EARTH/Orbital Variation (Including Milankovitch Cycles) 415 Note that the components of climatic precession can be constructed from the precession constant p and the fundamental frequencies gi Figure illustrates the variation in the climatic precession index, and its modulation in amplitude by eccentricity, over 1.2 million years The frequency analysis, shown on the right-hand side of the plot, reveals three peaks corresponding to frequencies given in Table Insolation Conceptually, the actual forcing of Earth’s climate by orbital variations is applied through the radiative flux received at the top of the atmosphere at a particular latitude and time, which is then transferred through oceanic, atmospheric, and biological processes into the geological record The integral of the radiative flux over a specified interval of time, termed ‘insolation’ (French from the Latin insolare), can be computed from the eccentricity e, the obliquity e, and the climatic precession e sin(o) The amount of ˜ solar radiation received at a particular location depends on the orientation towards the Sun of that location Calculation of insolation becomes complex Table Five leading terms for Earth’s climatic precessiona Term Frequency ( 00 year 1) Period (ky) Amplitude p ỵ g5 p ỵ g2 p ỵ g4 p ỵ g3 p ỵ g1 54.7064 57.8949 68.3691 67.8626 56.0707 23.680 22.385 18.956 19.097 23.114 0.0188 0.0170 0.0148 0.0101 0.0042 a Principal climatic precession components analysed over the past My The frequency terms gi refer to those given in Table Data from Laskar J (1999) The limits of Earth orbital calculations for geological time scale use Philosophical Transactions of the Royal Society of London, Series A, Mathematical, Physical and Engineering Sciences 357(1757): 1735 1759 if it is to be calculated over a particular time interval Averaged over year and the whole Earth, the only factor that controls the total amount of insolation received, apart from the solar constant, is the changing distance from Earth to the Sun, which is determined by Earth’s semi-major axis a and its eccentricity e If insolation variations are computed for a particular latitude, and over a particular length of time, the main contribution arises from the climatic precession signal, with additional contributions from the variation in obliquity The exact nature of the insolation signal is complicated Certain general statements can be made, though The signal arising from the climatic precession is always present in insolation time series Also, if the obliquity signal is present, it typically shows a larger amplitude towards high latitudes In addition, the climatic precession signal in the insolation calculation depends on the latitude at which it is calculated, such that the signal in the southernhemisphere summer shows opposite polarity to that in the northern-hemisphere summer (see Figure 7) If the mean monthly insolation is computed for a particular latitude, each month corresponds to a difference in phase (i.e., a difference in time of a particular insolation maximum or minimum) of approximately ky (12 months approximately correspond to the (on average) $24-ky-long climatic precession cycle) It is unlikely that geological processes that encode the insolation signal are driven by variations at the same latitudes and times of the year throughout geological time Depending on the latitude and the time interval over which insolation quantities are computed, the calculation can be very complex, and the question of time lags and forcing can be resolved only through the application of climate models A very revealing study to this effect was reported by Short and colleagues in 1991 At the present level of understanding, it is probably appropriate to avoid a strict Figure Climatic precession index and eccentricity envelope over time (1.2 million years) and frequency analysis for a 10 My time span The peaks in the frequency analysis correspond to the frequencies given in Table 4; the numbers over the peaks represent the periods (in thousands of years)