4.61 | −5.22 |

23 | 1996.9 | 121 | 12.2 | 1997–2008 | −4.20 | −11.20 | −8.33 | 5.45 | −3.03 |

24 | 2008.9 |

Solar cycle 14 (SC14) began in 1901 and was nearly finished when the Svalbard temperature observations started. Our analysis therefore starts with SC15 which began in 1914. Table

We have also calculated mean temperatures for four seasons as given in the table. Figure

Statistics on Svalbard temperature series.

Model 1 | Model PSCL | Bootstrap (1000 samples) | ||||

95% confidence | ||||||

^{−1} | ^{−1} | limit | ||||

Year | 0.43 | − | 0.75 | 0.79 | 0.54 : 0.96 | |

Winter | − | 0.02 | − | 0.82 | 0.81 | 0.52 : 0.97 |

Spring | 0.85 | − | 0.57 | 0.57 | 0.04 : 0.93 | |

Summer | 0.54 | − | 0.28 | 0.33 | 0.02 : 0.70 | |

Fall | 0.33 | − | 0.65 | 0.60 | 0.15 : 0.94 |

The calculated linear trend is given by

The number of observations in the regression analysis is 9. Usually the degree of freedom is the number of observations minus the number of parameters in the model. However, analysis of the sunspot length effect on different lags of delayed temperature has been performed on beforehand, which resulted in a model where the previous sunspot cycle period explains the temperature in the next sunspot cycle. Hence, the regression model is reduced with one additional degree of freedom which results in

The lengths of solar cycles since 1900 are shown with an inverted scale in Figure

We recognize some qualitative similarities: the SCL shortened in 1910–20, while the average temperature, and in particular the winter temperature, increased until about 1935. When the SCL became longer around 1970 a temperature minimum appeared a few years later. The short period SC22 which ended early in 1996 was followed by a temperature maximum around 2005.

Correlating the 11-year averaged Svalbard MAAT with the lengths of the solar cycles shows that the correlation (

Linear least square fits between the length of a solar cycle and the average temperature in the next cycle (weighted with

Residuals from PSCL model for the SValbard temperature series and the seasonal series. The sunspot-cycle number is shown by the winter series.

Table

temperatures explained as a function of time (secular trend) (Model 1),

temperatures explained by the previous solar cycle (Model PSCL).

Analytical correlations coefficients (

We have therefore determined a correlation coefficient

Comparing

The model fitting is not complete without examining the residuals. We have performed a Durbin-Watson (DW) statistical test [

Durbin Watson test on the autocorrelations in the PSCL model residuals.

Series | DW | Level result | Result |
---|---|---|---|

Year | 2.10 | 4-D(U) > DW > D(U) | No autocorrelation |

Winter | 2.44 | 4-D(U) > DW > D(U) | No autocorrelation |

Spring | 0.56 | DW < D(L) | Positive autocorrelation |

Summer | 0.64 | DW < D(L) | Positive autocorrelation |

Fall | 3.24 | DW > 4-D(L) | Negative autocorrelation |

The number of observations in each series is 9. Because of inspection of the data on beforehand one degree of freedom has been subtracted which corresponds to 8 instead of 9 “effective” observations. The model has one parameter in addition to the intercept. Then the 5% significance levels for the DW test are D(L) = 0.763 and D(U) = 1.332. The DW test is considered to have no significant autocorrelations if D(U) < DW < 4-D(U), indifferent if D(L) < DW < D(U) and 4-D(L) > DW > 4-D(U), positive autocorrelations if DW < D(L), and negative autocorrelations if DW > 4-D(L).

For two of the series, the yearly average and the winter temperatures, we find no autocorrelations in the residuals, which means that the model can be accepted by using the traditional statistical tests and confidence limits estimation without reduction of degrees of freedom. Then the

For the three other series: spring, summer, and fall, the DW test gives positive or negative autocorrelations, indicating that the linear relation found is not a complete description. These series should be further analyzed for development of better models. The Durbin-Watson tables [

The residuals from the PSCL-model are shown in Figure

The average temperature during a solar cycle as a function of the length of the previous cycle for Svalbard yearly and seasonal mean temperatures 1914–2008. Trends (

Of the 5 series investigated, the yearly mean and the winter mean temperatures are completely described by the PSCL-model. This model can be used to give forecasts for SC24 based on SCL23. The resulting forecasts show that the mean yearly temperature will decrease from −4.2°C in SC23 to −7.8°C, with a 95% confidence interval [−5.8 : −9.6]°C in SC24. This is the same result as with unweighted relations in SSH11 [

Our main result is a strong correlation between the mean air temperature at Svalbard in a solar cycle and the length of the previous solar cycle. The relation is highly significant for the yearly and winter mean temperatures. This is documented by stringent statistical tests showing no significant autocorrelations in the residuals, and small standard deviations in the

The yearly and winter solar influence on the Svalbard temperature is estimated to

In the spring (MAM) the landscape at Svalbard is almost completely snow covered, which means that most of the incoming short wave radiation from the Sun will be reflected, which results in little direct solar warming in the spring. On the other hand spring is normally the driest period of the year and dominated by an Arctic anticyclone, which prohibits warm air advection from lower latitudes. Here is a marked difference between winter (DJF) and spring (MAM). The spring relation is modulated by ice or no ice in the fjord. In the summer, fall, and winter the fjord has been ice-free since 1912, but ice usually appears some times in the spring months (MAM). The increasing spring temperatures may be related to less ice in the fjord and the general reduction of the Arctic ice.

The summer air temperature recorded at Svalbard Airport is highly influenced by local wind conditions, partly controlled by a land-sea breeze effects because of relatively small regional air pressure differences during the summer. By this the summer air temperature is controlled mainly by local conditions in the neighbourhood of the meteorological station (topography, land surface characteristics, and surface temperature in the adjoining fjord), which are relatively stable from summer to summer.

Looking at the observed and averaged temperatures in Figure

The strong trend in the spring residuals of 3.2°C/100 yrs may be explained as a Polar amplification as described by Bekryaev et al. [

The result of our PSCL model, explaining more than 60% of the temperature variance for annual and winter temperatures for Svalbard, can be compared with a solar forcing well over 75% of the variance for the decadally smoothed Arctic mean or spring temperatures as determined by Soon [

The lag of one solar cycle for the temperature response may have two explanations. The first is a relation between solar cycle length and the amplitude (

Based on the PSCL relation we predict a temperature decrease at Svalbard of about

A linear relation exists in the temperature series from Svalbard between the length of a solar cycle and the average temperature in the next solar cycle.

The yearly average and the winter temperatures can be modelled as a function of the length of the previous solar cycle, with highly significant negative trends.We call this the PSCL regression model.

The residuals from the PSCL model show no positive autocorrelation using the Durbin Watson test. The estimated correlation coefficients between the observed temperatures and the temperature from the fit to the regression models are reasonably high for yearly average and winter temperatures. Also the uncertainty levels of the estimated correlations coefficients calculated by Bootstrap analysis are on an acceptable level. Hence, the winter model and the yearly average model are considered to be acceptable, which means that no additional variables are needed.

A measure of the solar contribution is the coefficient of determination

For the average winter temperature the residuals show a negative linear trend, which indicates that cooling might have taken place the last 100 years if the solar activity did not increase as observed by the shortening of the solar cycle.

The solar cycle/temperature relation (our Model PSCL) can, when a sunspot cycle is finished, be used to predict the temperature in the next solar cycle. For Svalbard it means an estimated cooling of

This regression forecasting model benefits, as opposed to the majority of other regression models with explanatory variables, to use an explanatory variable—the previous sun cycle length—nearly without uncertainty. Usually the explanatory variables have to be forecasted, which of cause induce significant additional forecasting uncertainties.

The negative trends in the spring and fall PSCL models are significant on 80% level. With positive and negative autocorrelations in the residuals, one may expect also other variables could be present for these series. The spring model residuals show a significant secular trend of 0.032°C/yr, which indicates an amplification of some kind, probably related to diminishing Arctic and local ice cover in the spring season with an albedo effect. The residuals from the fall series show no significant trend. This may be explained by the nearby fjord (Isfjord) which never has been frozen in the fall and winter seasons since the start of the temperature series in 1912.

The Svalbard temperature data series used in this study was obtained from the