Chemical Weathering of Loess and Its Contribution to Global Alkalinity Fluxes to the Coastal Zone During the Last Glacial Maximum, Mid‐Holocene, and Present

Loess sediments are windblown silt deposits with, in general, a carbonate grain content of up to 30%. While regionally, loess was reported to increase weathering fluxes substantially, the influence on global weathering fluxes remains unknown. Especially on glacial‐interglacial time scales, loess weathering fluxes might have contributed to land‐ocean alkalinity flux variability since the loess areal extent during glacial epochs was larger. To quantify loess weathering fluxes, global maps representing the loess distribution were compiled. Water chemistry of rivers draining recent loess deposits suggests that loess contributes over‐proportionally to alkalinity concentrations if compared to the mean of alkalinity concentrations of global rivers (~4,110 µeq L−1 for rivers draining loess deposits and ~1,850 µeq L−1 for the total of global rivers), showing comparable alkalinity concentration patterns in rivers as found for carbonate sedimentary rocks. Loess deposits, covering ~4% of the ice‐ and water‐free land area, increase calculated global alkalinity fluxes to the coastal zone by 16%. The new calculations lead to estimating a 4% higher global alkalinity flux during the Last Glacial Maximum (LGM) compared to present fluxes. The effect of loess on that comparison is high. Alkalinity fluxes from silicate‐dominated lithological classes were ~28% and ~30% lower during the LGM than recent (with loess and without loess, respectively), and elevated alkalinity fluxes from loess deposits compensated for this. Enhanced loess weathering dampens due to a legacy effect changes in silicate‐dominated lithologies over the glacial‐interglacial time scale.


Introduction
Loess sediments cover extensive areas on the Earth's surface (Muhs et al., 2014). They can provide insights into dynamical sedimentation processes of the past and serve as terrestrial archives for studying dust deposition and atmospheric circulation (Muhs & Bettis, 2000;Muhs et al., 2014;Schaetzl et al., 2018). While loess sediments are widespread around the globe, they are mainly abundant in middle latitudes. Nowadays, they cover about 4.9 × 10 6 km 2 , which represents about 4% of the total ice-free land area (i.e., relative to the Global Lithological Map [GLiM] area without ice and water bodies; Hartmann & Moosdorf, 2012).
In this study, loess deposits are defined as windblown silt deposits which typically contain quartz, feldspar, mica, and clay minerals, but also carbonate minerals (Muhs et al., 2014;Pye, 1984;Smalley et al., 2011). Besides their significance to climate-related studies, loess sediments are assumed to be important regarding chemical weathering fluxes, and their weathering behavior, including, for example, weathering proxies, has to be understood (e.g., Buggle et al., 2011). Because surfaces of loess sediments are often only slightly weathered, and because of their carbonate content and high surface area due to fine grainsize, loess might have a high influence on global weathering fluxes. Kump and Alley (1994) mention the possible significance of loess deposits in glacial chemical weathering studies. Goddéris et al. (2013) applied numerical models to quantify the weathering of the Mississippi Valley loess to simulate climate, the continental biosphere, and the weathering processes within the pedon. They calculated similar CO 2 consumption rates from Mississippi Valley loess than those from carbonate sedimentary rocks globally, because of dolomite dissolution being the major contributor to CO 2 consumption, which underlines the possible importance of loess weathering. Zhang et al. (2013) concluded that even in slightly loess-covered areas (18% loess coverage in a lake catchment on the northeastern Chinese Loess Plateau), the weathering processes of loess dominate the weathering fluxes.
Since loess sediments can have a generally high content of carbonate minerals (up to 30% carbonate grains after Pye, 1984), it has to be tested whether they show in general a similar weathering behavior as carbonate rocks. Therefore, alkalinity fluxes from loess areas were studied by analyzing river chemistry data of catchments dominated by loess deposits and compared with alkalinity fluxes derived by applying previous carbonate weathering models (Amiotte-Suchet & Probst, 1995;Bluth & Kump, 1994;. The quantification of riverine alkalinity inputs to the ocean is relevant, since it directly influences marine biogeochemical cycles. Moreover, alkalinity fluxes provide insight into the amount of atmospheric CO 2 that is being consumed by chemical weathering of rocks. To quantify global changes of alkalinity flux and CO 2 consumption rates, comparing the time of the Last Glacial Maximum (LGM), the Mid-Holocene, and the recent setting, a spatial reconstruction of loess deposits is needed. For this purpose, a map of loess distribution during the LGM was created by extrapolating geographically the recent loess distribution . This extrapolation includes, for example, alluvial areas which accumulate material from catchment loess deposits during the LGM. For the LGM loess map, present-day inundated continental shelf areas were also considered, since the sea level was~134 m lower during the LGM (Lambeck et al., 2014), leading to the exposition of large shelf areas to terrestrial weathering. Information about loess sediments on previously exposed continental shelves is included in the LGM loess map in this study.
In the presented study, global alkalinity fluxes and according CO 2 consumption rates by weathering were calculated and compared for the LGM, the Mid-Holocene, and the present day. The comparison of loess weathering areas with carbonate and silicate rock areas was used to address the question if loess has a relevant influence on global alkalinity weathering fluxes for the chosen time slices, considering changes in global climate on hydrology and temperature.

Current Loess Distribution
The current time loess distribution was obtained from the Global Unconsolidated Sediments Map database (GUM) . The map distinguishes between subclasses of primary loess deposits, loess derivates, and loess-like silt deposits. In the further analysis, we do not distinguish between the different subtypes of loess. Most of the loess deposits can be found in the middle latitudes, 35-70°N and 25-40°S, respectively . For the Mid-Holocene scenario, we assume that the loess distribution is similar to the recent one.

Loess Distribution at the LGM
For the LGM, the land area that is equal to the recent continents had to be increased by the exposed continental shelves due to a lower sea level.

Loess Distribution of the LGM on Continents
Due to a lack of map data, the global loess distribution for the LGM cannot be reconstructed based on ground mapping but can be estimated. Mahowald et al. (1999) state that eolian deposition rates were up to 2-20 times higher during glacial periods, and Rousseau et al. (2014) conclude that the dust deposition fluxes during the LGM might have been 2-3 times higher. Since the Chinese Loess Plateau was reported to be extended to the south of the Yangtze River (25-30°N) (Pinxian & Xiangjun, 1994, and references therein) and river valleys were reported to have once been covered with loess deposits in some regions, before they were eroded (United States Army Corps of Engineers, 1974), the recent loess extent  had to be larger during the LGM period. As a conservative approach, reconstruction of past loess areas was done using Esri ArcMap (v10.6) by extrapolating the recent time loess shapefile, using the Euclidean Distance Tool with a maximum distance of 10 km. By doing this, river valleys within loess deposits, for example, were filled with loess. The constant extrapolation distance might cause additional regional biases because a constant Holocene erosion for all global loess regions is assumed and different depositional environments are neglected. The sensitivity of the loess extrapolation method was tested for different scenarios and is additionally discussed in section 3.4.1.

Loess Distribution on Exposed Continental Shelves
To analyze weathering on exposed continental shelves during the LGM, the subaerial shelf extent was determined using the global relief model ETOPO1 (Amante & Eakins, 2009). By setting the bathymetric line to −130 m (a rounded value derived from Lambeck et al., 2014), an exposed continental shelf area of about 23 × 10 6 km 2 was calculated. After subtracting the area that was covered by ice sheets (Ehlers et al., 2011), the total area of exposed shelves that were affected by weathering is therefore 19 × 10 6 km 2 .
For several regions of the continental shelves, it was possible to reconstruct loess deposits from literature studies and digitize these areas with GIS. In the English Channel, evidence for loess deposits was described by Lefort et al. (2013). Extensive loess deposits on the Arctic shelf were made available by Biryukov et al. (1988). For most of the Black Sea, data of shelf loess deposits were made available in Ryan et al. (1997) and for the Argentinian continental shelf by Violante et al. (2014). Besides, data about loess deposits in the China Sea, on the shelves off West Africa, and in the Indian Ocean and Western Pacific ( Figure 3) were made available by Li et al. (2013) and references therein. Details on the compilation of loess data of the continental shelves can be found in the supporting information.

Carbonate Content of the Shelves' Sediments
To quantify alkalinity fluxes from the total continental shelves, which were exposed during the LGM, additional sediment types besides loess were considered. Reconstruction of the sedimentary pattern that was exposed during the LGM is challenging due to strong erosion of the subsequent transgressional phases. As a first assumption, the modern sediments might represent the sediments that were accumulated in the previous sea-level high-stand interglacial period. A global database of chemical, physical, and mineralogical data about the ocean sediments from surface samplings and shallow stratigraphy-penetrating cores was used (dbSEABED, Bostock et al., 2018;Goff et al., 2008;Jenkins, 1997Jenkins, , 2018. The database includes the world distribution of coral reefs, which are mostly growing on old karstic low sea-level landscapes (Purdy, 1974), also composed of carbonate. The point data of the carbonate content of all the sediments were interpolated to all shelf areas at a resolution of 0.25°× 0.25° (Figure 1).

Hydrochemical Database
To analyze alkalinity fluxes from loess deposits, the Global River Chemistry Database (GLORICH) was used Hartmann et al., 2019). This database comprises 1.27 million samples from over 17,000 sampling locations . The watersheds of the GLORICH database sampling locations were geometrically intersected with the recent loess areal extent and the hydrochemical data extracted and analyzed. For each sampling location the mean and median values were calculated. In the following, all analyses are based on the mean values since the median values are not significantly different (see Supplemental Material B). Additional data on some rivers draining the Chinese Loess Plateau were added by extracting chemical data from literature (Ran et al., 2015Ran, Lu, et al., 2017;Xiao et al., 2016;Zhang et al., 2013) and creating watersheds for the sampling points in ArcMap. The fractions of loess as well as all other lithologies from the Global Lithological Map Database (GLiM) (Hartmann & Moosdorf, 2012) within the watersheds were calculated. Mean annual runoff and temperature values were extracted for the sampling locations from Fekete et al. (2002) and Hijmans et al. (2005), respectively.

Global Calculations of Alkalinity Flux Rates and CO 2 Consumption
The calculations of alkalinity fluxes and CO 2 consumption were done twice for each time step (LGM, Mid-Holocene, and recent times), one scenario considering loess deposits and one scenario neglecting loess deposits, using only the lithology from the Global Lithological Map Database (GLiM, Hartmann & Moosdorf, 2012, only considering the first level information "xx" for all polygons and therefore substituting possible loess deposits reported in the GLiM by other or generalized lithologies, because loess is only reported in sublevel information "yy"). The lithological maps were compiled in ArcGIS and merged following a specific order ( Figure 2). If loess data were available from the GUM database (attributes: xx = El/Er/Ea), these polygons were merged with the GLiM shapefile, which serves as a background lithological map.
For all lithologies, apart from carbonate sedimentary rocks and loess deposits, an alkalinity flux model was applied, which is based on a spatially explicit runoff-dependent model of chemical weathering, calibrated for 381 catchments in Japan (Hartmann, 2009) and which was later enhanced by considering temperature and a soil-shielding effect . The different weathering model equations for each lithological class applied to calculate alkalinity fluxes are described in the supporting information (Supplemental Material C, Table S1) and were first used to quantify global alkalinity fluxes by Goll et al. (2014). These equations distinguish between alkalinity fluxes from carbonate and silicate weathering.
For the carbonate sedimentary rocks, the following carbonate weathering functions were applied and the results compared: 1. Romero-Mujalli, Hartmann, and Börker (2018) The range of uncertainty in the global calculations was calculated using the standard deviation of the function as follows: Uncertainty of the global flux ¼ ∑ Flux per grid * 0:2 * log 10 ð Þ ð Þ 2. Amiotte-Suchet and Probst (1995) with alk = alkalinity rate in meq alkalinity m −2 a −1 and q = runoff in mm 3 mm −2 a −1 .
The residual standard deviations for the models in this study were calculated after with residuals = observed flux − estimated flux.
The ice sheet extent for the LGM was taken from Ehlers et al. (2011), and the LGM land mask was given by the shelves extent calculated from ETOPO1 (see section 2.2.2). For the Mid-Holocene the same land-sea LGM and recent times. The recent loess distribution is shown in red, and the extrapolated areas for the LGM are shown in blue. The orange color represents the redrawn loess on the continental shelves, and the gray color represents the general shelves extent that was exposed during LGM. The LGM ice cover is shown in light blue. mask as for nowadays was applied (land coverage derived by GLiM coverage, Hartmann &Moosdorf, 2012, andGUM coverage, Börker et al., 2018, respectively). Temperature and runoff data for each time period were taken from Earth System Model outputs of the Max-Planck-Institute (surface runoff and near-surface air temperature for the LGM, Mid-Holocene, and pre-industrial, Jungclaus et al., 2012aJungclaus et al., , 2012bJungclaus et al., , 2012c. These data had to be pre-processed by calculating the annual mean values of monthly data. The runoff data for the LGM had to be extrapolated from the continents to the exposed continental shelf areas in ArcMap, because the shelf areas were not fully covered by runoff data due to the raster resolution of the input data set.
The lithological coverage, as well as the ice extent, LGM land mask, carbonate content of the ocean sediments, soil-shielding, temperature, and runoff data were converted to a 20 × 20 km grid to run the global calculations.

Changes in Loess Area
While the recent loess coverage is about 5 × 10 6 km 2 , the areal extent during the LGM was~11 × 10 6 km 2 in our 10 km extrapolation ( Figure 3 and Table 1).
Extrapolating the recent loess area to the LGM is a theoretical approximation, because a constant increase in the areal extent around recent loess deposits is assumed. Kohfeld and Harrison (2001) (DIRTMAP database) report on an expansion of loess deposits downwind of deserts and ice sheets and a general increase of loess mass accumulation rates of 1-5 times during the LGM. The Chinese Loess Plateau was extended to the south of the Yangtze River (25-30°N) (Pinxian & Xiangjun, 1994, and references therein), which is resulting in about a doubling of the extent of the modern Chinese Loess Plateau. In order to get a global doubling of the loess extent for LGM times as first-order approximation, the value of 10 km was chosen for the extrapolation method.
Since there exists no paleogeographic sedimentary pattern for all the continental shelves, which are submerged nowadays, or the continental land area during the LGM, it might also be possible that the LGM loess extent is underestimated or overestimated. Besides, loess, which might be present in alluvial sediments, for example, and which would have an influence on alkalinity fluxes as well, is not considered separately as loess in our calculations for the scenario of recent times.
The classification of carbonate content in marine sediments reveals the following proportions of lithologies on the exposed continental shelves: 1. without loess: 24% siliciclastic sediments, 21% mixed sediments, and 55% carbonate sediments 2. with loess: 20% siliciclastic sediments, 18% mixed sediments, 51% carbonate sediments, and 11% loess sediments The lithological map of Gibbs and Kump (1994), used in various studies (Ludwig et al., 1999;Munhoven, 2002) to quantify weathering fluxes from the exposed continental shelf areas, provides similar results (55% of siliciclastic sediments and 45% of carbonate sediments as described in Ludwig et al., 1999). Zhang et al. (2013) observe a dominance of loess weathering on the weathering fluxes even at 18% watershed loess coverage. Therefore, here a rounded value of 20% loess coverage as boundary condition to identify catchments with significant loess weathering contribution is used in the following analysis.

Chemical Weathering of Loess
Of the geospatial data of the recent loess distribution and the watersheds of the GLORICH sampling points, and the additional data for the Chinese Loess Plateau, 1,032 sampling locations have watersheds that are covered by more than 20% loess; 683 sampling locations feature alkalinity and/or major ion data (Ca 2+ ). The majority of data points are from the United States and China ( Figure 4).

Geochemistry, Geophysics, Geosystems
Mean alkalinity concentrations and standard deviation in samples with a significant loess coverage of >20% is~4,110 ± 2,400 μeq L −1 , whereas the global average river alkalinity concentration and standard deviation is~1,850 ± 1,920 μeq L −1 , suggesting that loess weathering contributes disproportionally to alkalinity in river water and therefore to elevated fluxes compared to the lithological base below the loess deposits.

Regional Observed Differences in Loess Weathering
The different lithologies below the loess (loess fraction >0.2) do not show a significant pattern in their influence on the alkalinity concentration in global river waters ( Figure 5a). Therefore, it is assumed that the base lithology below the loess does not affect significantly the study of loess weathering and is neglected, which is also supported by the study of Zhang et al. (2013). However, where carbonate sedimentary rocks underlie loess deposits, this may not be the case, and their possible effect on loess weathering fluxes is additionally considered.
Furthermore, it was tested whether loess sediments show globally homogeneous weathering patterns. Alkalinity in rivers draining catchments with loess (areal loess fraction >0.2) shows a distinct land surface temperature dependency, comparable to carbonate weathering patterns (Romero-Mujalli, , with some deviations from the patterns for Argentina (Figures 5a and 5b). The analysis of major ions reveals some regional differences in the composition of the water (Figures 5c-5f), which will be explained below.
The Ca 2+ /Mg 2+ concentrations in the river water (Figure 5c), above the dashed line, representing the ratio of Ca 2+ /Mg 2+ = 2, indicate that carbonate minerals other than calcite (e.g., dolomite) or silicate minerals may be a relevant Ca 2+ source (Romero-Mujalli, . While the loess regions of France, Germany, Venezuela, Canada, and Argentina seem less affected by non-calcite contributions, data from China show the largest positive deviation from the 2:1 ratio. For the United States, Goddéris et al. (2013) report that dolomite weathering occurs in the loess pedons, which might be reflected here. Dolomite occurrences are also reported for the Chinese Loess Plateau (e.g., Meng et al., 2015). The Ca 2+ /SO 4 2− ratio ( Figure 5d) shows that most of the water sampling points lay above the 10:1 ratio (mentioned by Romero-Mujalli, Romero-Mujalli, Hartmann, Börker, Gaillardet, et al., 2018;, as a border for calcite weathering evaluation), which may indicate an influence of sulfate mineral dissolution (Romero-Mujalli,  or anthropogenic inputs as pyrite oxidation might be excluded, assuming that particles transported via air are oxidized quickly. Especially Argentinian and Chinese loess deposits show elevated SO 4 2− concentrations (ratio of Ca 2+ /SO 4 2−~1 ), which could be related to evaporation processes. In addition, data points with a Ca 2+ /Na + < 10 (Figure 5e) might be influenced by evaporite dissolution or silicate weathering (Gaillardet et al., 1999),

10.1029/2020GC008922
Geochemistry, Geophysics, Geosystems which is the case for almost all samples. Many data points have a ratio different from Na + /Cl −~0 .86 (Figure 5f), which indicates that the Na + and Cl − concentrations are affected by other sources than sea salt (ratio molar Na + /Cl −~0 .86; Möller, 1990).
The general cation distribution pattern suggests that Ca 2+ is the primary cation released (Figure 6), supporting that calcite might be the dominant contributor, whereas Na + contributes~20% to the total cation equivalent concentration. Ternary diagrams of the distribution of major cations in the water samples draining loess deposits (fraction >0.2) can be additionally seen in the supporting information, showing that carbonate sedimentary rocks provide in general lower concentrations of Na + and K + compared to loess deposits.
Since loess mineralogy is dependent on the provenance and the primary lithologies that it is derived from, it is challenging to find the one typical weathering signature for all regions of loess. The Argentinian loess might be influenced by an input of volcanic ash (Zárate, 2003) or evaporitic processes within the river catchments and therefore shows elevated concentrations of Na + or SO 4 2− . Evaporation can be expected in some regions of the Chinese Loess Plateau since it is the largest arid and semi-arid zone in China (Huang et al., 2008), which might explain elevated concentrations of SO 4 2− or Na + . Moreover, dolomite contribution to alkalinity fluxes, which is represented by elevated Mg 2+ concentrations, might be expected for regions of

Comparison With Previous Carbonate Weathering Functions
To test the hypothesis that loess weathering derived alkalinity fluxes are comparable to carbonate rock alkalinity fluxes at the broader scale, previous global carbonate weathering models were compared with the new data set compiled here. Used global carbonate weathering functions are runoff dependent (Amiotte-Suchet & Probst, 1995;Bluth & Kump, 1994) and include in case of the function for calcite weathering (Romero-Mujalli, Hartmann, & Börker, 2018) a temperature adjustment, comparable in shape as shown for loess alkalinity in Figures 5a and 5b. The general increase in alkalinity with increasing temperature up to~11°C in the model of Romero-Mujalli,  can be explained by increasing biological activity and hence elevated soil-rock pCO 2 driving the weathering reactions. However, for higher temperatures (>11°C) alkalinity concentrations in rivers seem to decrease, which is related to the temperature effect on the carbonate system (Romero-Mujalli, . Gaillardet et al. (2018) analyzed the climate control on carbonate weathering using Ca 2+ + Mg 2+ concentrations to display the intensity of carbonate weathering and found that the maximum of carbonate weathering intensity can be observed with mean annual air temperatures between 5°C and 15°C following a bell-shaped curve, which is consistent with the results of Romero-Mujalli, .
These identified bell-shaped patterns for calcite weathering conditions are also observed using all water samples whose catchments have a loess fraction >0.2 and showing alkalinity and Ca 2+ + Mg 2+ concentrations dependent on temperature (Figures 7 and 8). Both figures show the identified function of Romero-Mujalli,  with its range of the calculated uncertainty for comparison.
Despite the above identified bell-shaped pattern, it has to be stressed out that the function of Romero-Mujalli,  was trained for catchments with predominant calcite weathering, while catchments with significant Mg 2+ contribution showed a tendency to elevated alkalinity values.

Geochemistry, Geophysics, Geosystems
Therefore, this approach is reasonable for weathering from lithologies with dominant calcite weathering but might underestimate alkalinity fluxes for other sources that add, for example, Mg 2+ . The elevated concentrations in both alkalinity data and Ca 2+ + Mg 2+ data (Figures 7 and 8), in comparison to the idealized calcite weathering function, might be due to the dissolution of further carbonate minerals (e.g., dolomite, indicated by elevated Mg 2+ concentrations), silicate minerals, or catchment internal processes like evaporation. However, low runoff areas have a tendency to elevated concentrations (Figure 9). For temperatures between 15°C and 20°C some data points show clearly elevated alkalinity values in comparison to the model of Romero-Mujalli,  and are mostly data from Argentina, which might be dominated by silicate weathering due to an input of volcanic ash and predominantly volcanic rocks as source rock (Zárate, 2003). Nevertheless, the bias in the global calculations might be small considering that regions with mean annual temperatures between 15°C and 20°C cover nowadays only~13% and for the LGM~20% of the ice-and water-free land area (temperature data set used for the pre-industrial and LGM in this study, resolution 20 × 20 km, land mask derived by the consideration of all lithologies used for calculations in this study), and this tendency is mostly restricted to the Argentinean area.
While the alkalinity concentration patterns seem to show a bell-shaped pattern, dependent on temperature, runoff is in general the dominant control on the flux, which is intended to be modeled in the following. Alkalinity concentrations of river waters draining loess sediments (fraction >0.2) generally decrease with increasing runoff (Figure 10a). The dilution effect seems to be strong after a threshold of about 200 mm a −1 (Figures 10a and 10b), and~26% of all recent global loess deposit areas have runoff values >200 mm a −1 , indicating that a dilution effect should be considered in global calculations of loess weathering.  Figure 5b). Additionally, the moving mean value of alkalinity concentration is shown (in orange) with the range of the standard deviation (in gray).

Geochemistry, Geophysics, Geosystems
Therefore, a new alkalinity flux function was developed, based on a nonlinear regression method for observed alkalinity flux rates ( Figure 10b) applying a four-parameter logistic function, which fits best the observed data points and allows to project alkalinity flux rates for high runoff areas. One parameter was set manually to 9 to represent the maximum values of alkalinity flux rate in the observations: log 10 alkalinity flux rate ¼ 9 1 þ exp −a log 10 runoffþb ð Þ þ c ; MSE ¼ 0:08 (6) with log 10 alkalinity flux rate in μeq km −2 a −1 , log 10 runoff in mm 3 mm −2 a −1 , a = 0.63, b = 0.76, and c = −2.00.
The residual analysis of the modeled alkalinity flux rates for the four carbonate weathering models compared to different variables ( Figure 11) shows in general no clear trend with temperature, but a tendency toward overestimation with elevated runoff (Figures 11b, 11f, 11j, and 11n). The relative residual distribution is additionally shown in the supporting information.
The new loess function (Equation 6) provides the best estimation for the observed alkalinity flux rates with an R 2 = 0.

Geochemistry, Geophysics, Geosystems
Probst, 1995; and R 2 = 0.34 for Bluth & Kump, 1994). The model of Romero-Mujalli, , however, shows a reduced dispersion for temperature (excluding extreme values), while for the runoff-dependent models the residuals show a higher dispersion and seem to display the "bell-shaped pattern" (Figures 11e, 11i, and 11m). They might underestimate alkalinity flux rates for temperatures about 10°C, but for lower and higher temperatures, the runoff-dependent models might overestimate alkalinity fluxes. Moreover, it can be seen that all previous models for carbonate weathering overestimate fluxes for high runoff values significantly at the p < 0.05 level (Figures 11b, 11f, and 11j), whereas the new loess function (Equation 6) considering the dilution effect is not (p = 0.25). Still, for high runoff values the loess function overestimates alkalinity fluxes. But this bias might be relatively small considering that alkalinity fluxes from elevated runoff regions (>200 mm a −1 ) contribute with~30% to total alkalinity fluxes from loess deposits, while their areal extent is about 26% of the global loess area. Nevertheless, although the new loess function overestimates alkalinity flux rates for high runoff values (Figure 11n), most of the alkalinity flux rates (~80% of the loess grids in the global calculation for the recent setting) are underestimated. This might be related to the residuals of the new function comparing for alkalinity concentration in the rivers (Figure 11p).
Although the model of Romero-Mujalli,  considers as well the climate variable temperature, it might underestimate global alkalinity fluxes from loess deposits because the inputs of, for instance, Mg-minerals like dolomite are neglected. The carbonate weathering functions of Amiotte-Suchet and Probst (1995) and Bluth and Kump (1994) represent total carbonate weathering fluxes, including other carbonate minerals than calcite. Nevertheless, they assume almost constant alkalinity values (the dilution effect in the equation of Bluth & Kump, 1994, is relatively weak), which is not consistent with the observed alkalinity concentrations in rivers draining loess deposits (Figure 12). For the global alkalinity

Global Alkalinity Fluxes Including Loess Deposits
For the global calculations of alkalinity flux and CO 2 consumption rates from loess deposits the new function (Equation 6), whereas for carbonate sedimentary rocks the models of Romero-Mujalli, , Amiotte-Suchet and Probst (1995), and Bluth and Kump (1994) were used, and their results are listed in Tables 2 and 3 and Figure 13. For simplicity, in the following, the global alkalinity flux and CO 2 consumption values are compared for the different time slices applying the model of  for carbonate sedimentary rocks. For all other lithologies the model of Goll et al. (2014) was applied. For comparison, the calculations were done for two scenarios: one scenario where loess lithologies are considered for weathering and one where they are neglected. Note that the CO 2 consumption rates of loess deposits might be regarded as the lower boundary, because additional silicate weathering happening in the loess sediments can increase the CO 2 consumption rates.
It can be shown that loess weathering increases the global alkalinity fluxes compared to the base lithology below (~36% for the LGM,~15% for the Mid-Holocene, and~16% for recent times). This increase in alkalinity fluxes because of loess weathering might partly explain the gap between the proportion of carbonate Figure 10. Relationship between runoff and loess-derived alkalinity concentration (a) and relationship between runoff and loess-derived alkalinity flux rate (b) with the previous models of Amiotte-Suchet and Probst (1995), Bluth and Kump (1994), and Romero-Mujalli,
The calculated global weathering fluxes are generally lower than estimates from previous studies, which can be explained by in general lower runoff values in the data sets used for the global calculations in this study (Jungclaus et al., 2012a(Jungclaus et al., , 2012b(Jungclaus et al., , 2012c to allow a comparison with runoff as a forcing parameter based on the same model outputs. Applying a runoff data set, which was used to calibrate the new loess function (Equation 6) and which includes observed river discharge information (Fekete et al., 2002) for the recent time, yields 106% to 124% higher values (Table 4). Therefore, only the relative changes between time slices are interpreted here.
The differences in alkalinity flux rates between the Mid-Holocene and the present day are generally low ( Figure 13); only for loess deposits the alkalinity flux rates during the Mid-Holocene decrease by~9%. Alkalinity flux rates from silicate weathering are decreasing during the LGM (~30% for the scenario neglecting loess weathering and~28% for the scenario considering loess weathering if compared to recent times). Moreover, the alkalinity fluxes derived by the carbonate weathering proportion of the model of Goll et al. (2014), which was applied for other lithologies than carbonate sedimentary rocks (sc) and loess, are decreasing during the LGM as well (~25% for the scenario neglecting loess weathering and~26% for the scenario considering loess weathering).

Geochemistry, Geophysics, Geosystems
The global alkalinity flux rates from carbonate sedimentary rocks (sc) for the different applied models are regarded separately in the following. Generally, the alkalinity fluxes from carbonate sedimentary rocks are higher for all three models for the LGM compared to the recent time ( Figure 13). The values derived by applying the carbonate weathering functions of Amiotte-Suchet and Probst (1995) and Bluth and Kump (1994) show the higher positive deviations (mean of both models:~55% increase for the scenario considering loess weathering and~60% increase for the scenario neglecting loess weathering) than the model of Romero-Mujalli, Hartmann, and Börker (2018) (~34% increase considering loess weathering and~31% increase neglecting loess weathering).
These differences might be explained by the alkalinity flux rates derived from carbonate sedimentary rocks (sc) on the exposed continental shelf areas. Previous studies on changes of weathering fluxes at glacial-interglacial time scales report an increase of global fluxes of about 20% for the LGM time, mostly because of the abundance of carbonate sedimentary rocks on the continental shelves (Gibbs & Kump, 1994;Ludwig et al., 1999). Here, the carbonates of the continental shelf areas contribute to global alkalinity fluxes by about 21% (considering loess weathering, mean of the two runoff-dependent models). This contribution from carbonate sedimentary rocks (sc) on the continental shelves to global alkalinity flux rates is less if applying the model of Romero-Mujalli, Hartmann, and Börker (2018) (~11% considering loess weathering). These differences might be related to an overestimation of the fluxes of the runoff-dependent models for the carbonate sedimentary rocks (sc), mostly located in high temperature regions, on the exposed continental shelf areas because the models do not consider temperature. Runoff as possible reason can be excluded because all three models show a comparable bias for runoff in the residuals (Figures 11b, 11f, 11j, and 11n).
Nevertheless, there remains uncertainty due to the classification of the sediments on the exposed continental shelves. The equations that were used to consider the carbonate content of the shelf sediments were calibrated for consolidated sedimentary rocks (sc), which might not reflect properly the alkalinity flux rates from the continental shelves. However, loess deposits on the continental shelves do not contribute significantly to global alkalinity flux rates (~2% applying the mean of the three models).

Geochemistry, Geophysics, Geosystems
The elevated alkalinity fluxes during the LGM from loess sediments including those from shelves (approximately +78% compared to recent times) might be slightly too high because the loess regions during the LGM show colder temperatures (with a mean of about −3°C), which might lead to an overestimation of fluxes for the runoff-dependent new function (Equation 6). Applying the temperature-and runoff-dependent model of  for the loess deposits shows an increase of about 20% of loess-derived alkalinity fluxes compared to recent times. Nevertheless, there exists a lack of data points for low temperature regions, but because the residuals of the new loess function (Equation 6) show a smaller range for the parameter temperature than the other models, it might be reasonable to apply the new loess function for loess weathering (Equation 6) as first-order approximation.
With the new loess weathering function and applying the model of Romero-Mujalli,  for carbonate sedimentary rocks (sc) to avoid an overestimation of alkalinity fluxes from the exposed continental shelves during the LGM, the differences in the total global alkalinity fluxes between the LGM and recent times become small (~4% increase for the LGM). Without the consideration of loess weathering the differences in alkalinity fluxes between the LGM and recent times become larger (~11% decrease during the LGM). However, the estimated extent of the continental loess area represents conservative assumptions, discussed in the next section.

Sensitivity of Loess-Derived Alkalinity Fluxes to Their Areal Extent
Increased alkalinity fluxes due to loess deposits are especially interesting because mapped loess deposits (excluding the shelves) nowadays cover only about 4% of the global ice-free land area (relative to the GLiM area without ice and water bodies; Hartmann & Moosdorf, 2012). Still, the influence on global alkalinity fluxes and CO 2 consumption rates could become even larger because the loess areal extent reported Note. For Romero-Mujalli,   Values that are calculated for the exposed continental shelves.

10.1029/2020GC008922
Geochemistry, Geophysics, Geosystems in the Global Unconsolidated Sediments Map (GUM)  underestimates the land area where loess weathering occurs due to neglected thin loess covers that were not mapped in the input geological maps. Some literature studies report a recent global loess cover of even about 10% (Muhs & Bettis, 2003;Pécsi, 1990). Nevertheless, these maps are of a coarser resolution.
Taking the LGM loess cover derived by the 10 km extrapolation method (without loess on the shelves) and applying it for the recent climate setting results in a mean increase of about 34% for alkalinity flux rates and about 25% for CO 2 consumption rates if compared to the recent alkalinity flux and CO 2 consumption rates without loess. Because the extrapolated LGM loess cover partly includes river valleys and therefore alluvial sediments, which might contain relevant amounts of loess nowadays, the approach of comparing global alkalinity fluxes derived by loess deposits might be seen as conservative, since the distributed LGM loess might still influence recent weathering fluxes. This aspect should be further studied, to quantify the legacy contribution of old loess deposits to differently mapped lithological units in recent global maps.
Further, to test the influence of the extrapolated LGM loess area on the global alkalinity fluxes, a sensitivity experiment was conducted. The extrapolation method was, additionally to 10 km, also done with 5 and 20 km. Besides, the alkalinity fluxes for the LGM were calculated assuming the same loess distribution than for recent times (in the following named "0 km"). A possible upper boundary of loess weathering might be given by applying modeled dust output data. Kohfeld and Harrison (2001) report eolian mass accumulation rates (MARs) for loess deposits during the LGM of 50 to more than 1,000 g m −2 a −1 . Taking the dust model output data for the LGM from Albani et al. (2016) and applying a lower boundary of 50 g m −2 a −1 as a specific minimum of total dust deposition in order to form a loess deposit show elevated loess alkalinity flux rates (in Values that are calculated for the exposed continental shelves.

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Geochemistry, Geophysics, Geosystems the following simulations named after the method "50MAR"). But results from this method might be too high because the dust MARs include as well smaller particles than those typical for loess deposits. Nevertheless, taking the output data of the same model (Albani et al., 2016) for the pre-industrial time, it can be seen that the areal extent for dust deposits with a deposition rate of more than 50 g m −2 a −1 is about half as large as the extent during the LGM. This observation underlines the reasonability of the 10 km loess extrapolation method. The differences between the scenarios are shown in Table 5 and Figure 14.
The sensitivity of the global alkalinity flux rates to the loess areal extent scenarios becomes evident when comparing the differences between global alkalinity fluxes of the LGM and recent times (Figure 14d). While the application of the possible lower boundary (0 km) of loess areal extent suggests almost no changes between the global alkalinity fluxes as if compared to neglecting loess deposits, the increase of the loess areal  . Panel (c) shows the changes in alkalinity flux rates, without the continental shelves. Note that the two dashed lines showing the alkalinity flux rate calculations for the models of Amiotte-Suchet and Probst (1995) (in pink) and of Bluth and Kump (1994) (in green) for carbonate sedimentary rocks (sc) overlap. Additionally, note that the equations used to calculate alkalinity fluxes for all other lithologies apart from carbonate sedimentary rocks (sc) and loess from Goll et al. (2014) distinguish between alkalinity fluxes derived by carbonate weathering and by silicate weathering (explanation in the supporting information).

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Geochemistry, Geophysics, Geosystems LGM alkalinity flux rates from loess deposits [Mt C a −1 ] Global total alkalinity flux rates at the LGM considering three different models for carbonate sedimentary rocks (sc) and including loess alkalinity flux rates [Mt C a −1 ]; with their relative change to the global alkalinity flux rates for the recent time, including loess weathering Romero-Mujalli, Hartmann, and Börker (2018) Amiotte-Suchet and Probst (1995) Bluth and Kump (1994)  Note. For all calculations in this study a modeled runoff data set was used, in which runoff is generally underestimated and hence generally lower weathering flux values are produced as if compared to values reported in previous studies. Therefore, the key information from the table is the relative change between the scenarios, which are shown in Figure 14d.

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Geochemistry, Geophysics, Geosystems extent during the LGM (scenario 10 km to 50MAR), increases the global alkalinity flux rates up to 22-28% during the LGM compared to recent times.

Conclusion
Loess sediments are widespread around the globe nowadays. Although they can be very heterogeneous regarding their mineralogy, depending on their provenance or internal processes like evaporation, they show, in general, a similar weathering behavior than carbonate sedimentary rocks. Studying the chemical composition of river water draining loess areas shows elevated alkalinity fluxes if compared to idealized calcite weathering and points to the importance of recognizing further minerals and their weathering behavior into more detailed global loess weathering models like dolomite, silicates, or sulfate minerals because they would affect alkalinity concentrations. Furthermore, it can be noticed that more data on cold temperature regions, especially interesting for the LGM, are needed to improve the quantification of loess weathering fluxes. Based on the river chemical data used in this study, a new empirical function for loess weathering was developed, which considers a dilution effect for elevated runoff areas.
Applying the new loess weathering function in global calculations suggests that loess contributes significantly to global alkalinity flux rates, with about 16%. But it remains to be tested if the global alkalinity fluxes from loess deposits are possibly underestimated, because small and/or thin loess covers might not be mapped as loess but still influence the water chemistry. Gaillardet et al. (1999) report on a larger proportion of carbonate weathering on global CO 2 consumption fluxes than calculated by Hartmann et al. (2009) taking a different approach. This gap could be partly explained by loess weathering.
Comparing the LGM and recent times shows very similar global alkalinity flux rates (~4% higher alkalinity flux rates during the LGM for one of the discussed scenarios). The suggested enhanced fluxes from loess sediments during the LGM are hereby counteracting the modeled and in general lower silicate weathering rates during the LGM. Thus, loess sediments might be involved in stabilizing the alkalinity fluxes at glacial-interglacial time scales, which points to the importance of further consideration of sediments, and specifically their origin, in global weathering models.

Data Availability Statement
Data for this research are archived in the PANGAEA database (https://doi.org/10.1594/PANGAEA.915793).