Decoupling of water and air temperature in winter causes warm season bias of lacustrine brGDGTs temperature estimates

Abstract. It has been frequently found that lacustrine brGDGTs-derived temperatures are warm season biased relative to measured annual mean air temperature (AT) in the mid to high latitudes, the mechanism of which, however, is not very clear. Here, we investigated the brGDGTs from catchment soils, and suspended particulate matter (SPM) and surface sediments in the Gonghai Lake in north China to explore this question. Our results showed that the brGDGTs distribution in sediments resembled that in the SPM but differed from the surrounding soils, suggesting a substantial aquatic origin of the brGDGTs in the lake. Therefore, established lake-specific calibrations were applied to estimate local mean annual AT. As usual, the estimates were significantly higher than the measured mean annual AT. However, they were similar to, and thus actually reflected, the mean annual lake water temperature (LWT). Interestingly, the mean annual LWT is close to the measured mean warm season AT, hence suggesting that the apparent warm season bias of lacustrine brGDGTs-derived temperatures could be caused by the discrepancy between AT and LWT. In our study region, ice forms at the lake surface during winter, leading to isolation of the underlying lake water from air and hence higher LWT than AT, while LWT follows AT during warm seasons when ice disappears. Therefore, we believe what lacustrine brGDGTs actually reflected is the mean annual LWT, which is higher than the mean annual AT in our study location. Since the decoupling between LWT and AT in winter due to ice formation is a universal physical phenomenon in the mid to high latitudes, we propose this phenomenon could be also the reason for the widely observed warm season bias of brGDGTs-derived temperatures in other lakes, especially the shallow lakes.



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In fact, brGDGTs-based temperature indices should directly record lake water temperature (LWT), rather than AT, if the brGDGTs in lake sediments solely or mainly sourced from the lake environments (Tierney et al., 2010;Loomis et al., 2014). So, the mean annual AT estimate based on lake sedimentary brGDGTs is valid only when LWT is tightly coupled with AT. However, the relationship between LWT 90 and AT is potentially complex in cold regions, as well as in deep lakes, and the coupling between the two is not always the case, which would hamper the application of brGDGTs for temperature estimates (Pearson et al., 2011;Loomis et al., 2014;Weber et al., 2018). In deep lakes, bottom water temperature usually decouples with AT, together with the predominant production of brGDGTs in deep water and sediments, causing weak correlations between brGDGTs-derived temperature and AT (Weber et al.,95 2018). For shallow lakes, LWT does not always follow AT either, specifically in winter when AT is below freezing, in cold regions, as has been shown in the Lower King pond (Loomis et al., 2014).
However, the decoupling between LWT and AT has not been recognized as a key mechanism for the warm bias of brGDGT-derived temperatures observed widely in the mid-and high-latitude lakes, and seasonal production or deposition of brGDGTs is usually invoked as a cause (e.g., Pearson et al., 2011; 84/16 A/B to equilibrate it for 30 min. The flow rate was at a constant 0.2 ml/min throughout. BrGDGTs were ionized and detected with single ion monitoring (SIM) at m/z 1050, 1048,1046,1036,1034,1032,160 1022, 1020, 1018 and 744. The brGDGTs were quantified from comparing retention time and peak areas with the C46 GDGT internal standard.
In this study, we used two silica columns in tandem and successfully separated 5-and 6-methyl brGDGTs. However, many previous brGDGTs studies on lake materials used one cyano column, 180 which cannot separate 5-and 6-methyl brGDGTs (e.g., Wang et al., 2012;Loomis et al., 2014;Hu et al., 2015Hu et al., , 2016Cao et al., 2017). In order to facilitate comparison with previous studies, we reanalyzed the published brGDGTs data in the Gonghai Lake (Cao et al., 2017). For temperature estimations, we listed the Eqs. (8-16) used in this study in Table 2.

Seasonal changes in environmental parameters
The AT in our study area ranged from −12.2 to 21.6°C, below freezing in winter (November to The brGDGTs in soils, sediments and SPM were dominated by brGDGTs II and III series, with acyclic compounds dominant in every series (Fig. 3a). In comparison, the mean IIIa/IIa ratio value in sediments (1.30) was higher than in SPM (0.99) and soils (0.70). In addition, 6-methyl brGDGTs dominated over 5-methyl brGDGTs in soils, exhibiting mean IR6ME of 0.62; whereas the two isomers were similar in contents in sediments (IR6ME = 0.51) and SPM (IR6ME = 0.47~0.48) (Fig. 3a). Notably, also identified in the Gonghai Lake sediments and SPM, but not found in catchment soils (Fig. 3a).

Cyclisation ratio, methylation index of brGDGTs
The  (Fig. 3b). The #Ringspenta 5ME showed the same increasing trend as #Ringstetra from soils to SPM and then to sediments (Fig. 3b). In contrast, #Ringspenta 6ME in soils was similar to that in sediments and SPM (Fig. 3b).

Different sources of lacustrine brGDGTs from surrounding soils
Although brGDGTs have a strong potential to record temperature in lacustrine regions (Tierney et al., 2010;Pearson et al., 2011;Sun et al., 2011;Loomis et al., 2012;Dang et al., 2018;Russell et al., 2018), the sources of brGDGTs in lake sediments should be carefully identified. There are two potential sources, including allochthonous input from soil and autochthonous production in lake water 225 or surface sediments, which can be distinguished by comparison of brGDGTs concentration and compositional distribution between surface sediments and soils (Tierney and Russell, 2009;Loomis et al., 2011;Wang et al., 2012;Hu et al., 2015;Sinninghe Damsté, 2016).
In the Gonghai Lake, the average content of brGDGTs in surface sediments was significantly higher than that in surface soils (Table 1), suggesting a possible autochthonous contribution, even 230 though soil brGDGTs input cannot be ignored. Moreover, the composition distribution of brGDGTs in surface sediments was similar to SPM, but quite different from soils ( Fig. 3a). Several lines of evidence could suggest a substantial in situ production of brGDGTs in the Gonghai Lake. (I) The presence of IIIa'' in the Gonghai Lake sediments (Fig. 3a), which has been only identified in lake sediments but not found in catchment soils previously (Weber et al., 2015), could be a direct evidence 235 of in situ production in lake. (II) The values of IIIa/IIa in sediments was higher than 0.92, which was regarded as the evidence of aquatic production as previous reported (Xiao et al., 2016;Martin et al., 2019;Zhang et al., 2020). In the Gonghai Lake, IIIa/IIa was higher than 0.92, and significantly higher than that in catchments (Fig. 3a). (III) The average values of IR6ME in surface sediments is significantly lower than in catchment soils ( Fig. 3a), suggesting at least some of 5-methyl brGDGTs 240 in lake sediments were produced in situ. (IV) The cyclisation ratio of brGDGTs has been also used to distinguish the aquatic production, although applied to marine sediments, from soil input (Sinninghe Damsté, 2016). In the Gonghai Lake, #Ringstetra and #Ringspenta 5ME were clearly higher in sediments than in catchment soils, although #Ringspenta 6ME in sediments was similar to that in catchment soils ( Fig. 3b).

Soil brGDGTs reflect mean annual AT
Based on the new global soil calibration of Eq. (9) excluding 6-methyl brGDGTs, the brGDGTs-derived AT in the Gonghai catchment soils ranged from 1.18-2.75°C (average 2.33 ± 0.65; Fig. 4a). Considering the ±4.8°C uncertainty of the calibration, thus estimated temperature is close to the mean annual AT of 4.3°C, thereby reflecting mean annual AT in our study lake catchment. 250 For some lakes, soil brGDGTs input may be significant and predominant over aquatic production, yielding similar brGDGTs composition distributions between lake sediments and surrounding soils. In such cases, soil calibrations could be still applicable to lake sediments for AT reconstruction (Niemann et al., 2012;Li et al., 2017;Ning et al., 2019;Tian et al., 2019). In our results, using soil-derived calibration of Eq. (9), the estimated temperatures from surface sediments (−0.50 ± 255 0.78°C; Fig. 4a) and SPM (−0.55 ± 0.52°C; Fig. 4a) were much lower than those from surface soils (2.33 ± 0.65°C; Fig. 4a). Similarly, temperature underestimation has been widely reported in global lakes (e.g., Tierney et al., 2010;Loomis et al., 2012;Pearson et al., 2011;Russell et al., 2018), which is likely associated with in situ production of brGDGTs in the lakes.

Lacustrine brGDGTs reflect warm season AT
The above evidence suggests that the application of temperature calibrations based on soil brGDGTs (by De Jonge et al. (2014)) to lake sediments is risky. Therefore, lake-specific temperature calibrations, although not differentiated quantitatively the relative contributions of aquatic vs.
soil-derived brGDGTs, are likely to be more appropriate than soil calibrations. In fact, in situ aquatic 265 production of brGDGTs has been noticed by numerous authors in their works for making lake-specific calibrations (Tierney et al., 2010;Pearson et al., 2011;Sun et al., 2011;Loomis et al., 2012;Dang et al., 2018;Russell et al., 2018). Therefore, we preferred application of lake-derived calibrations to our lacustrine brGDGTs.
In September, the values of MBT'5ME and MBT'6ME in SPM gradually decreased with depth, 270 similar to the measured water temperature profile in the water column (Fig. 2). In January, the values of MBT'5ME and MBT'6ME in SPM remained constant at different depths, also similar to the measured water temperature profile in water column (Fig. 2). In addition, the values of MBT'5ME and MBT'6ME in SPM in September were higher than in January, corresponding to the warmer water temperature in Although the MBT'5ME and MBT'6ME in SPM in the lake may reflect temperature changes in the water column, the difference of brGDGTs-derived temperatures based on lake-specific calibrations between September and January (0.3°C) were much smaller than the measured difference (~13°C), independent of the calibration of (14), (15)  indices such as IIIa/IIa, IR6ME, #Ringstetra and #Ringspenta in SPM were all in-between the soil and sediment values, suggestive of more impact of soil input on brGDGTs in SPM than in sediments, which could also reduce the seasonal contrast in estimated temperatures.
Using the new proposed 5-and 6-methyled brGDGTs temperature calibrations, we got 300 temperature estimates from the Gonghai surface sediments in ranges of 6.9-8.0°C (average 7.5 ± 0.4°C; Eq. (14); Fig. 4b) and 10.1-13.2°C (average 11.4 ± 1.4°C; Eq. (15); Fig. 4b). These values are significantly warmer than the mean annual AT and close to the mean warm season AT in the Gonghai Lake region (Fig. 4b). This is consistent with the recent results from Dang et al. (2018), who investigated 35 Chinese lakes and found that warm season AT correlated well with brGDGTs 305 composition in relatively cold regions.
Many previous brGDGTs instrumental analyses on lake materials used one cyano column, which cannot separate 5-and 6-methyl brGDGTs. Using the data published in the same lake from Cao et al.
(2017), we re-calculated temperature using different calibrations. The results showed that the absolute temperature estimates were all significantly warmer than the mean annual AT (Table 3), with the 310 temperature offsets varying from 4-10°C, which cannot be fully explained by the uncertainty of each calibration. Therefore, it appears that sedimentary brGDGTs-derived temperature is warm season biased in the Gonghai Lake irrespective of whether or not 5-and 6-methyl brGDGTs are separated.  (Hu et al., 2015(Hu et al., , 2016 and Lake Towuli (Tierney and Russell, 2009). Applying the global lake surface sediment calibration (Eq (10); Sun et al., 2011) to these lakes, we also re-calculated temperatures from published data of sedimentary brGDGTs (Fig.   5). Interestingly, the brGDGTs-inferred temperatures were generally higher than the measured mean annual AT, with greater differences in higher latitude lakes (including the Gonghai Lake in this study) 320 and close to the mean annual AT in low-latitude or low-altitude lakes (i.e. the warm region; Fig. 5a).
Investigations on specific lake studies have also pointed out that brGDGTs-inferred temperatures are higher than mean annual AT, close to warm season AT or summer AT in mid-and high-latitude lakes (Shanahan et al., 2013;Peterse et al., 2014;Foster et al., 2016;Dang et al., 2018), but close to mean annual AT in low-latitude lakes (Tierney et al., 2010;Loomis et al., 2012).

Ice cover formation as a mechanism for the apparent warm bias of lacustrine brGDGTs-derived temperature
One explanation for the warm season biases of the lacustrine brGDGTs-derived temperature has been proposed as the excessive production of brGDGTs during the warm/summer season relative to winter season (Pearson et al., 2011;Shanahan et al., 2013;Peterse et al., 2014;Foster et al., 2016;330 ng/l in September and 5.2 ± 2.3 ng/l in Jannuary (Fig. 2) with no significant difference. It appears not to support preferential production of brGDGTs in warm season, although the interference from fossil brGDGTs due to longer residence time and sediment resuspension cannot be fully ruled out. Besides, the season of higher brGDGTs concentration has been found different in different lakes, e.g., in spring 335 and autumn in Lower King pond (Loomis et al., 2014), in winter in Lake Huguangyan (Hu et al., 2016) and Lake Lucerne (Blaga et al., 2011), and in summer in Lake Donghu in central China (Qian et al., 2019). However, in all these lakes, brGDGTs-derived temperatures have been found to be slightly or obviously warm season biased. The inconsistency of seasonality of particulate brGDGTs concentrations suggests that other than seasonality in the production of brGDGTs in the lakes, there 340 should be another factor responsible for the bias of brGDGTs-inferred temperature toward warm season ( Fig. 5a and b).
Another explanation is that lake water depth (wd), especially water stratification, can affect  Weijers et al., 2006bWeijers et al., , 2010Weber et al., 2015Weber et al., , 2018, implying that a potentially anoxic environment in deep water favors the production of brGDGTs (Woltering et al., 2012;Zhang et al., 2016;Weber et al., 2018), which could lead to higher proportion of 'colder temperature' brGDGTs in surface sediments. Normally, stratified lakes are deep, which is not the case for the Gonghai Lake, as well as 350 for Lower King pond (Loomis et al., 2014) and Lake Donghu (Qian et al., 2019) that have maximum water depths of ca. 8 m and 6 m, respectively. Therefore, the influence of lake water depth on the molecular distribution of brGDGTs can be ruled out in these shallow lakes. In deeper lakes, such as Lake Huguangyan (20 m wd), Qinghai Lake (27 m wd) and Lake Towuli (200 m wd) (Tierney and Russell, 2009;Wang et al., 2012;Hu et al., 2016), the relatively high concentration of brGDGTs in 355 bottom water (Hu et al., 2016) could record relatively low temperature of deep water in sediments.
However, the MBT/CBT-inferred temperature in these lakes' sediments are higher, not lower than the mean annual AT, irrespective of whether the global or regional calibrations are used ( Fig. 5a and Table   3). Consequently, lake water stratification should be not responsible for the warm bias of MBT/CBT-inferred temperature of surface sediments, at least in these lakes. 360 Since the brGDGTs in surface sediments of the Gonghai Lake mainly derived from in situ production, the brGDGTs-derived temperature proxies should directly record LWT, rather than AT, as has been demonstrated by the study of Lower King Pond in temperate northern Vermont, U.S.A. However, previous studies assumed that the estimated temperatures can still reflect AT due to the tight 365 coupling between LWT and AT. In fact, such tight coupling can be found in tropical-subtropical lakes such as Lake Huguangyan and Lake Donghu ( Fig. 6c and d), where AT is always above freezing, but is not true in higher-latitude lakes such as Lower King pond and Gonghai Lake with lake surface freezing in winter ( Fig. 6a and b). The reason is that lake surface ice prevents the thermal exchange between water and air, leading to decoupling between LWT and AT in winter in those cold regions. 370 The decoupling makes annual mean LWT higher than mean annual AT. Therefore, the greater warm biases of brGDGT-derived temperatures from surface sediments in higher latitudes (Fig. 5a) could be due to the stronger decoupling (e.g., longer freezing time) between LWT and AT. Nevertheless, annual mean LWT appears close to the mean AT in warm season (monthly temperature >0°C) (Fig. 6f), which could be the reason why the brGDGTs-inferred temperatures are similar to the mean warm 375 season AT. Due to lack of detailed AT and LWT data in literature, we failed to show more examples than as shown in Fig. 6, especially those from even higher latitudes. However, we proposed a simple model for the relationship between LWT and AT in a year cycle (Fig. 7), which may be a universe physical phenomenon in shallow lakes. In mid-and high-latitude region, we believe the decoupling between AT and LWT caused by ice formation in winter may be applied to explain the observed 380 seasonality of the brGDGTs temperature records. For example, the biases of brGDGTs derived temperatures toward summer AT observed extensively in the Arctic and Antarctic lakes (Shanahan et al., 2013;Foster et al., 2016) are compatible with our suggested mechanism here.
We noticed that the seasonality of brGDGTs-derived temperature occurs also in tropical lakes;  between mean warm season AT and mean annual LWT. In the mid-latitude Gonghai Lake and Lower King pond, the surface LWT follows AT only when the AT is above freezing. In the low-latitude Lake Donghu and Lake Huguangyan, the surface LWT follows AT for the whole year.