周衛(wèi)健，陳茂柏，孔祥輝，鮮 鋒，杜雅娟，武振坤，宋少華，康志海

（1. 中國(guó)科學(xué)院地球環(huán)境研究所 黃土與第四紀(jì)地質(zhì)國(guó)家重點(diǎn)實(shí)驗(yàn)室，陜西省加速器質(zhì)譜技術(shù)及應(yīng)用重點(diǎn)實(shí)驗(yàn)室，西安 710061； 2. 西安加速器質(zhì)譜中心 ，西安 710061；3. 北京師范大學(xué)，北京 100875；4. 西安交通大學(xué) 人居環(huán)境與建筑工程學(xué)院，西安 710049）

基于“平均值概念”的“殘差示蹤法”
——黃土高原降水重建的應(yīng)用

周衛(wèi)健1,2,3,4，陳茂柏1,2，孔祥輝1,2，鮮 鋒1,2，杜雅娟1,2，武振坤1,2，宋少華1,2，康志海1,2

（1. 中國(guó)科學(xué)院地球環(huán)境研究所 黃土與第四紀(jì)地質(zhì)國(guó)家重點(diǎn)實(shí)驗(yàn)室，陜西省加速器質(zhì)譜技術(shù)及應(yīng)用重點(diǎn)實(shí)驗(yàn)室，西安 710061； 2. 西安加速器質(zhì)譜中心 ，西安 710061；3. 北京師范大學(xué)，北京 100875；4. 西安交通大學(xué) 人居環(huán)境與建筑工程學(xué)院，西安 710049）

本文對(duì)定量重建黃土高原降水的傳統(tǒng)方法進(jìn)行了回顧分析，提出了利用新發(fā)展的“殘差示蹤法”定量重建黃土高原古降水變化的兩種新方法。一種是利用黃土磁化率和粉塵通量指標(biāo)的關(guān)系進(jìn)行降水重建的磁化率方法（SUS-approach），另一種是利用黃土10Be濃度與10Be產(chǎn)率和粉塵通量指標(biāo)的關(guān)系進(jìn)行降水重建的10Be方法（10Be-approach）。上述兩種方法定量重建的洛川地區(qū)13萬(wàn)年以來(lái)降水變化曲線高度一致，但與前人利用現(xiàn)代觀測(cè)數(shù)據(jù)建立的氣候回歸方程等傳統(tǒng)方法重建的降水記錄具有明顯的差異。本文所建立的降水曲線具有明顯的細(xì)節(jié)特征，揭示了粉塵稀釋作用對(duì)降水指標(biāo)的影響，顯示了該方法的優(yōu)勢(shì)。文章同時(shí)指出，“殘差示蹤法”的數(shù)學(xué)涵義是基于“平均值概念”（MVC），并對(duì)此從統(tǒng)計(jì)學(xué)角度進(jìn)行了論證。最后，就本文所提出的運(yùn)用線性回歸后的殘差進(jìn)行示蹤的新方法與傳統(tǒng)的示蹤方法之差異作了對(duì)比分析。

黃土高原；SUS-approach；10Be-approach；平均值概念（MVC）；殘差示蹤法；古降水

1 Background of the traditional approach for paleoprecipitation reconstruction over the Chinese Loess Plateau

The magnetic susceptibility records in Chinese loess-paleosols are very similar to the δ18O records from deep-sea sediments. This similarity led to the suggestion that magnetic susceptibility records from loess-paleosols could be used for paleoclimate change research (Kukla et al, 1988). For more than two decades, a number of studies (Maher et al, 1994; An and Sun, 1995; Sun et al, 1995; Han et al, 1996; Porter et al, 2001) have pursued this approach, with magnetic susceptibility as a proxy of paleoprecipitation over the Chinese Loess Plateau (CLP). These studies took important steps towards the spatial and temporal reconstruction of paleoprecipitation over the CLP. However, it becomes clear that the magnetic susceptibility signal in loess includes a dustfall induced susceptibility from the dust source regions that is not related to precipitation, and that the rainfall-induced pedogenic susceptibility is controlled by chemical/ biochemical pedogenic processes. Because it is not yet possible to collect information on all of the variables involved in pedogenic susceptibility, they cannot be quantitatively accounted for through conventional regression analysis (Porter et al, 2001). Therefore most studies have considered precipitation as the dominant factor that controls the pedogenic processes, and have adopted different simplifying assumptions to rule out other non-precipitation factors, and to reconstruct paleoprecipitation. These studies have given rise to a diverse set of climofunctions and results (Maher et al, 1994; An and Sun, 1995; Sun et al, 1995; Han et al, 1996; Porter et al, 2001) (Tab.1).

Tab.1 Different types of climofunction in published papers

All of the climofunctions cited in Tab.1, with the exception of Porter et al (2001), were established using a best fit between present (most recent 10 ～ 30 years) precipitation and total magnetic susceptibility (or pedogenic susceptibility) in the modern soil (near surface) from different locations, without consideration of the dust dilution effect. Namely, all these papers through burdensome work have ruled out all non-precipitation factors in regression calculations, leaving the latest 10 ～ 30 years’ precipitation alone. As a result, the effect of non-precipitation factors, including dustfall-induced susceptibility SUS(D) and the dilution effect (Kukla et al, 1988; Porter et al, 2001) of the slow dust deposition during pedogenesis (An and Sun, 1995; Porter et al, 2001), have altogether been taken as the rainfall-related composition to be fitted with the measured present precipitation P in their regression, which has resulted in that the inherentlinear correlation between the precipitation and the pedogenic susceptibility (Beer et al, 1993; Heller et al, 1993; An and Sun, 1995; Shen et al, 2000; Zhou et al, 2007a) was incorporated into a nonlinear climofunction (polynomial type or logarithmic type) depending on the local and temporal climate conditions being considered (Tab.1). These different types of nonlinear climofunctions did not achieve a perfect correlation between precipitation and pedogenic susceptibility in nature as they only reflected the best fit between the present precipitation and near surface susceptibility for a specifi c locality over the past 10 ～ 30 years.

A basic question that arises from the aforementioned approach is whether climofunctions from the latest 10 ～ 30 years’ data can be extended to include past glacial and interglacial periods. Such an approach implies that all non-precipitation factors have been constant or have negligible changes from glacial and interglacial ages through the present. This is obviously not a valid assumption. For example, Fig.1a shows the dust flux (D) from the Louchuan loess profile for the past 130 ka, with a relative standard deviation RSD = 25%. This record features an abrupt change in dust flux at circa 80 ka that reached up to 200%. The large fluctuation of the dust flux indicates that it is inappropriate to apply the climofunctions in Table 1 through this interval. This includes the formula of Porter et al (2001), which accounts for the dust dilution effect, but still refers to recent accumulation rates.

In addition to the susceptibility-based approach for paleoprecipitation reconstruction, Heller et al (1993) exploited a “10Be-Susceptibility similarity” approach to extract the pedogenic susceptibility. In their approach, they used both susceptibility and10Be to reconstruct regional paleorainfall in the CLP (Beer et al, 1993; Heller et al, 1993; Shen et al, 2000). However, their approach did not consider both dust flux variations and10Be changes associated with geomagnetic field changes. The latter account for 10% ～ 20% of the total10Be signal.

Fig.1 The dust fl ux D (a), magnetic susceptibility (b),10Be concentration (c) for the past 130 ka of the Louchuan loess profi le. The RSD (relative standard deviation) of D, i.e. the ratio of the mean root square of the fl uctuation ΔD to their average value, is 25%, an abrupt change occurred at circa 80 ka. The high magnetic susceptibility during 80 ～ 110 ka was formed by a combination of high precipitation and low dust fl ux (Fig.1a) rather than by high precipitation alone.

Authors have used the correlation between7Be in modern precipitation (Wallbrink and Murray, 1994; Ishikawa et al, 1995; Caillet et al, 2001) and tropospheric10Be/7Be ratio to derive quantitative estimates of the past 80 ka precipitation over the Luochuan profile (Zhou et al, 2007a). The results were comparable to speleothem δ18O records from Dongge and Hulu caves (Wang et al, 2001, 2008), however the approach relies the correlation with7Be which again is only available from modern observations. Hence the method cannot fully account for geomagnetic field changes and dust dilution effects that one may expect when extending a model to the past 80 ka.

Hence, a quantitative reconstruction of paleoprecipitation remains a crucial goal towards understanding changes in East Asia Monsoon intensity through time. Here we introduce a new method to reconstruct paleoprecipitation by using loess magnetic susceptibility and10Be records.

In order to make it clear, we explain a few terms used in the text as following (Tab.2).

Tab.2 The explanation of terms used in this study

2 Application of the “Residual Trace Approach”to the paleoprecipitation reconstruction over the past 130 ka from Luochuan loess prof le

We describe next two approaches based on what we term the “Residual Trace Approach” (RTA) for paleoprecipitation reconstruction, and demonstrate their application over the past 130 ka in the Luochuan loess profile. The first is the SUS-approach where the dust dilution effect on pedogenic susceptibility is considered. The second is10Be-approach, which arose from10Be production rate reconstruction studies (Zhou et al, 2007a, 2007b, 2010a, 2010b). In the10Be-approach, the influences of both atmospheric10Be production rate and loess dust flux on the wet deposited10Be records are considered.

2.1 SUS-approach

In the SUS-approach we use magnetic susceptibility SUS(M ) = SUS(D, P) (Fig.1b) and dust fl ux D (Fig.1a) to reconstruct precipitation P at Luochuan for the past 130 ka. As stated above, this approach is different from previous methods that ignored dilution effects of the loess component on the pedogenic susceptibility (Maher et al, 1994; An and Sun, 1995; Sun et al, 1995; Han et al, 1996), and considers the dilution effect of the dust deposition on the pedogenic susceptibility SUS(P).

We first assume that the dustfall-induced susceptibility SUS(D) is independent of precipitation and is homogenous in both its spatial and temporal distributions (Zhou et al, 2007a), it is reasonable to use the measured SUS(M ) =SUS(D, P), instead of the SUS(P) for precipitation reconstruction, since the pure SUS(P) is diffi cult to be extracted from the total SUS(M ).

A linear regression of SUS(M ) vs. D for the Luochuan loess profi le during the past 130 ka is:

According to Mean Value Concept (MVC) (Zhou et al, 2007b), the estimated SUS(M )eis determined by the varying dust fl ux D under the average precipitationfor the past 130 ka. The negative slope of the regression line refl ects the dilution effect of D on the magnetic susceptibility.

We can then compute residual values compared to those foras:

These are fl uctuations of pedogenic susceptibility caused by changes in monsoon precipitation relative to the mean precipitation(Zhou et al, 2007b).

We next assert that the residual ΔSUS(ΔP) should be linearly correlated to precipitation variations ΔP about the mean,,

Thus the absolute precipitation at age T is:

And the absolute precipitation during the present day T0is:

The [0, 1] normalization is introduced in order to delete the unknown constants in (4).

where the symbol ＜ ＞ denotes the normalized precipitation value, and the footprint ‘max’ and ‘min’is the maximum and minimum residual or P within the regression interval.

Then the ratio of (5-1) to (5-2) would be the relative precipitation to be reconstructed to the present, if the smallest precipitation is Pmin= 0 within the regression interval.

where the present relative precipitation P(T0) =1.

The next step is how to determine the ΔSUS(ΔP)mincorresponding to the Pmin= 0, that will be discussed in section 2.3.

2.210Be-approach

In10Be-approach, we will extract the precipitation P signals from the measured Be(M ) = Be(D, P, Pr) (Fig.1c) by using both the loess dust flux D (Fig.1a) and the reconstructed atmospheric10Be production rate Pr (Fig.2) synthesized from two Pr curves reconstructed from the Luochuan and Xifeng loess10Be records (Zhou et al, 2010a) which are closely comparable with the calculated10Be production rate from marine10Be (Christl et al, 2010) and SINT 800 paleointensity records (Guyodo and Valet, 1999).

Fig.2 The reconstructed10Be production rate Pr curve synthesized from two Pr curves reconstructed from the past 130 ka of Luochuan and Xifeng10Be records (Zhou et al, 2010a)

In the10Be-approach (Zhou et al, 2014a), we fi rst carried out binary linear regression of Be(M ) with Pr and D over the past 130 ka Luochuan loess profi le:

where the estimated value Be (M)eis determined byvarying Pr and D under the average precipitationof the past 130 ka according to the MVC (Zhou et al, 2007b) and the dust dilution effect is apparent in the negative slope before D in equation (7).

Next, we obtain the residual:

which is the loess10Be concentration fluctuations caused by the precipitation variations ΔP relative to the averageof past 130 ka according to MVC.

Similar to (3)～(6), the ratio in (9) would be the relative precipitation to be reconstructed to the present, if the smallest precipitation is Pmin= 0 within the regression interval.

where the present relative precipitation P(T0) =1.

The next step is how to determine the ΔBe(ΔP)mincorresponding to the Pmin= 0, that will be discussed in section 2.3.

2.3 Normalization and Scaling

As mentioned above, the ratios in (6) and (9) would be relative precipitation when reconstructed to the present. If the smallest precipitation within the regression interval is Pmin= 0 then the corresponding residual would be Δymin(ΔSUS(ΔP)minor ΔBe(ΔP)min) (10),

Under the limiting condition that precipitation P = 0, the corresponding composition of the pedogenic susceptibility in loess would be SUS(P)=0, and the measured contemporary total susceptibility SUS(M ) is the smallest and is only related to dustfall-induced susceptibility, i.e. SUS(M) = SUS(D). According to the comparison of loess magnetic susceptibility versus coercivity (Evans and Heller, 2001) from a wide range of locations on the Chinese Loess Plateau for the last 135 ka, the endmember of high coercivity represents a dry dust component of loess susceptibility. We note the corresponding SUS(D) ≈ 25×10-8(m3· kg-1) (driest period) (Zhou et al, 2007a).

Consequently, we can f ind the age corresponding to the smallest susceptibility SUS(M )≤25 (10-8m3· kg-1), and we can obtain the corresponding residual Δyminfrom the regression equation, i.e., ΔSUS(ΔP)minin SUS-approach, ΔBe(ΔP)minin10Be-approach. If the measured datum error is moderate, the residual Δymin(ΔSUS(ΔP)minor ΔBe(ΔP)min) should be the smallest (most negative) within the concerned regression interval. With the value of ΔSUS(ΔP)minor ΔBe(ΔP)min, the relative precipitation to the present can be reconstructed from equations (6) or (9).

On the other hand, it has been acknowledged through modern observation that the average precipitation at present is about≈ 650 mm in Luochuan, thus, we can calculate the absolute precipitation through scaling the present relative precipitation to= 650 mm, noting the present relative precipitation P(T0)=1.

Or through scaling the present normalized precipitationto 650 mm (Zhou et al, 2014a), which will introduce the ΔSUS(ΔP)maxor ΔBe(ΔP)max.

2.4 Cross check and inter-comparison

The correlation coefficient of the reconstructed precipitation curves (Fig.3 a, b) by the two approaches are 0.96. The relative differences of their average values are 13.0% (0 ～ 130 ka) and 12.7% (0 ～ 80 ka), and the RSDs (relative standard deviation of their difference to the average) are 9.6% (Tab.3).

In order to compare our results with other susceptibility-reconstructed precipitation records, we substituted our measured magnetic susceptibility value SUS(M ) (Fig.1b) (or approximate pedogenic SUS(P)= SUS(M ) -25) into the individual climofunctions introduced by previous studies (Maher et al, 1994; Han et al, 1996; Porter et al, 2001) to calculate the past 130 ka precipitation over the Louchuan loess profi le. These results are superimposed on our curves as shown in Fig.3. The differences are apparent, especially at age ranges between 80 ～ 110 ka where the alternernative curves are higher than ours (Fig.3 c, d, e).

In our view, the high pedogenic susceptibility during 80 ～ 110 ka (Fig.1b) formed through a combination of high precipitation and low dust flux (Fig.1a) rather than by high precipitation alone, so the horizontal sections of the precipitation curves during 80 ～ 110 ka should follow a lower trend, such as ours (Fig.3 a, b). The previous approaches follow a trend above these values because they failed to account for the abrupt drop in dust fl ux from 80 ～ 110 ka (Fig.1a).

In addition, our reconstructed precipitation records (Fig.4 a, b) compare well with the δ18O records from Hulu-Sanbao caves (Fig.4c) (Wang et al, 2001, 2008), which is widely regarded as a reliable record of Asian Monsoon intensity. Like speleothem δ18O records,10Be precipitation records in loess during MIS 5 clearly reveal sub-cycles (MIS 5a—MIS 5e) of precipitation changes, providing further proof that our approaches are reliable.

Fig.3 The comparison of the reconstructed precipitation curves by the SUS-approach (a) and the10Be-approach (b) with individual precipitation curves (c-e) reconstructed by substituting our measured magnetic susceptibility values into the climofunctions reported in previous studies

Tab.3 The average precipitation () and their relative differences (σ, RSD) and correlation coeffi cient (R2) of the reconstructed precipitation curves by two approaches

Tab.3 The average precipitation () and their relative differences (σ, RSD) and correlation coeffi cient (R2) of the reconstructed precipitation curves by two approaches

Correlation (R2) σRSD (SUS-approach)(10Be-approach)0 ～ 130 ka440.7506.313.0%0.92 (r = 0.96)48.69.6% 0 ～ 80 ka444.4508.914.9%0.91(r = 0.96)48.79.6%

Fig.4 The reconstructed past 130 ka precipitation over the Louchuan loess profi le by a)10Be-approach and b) SUS-approach, and their correlation with speleothem δ18O records (c) from Hulu-Sanbao caves (Wang et al, 2001, 2008)

2.5 Summary for the paleoprecipitation reconstruction

Using the loess susceptibility alone for precipitation reconstruction in previous studies based on the traditional trace methods has derived a number of climofunctions which have neglected to include the infl uence of dust dilution on pedogenic susceptibility, and on the reconstructed precipitation. The paired measurements of loess susceptibility and loess dust fl ux can be used to reconstruct glacial and interglacial precipitation by using the SUS-approach, in which the dust dilution influence on the reconstructed precipitation is accounted for.

As a byproduct of reconstruction global10Be production rate (or geomagnetic intensity) reconstruction, we can use the10Be-approach to reconstruct precipitation over the loess plateau. The coincidence of the reconstructed precipitation curves by the two approaches is marked. Nevertheless, as speculated by previous workers (Heller et al, 1993; Maher et al, 1994), difficulties are also encountered with the SUS-approach and10Be-approach in determining precise estimates of dust fl ux through the loess accumulation rates and the dry bulk density.

3 Mathematical explanation of the“Residual Trace Approach”: Mean Value Concept

Variables SUS(P, D), P, D used in the SUS-approach, or variables Be(P, D, Pr), (P, D), Pr used in the10Be-approach constitute multiple variables y(x1, x2), x1, x2. Other than conventional multivariable regression analysis or traditional tracer research, in the“Residual Trace Approach”, we carry out the linear regression analyses between y(x1, x2) and x1to remove the effect of x1, and then carry out a calculation to quantify the variation due to the second variable x2through the calculated residual Δy(Δx2).

Usually, the estimated regression equations (1) and (7) are expressed as the only correlation betweeny(x1, x2) and x1.

Obviously, the second variable x2“uninvolved”in regression equation (12), must be a constant xCin the estimated values y(x1, x2= xc)eor on the regression line, otherwise the regression analysis (12) would be meaningless, and the calculated residuals Δy(Δx2) are caused only by the difference between the measured x2and the constant xCon the regression line.

How much is the constant xCon the regression line? According to our study (Zhou et al, 2007b), this constant is taken to be xC=, the arithmetic mean value of x2over the concerned regression interval. Namely, all x2values corresponding to estimated values on the regression line are equal to the arithmetic mean value(Fig.5). This is the root of the MVC (Mean Value Concept) (Zhou et al, 2007b), which can be further explained from a statistical view as following.

The top and middle panels of Fig.5 are the scatter diagrams of y(x1, x2) vs. x1(Fig.5a) and y(x1, x2) vs. x2(Fig.5b) respectively. The decline line in Fig.5a is the regression line of y(x1, x2) vs. x1and the vertical line in Fig.5b is the constant x2line xCcorresponding to the value on the regression line. Even though assuming the complete correlation between y(x1, x2) and x1and without datum errors, all measured data y(x1, x2) are distributed around the two sides of the regression line (Fig.5a). They are located at different distance Δy(Δx2) from the regression line depending on the Δx2, the deviation of the x2values from the constant value xC(Fig.5b). No matter whether the correlation between y(x1, x2) and x2is linear or nonlinear, the further the Δx2, the bigger the Δy (Δx2), and vice versa.

Fig.5 Scatter diagrams of y(x1, x2) vs. x1

If we define the Δy(Δx2), the deviation from the regression line caused by the Δx2, as a“residual”, like the conventionally defi ned residual in statistics due to datum error or incomplete similarity correlation, the regression equation derived by computer programs must be determined in compliance with the minimum of the sum of the“residual” square Δy(Δx2)2or the deviation square Δx2

2according to the well-known principle of least square method, applicable to linear correlations. Moreover, the statistics indicates that the summation of the squares of the deviation from arithmetic mean value is the least among the sum of various deviation squares. Thus the constant xCon the regression line (Fig.5c) or on the vertical line (Fig.5b) must be the arithmetic mean valueso as to meet the minimum of the sum of the “residual” squares Δy(Δx2)2or the deviation squares Δx22. That is the virtual MeanValue Concept (MVC) deduced from the statistical point of view. The more the number of specimens, the more accurate the MVC.

According to the MVC, a linear regression of a multivariable system, such as y(x1, x2) vs. x1, is carried out around the average, and the estimated value y(x1, x2) of the regression equation (12) is the correlation between y(x1, x2) and x1under the condition of constant(Fig.5c).

With introduction of the MVC, we realize the residual in RTA,

is the variations of y(x1, x2) caused by the Δx2, variation of x2relative to its average valuewithin concerned regression interval, which becomes the mathematic connotation of the “Residual Trace Approach”.

4 Other successful application examples of the “Residual Trace Approach”

By taking the loess susceptibility as climate (P, D) proxy, this new approach has successfully been applied to reconstruct the past 80 ka, 130 ka paleogeomagnetic intensities by using the10Be records in Luochuan and Xifeng loess profiles (Zhou et al, 2007a, 2010a). By using this approach, we have determined the Brunhes/ Matuyama (B/M) geomagnetic reversal at circa 780 ± 3 ka BP in Xifeng and Luochuan loess profi les, this timing is synchronous with the B/M reversal timing seen in marine records, facilitating the resolution of the long standing debate about the discrepancy of the B/M magnetic records between Chinese loess and marine sediments by paleomagnetic studies (Zhou et al, 2014b).

In addition, taking the radioisotope90Sr as proxy of the sea surface temperature, we have applied this new approach to quantitatively reconstruct the past 90 years’ sea salty in the Xisha and Hainan islands with δ18O (Song, 2006) records.

There is no doubt that the “Mean Value Concept”based “Residual Trace Approach” has opened a new way in environment tracing studies. The differences of the developed “Residual Trace Approach” from the traditional trace method are compared in tab.4, both of which can be applied to the trace research under the respect appropriate condition and with its own advantage and disadvantage, and the “Residual Trace Approach” is especially suitable to the trace research for a multivariable geosystem where all variables are changeable and their distribution have been known except the one to be reconstructed. However, it is important for RTA that the linear correlation between the dependent variable y and independent variables x1, x2… should be high, the higher the linear correlation, the more accurate the traced/ reconstructed results.

Tab.4 Comparison of the “Residual Trace Approach” with the traditional trace approach

References

孫東懷, 周 杰, 吳錫浩. 1995. 全新世氣候適宜期黃土高原及黃土／沙漠過(guò)渡區(qū)年降水量的初步恢復(fù)[J].中國(guó)沙漠, 15: 339 - 344. [Sun D H, Zhou J, Wu X H. 1995. Preliminary reconstruction of annual rainfall in loess plateau and loess-desert transitional regions in suitable climatic period of Holocene [J]. Journal of Desert Research, 15: 339 - 344.]

周衛(wèi)健, 孔祥輝, 鮮 鋒, 等. 2010b. 中國(guó)黃土10Be重建古地磁場(chǎng)變化史的初步研究[J]. 地球環(huán)境學(xué)報(bào)，1(1): 20 - 27. [Zhou W J, Kong X H，Xian F, et al. 2010b. Preliminary study on the reconstruction of the plaeogeomagnetic intensities by10Be in Chinese loess [J]. Journal of Earth Environment, 1(1): 20 - 27.]

An Z S, Sun D H. 1995. Discussion on the monsoon variation over the Loess Plateau in the Last Glacial Cycle [M]. Beijing: Science Press.

Beer J, Shen C D, Heller F, et al. 1993.10Be and magnetic susceptibility in Chinese Loess [J]. Geophysical Research Letters, 20: 57 - 60.

Caillet S, Arpagaus P, Monna F, et al. 2001. Factors controlling7Be and210Pb atmospheric deposition as revealed by sampling individual rain events in the region of Geneva, Switzerland [J]. Journal of Environmental Radioactivity, 53: 241 - 256.

Christl M, Lippold J, Steinhilber F, et al. 2010. Reconstruction of global10Be production over the past 250 ka from highly accumulating Atlantic drift sediments [J]. Quaternary Science Review, 29: 2663 - 2672.

Evans M E, Heller F. 2001. Magnetism of loess/palaeosol sequences: recent developments [J]. Earth-Science Reviews, 54: 129 - 144.

Guyodo Y, Valet J P. 1999. Global changes in intensity of the Earth’s magnetic fi eld during the past 800 kyr [J]. Nature, 399: 249 - 252.

Han J M, Lu H Y, Wu N Q, et al. 1996. The magnetic susceptibility of modern soils in China and its use for paleoclimate reconstruction [J]. Studia Geophysica et Geodaetica, 40: 262 - 275.

Heller F, Shen C D, Beer J, et al. 1993. Quantitative estimates of pedogenic ferromagnetic mineral formation in Chinese loess and palaeoclimatic implications [J]. Earth and Planetary Science Letters, 114: 385 - 390.

Ishikawa Y, Murakami H, Sekine T, et al. 1995. Precipitation scavenging studies of radionuclides in air using cosmogenic7Be [J]. Journal of Environmental Radioactivity, 26: 19 - 36.

Kukla G, Heller F, Liu X M, et al. 1988. Pleistocene climates in China dated by magnetic susceptibility [J]. Geology, 16: 811 - 814.

Maher B A, Thompson R, Zhou L P, et al. 1994. Spatial and temporal reconstructions of changes in the Asian palaeomonsoon: A new mineral magnetic approach [J]. Earth and Planetary Science Letters, 125: 461 - 471.

Porter S C, Hallet B, Wu X H, et al. 2001. Dependence of nearsurface magnetic susceptibility on dust accumulation rate and precipitation on the Chinese Loess Plateau [J]. Quaternary Research, 55: 271 - 283.

Shen C D, Beer J, Heller F, et al. 2000.10Be-susceptibility model and quantitative estimates of pedogenic ferromagnetic material fl ux in Chinese loess [J]. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 172: 551 - 554.

Song S H. 2006. Reconstruction of climatic history based on coral in South China Sea and the related data analysis method [D]. Beijing: Graduate University of Chinese Academy of Sciences.

Wallbrink P J, Murray A S. 1994. Fallout of7Be in South Eastern Australia [J]. Journal of Environmental Radioactivity, 25: 213 - 228.

Wang Y J, Cheng H, Edwards R L, et al. 2001. A high-resolution absolute-dated Late Pleistocene monsoon record from Hulu Cave, China [J]. Science, 294: 2345 - 2349.

Wang Y J, Cheng H, Edwards R L, et al. 2008. Millennial- and orbital-scale changes in the East Asian monsoon over the past 224,000 years [J]. Nature, 451: 1090 - 1093.

Zhou W J, Priller A, Beck W, et al. 2007a. Disentangling geomagnetic and precipitation signals in an 80-kyr Chinese loess record of10Be [J]. Radiocarbon, 49: 139 - 160.

Zhou W J, Chen M B, Xian F, et al. 2007b. The mean value concept in mono-linear regression of multi-varaibles and its application to trace studies in geosciences [J]. Science in China Series D: Earth Sciences, 50: 1828 - 1834.

Zhou W J, Xian F, Beck W, et al. 2010a. Reconstruction of 130-kyr relative geomagnetic intensities from10Be in two Chinese loess sections [J]. Radiocarbon, 52: 129 - 147.

Zhou W J, Xian F, Du Y J, et al. 2014a. The last 130 ka precipitation reconstruction from Chinese loess10Be [J]. Journal of Geophysical Research: Solid Earth, 119: 191 - 197.

Zhou W J, Beck W, Kong X H, et al. 2014b. Timing of the Brunhes-Matuyama magnetic polarity reversal in Chinese loess using10Be [J]. Geology, 42: 467 - 470.

“Mean Value Concept” based “Residual Trace Approach” — application to paleoprecipitation reconstruction over the Chinese Loess Plateau

ZHOU Wei-jian1,2,3,4, CHEN Mao-bai1,2, KONG Xiang-hui1,2, XIAN Feng1,2, DU Ya-juan1,2, WU Zhen-kun1,2, SONG Shao-hua1,2, KANG Zhi-hai1,2
(1. State Key Laboratory of Loess and Quaternary Geology and Shaanxi Key Laboratory of Accelerator Mass Spectrometry Technology and Application, Institute of Earth Environment, Chinese Academy of Sciences, Xi’an 710061, China; 2. Xi’an Accelerator Mass Spectrometry Center, Xi’an 710061, China; 3. Beijing Normal University, Beijing 100875, China; 4. School of Human Settlements and Civil Engineering, Xi’an Jiaotong University, Xi’an 710049, China)

The traditional trace methods for paleoprecipitation reconstruction over Chinese Loess Plateau are fi rst analyzed. Then, two practical applications of the newly developed “Residual Trace Approach” to quantitatively reconstruct the paleoprecipitation over the Chinese Loess Plateau are described. One is the “SUS-approach” that uses paired measurements of magnetic susceptibility and dust flux in loess-paleosol sediments as proxies, the other is the “10Be-approach” that uses both atmospheric10Be production rate and loess dust fl ux as proxies. The reconstructed precipitation curves of the past 130 ka over Luochuan loess plateau site by the two approaches are highly correlated. However, they are different to some extent from the other precipitation curves calculated by theindividual climofunctions of the previous studies using traditional trace methods, and the detailed variations evident in the new approach offer an advantage over the traditional methods in revealing the dust dilution effect on the reconstructed precipitation. Furthermore, it is pointed out that the mathematical connotation of the “Residual Trace Approach” is equivalent to the “Mean Value Concept (MVC)” which is further explained from a statistical point of view. Finally, the difference of the “Residual Trace Approach” from the traditional trace method is compared.

Chinese Loess Plateau; SUS-approach;10Be-approach; Mean Value Concept; Residual Trace Approach; paleoprecipitation

ZHOU Wei-jian, E-mail: weijian@loess.llqg.ac.cn

P532

A

1674-9901(2015)06-0382-11

10.7515/JEE201506002

Received Date:2015-09-29

Foundation Item:National Basic Research Program of China (2013CB955904); National Natural Science Foundation of China (41230525); MOST (Ministry of Science and Technology) Special Fund for State Key Laboratory of Loess and Quaternary Geology.