The Earth's climate is influenced by the manner in which solar radiation is absorbed and reflected in the atmosphere. In the study, the approach evaluating the radiative forcing of aerosol was used to analyze the climatic effect of dust over the last 140,000 years in the southern Chinese loess plateau. (1) Radiative effect of dust aerosol was to reduce the solar radiation arriving at the surface and thus to lead earth cooling. However, the grain size-driven climatic feedback of dust aerosol was negative on short-term scale, i.e., to weaken the amplitude of climate fluctuation. (2) Glacial-interglacial fluctuation was marked in most optical properties of dust over the last 140,000 years. High-frequent millennial scale fluctuations corresponding to Younger Dryas, Heinrich events and D-O cycles dominated most optical properties of dust aerosol. (3) The climatic feedback of dust aerosol may be a contributor for the climatic transition between glacial and interglacial periods.
 Solar radiation plays an important role for the Earth's climate that is strongly influenced by radiative absorption and reflection of atmosphere [Chylek and Wong, 1995]. In recent years, there has been a substantial increase in interest in the influence of aerosols on climate through direct effect. On a global scale the abundance of natural aerosols is several times greater than that of the major anthropogenic aerosols (sulphate, soot and organics). Soil dust constitutes an important portion of the global natural aerosol abundance [Tegen and Fung, 1994; Haywood et al., 2003]. As a strongly-scattering aerosol, dust aerosol absorbs sunlight to a greater extent than industrial sulphate and sea salt aerosols [Tegen et al., 1997]. Recent studies have revealed that mineral dust exert significant radiative forcing [Highwood et al., 2003; Hess et al., 1998].
 Direct climatic impact of dust aerosols is to change the energy balance of earth-atmospheric system by scattering and absorbing [Hinds, 1999]. Scattering increases the fraction of sunlight reflected to space and consequently leads the decrease of energy gotten by the earth-atmospheric system and thereby the cooling of whole earth system. Absorption reduces both the reflection at the top of atmosphere (TOA) and the surface illumination [Zhang and Zhou, 1995].
 For weak-absorption dust aerosols, the climate response depends not only upon radiative forcing at TOA, but also its difference with respect to the surface value, which represents radiative heating within the atmosphere [Miller et al., 2004]. Further, dust aerosol could also lead the difference between the surface and the lower atmosphere [Tegen et al., 1997]. Satheesh and Moorthy  analyzed the process, i.e., mineral dusts may cause lower atmospheric heating due to aerosol absorption and simultaneous surface cooling due to reduced surface illumination, in turn to reduce the sensible heat flux, intensify a low-level inversion and increase atmospheric stability, eventually to lead perturbations of atmospheric circulations and thereby changes of regional or global climate. The phenomenon that a net cooling at the surface was accompanied by an increase in atmospheric heating has been observed [Tegen and Fung, 1994], particularly over the desert regions [Mohalfi et al., 1998]. Miller et al.  reported that while global evaporation and precipitation are reduced in response to surface radiative forcing by dust, precipitation increases locally over desert regions, so that dust emission can act as a negative feedback to desertification.
 Aerosol direct forcing at the TOA may be positive (warming) or negative (cooling), depending on surface albedo, single scatter albedo, backscattering fraction of aerosol [Satheesh and Moorthy, 2005], the altitude at which the dust layer is located and the relative altitude from the cloud layer [Liao and Seinfeld, 1998]. Dust aerosols have significant contribution to radiative warming below 500mb due to short-wave absorption but less effect on long-wave radiation [Mohalfi et al., 1998; Alpert et al., 1998]. Dust approximately doubles the short-wave radiation absorption under clear-sky conditions [Tegen and Miller, 1998].
 However, all these studies were focused on modern dust aerosol and there are few studies on paleo-natural aerosols. Paleo-natural aerosols are particularly important because they provide a background level of aerosol effect. It was unclear how dust aerosols impacted paleo-climate. Loess and paleosol formations recording the history of Quaternary climatic change, is a windblown dust deposition [Liu et al., 1985]. Chinese Loess Plateau is the largest loess area in the world. Nevertheless, it was unknown whether or not dust aerosols of Eastern Asia could influence paleo-global climate and how the radiative effect of dust aerosols fluctuated in glacial-interglacial cycles. In the study, the climate effect of dust aerosol in southern Chinese loess plateau over the last 140000 years was analyzed from the loess-paleosol sequence at Weinan, Shanxi province.
2. Studied Site and Sample Measurement
 The study section (34°34´N, 109°32´E) is located at Yangge, Weinan, Shanxi in the southern Chinese Loess Plateau and has been reported by Qin et al. . In the study, the 12.0m section was re-sampled at intervals of 2cm for the upper part 2.0m and 5cm for others.
 The sequence was divided 4 sections, S0, L1, S1 and L2, based on field observation and magnetic susceptibility (MS). The loess formation L1 was divided into five sub-layers again, i.e., 3 loess layers L1−1, L1−3 and L1−5 and paleosol-like layers L1−2 (poorly developed) and L1−4. Measurements of MS and grain size of samples followed methods of Qin et al. .
 By comparing MS sequence of the section with Weinan section reported by Liu et al.  and stacked δ18O time series of Specmap [Imbrie et al., 1990], important age-controlling points were chosen. Particularly, the age-control points in S1 were chosen by referring to the top and bottom ages of S1 [Ding et al., 1994] and stalagmite ages [Wang et al., 2008]. The age of samples between two adjacent control points is interpolated by following Kukla et al.'s  MS age-model.
3. Method and Parameters
 Direct radiative forcing of dust aerosol refers to the difference in the radiation budgets with and without the presence of aerosol. In the radiative theory of dust aerosols, scattering coefficient (SC), absorption coefficient (AC), extinction coefficient (EC), atmospheric optical depth (AOD), single scatter albedo (SSA) (ratio of scattering to extinction) and scattering asymmetry coefficient (SAC) are important optical properties for direct radiative effect and are the function of the real and imaginary components of the aerosol refractive index and light wavelength [Hinds, 1999]. Aerosol particle size plays a major role in the radiative effect of dust aerosols [Zhang and Zhou, 1995]. Mie scattering theory of dust aerosol describes the radiative effect of particles with diameter 0.03∼100μm that covers the grain size range of loess.
 Following Coakley and Cess  and Li , optical properties, transmittance t, reflectance r of dust aerosol, the difference ΔRs between the albedo of earth-atmospheric system (EAS) with aerosol and the surface albedo, the radiative difference ΔFEAS (W·m−2) led by ΔRs and its temperature effect ΔTannual can be calculated (see Supplement). Further, dust aerosol layer was assumed to locate at the bottom of atmosphere because dust deposited on the surface to form loess. The ratio Fa,s/Fa,a of surface absorption Fa,s and aerosol absorption Fa,a of solar radiation indicates the dust-driven atmospheric instability (DDAI). The bigger the ratio, the larger the heat gradient from surface to atmosphere, the stronger the air upward current, and thus the lower the atmospheric stability. Parameters of paleo-dust storms were determined by referring to observations of modern dust storms (See Supplement).
 Similarly, estimated SC (δs = 0.99∼2.18) and AC (δa = 0.22∼0.30) are close to measured values of modern dust aerosol, 0.1∼1 and 0.01∼0.4 [Liu and Shao, 2004], respectively. Chen and Shen  gave out the measured value of daily mean radiative forcing in desert and oasis areas in the northwestern China, 67.67 W·m−2 and 48.67 W·m−2 which are slightly less than our estimation 60∼93.6 W·m−2. It's reasonable because the radiative forcing of dust storm is larger than that of dust aerosol in clear atmosphere. Estimated SSA was 0.820∼0.881 and the average value 0.863 is close to 0.84 reported by Hess et al.  but lower than 0.97 of Saharan dust inferred by Kaufman et al.  and 0.95–0.99 given by Haywood et al. . It may be because the refractive index used in the study is different from the latter. Consequently, the estimation of optical properties of paleo-dust aerosol was reasonable.
4.2. Grainsize-Controlled Optical Properties of Dust Aerosol Over the Past 140,000 Years
 AC shows an almost complete reverse fluctuation trend to median size (Md) (the correlation coefficient R = −0.98) but EC and SC fluctuated more violently than Md (R = −0.75 and −0.72) on Figures 1 and S1. Similar to SC, reflectance r high-frequently fluctuated. The transmittance t fluctuated obviously on long-term scale, similar to Md, implying that coarse dust particles were in favor of solar radiation traversing through the aerosol layer.
 1. ΔRs was always larger than zero, indicating that the radiative effect of dust aerosol was to reduce the solar radiation arriving at the surface and thus to lead earth cooling.
 However, ΔRs in the last glacial maximum (LGM) was not the lowest. The difference between glacial and interglacial periods was unnoteworthy for SSA, ΔRs, and ΔFEAS, suggesting that the albedo effect of dust aerosol in glacial and interglacial periods was close.
 2. Glacial-interglacial fluctuation was marked in most optical properties of dust aerosols over the last 140,000 years. Values of AC, SC, EC and AOD were low during the last glacial period (LGP) and the late Holocene and large in the last interglacial period (LIGP) and Holocene Optimal. AC during LGM is the lowest. The fluctuation amplitudes of EC and SC during LGM were close to that during marine oxygen isotope 3∼4 stages (MIS3∼4) (L1−2 ∼ L1−5).
 3. High-frequent fluctuations dominated EC, SC, SSA and AOD during LGP. EC, SC, SSA and AOD decreased rapidly in periodic short-intervals within LGP to form obvious events which were similar to Younger Dryas (YD) and Heinrich cooling events (H-events). Nineteen low-SC (low-SC and low-AOD) events have been identified over the last 140000 years, of which 13 low-SC events after 60000a B.P. were corresponding to 13 strong turbulence periods reported by Qin et al. . Thus, the grain size-driven cooling effect of dust was weak in cold events. It is because strong winter monsoon in cold events transported much more coarse particles to lead a decrease of scattering efficiency. Thus, the grain size-driven radiative feedback of dust to cooling events was negative and to weaken the cooling effect.
 Most decreases of SC, EC, SSA and AOD in cooling events after L1−2 were rapid, sudden and not sinusoidal, suggesting that they were periodic abrupt cooling events in Chinese loess plateau area and implied a strong instability of the period's climate.
 4. The dust-driven annual temperature difference (ΔTannual) represented that cooling effect was weak in S1 and S0 and strong in L1−4. The annual climatic effect of dust aerosol seems to amplify the cooling effect on long-term scale. It may be because the annual temperature effect was determined by both the grain-size distribution of dust particles and especially the annual frequency of dust storms. Thus, the precise of time scale dominated the estimation's reliability.
 5. DDAI was the lowest in L1−2 ∼ L1−3 (MIS 3) not in L1−1 (LGM) and large in S1 and S0. The dust radiative absorption (Fa,a) marked by high-frequent fluctuations, was low during warming periods and large during cooling periods. The surface radiative absorption (Fa,s) was different from Fa,a on long term scale and its high-frequent fluctuations were unobvious.
 DDAI (Fa,s/Fa,a) was low in L1−2,3 and the bottom of L1−5 (MIS-4∼5) not in L1−1 (LGM) and large in the middle S0 (Holocene Optimal) and the bottom of S1 (the early LIGP), indicating that DDAI was strong during warm interglacial periods and weak during the cool glacial period. LGM was not a special stage for the dust-driven atmospheric instability. On short-term scales, DDAI was also low in rapid cooling events such as H-events. On the long-term scale, DDAI gradually decreased from S1 to L1−5 and gradually increased from L1−3 to S0. It seems to imply that the climatic feedback of dust aerosol was also negative not only in short-term events but also in the climatic transition between glacial and interglacial periods.
 EC, AOD, r, ΔRs and Fa,s/Fa,a are compared with GISP2 ice core, marine and stalagmite records. It was found that millennial scale fluctuations were similar in those records. Low-value periods of EC, SC, SSA and AOD were corresponding to H-events and Dansgaard-Oeschger (D-O) cycles. In particularly, some high-frequent fluctuations that are similar to low-SC events within L1−4, L1−5, and S1, were also found in records of stalagmite δ18O.
 In general, most optical indices of dust aerosol changed synchronously with MS on longer term scale. However, in the bottom of S1, optical indices of dust aerosol rapidly increased to form a peak but MS ascended slowly and lagged behind AOD. The inconsistency may result from two likely reasons. In Chinese loess plateau, MS is usually positively correlative with the intensity of pedogenesis and chemical weathering [Heller and Evans, 1995]. However, MS would rapidly reduce if pedogenesis and chemical weathering are strong enough to overstep the linear-correlation range between MS and pedogenesis [Han, 1991]. Thus, the first likely reason is that pedogenesis and chemical weathering in the beginning of S1 were excessive. Another reason may be that the summer monsoon (shown by MS) reinforcing from L2 to S1 lagged behind the winter monsoon (represented by SC) weakening after L2.
 Coherence analysis demonstrates that GISP2 ice core δ18O and AOD of Weinan section were correlative at the periodicities of ∼1.3ka and 5-6ka, which are close to D-O cycles and H-events respectively. However, it is not appropriate to discuss more details due to time- scale precise' limit. Whatever, the similarity of high-frequent fluctuations between different records reveals that the millennial-scale climatic fluctuations (H-events and D-O cycles), occurred not only at Polar and oceanic areas but also at East-Asian monsoon area. It implies a global mechanism to link different regional climatic sub-systems together.
 In short-term cooling events, such as H-events and D-O cycles, ice core δ18O, TOC of marine sediments and SC of dust aerosol decreased but stalagmites δ18O, ice core B10 and the turbulent intensity of dust aerosol [see Qin et al., 2005] increased. Usually, strong winter monsoon would result in more coarse dust particles to deposit, thus to reduce fine particles' proportion [Qin et al., 2005], suggesting that a low SC may indicate a strong winter monsoon. Therefore, a reasonable explanation is that the strong winter monsoon would lead atmospheric turbulent intensity strengthening and more coarse particles settling, in turn to cause weak dust-scattering and more B10 adhered on dust particles. Low temperature in cold events resulted in a low bio-productivity in ocean, in turn to lead less TOC deposition in marine.
 However, stalagmite δ18O was more complicated. Modern observations revealed that the larger the summer precipitation, the lighter rain δ18O [Johnson and Ingram, 2004]. Thus, stalagmite δ18O of the south of China is used as a proxy of summer monsoon's intensity [Wang et al., 2001; Yuan et al., 2004]. The similarity of millennial scale fluctuations between stalagmite δ18O and dust SC implies several likely mechanisms. The first likely explanation is that the Eastern Asian summer and winter monsoons fluctuated reversely on millennial scales.
 However, stalagmite δ18O and dust SC may be forced by same monsoon. Mie scattering theory shows that fine particles (<2 μm) are major contributors of scattering and extinction [Hinds, 1999]. Fine dust particles' settlement was controlled by the atmospheric turbulent intensity in dust deposition areas far away from sources in the north [Qin et al., 2005]. It implies that the summer monsoons derived from the south may dominate stalagmite δ18O and SC.
 However, dust storms always take place in winter and especially spring. It seems to be impossible that summer monsoons influenced dust deposition during winter and spring. Recent observations of cave precipitation show that carbonate deposition in cave during July and August with the largest rainfall in a year, was low in China (Cai, personal communication). It is because large rainfall of July and August results in drip water in cave to be unsaturated and in turn few carbonate to deposit. Thus, efficient drip-water of stalagmite growth may mainly come from other months except July and August. Rainfall measurements reveals that δ18O of winter precipitation is heavier than that of summer precipitation in monsoon rainfall-dominated areas [Araguás-Araguás et al., 1998]. The precipitation proportion between winter-spring and summer may dominate stalagmite δ18O. The heavier stalagmite δ18O, the larger the precipitation amount of winter-spring when is the dust storm season in the northern China. In the case, both stalagmite δ18O and dust SC indicated fluctuations of winter monsoon.
 Further, stalagmite δ18O may be indirectly affected by dust aerosol's climatic feedback. In cooling events, the grain size-driven low SC would lead high surface illumination and large solar radiative absorption of surface during winter/spring, in turn more water to be evaporated and more heavy δ18O rain to subsequently precipitate during spring and early summer, eventually to result in heavier stalagmite δ18O during cooling events. These mechanisms are unapproved and disputable but they are valuable and helpful for the study in future.
 We thank Wang and Cai for their comments on the manuscript. The study is supported by projects (40472094, 40772212) of the National Natural Science Foundation of China.