Climate changes are driven largely by variations in the distribution of solar insolation associated with changes in the Earth's orbital parameters. Here we define the rate of solar insolation change (RSIC) as a parameter to evaluate and quantify solar heating changes through time. We propose that RSIC may control the timing of transitions between warm and cold periods through its control on the rate of climate changes. Specifically, the glacial/interglacial transitions took place when the 65°N July insolation experienced the most rapid changes; interglacials start with a maximum positive RSIC and end with a maximum negative RISC. The RSIC curve thus provides a new astronomically tuned method for dating interglacials. The 65°N July RISC curves average a 4.7 ky lead compared to ice sheet changes as indicated by Bassinot et al.  for the last 0.9 Ma, possibly implying a more rapid response of monsoonal climate to the insolation heating.
 Radiation from the sun is the primary source of energy for the Earth's climate system. Changes in the Earth's orbit around the sun cause variations in the seasonal distribution and amount of solar radiation reaching the earth. Records of past climate show that there is a correlation between these variations and long-term climate changes [Hays et al., 1976; Imbrie et al., 1992]. Interglacial conditions begin with increasing mid-latitude summer insolation and end as mid-latitude summer insolation decreases. Orbital-scale climate cycles are driven largely by variations in solar radiation associated with precession, obliquity and eccentricity of the Earth's orbit. Recent studies of the Asian monsoon show that the transitions between the glacial and interglacial conditions took place abruptly, perhaps only in century-long events [Wang et al., 2001; Yuan et al., 2004]. However, it generally takes about 10 ka for the insolation to change from a minimum to maximum and vice versa.
 How climate reacts to insolation change is a matter of continuing investigation. Kukla  stressed that the absolute value of incoming radiation will be of little significance in judging the amplitude of the climate change, and argued that the year-to-year or season-to-season gradient of change will be the critical trigger of any multiplying mechanism involving insolation. Berger  suggested that the insolation signature of Quaternary climatic changes is precisely the time change of the seasonal gradient. In this paper we employ the time rate of solar insolation change (RSIC) to evaluate and quantify solar heating changes through time at orbital and sub- orbital scales and characterize times when these abrupt climate transitions took place. We report that the beginning and ending of the interglacial monsoons coincide remarkably well with the timing of the maximum positive and the maximum negative 65°N July RSIC. This may suggest that the 65°N July RSIC extremes control the timing of the transition between warm and cold conditions.
2. RSIC and Climate Change
 Changes in solar insolation can be calculated from the equations of planetary mechanics and are accurately dated [Berger, 1978]. The RSIC parameter was developed by calculating the first derivative of the insolation curve and is defined as the variation in the rate of solar energy reaching the upper atmosphere per thousand years, that is Wm−2ka−1. High and low positive RSIC values indicate, respectively, quick and slow insolation increases with time; whereas high and low negative RSIC values represent rapid and slow insolation declines, respectively. The RSIC curve exhibits variations similar to the insolation curve change with latitude and month as discussed by Berger et al. , but has a phase lead of about 4-5 ka (Figure 1). For a given month, RSIC at different latitudes are in phase, but intensity differs with latitude. RSIC of a specific month leads the RSIC of the next month by about 2 ky (Figure 1).
 In comparing changes in RSIC to climate, the use of independent and precisely dated climate records is crucial. The recent 230Th dated stalagmite records from Dongge and Hulu caves of China [Wang et al., 2001; Yuan et al., 2004] contain thoroughly dated, high resolution climate records from the penultimate glacial, through the last interglacial and glacial cycle and into the Holocene. We also use the sediment record from Qinghai Lake which provides a high resolution, AMS 14C-dated monsoon record from the late glacial and the entire Holocene [Ji et al., 2005]. The comparison of RSIC with the two monsoon records displays two significant characteristics (Figure 2):
 First, the start and end of major warm climate changes for the last 140 ka precisely coincide, respectively, with the timing of the maximum positive and maximum negative RSIC of the 65°N July mid-month. The Last Interglacial starts with an abrupt decrease of stalagmite δ18O at 129.3 ka BP (the monsoon Termination II [Yuan et al., 2004]), is coincident with the maximum positive RSIC of the 65°N July mid-month at 130.5 ka BP, ends with a rapid rise of stalagmite δ18O at 119.6 ka BP [Yuan et al., 2004] and is synchronous with the maximum negative RSIC between 119.5 and 120.5 ka BP (Figure 2). Therefore, the timing and duration of the Last Interglacial period are bracketed by major changes in the rate of insolation.
 The maximum positive RSIC of the 65°N July mid-month between 14.5 and 15.5 ka BP coincides with the sharp decrease of stalagmite δ18O at 14.645 ka BP (monsoon Termination I [Wang et al., 2001; Yuan et al., 2004]) and the rapid temperature rise of the Bölling-Alleröd warming at 14.68 ka BP noted in the Greenland Ice Sheet Project Two core (GISP2 [Grootes et al., 1993]). Likewise, the maximum negative RSIC at 4.5 ka BP correlates well with 1) the abrupt decrease of runoff into Qinghai Lake as indicated by the decreased sediment redness at 4.2 ka BP [Ji et al., 2005] (Figure 2), 2) the recent stalagmite record of abrupt lowering of Asian monsoon intensity at 4.4 ka BP [Wang et al., 2005] and 3) the well-known and historically recorded drought at about 4 ka BP in tropical Africa, the Middle East and western Asia [Thompson et al., 2002], suggesting an end of the solar insolation controlled Holocene interglacial at this time. More recently Ruddiman  proposed that greenhouse effect from human activities has warded off a glaciation that otherwise would have begun about 5,000 years ago, and current temperatures would be well on the way toward typical glacial temperatures had it not been for the greenhouse gas contribution from early farming practices and later industrialization.
 Second, warm periods correlate with high insolation and a gradually declining 65°N July mid-month RSIC, whereas cold times correspond to a continuously increasing RSIC and a lowering of solar insolation (Figures 2 and 3) . The transition from glacial conditions to interglacial conditions took place when the RSIC varied from a gradual increase to a continual decrease (Figure 3). Therefore, we argue that a change from an increasing to decreasing RSIC trend and vice versa may constitute insolation threshold itself for the Earth's climate system, or that a quick insolation change may increase the probability per unit time of crossing a threshold.
 From the simple energy balance model [Budyko, 1969], the climate system of the Earth is controlled by the variation of solar radiation:
 Here Q is the solar irradiance at the top of the atmosphere, αp is the albedo of the Earth system, and I = A + BT is the outgoing long wave radiation of the Earth system. A and B are the constants. Based on this equation, the condition for reaching the maximum positive or negative extreme is = 0, and the equation can be rewritten:
where RSIC = , and can be neglected since it is a very small term compared with B. This formula implies that the rate of temperature change is function of RSIC; higher RSIC causes a faster temperature change of the climate of the Earth and vice versa. Therefore, we propose that the maximum positive RSIC may produce the highest rate of surface temperature increase and the most rapid decay of the snow cover and sea ice thereby triggering the warming to an interglacial climate. Likewise, the maximum negative RSIC values cause a large temperature decrease resulting in the fast growth of continental snow cover and sea ice and forcing glacial conditions.
3. RSIC and Ages of Interglacial Timing
 If these transitions between warm and cold conditions are paced at a RSIC rhythm, the times of RSIC extremes can be compared to the ages of past interglacials. Support for this idea is found in SPECMAP record for the last 300 ka which shows a strong correlation between the timings of the marine oxygen isotope (MIS) events and the 65°N July mid-month RSIC extremes (Figure 3), e.g., the ages for MIS5/MIS6, MIS6/MIS7 and MIS7/MIS8 boundary are 127 ka, 186 ka and 242 ka from Bassinot et al. , whereas the ages of correlated RSIC extremes are 130.5, 191.5 and 245.5 ka respectively.
Bassinot et al.  developed the low latitude, late Pleistocene δ18O reference record by using the 65°N July insolation curve of Berger and Loutre , the same curve we used to calculate RSIC. We calculated the difference between the 65°N July RSIC curve and the stacked marine oxygen isotope record for the ages of the timing of past interglacials and monsoon terminations for the last 0.9 Ma (Table 1). There is an average 4.7 ky lead of the monsoon timing to the ice sheet changes for the last 0.9 Ma, indicating a fast response of monsoonal climate to the insolation heating. The use of RSIC extremes as age controlling points may also help to solve the problem of variable age estimates of MIS events and glacial Terminations that result from using different MIS stratigraphy and orbital tuning techniques [Martinson et al., 1987; Bassinot et al., 1994; Raymo, 1997].
Table 1. Comparison of Ages of the Monsoon Interglacials and Terminations for the Last 0.9 Ma Based on the 65°N July Mid-Month RSIC With Ages of MIS Events of Bassinot et al. a
RSIC was calculated from 1 ky increment of the July mid-month insolation data of Berger and Loutre . T, Termination.
Average monsoon phase lead to the ice volume change
 As the RSIC can be calculated for the future, it can also be used to create scenarios of future climate changes. Further study is needed to explore and understand the connections between RSIC and climate change.
 1. RSIC is a new parameter to evaluate and quantify the insolation change with time, and provides a history of time rate changes of solar heating to the Earth's climate system. The glacial/interglacial transitions took place during the most rapid changes of the 65°N July insolation, which is critical to buildup or decay of continental ice.
 2. The 65°N July mid-month RSIC may control the timing of the transition between warm and cold times. Interglacial conditions start with a maximum positive RSIC and end with a maximum negative RSIC, whereas glacial conditions began with a maximum negative RSIC and end with a maximum positive RSIC. The 65°N July mid-month RSIC curve thus provides a new, astronomically tuned method for dating the interglacials.
 3. Comparison of the 65°N July mid-month RSIC curve with the stacked marine oxygen isotope stratigraphy of Bassinot et al.  produces new ages for the past interglacials (Table 1) and displays an averaging 4.7 ky lead of the monsoon timing to the ice sheet changes for the last 0.9 Ma, possibly implying a more rapid and sensitive response of monsoonal climate to the insolation heating.
 This study was funded by the National Basic Research Program of China (2004CB720204 and 2001CCB00100) and the National Natural Science Foundation of China (grants 40331001 and 40475035). We thank A. Berger and two anonymous reviewers for critically commenting on the manuscript, and Xianfeng Wang for providing the summer solstice insolation data.