0340-5442/93 $6.00 + 0.00 Copyright @ 1993 Pergamon Press Ltd
Energv Vol. 18, No. 12, pp. 1273-1284, 1993 Printed in Great Britain. All rights reserved
Eigil Friis-Christensen Solar-Terrestrial Physics Division, Danish Meteorological Institute Lyngbyvej 100, DK-2100 Copenhagen, Denmark (Received 29 January 1993)
Abstract - Variations in the activity of the Sun have long been suspected to affect the climate of the Earth, and a number of correlations have been presented that indicate a link. In many cases, the presented correlations have been associated with poor statistical significance. Recent results, however, have indicated strong correlations between climate parameters and solar activity. Upper troposphere and stratosphere temperatures have been found to vary in phase with the lo- to 1Zyear solar activity cycle. On a longer time scale, the global temperature, particularly the Northern Hemisphere land air temperature, has been found to be nearly perfectly correlated with the long-term variation of solar activity. The solar activity itself cannot be represented by only one parameter. Different representations of solar activity have different and not understood, long-term variations. It has been found that the longterm variation of solar activity represented by the varying length of the approximately 11-year solar cycle is the parameter that is probably best correlated with global temperature, both with respect to the modem instrumental temperature record from 1860 to 1990 and with respect to a reconstructed temperature record extending back to 1750 when sunspot observations are believed to have been reliable.
1. Introduction The climate of the Earth is the result of the physical response of the combined system of the atmosphere, the ocean, and the landmasses to the energy received from the Sun and partly lost to space again through radiation. Any changes in the energy received and lost and any changes in the distribution of the energy on the surface of the Earth will therefore have an effect on climate. The composition of the atmosphere is of fundamental importance for the radiative balance that determines climate. A main issue in the public as well as in the scientific community is therefore the changes in climate that could be due to anthropogenic changes in the composition of the atmosphere, the so-called enhanced greenhouse effect. In order to evaluate this effect in terms of for example the global mean temperature, it is of importance to evaluate the temperature variations of natural origin including those that could be due to changes in the energy received from the Sun and its distribution on the surface oftheEarth. On time scales of ten thousand years, it is well known that the Earth’s climate changes considerably. It is generally accepted that these changes occur as results of changes in the orbit of the Earth relative to the Sun. Although small, these changes seem sufficient to have initiated large oscillations in the Earth’s climate in a manner still poorly understood. Only during recent years has it finally been proven that the energy emitted through radiation from the Sun is not constant, as one might think. This proof was made possible after a continuous period of about 12 years of direct measurement of the total solar irradiance from a satellite in space where radiation measurements are not contaminated by the varying opacity of the Earth’s atmosphere. For centuries, the possibility of climatic changes due to changes in solar activity has been discussed. But even today it has not been possible to demonstrate any physically plausible mechanism whereby changes in solar activity could influence climate. 1273 EGY 18:12-G
The 11-year activity of the Sun was first demonstrated through observations of sunspots, which are dark areas associated with strong local magnetic fields at the surface of the Sun. Intuitively, one might think that these dark spots would reduce the solar radiation. This is in fact true, but satellite measurements show that although the “shadow effect” does exist, the effect is more than compensated by intense radiation from the faculae that tend to brighten during higher solar activity.’ In recent time, solar activity is monitored in a number of ways including the 10.7 cm radio wave emission from the Sun. This emission has been observed continuously since the fifties and is well correlated with the sunspot number. Knowledge of solar activity on a long-term basis, however, is mainly based on observations of sunspot numbers, which have been systematically observed since 1750. In Figure 1 is shown the average monthly sunspot number from 1750 to 1992. It is evident that the monthly mean sunspot number is affected by noise that is superposed on an assumed and apparent quasi-regular 1l-year period. In applications of the sunspot number a method of a weighted 13-months running mean has traditionally been used in order to avoid the month-to-month variations.
Monthly mean sunspot number
150 100 SO 0~
Fig. 1. The monthly mean of the sunspot number 1750 to 1991. For investigations of long-period variations of solar activity, as well as of relationships between this activity and terrestrial phenomena, a particular smoothing procedure called “secular smoothing” was introduced by Gleissberg. * This procedure is based on the assumption that, as the course of the spot frequency during each sunspot cycle is disturbed by short term variations of accidental character, the cycles themselves are disturbed also by accidental variations. In addition to the very clear approximately 1l-year period in the monthly sunspot number, it is observed that the magnitude of the maximum sunspot number in each 1l-year cycle changes in an apparently oscillatory way. This oscillation with a period of about 80 to 90 years has been named after Gleissberg. This Gleissberg period is not only seen in the number of sunspots but also in a completely different parameter, namely, the number of auroras, which has been observed more or less systematically during centuries. Careful studies of independent observations from the Orient and from Europe have demonstrated simultaneous long-term variations in the number of observed auroras3 This shows that the long-term variations are not just due to a changing quality of the observations but that they do reflect a varying energy transport from the Sun. A spectral analysis of published auroral observations during 2000 years by Feynman and Fougere’ resulted in a clear 88 year peak which is also seen in variations of the radioactive “C isotope. This isotope has its origin in the cosmic radiation, which causes the transformation of nitrogen atoms to this isotope. Since the cosmic radiation from deep space is supposed to be constant over these time scales, the reason for the varying effectiveness of this process in the atmosphere is that the Earth’s environment is shielded from the cosmic radiation by the
Solar activity variations and global temperature
varying magnetic field in the solar wind. A strong solar wind magnetic field will be more effective and thus decrease the production of the 14Cisotope. The occurrence of aurora is known to be closely connected to increased magnetic activity, for example in cases of “magnetic storms”. During more than 120 years systematic observations of the geomagnetic field on the surface of the Earth have been performed. In Fig. 2, an annual index of magnetic activity, the aa index, is shown for 1867 to 1991. From this plot, it is clear that also the geomagnetic activity shows an approximately 1l-year cycle. Contrary to the sunspot variation, which shows a dominant 1l-year cycle with a less pronounced long-term variation, the geomagnetic 1l-year cyclic variations are superposed on a long-term (Gleissberg) variation of similar amplitude including a nearly monotonic increase from l!MKlto 1960. The main difference between the sunspot record and the record of magnetic activity is that the sunspot number decreases to values very close to zero at each sunspot miniium whereas the magnetic activity at different solar minima is rather different and does show a distinct long-term variation. This indicates that low sunspot numbers do not necessarily mean that solar activity is close to a possible lower threshold. The general solar activity at different sunspot minima may be rather different, even if it does not manifest itself in the observed sunspot number directly. The approximately 88-year Gleissberg period is also found in another parameter of solar activity, namely, the length of the approximately 1l-year period, which in reality is between 8 and 14 years long. Short solar cycles are associated with a high level of the long-term solar activity whereas long periods are typical for low solar and auroral activity. In order to reveal the essential behavior of the sunspot cycle, Gleissberg introduced a low-pass filter to the data. This filter corresponds to a running mean filter with the weights of 1,2,2,2,1. He applied the filter to the series of individual sunspot maximum and minimum epochs, respectively, and presented a table of these secularly smoothed epochs as well as the corresponding smoothed lengths of the individual sunspot periods.
35 I 30 1 25 1 20 1 1 15 L 10 1 5-
1920 1940 Year
Fig.2. AMU~ average of the geomagnetic activity index aa 1867-1991. In Fig. 3 is plotted the length of the sunspot cycle based on data after 1750, determined separately by means of the sunspot minima and maxima, respectively.5 The 1,2,2,2,1 filter has been applied to the data. Noticeable in the plot is that the lengths determined by means of epochs of minima display a variation of amplitude that is systematically less than those determined by means of epochs of maxima. The phenomenon is particularly obvious before about 1850, which is the time after which sunspot numbers are first thought to be fully reliable.6
The most obvious part of the solar variability is associated with the 1l-year solar cycle. Therefore, it was this cycle that might also be supposed to have the most conspicuous climatic effect. However, in spite of many attempts it has been difficult to find a convincing statistical indication of an effect in the surface temperature. A reason for that could be that the temperature is affected by large short-time variations caused by volcano eruptions and internal variations in the coupled atmosphereocean system as for example expressed in the El Niflo phenomenon. In the upper troposphere and in the stratosphere, however, the temperature conditions are simpler, and this may be a reason why the first statistically convincing results of a solar activity effect were based on this type of data. Labitxke’ reported on a very distinct lO- to 12-year period in these data which was phase-locked to the solar activity cycle during the last thirty years. Before this, systematic temperature measurements in these altitudes do not exist. Although some meteorologists rejected the association, careful statistical tests demonstrated that the probability of the effect being just a coincidence is less than 1% .*
Sunspot cycle length
Year Fig. 3. Variation of the sunspot cycle length 1750-1990 determined independently by means of sunspot minimum (m-m) and sunspot maximum (M-M) epochs, respectively. A smoothing filter with the coefficients 1,2,2,2,1 has been applied to the data. All values have been plotted at the centre of each cycle. Regarding long-term variations in climate, Eddy drew attention to the coincidence of the so-called Maunder minimum in solar activity with the coldest excursion of the “Little Ice Age”. Eddy pointed out that this apparent long-term relationship might be due to changes in the total solar irradiance. Reid9 noticed a striking similarity between the globally-averaged sea-surface temperature (SST) and the long-term variation of solar activity represented by the 1l-year running mean Zurich sunspot number. He pointed out that the two time series had several features in common. Most noteworthy was the prominent minimum in the early decades of this century, the steep rise to a maximum in the 195Os, and a brief drop during the 1960s and early 1970s followed by a final rise. Based on this comparison, Reid suggested that the solar irradiance may have varied by approximately 0.6% from 1910 to 1960 in phase with the 80-90 year cycle (the Gleissberg period) of solar activity represented by the envelope of the 1l-year solar activity cycle. He found that the necessary range of variation in the solar constant during the 130 year period is less than 1%. This order of
Solar activity variations and global temperature
magnitude is consistent with the long-term trend which could be derived from existing observations of the solar irradiance during the recent years by means of satellites, rockets, and balloons. Satellite measurements over approximately one solar cycle have shown that the irradiance is not constant, but model calculations show that it varies too little (less than 0.1%) during a solar cycle to be of major importance for climate.” However, no measurements yet exist that do exclude the possibility of larger variations in total irradiance over a longer period of time. The statistical correlation between the two time series used by Reid was reported to be 0.75. Although this is apparently better than the correlation between the observed mean global temperature and the modelled temperature caused by the increased greenhouse effect, Friis-Christensen and Lassen ” pointed out a major difficulty with this interpretation. They examined the Northern Hemisphere land air temperature” l3 and noted that this record was leading both the SST record and the sunspot record, in fact by as much as 20 years as seen in Fig. 4. From this discrepancy they concluded that if a cause and effect relation between solar activity and terrestrial climate is to be maintained, it is unlikely that longterm variations of solar activity can be sufficiently well represented by some average value of the sunspot number itself.
N. Hemisph. land T and sunspot number - loo
1920 1940 Year
Fig. 4. 1l-year running mean of the annual average Northern Hemisphere land air temperature relative to the average temperature 1951-1980, and the 1l-year running mean of the yearly sunspot number R.
But, as they pointed out, other parameters of solar activity exist that do have a different long-term variation. In particular, they examined the long-term variation of the variable length of the ‘1 l-year’ sunspot cycle (see Fig. 3) and found that this parameter was nearly perfectly correlated with the Northern Hemisphere land-surface temperature during the entire interval of systematic temperature measurements from 1860 to 1990. This is demonstrated in Fig. 5 showing the variation of the sunspotcycle length together with the 1l-year running mean of the Northern Hemisphere land air temperature from 1860. The 1l-year running mean filter was chosen in order to suppress the temperature variations within a solar cycle, which obviously cannot be ascribed to a possible long-term external forcing of the climate. The filtered temperature record appears to follow closely the record of the sunspot-cycle length. Also, the sunspot-cycle length record is subject to ‘noise’, due to the fact that the time of the start of a cycle
cannot be exactly defined because of the presence of short-term variations in solar activity that obscure this. This is the case when the minimum activity in the ’ 11-year’ cycle is regarded as the start of a cycle, but it is even more difficult to define the start of a cycle by means of the time of maximum solar activity. Therefore, the cycle-length record must also be filtered. In this presentation, the low-pass filter introduced by Gleissberti has been used. Based on the close association between the solar cycle length and the mean land-surface temperature of the Northern Hemisphere, Friis-Christensen and Lassen ‘I proposed that the solar cycle length could provide a better indicator of long-term variations in solar luminosity than the sunspot number itself.
N. Hemisph. land T and sunspot cycle length 9.5
1920 1940 YC%U
Fig. 5. 1l-year running mean of the annual average Northern Hemisphere land air temperature relative to the average temperature 1951-1980, and the filtered length of the sunspot cycle.
Although the Northern Hemisphere temperature record is based on a larger data set than that for the Southern Hemisphere, an inclusion of the Southern Hemisphere land air temperature to yield a global average land air temperature record only changes the temperature curve by a minor amount, as seen in Fig. 6. The temperature records, however, behave significantly differently when the sea-surface temperatures are taken into account. Fig. 7 shows a plot similar to Figs. 5 and 6, but here the temperature record consists of the combined land and sea-surface temperatures, the global temperature.” A marked delay of the global average combined land and ocean temperature variations relative to the land air temperature of Fig. 6 is obvious. This delay may, however, be understood as due partly to a delayed response of the ocean to external forcing. A delayed response of the ocean could also be the reason for the slight delay of the global land air temperature in Fig. 6 relative to the Northern Hemisphere land air temperature in Fig. 5. Due to the different distribution of land and ocean in the two hemispheres, the Southern Hemisphere observations would probably be more affected by the ocean thermal inertia. In addition to the long-term variation of the climate illustrated by the 1l-year running mean temperature, the climate has, of course, a significant component of short-term variations. These include the large year-to-year variations also shown in Fig. 7 that are due to internal oscillations in the climate. Apart from the variance associated with this component, the long-term variations of interdecadal and longer periods indicate the possibility of a significant component associated with a variation in the solar energy output.
Solar activity variations and global temperature
Global land T and sunspot cycle length _._ -
YeerS - 11.0
- 11.5 ,
1920 1940 YW
Fig.6. 1l-year running mean of the annual average global land air temperalture relative to the average temperature 1951-1980, and the filtered length of the sunspot cycle.
Global land/sea T and sunspot cycle length 9.5
3 0.1” B 8 0.0”
g,.2° 8 -0.3” k
Fig.7. AMU~ average and 11-year running mean of the annual average global temperature (land and sea) relative to the average temperature 19511980, and the filtered length of the sunspot cycle.
The limited extent of instrumental temperature records and the possible complex bebaviour of a solar-climate relationship that makes a filtering of the time series necessary means that the statistical significance of the correlation is not sufficiently strong to prove that the found correlation is not just a coincidence. Since the shorter term variations in solar activity and temperature may have quite different characteristics, the only possible way to obtain an increased significance is to try to use a longer time series of temperature data. For lack of direct systematic temperature measurements over a large region, attempts have been made to reconstruct past climate by using sporadic temperature measurements in conjunction with non-
instrumental proxy data. A comprehensive reconstruction of the Northern Hemisphere temperature covering a 300-year period prior to the modern instrumental record was achieved by Groveman and Landsberg.” They used several local temperature measurements together with proxy data from many places in the Northern Hemisphere and performed a multiregressional analysis of the data that resulted in a set of empirical formulas relating each proxy data series to the measured Northern Hemisphere temperature. Using this set of empirical relations, they then calculated the temperature for the Northern Hemisphere. In Fig. 8, reproduced from Friis-Christensen and Lassen,’ the reconstructed annual temperature series of Groveman and Landsberg from 1750 to 1860 is plotted together with the modem instrumental temperature record for the Northern Hemisphere and together with the variation of the sunspot cycle length taken from Fig. 3. As discussed in a previous section, the latter has been derived from minimum epochs covering the whole period, supplemented by maximum values for the years after 1850. A reduction to the modern instrumental temperature record, expressed as anomalies relative to 1951-1980, has been done by applying a correction of 4.1 “C to the values of Groveman and Landsberg, which were originally given as departures from the average Northern Hemisphere temperature 1881-1975. Naturally, the reconstruction of the global temperature must be less confident than the modem record. Groveman and Landsberg give a standard error of 0.2 to 0.3 “C for the single annual averages plotted in Fig. 8. Besides this, there exist, of course, year-to-year variations due to internal oscillations in the climate, El Nifio effects, volcanic eruptions, etc. Taking these variations into consideration, the comparison between the temperature record and the solar activity during the pre-instrumental period reveals that there is a good association between the trends in the temperature and in the solar cyclelength record, although the coincidence may be leas obvious than for the modem instrumental record. This independent result for a separate time interval indicates that the association found for the last 130 years” has probably been present for at least 240 years.
N. Hemisphere T and sunspot cycle length (12221) . I
Proxy 1 -m-m-M4
Fig. 8. AMU~ average values of the Northern Hemisphere land air temperature. For 18651990, the temperature is the instrumental record; prior to 1865, the temperature has been reconstructed by Groveman and Landsberg. Also plotted is the filtered value (1,2,2,2,1 filter) of the sunspot cycle length 1750-1980 (see text).
Solar activity variations and global temperature
4. Discussion Research in possible Sun-climate relationships has been dominated by the unsuccessful attempts to identify a physical mechanism that could account for the hypothesized effects on climate based on a large number of correlations between various solar and climate parameters. Still today, no single physical parameter has been found that could serve as an indicator of the hypothesized solar forcing. The correlation between the length of the solar cycle and Northern Hemisphere land-surface temperature has been illustrated by using the best data that are probably available for such an exercise. It is recognized that data prior to the modem instrumental temperature record are by no means perfect but the fact that the correlation found for the last 130 years of systematic temperature measurements is in agreement with the data for the last 250 years does indicate that a significant part of the ‘natural’ variability is not of internal but of external origin. The simplest physical mechanism for the found correlation is the possibility of a long-term variation of total solar irradiation that is sufficiently large to have an observed temperature effect on climate. Satellite measurements over approximately one solar cycle have shown that the irradiance is not constant, but model calculations show that it varies too little (less than 0.1%) during a solar cycle to be of major importance for climate. However, no measurements yet exist that do exclude the possibility of larger variations in total irradiance over a longer period of time. On the contrary, Lean et al,16 from correlations between total solar irradiance measurements and Ca II solar emissions estimate that in the absence of surface solar magnetism (like what was probably the case during the Maunder sunspot minimum period around 1700), the total solar irradiance may have been reduced by 0.24%. The hypothesis of a solar forcing through total irradiance variations may be tested using climate models. Much experience has been gained using climate models of various sophistication and size to simulate climatic response to different forcing factors including the effect of an increase in atmospheric greenhouse gases. The most comprehensive models are the large general circulation models (GCMs), and in particular those that include a coupling to the ocean (CGCMs). Although these models have continued to improve in their ability to simulate present climate on large scales, there is still a major uncertainty regarding the role of some of the important processes, including the treatment of watervapour feedback, effects of clouds, and realistic atmosphere-ocean coupling processes. One of the crucial results of these models is the climate sensitivity, which is usually expressed in terms of the equilibrium response of the global temperature corresponding to a radiative forcing equivalent to that for a doubling of the COz concentration in the atmosphere. The range of climate sensitivity that results from different models is still relatively large, varying by a factor of three from 1.5 to 4.5 “C for a doubled CO,. A different approach is to use simpler energy-balance climate models. In these models, a specific global climate sensitivity has to be assumed. Such models were used in the investigations by Kelly and Wigley” and Schlesinger and Ramankutty’* who explore the relative role of possible solar forcing vs greenhouse forcing. Schlesinger and Ramankutty find strong circumstantial evidence that there have been intercycle variations in solar irradiance which have contributed to the observed temperature changes since 1856, but their model calculations indicate, also in agreement with Kelly and Wigley, that since the nineteenth century greenhouse gases have been the dominant contributor to the observed temperature changes. Kelly and Wigley conclude that the combination of greenhouse forcing and solar cycle-length forcing can explain many features of the observed temperature record. They do call for caution, however, regarding the interpretation of this result because the cycle-length history is not uniquely defined and because implied irradiance changes prior to 1900 are unrealistically large. The latter result is particularly evident when using their own proposed cycle-length record based on applying a 7-term binomial filter to the mixed raw maximum-to-maximum and minimum-to-minimum length series. However, as discussed in a previous section, the length series determined by means of maximum sunspot epochs is probably less reliable than the series determined by means of minimum epochs. Figure 3 shows that the difference in amplitude between these two independent series is particularly large prior to 1850.
This partly explains why Kelly and Wigley infer a large solar forcing of 2.8 Wm-* (more than 1Z) over this period. In both studies, the effect from sulphate aerosol forcing was taken into account in addition to the greenhouse and solar forcing. Whereas Kelly and Wigley explored one particular estimated sulphate aerosol forcing record, Schlesinger and Ramankutty in their similar modelling approach explicitly demonstrate the importance of this highly uncertain forcing of anthropogenic origin by investigating a range of different sulphate aerosol forcings. They point out that regardless of the exact magnitude of the sulphate aerosol forcing, the inclusion of the Sun’s past influence reduces the best estimate of the climate sensitivity by at least 48 % . This result demonstrates the importance of establishing a firm basis for the possible solar forcing. Both of the above results based on simple climate models are particularly influenced by the global warming during the last 15 years, which does fit very well to the increased greenhouse effect. A considerable part of this warming, however, may be due to the intradecadal variation that is so dominant in the temperature record. For obvious reasons, a filtered solar cycle length may not be available for some time, but it is noteworthy that the activity of the Sun has increased drastically during the last 20 years. The merits of the energy-balance models are that they are simple and inexpensive in terms of computer resources. The problem with these models is that it is assumed that the global climate can be calculated simply by means of global averages of radiative forcings, some of which are assumed to be relatively well described. As a first-order approximation, these models may constitute an appropriate tool but caution must be exercised in the interpretation of the results. It must be realized that average global values may not constitute an adequate description of the very complex atmospheric processes that determine the average global temperature. Even if energy-balance models only intend to consider global-mean response to different forcings, a global-mean climate sensitivity is not necessarily appropriate, taking into account the multitude of non-linear effects that is characteristic of the Earth’s climate. It is conceivable that a comparatively small rise in the Sun’s irradiation may result in a steeper tropical to polar temperature gradient, because of the different Solar zenith angles at low and high latitudes. If so, this would increase the Hadley circulation and in this way influence the global temperature distribution. The different radiative forcings, including solar irradiance, greenhouse gases, and anthropogenic sulphate aerosols, all have different spatial distributions and, in case of the latter, a particularly inhomogeneous distribution that makes it rather dubious if a one-dimensional climate model is at all appropriate in a quantitative distinction of the effects of these different forcings. In particular, the fact that most of the rise in global temperature during the present century had its origin in a very fast increase in the temperature in the Northern polar regions during 20 years from 1920 to 1940, simultaneous with a similarly fast rise in the solar activity expressed in the variation of the length of the sunspot cycle, suggests a more direct solar effect than the climate models indicate. Nevertheless, the temperature variations simulated by realistic combinations of greenhouse, solar and sulphate aerosol forcing leaves very little room for the low-frequency internal variability corresponding to periods larger than decadal scale variations. This fact could become an important issue in the validation of the various GCMs regarding confidence in their use for simulations of future climate change. 5. Summarv In this paper, several aspects of solar activity has been reviewed and it has been demonstrated that the sunspot number itself is not necessarily an appropriate indicator of solar activity, particularly not regarding its long-term variation. One of the other indicators of solar activity, the length of the sunspot cycle, seems to have a well-defined long-term variation which appears to be well correlated with the long-term variation of global temperature, particularly the Northern Hemisphere land air temperature,
Solar activity variations and global temperature
not only during the instrumental period 1860 to 1990 but also during the pre-instrumental period, where only sporadic or proxy temperature data are available. At least since the introduction of reliable sunspot data in 1750, the variation of the Northern Hemisphere land air temperature appears to have been modulated by the varying solar activity as represented by the sunspotcycle length. An expected contribution to the greenhouse effect due to anthropogenic sources seems to be less dominant in the observational temperature records compared to solar influences, except maybe during the last 20 years. The obscurity of the hypothesized increased greenhouse effect could be due to the fact that simultaneously with the increased atmospheric content of CO, in the atmosphere, an increase in the content of aerosols, particularly in the Northern Hemisphere, has taken place that could result in a significant cooling,” which could have offset an increased greenhouse effect. The observations have been compared with published results of simple climate models that take into account various forcing factors in addition to solar forcing, including greenhouse forcing and anthropogenic sulphate aerosol forcing. The results of these models are consistent with a noticeable effect of total solar irradiance changes, but the model results also indicate that, since the nineteenth century, greenhouse gases have been the main contributor to the observed temperature changes. The validity of the results of these model calculations does, however, rely on the assumption that the solar forcing manifests itself purely by means of total solar irradiance and the further assumption that the solar radiative forcing in its global effect is equivalent to the corresponding radiative effect from increased greenhouse gases. These assumptions must be taken into account in the interpretation of the results of the model calculations. 6. References 1.
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