Astronomical frequencies for climate research at the decadal to century time scale

Short-term variations of the elements representing the Earth's motion around the Sun and its rotation have been analyzed over the last 6000 years using 1-year steps. Their low-frequency part is compared first to the values obtained from a secular theory of the planetary long-term motion showing that they can be considered reliable enough to represent adequately the motion of the Earth over the last 5000 years. Spectral analysis of these values shows that the main periodicities are 2.67, 3.98, 5.26, 5.93, 7.9, 9.8, 11.9, 14.7, 15.8, 29, 42, 61, 122, 165 and 250 years for the eccentricity as well as for the climatic precession, with an additional component at around 930 years for the eccentricity and around 840 years for the climatic precession. Periodicities at 2.67, 3.8, 5.9, 8.0, 9.3, 11.9, 14.7, 18.6, 29, 135, 250 and 840 yr are also shown for the obliquity. Spectral analyses of the daily July mid-month insolation at 65°N show essentially the same periodicities as the climatic precession and the obliquity, i.e. 2.67, 3.98, 5.92, 8.1, 11.9, 15.7, 18.6, 29, 40, 61 and around 900 years. Finally a wider analysis of the insolation pattern was performed related to the large periodicity band of the insolation time series for the solstices and the equinoxes for 7 different latitudes. In equatorial latitudes the insolation variance is largely explained by precession. But precession dominates everywhere with the obliquity signal being stronger at polar latitudes at the solstices. The amplitudes of the insolation change at these frequencies is of the order of 0.2 Wm^–2 at the maximum. Offprint requests to: A Berger     

A comparison of the Vostok ice deuterium record and series from Southern Ocean core MD 88-770 over the last two glacial-interglacial cycles

Taking advantage of the fact that the Vostok deuterium (δD) record now covers almost two entire climatic cycles, we have applied the orbital tuning approach to derive an age-depth relation for the Vostok ice core, which is consistent with the SPECMAP marine time scale. A second age-depth relation for Vostok was obtained by correlating the ice isotope content with estimates of sea surface temperature from Southern Ocean core MD 88-770. Both methods lead to a close correspondence between Vostok and MD 88-770 time series. However, the coherence between the correlated δD and insolation is much lower than between the orbitally tuned δD and insolation. This reflects the lower accuracy of the correlation method with respect to direct orbital tuning. We compared the ice and marine records, set in a common temporal framework, in the time and frequency domains. Our results indicate that changes in the Antarctic air temperature quite clearly lead variations in global ice volume in the obliquity and precession frequency bands. Moreover, the average phase we estimated between the filtered δD and insolation signals at precessional frequencies indicates that variations in the southern high latitude surface temperature could be induced by changes in insolation taking place during a large period of the summer in northern low latitudes or winter in southern low latitudes. The relatively large lag found between Vostok δD variations and obliquity-driven changes in insolation suggests that variations in the local radiative balance are not the only mechanism responsible for the variability in surface temperature at those frequencies. Finally, in contrast to the cross-spectral analysis method used in previous studies, the method we use here to estimate the phases can reveal errors in cross-correlations with orbitally tuned chronologies. Received: 11 April 1995 / Accepted: 19 July 1995     

EMD analysis of solar insolation

Summary A new time series analysis technique, Empirical Mode Decomposition (EMD), which has been successfully applied to nonlinear and nonstationary data, is used to examine paleoclimate cycles in the Pleistocene (1 Ma bp–20 Ka bp). The purpose of this study is to improve knowledge of the climatic significance of solar insolation. The results show that the eccentricity band signal is much larger than previously estimated, having an amplitude of about 1% of solar irradiance which is comparable to the amplitude of the precession and obliquity band signals. This finding implies the need to reconsider the role of solar radiation on the formation and maintenance of quaternary ice sheet cycles.     

Improving the methodology for spectral analysis of climatic time series

The paper discusses a methodology able to estimate both the discrete and continuous spectra without any assumption on the shape of spectral densities. The approach to estimate the spectral density is based on a robust smoothing of the periodogram. Bandwidth, a quantity similar to the width of spectral windows traditionally used in spectral analysis, is estimated locally in contrast to intuitively chosen global window lengths. Detection and estimation of frequencies forming discrete spectra are also addressed. The procedure is applied to Central England temperature (CEt), North Atlantic Oscillation (NAO) index and Oxygen Isotope of North Greenland Ice Core Project (δ¹⁸O of NGRIP) data. Annual and half annual cycles were detected in CEt data, whilst 118.2- and 41.7-ky cycles were found in δ¹⁸O of NGRIP. This latter periodicity is almost as intense as the dominant longer cycle. Several local peaks of spectral densities were recognised in each time series that mostly cover earlier results. However, a few previous findings at low frequencies have not been reinforced by the present method. Identification of modest local peaks or discrete amplitudes at low frequencies is an extremely challenging task as climatic data generally have spectral densities rising to low frequencies.     

Autoregressive modelling of daily ragweed pollen concentrations for Szeged in Hungary

Studying airborne pollen concentrations is an essential part of aerobiology owing to its important applications in allergology. A time-varying first order autoregressive (AR(1)) model able to describe the annual cycle of both the expectation and variance as well as the highly skewed probability distribution of daily ragweed pollen concentrations conditioned on previous-day pollen concentration values is developed. Confidence bands for forecasts obtained with these conditional lognormal distributions are analysed. The probability of exceeding specific pollen concentration thresholds is also addressed with the model based on a refinement of the AutoRegressive To Anything process. In order to have more accurate forecasts for the next-day pollen concentration level, eight meteorological variables influencing pollen concentrations are considered. Based on a procedure similar to the stepwise regression method, only one predictor has been retained, namely the daily mean temperature. Using root mean square error, the percentage variance of the ragweed pollen concentration level accounted for by this extended AR(1) model is 53.5%, while the mean absolute error produced by the model is 32.2 pollen grains?m^?3. The probability of exceeding pollen concentration thresholds obtained from the conditional lognormal distributions under the extended AR(1) model fits well the observed exceedance events.     

CO2 and Northern Hemisphere ice volume variations over the middle and late Quaternary

 The atmospheric CO₂ concentrations have been reconstructed over the past 600 ka based on regression between the Vostok CO₂ data and the SPECMAP oxygen isotope values. A lag of 4.5 ka (CO₂ preceding δ¹⁸O) gives the best results. A polynomial of order 5 explains 66% of the Vostok CO₂ variance over the last 220 ka. The Northern Hemisphere ice-sheet volume was simulated over the past 575 ka using the LLN 2-D model, forced by insolation and these statistically reconstructed atmospheric CO₂ concentrations. The simulated ice volume fluctuations resemble the deep-sea oxygen isotope variations. CO₂ of interglacial level is necessary for explaining both the interglacial at oxygen isotopic stage 11 and our present-day interglacial.     

Is the astronomical forcing a reliable and unique pacemaker for climate? A conceptual model study

There is evidence that ice age cycles are paced by astronomical forcing, suggesting some kind of synchronisation phenomenon. Here, we identify the type of such synchronisation and explore systematically its uniqueness and robustness using a simple paleoclimate model akin to the van der Pol relaxation oscillator and dynamical system theory. As the insolation is quite a complex quasiperiodic signal involving different frequencies, the traditional concepts used to define synchronisation to periodic forcing are no longer applicable. Instead, we explore a different concept of generalised synchronisation in terms of (coexisting) synchronised solutions for the forced system, their basins of attraction and instabilities. We propose a clustering technique to compute the number of synchronised solutions, each of which corresponds to a different paleoclimate history. In this way, we uncover multistable synchronisation (reminiscent of phase- or frequency-locking to individual periodic components of astronomical forcing) at low forcing strength, and monostable or unique synchronisation at stronger forcing. In the multistable regime, different initial conditions may lead to different paleoclimate histories. To study their robustness, we analyse Lyapunov exponents that quantify the rate of convergence towards each synchronised solution (local stability), and basins of attraction that indicate critical levels of external perturbations (global stability). We find that even though synchronised solutions are stable on a long term, there exist short episodes of desynchronisation where nearby climate trajectories diverge temporarily (for about 50 kyr). As the attracting trajectory can sometimes lie close to the boundary of its basin of attraction, a small perturbation could quite easily make climate to jump between different histories, reducing the predictability. Our study brings new insight into paleoclimate dynamics and reveals a possibility for the climate system to wander throughout different climatic histories related to preferential synchronisation regimes on obliquity, precession or combinations of both, all over the history of the Pleistocene.     

Characterizing atmospheric circulation signals in Greenland ice cores: insights from a weather regime approach

Greenland ice cores offer seasonal to annual records of δ¹⁸O, a proxy for precipitation-weighted temperature, over the last few centuries to millennia. Here, we investigate the regional footprints of the North Atlantic weather regimes on Greenland isotope and climate variability, using a compilation of 22 different shallow ice-cores and the atmospheric pressure conditions from the twentieth century reanalysis (20CR). As a first step we have verified that the leading modes of winter and annual δ¹⁸O are well correlated with oceanic (Atlantic multidecadal oscillation) and atmospheric [North Atlantic oscillation (NAO)] indices respectively, and also marginally with external forcings, thus confirming earlier studies. The link between weather regimes and Greenland precipitation, precipitation-weighted temperature and δ¹⁸O is further explored by using an isotope simulation from the LMDZ-iso model, where the 3-dimensional wind fields are nudged to those of 20CR. In winter, the NAO+ and NAO? regimes in LMDZ-iso produce the largest isotopic changes over the entire Greenland region, with maximum anomalies in the South. Likewise, the Scandinavian blocking and the Atlantic ridge also show remarkable imprints on isotopic composition over the region. To assess the robustness and model dependency of our findings, a second isotope simulation from the isotopic model is also explored. The percentage of Greenland δ¹⁸O variance explained by the ensemble of weather regimes is increased by a factor near two in both LMDZ-iso and IsoGSM when compared to the contribution of the NAO index only. Similarly, weather regimes provide a net gain in the δ¹⁸O variance explained of similar magnitude for the whole set of ice core records. Greenland δ¹⁸O also appears to be locally affected by the low-frequency variations in the centres of action of the weather regimes, with clearer imprints in the LMDZ-iso simulation. This study opens the possibility for reconstructing past changes in the frequencies of occurrence of the weather regimes, which would rely on the sensitive regions identified here, and the use of additional proxies over the North Atlantic region.     

Responses of global monsoon and seasonal cycle of precipitation to precession and obliquity forcing

In this paper, the response of global monsoon to changes in orbital forcing is investigated using a coupled atmosphere–ocean general circulation model with an emphasis on relative roles of precession and obliquity changes. When precession decreases, there are inter-hemispheric asymmetric responses in monsoonal precipitation, featuring a significant increase over most parts of the Northern Hemisphere (NH) monsoon regions and a decrease over the Southern Hemisphere (SH) monsoon regions. In contrast, when obliquity increases, global monsoon is enhanced except for the American monsoon. Dynamic effects (caused by changes in winds with humidity unchanged) dominate the monsoonal precipitation response to both precession and obliquity forcing, while thermodynamic effects (caused by changes in humidity with winds unchanged) is related to the northward extension of the North African summer monsoon. During minimum precession, the seasonal cycle of tropical precipitation is advanced with respect to the maximum precession. The rainfall increase in the transitional season (April-June in the NH and October-December in the SH) is dominated by the dynamic component. From an energetics perspective, the southward (northward) cross-equatorial energy transport during April-June (October-December) corresponds to a northward (southward) shift of tropical precipitation, which results in a seasonal advance in the migration of tropical precipitation. Nonetheless, there is no significant change in the seasonal cycle in response to obliquity forcing.

     

Orbital forced frequencies in the 975 000 year pollen record from Tenagi Philippon (Greece)

Frequency analysis was applied to different time series obtained from the 975 ka pollen record of Tenagi Philippon (Macedonia, Greece). These time series are characteristic of different vegetation types related to specific climatic conditions. Time control of the 196 m deep core was based on 11 finite 14C dates in the upper 17 m, magnetostratigraphy and correlation with the marine oxygen isotope stratigraphy. Maximum entropy spectrum analyses and thomson multitaper spectrum analysis were applied using the complete time series. Periods of 95–99, 40–45, 24.0–25.5 and 19–21 ka which can be related to orbital forcing, as well as periods of about 68, 30 ka and of about 15.5, 13.5, 12 and 10.5 ka were detected. The detected periods of about 68, 30 ka and 16, 14, 12, 10.5 ka are likely to be harmonics and combination tones of the periods related to orbital forcing. The period of around 30 ka is possibly a secondary peak of obliquity. To study the stability of the detected periods through time, analysis with a moving window was employed. Signals in the eccentricity band were detected clearly during the last 650 ka. In the precession band, detected periods of about 24 ka show an increase in amplitude during the last 650 ka. The evolution of orbital frequencies during the last 1.0 Ma is in general agreement with the results of other marine and continental time series. Time series related to different climatic settings showed a different response to orbital forcing. Time series of vegetational elements sensitive to changes in net precipitation were forced in the precession and obliquity bands. changes in precession caused changes in the monsoon system, which indirectly had a strong influence on the climatic history of Greece. Time series of vegetational elements which are more indicative of changes in annual temperature are forced in the eccentricity band.     

A model for large glacial–interglacial climate-induced changes in dust and sea salt concentrations in deep ice cores (central Antarctica): palaeoclimatic implications and prospects for refining ice core chronologies

A semi-empirical model has been developed to reproduce glacial–interglacial changes of continental dust and marine sodium concentrations (factor of ∼50 and ∼5, respectively) observed in inland Antarctic ice cores. The model uses conceptual pathways of aerosols within the high troposphere; assumes the dry deposition of impurities on the Antarctic surface; uses estimates of aerosol transit times taken independent of climate; assumes a temperature-dependent removal process during aerosol pathways from the mid-latitudes. The model is fitted to the data over the last four climate cycles from Vostok and EPICA Dome C Antarctic sites. As temperature is cooling, the aerosol response suggests different modes of climate couplings between latitudes, which can be continuous or below temperature thresholds for sodium and dust, respectively. The model estimates a southern South America dust source activity two to three times higher for glacial periods than for the Holocene and a glacial temperature over the Southern Ocean 3–5 °C cooler. Both estimates appear consistent with independent observations. After removal of temperature effects, dust and sodium residuals for both sites show orbital frequencies in opposite phase at the precession timescale. Such long-term insolation-related modulation of terrestrial and marine aerosol input, could provide a chemical pacemaker useful for refining ice core chronologies.     

A note on orbital control of equator-pole heat fluxes

We note that orbital (Milankovitch) variations, in particular the precession of the equinoxes, can lead to profound variations in the flux of heat from the tropics to higher latitudes. The mechanism involves changing the intensity of the Hadley circulation by varying the maximum displacement from the equator of the zonally averaged surface temperature maximum in summer. The precession of the equinoxes causes this quantity to vary by more than a factor of 2. The intensity of the Hadley circulation has a major influence on the heat fluxes in the winter hemisphere. Summer heat fluxes are generally small. Although the precession cycle is characterized by periods in the neighborhood of 20000 years, the variations are modulated by the eccentricity whose variation is dominated by periods in the neighborhood of 100000 years and 400000 years. We show how the fact that both small and large heat fluxes lead to low snowfall (and, hence, small glacial accumulation) causes the demodulation of the heat flux leading to dominant eccentricity periods in the resulting glaciation.     

An application of the threshold autoregression procedure to climate analysis and forecasting

In this paper a nonlinear method of time series analysis-threshold autoregressive (TAR) model in discrete time is used. The TAR procedure consists of four parts: model building, statistical identification, parameter estimation and forecasting.The object of this study is to estimate monthly total precipitation of Shanghai and Beijing by using open loop TAR model. We can see that the trend of forecasting is in agreement with observations.     

Orbital Forcing and Endogenous Nonlinearity in the Pleistocene: The Greenland Ice Core

The succession of ice ages and interglacials during the Pleistocene is understood to have been caused primarily by shifts in the earth's orbit. At the same time, there is evidence of high variability in climate at suborbital frequencies. This paper conducts a statistical analysis of Pleistocene climate using the Greenland Ice Core Research Project (GRIP) data. Factoring temperature into the component explained by orbital forcing and a residual demonstrates that variations at suborbital frequencies are nonlinear and aperiodic. There is evidence of a regular cycle at 7.9 kyr, evidently a subharmonic of the orbital frequencies. Apart from this, however, the proximate memory of both the actual data and the residual decays slowly over a period of 15 kyr. Residual variations in temperature show two prominent features, alternating periods of high and low volatility, and states of distance from and proximity to the path implied by orbital forcing. A parametric model incorporating both of these properties is fit to the data, and is found to significantly improve the forecastability of climate. Transitions between states of proximity and distance from the orbital path can be partially predicted using the statistical model.     

Interpretation of short-term ice-sheet elevation changes inferred from satellite altimetry

Satellite altimetry offers means of directly measuring changes in surface elevation over the polar ice sheets of Greenland and Antarctica. By relating these changes to variations in ice mass, it becomes possible to detect short-term changes in the Earth's ice sheets. However, it is not immediately obvious that short-term changes in surface elevation are indicative of any (long-term) trend in ice mass. An increase in ice thickness may very well reflect the response of the glacier to random fluctuations in precipitation. The spectrum of this response is dominated by low frequencies, with the majority of the variance contained in the longer time scales. As a result, the ice-thickness record may exhibit trends that have no climatic significance, but are due to a low-frequency response to random forcing. A simple model for the interpretation of observed elevation changes is developed and applied to measurements made over the Greenland Ice Sheet. It appears to be unlikely that the difference between the rate of thickening derived by Zwally and others (1989) using repeat satellite altimetry, and significantly smaller previous estimates, can be explained as being the response of the ice sheet to random climatic forcing or that this difference can be attributed to a recent increase in accumulation rate.     

Analysis of the Moberg et al. (2005) hemispheric temperature reconstruction

The Moberg et al. (Nature 433(7026):613–617, 2005. doi:10.1038/nature03265; M05) reconstruction of northern hemisphere temperature variations from proxy data has been criticised; the M05 method may artificially inflate low-frequency variance relative to reality. We test this assertion by undertaking several pseudoproxy experiments in three climate model simulations—one control run and two forced simulations that include several time-varying radiative forcings. The pseudoproxy series are designed to have the same variance spectra as the real M05 proxies, primarily to mimic the low-resolution character of several series. A simple composite-plus-scale (CPS) method is also analysed. In the CPS case all input data behave like annually resolved proxies. The spectral domain performance of both M05 and CPS is found to be dependent on the noise type and noise level in pseudoproxies, on the variance spectrum of the climate model simulation, and on the degree of data smoothing. CPS performs better than M05 in most investigated cases with the control run, but leads to deflated low-frequency variance in some cases. With M05, low-frequency variance tend to be inflated for the control run but not for one of the forced runs and only very slightly with the other forced simulation. Hence, the M05 approach does not routinely inflate low-frequency variance. In our experiment, the M05 approach performs better in the spectral domain than CPS when applied to forced climate model simulations. The results underscore the importance of evaluating the variance spectrum of climate reconstructions.     

Glacial-interglacial water cycle, global monsoon and atmospheric methane changes

The causes of atmospheric methane (CH₄) changes are still a major contention, in particular with regards to the relative contributions of glacial-interglacial cycles, monsoons in both hemispheres and the late Holocene human intervention. Here, we explore the CH₄ signals in the Antarctic EPICA Dome C and Vostok ice records using the methods of timeseries analyses and correlate them with insolation and geological records to address these issues. The results parse out three distinct groups of CH₄ signals attributable to different drivers. The first group (~80% variance), well tracking the marine δ¹⁸O record, is attributable to glacial-interglacial modulation on the global water cycle with the effects shared by wetlands at all latitudes, from monsoonal and non-monsoonal regions in both hemispheres. The second group (~15% variance), centered at the ~10-kyr semi-precession frequency, is linkable with insolation-driven tropical monsoon changes in both hemispheres. The third group (~5% variance), marked by millennial frequencies, is seemingly related with the combined effect of ice-volume and bi-hemispheric insolation changes at the precession bands. These results indicate that bi-hemispheric monsoon changes have been a constant driver of atmospheric CH₄. This mechanism also partially explains the Holocene CH₄ reversal since ~5?kyr BP besides the human intervention. In the light of these results, we propose that global monsoon can be regarded as a system consisting of two main integrated components, one primarily driven by the oscillations of Inter-Tropical Convergence Zone (ITCZ) in response to the low-latitude summer insolation changes, anti-phase between the two hemispheres (i.e. the ITCZ monsoon component); and another modulated by the glacial-interglacial cycles, mostly synchronous at the global scale (i.e. the glacial-interglacial monsoon component). Although atmospheric CH₄ record integrates all wetland processes, including significant non-monsoonal contributions, it is the only and probably the best proxy available to reflect the past changes of global monsoon. However, the utility of CH₄ as a proxy of monsoon changes at any specific location is compromised by its bi-hemispheric nature.     

自回归模型的最优定阶及其在长期预报中的应用

对自回归模型的5种定阶方法（FPE、AIC、BIC、L1和L2准则）作了概述，并应用上述方法对青岛月平均温度序列进行了自回归模型定阶试验。结果指出，FPE、AIC和L1准则选择自回归模型的阶数较高，L2准则选择自回归的阶数为中等，BIC准则确定的阶数最低。文章还提出了一个应用自回归模型递推预报月平均温度的方法，预报实践证明，由BIC准则产生的低阶自回归模型的效果优于其它方法。     

Effect of seasonal adjustment on empirical rainfall distributions

Summary The empirical rainfall distributions of 42 monthly time series in Spain, for both raw data and for residual series, after removing the seasonal component, were fitted with six theoretical distribution functions (d f's). The distributions were fitted with 2, 3, and 4 parameters, which had been used previously with meteorological variables. The parameters of the probability density functions were calculated using maximum likelihood estimation procedures, and six statistics were examined to identify the bestd f to fit each series.The observations {X _t},t = 1,,N were assumed to consist of a seasonal componentS _t described by an harmonic process model, whose frequencies, number of terms, amplitudes and phases are unknown constants, plus a residualY _t which is a general linear process (for example, an autoregressive, moving-average, or mixed autoregressive/movingaverage process).The frequencies and number of terms in the harmonic process were chosen via a periodicity test, the Siegel test (1980). This is essentially a uniparametric family of periodicity tests which contains the Fisher test as a special case, which improves the results of the latter in cases of simultaneous periodicity at several frequencies. The remaining unknown parameters were determined by regression analysis.It is well known that precipitation has a positively skewed, non-Gaussian distribution. However, the results obtained here show that while the statistical techniques used to eliminate the seasonal component do not require the original data normal distribution, when they are normally distributed the quality of the estimates is better.With 7 Figures     

GCM simulations of the Last Glacial Maximum surface climate of Greenland and Antarctica

 The LMDz variable grid GCM was used to simulate the Last Glacial Maximum (LGM, 21 ky Bp.) climate of Greenland and Antarctica at a spatial resolution of about 100 km.The high spatial resolution allows to investigate the spatial variability of surface climate change signals, and thus to address the question whether the sparse ice core data can be viewed as representative for the regional scale climate change. This study addresses primarily surface climate parameters because these can be checked against the, limited, ice core record. The changes are generally stronger for Greenland than for Antarctica, as the imposed changes of the forcing boundary conditions (e.g., sea surface temperatures) are more important in the vicinity of Greenland. Over Greenland, and to a limited extent also in Antarctica, the climate shows stronger changes in winter than in summer. The model suggests that the linear relationship between the surface temperature and inversion strength is modified during the LGM. The temperature dependency of the moisture holding capacity of the atmosphere alone cannot explain the strong reduction in snowfall over central Greenland; atmospheric circulation changes also play a crucial role. Changes in the high frequency variability of snowfall, atmospheric pressure and temperature are investigated and possible consequences for the interpretation of ice core records are discussed. Using an objective cyclone tracking scheme, the importance of changes of the atmospheric dynamics off the coasts of the ice sheets, especially for the high frequency variability of surface climate parameters, is illustrated. The importance of the choice of the LGM ice sheet topography is illustrated for Greenland, where two different topographies have been used, yielding results that differ quite strongly in certain nontrivial respects. This means that the paleo-topography is a significant source of uncertainty for the modelled paleoclimate. The sensitivity of the Greenland LGM climate to the prescribed sea surface conditions is examined by using two different LGM North Atlantic data sets. Received: 23 October 1997 / Accepted: 17 March 1998