Global analysis of short- versus long-term drainage basin erosion rates

Measuring erosion rates, analysing their temporal variations, and exploring environmental controls are crucial in 10 the field of geomorphology because erosion through sediment transport in drainage basins shapes landforms and landscapes. Thus, important insights into landscape controls can be gleaned from analyses of erosion rates measured over different timescales. Suspended sediment flux and in situ cosmogenic radionuclides have been widely used for estimating shortand long-term erosion rates of drainage basins, respectively. Even though analyses of erosion rates have been conducted across the globe, there are still gaps in understanding of the links between environmental controls and erosion rates between 15 timescales, especially the influence of climate, which is complex and covaries with other factors. To begin unpicking controls on landscape evolution across the globe, we compiled shortand long-term erosion rates (estimated from suspended sediment yield and in situ beryllium-10, Be, respectively) and analysed their relationships with climate, topography, and anthropogenic activity. The results show that: 1) A non-linear relationship exists between aridity and long-term erosion rates, resulting from the balance between precipitation and vegetation cover; 2) Long-term erosion rates are higher in midand 20 high-latitude regions with high humidity, reflecting glacial processes during ice ages; 3) Long-term erosion rates are positively related to the steepness of drainage basins, showing that both climate and topography are the common factors; 4) Human activities increase short-term erosion rates which outweigh natural controls; and 5) The ratios of shortto long-term erosion rates are negatively related to basin area, reflecting the buffering capacity of large basins. These results highlight the complex interplay of controlling factors on land surface processes and reinforce the view that timescale of observation 25 reveals different erosion rates and principal controls.

whether there are identifiable patterns in these erosion rates that reflect the prevailing climatic regime and/or anthropogenic activities within basins.
Suspended sediment flux records, typically measured over annual to decadal timescales in the recent past, describe the history of fine sediment transport from uplands to lowlands within riverine flow (Milliman and Meade, 1983). In situ 35 cosmogenic radionuclide concentrations within riverine sediment can be used to estimate basin-averaged exposure ages for timescale of tens of thousands years or more, integrating long-term erosion and deposition signals (Granger and Schaller, 2014;von Blanckenburg and Willenbring, 2014). These two proxies for basin-wide erosion are commonly used independently in geomorphology to investigate spatial and temporal changes in erosion in response to climatic and tectonic forcing (Clapp et al., 2001;Pan et al., 2010;Wittmann et al., 2011;Yizhou et al., 2014) and to compare erosions rates 40 between basins (Milliman and Meade, 1983;Milliman and Syvitski, 1992;Summerfield and Hulton, 1994;Dedkov and Mozzherin, 1996;Portenga and Bierman, 2011;Harel et al., 2016). The combination of these proxies enables the investigation of potential drivers of erosion and consideration of the role of time averaging on erosion rates (Kirchner et al., 2001;Schaller et al., 2001;Covault et al., 2013). To quantify the pattern of erosion rates and the dominant controls on erosion rates at different timescales at the global scale, we compiled drainage basin erosion rates estimated from suspended 45 sediment yield (short-term) and cosmogenic nuclides (long-term) from several global databases. We then compared shortand long-term rates across the globe, classified by climate and anthropogenic activity, to explore the linkages between erosion and its primary drivers over different timescales.
Erosion rates based on suspended sediment yield are calculated by measuring the sediment concentration and discharge at a 50 gauging station over years to decades, and then converting their product into mean annual sediment flux, then to sediment yield (t ha -1 yr -1 ) normalised by upstream drainage area, and subsequently to erosion rate (mm yr -1 ), assuming a basinaveraged soil bulk density. This method provides an averaged value of erosion rate for the upstream area that neglects the storage of sediment during transportation and assumes that eroded sediments are all transported as suspended load. This is a reasonable approximation because 1) storage of sediment can be considered to be negligible over longer timescales, and 2) 55 suspended load dominates sediment flux (> 90%) for the majority of drainage basins, except high relief or dryland catchments (Milliman and Meade, 1983;Dedkov and Mozzherin, 1996;Singer and Dunne, 2004;Milliman and Syvitski, 1992;Laronne, 1993;Tooth, 2000;Singer and Michaelides, 2014). Suspended sediment records provide a record of recent and potentially transient responses within landscapes to climatic and/or anthropogenic forcing (Walling and Webb, 1996;Walling and Fang, 2003). 60 In situ cosmogenic radionuclides are a common tool for estimating erosion rates based on exposure age dating at timescales from 10 3 to 10 5 yr. In situ cosmogenic radionuclides are produced by the interaction of cosmic rays with minerals in rocks and soils in the uppermost few metres of the Earth's surface. The concentration of cosmogenic radionuclides near the surface https://doi.org/10.5194/esurf-2021-7 Preprint. Discussion started: 24 February 2021 c Author(s) 2021. CC BY 4.0 License.
is principally a function of the production rate, radioactive decay rate and erosion rate (or rate of surface stripping). 65 Therefore, cosmogenic exposure age dates can be used for estimating drainage basin erosion rates (Brown et al., 1995;Granger et al., 1996;Granger et al., 2013;Granger and Schaller, 2014;von Blanckenburg and Willenbring, 2014). This method, when applied to riverine sediments, also provides averaged erosion rate, assuming no sediment storage within the upstream basin. Furthermore, this method assumes that: erosion rate is faster than the radioactive decay rate (for 10 Be, erosion rate should be faster than 0.3 mm kyr -1 ); radionuclide concentration has achieved the balance between production, 70 erosion and decay rates (the landscape is in a state of equilibrium); the nuclide concentration has no dependency on grain size (a narrow range of grain sizes is typically used for analysis); there is no erosion-deposition cycle in the drainage basin; and quartz exists in sediments throughout the entire basin (Brown et al., 1995;Granger et al., 2013;Dosseto and Schaller, 2016;Struck et al., 2018). Erosion rates estimated using cosmogenic nuclides represent longer timescales than suspended sediment records (10 3 -10 5 yr versus 10 0 -10 1 yr), and are therefore suitable for analysing the influences of climate and 75 tectonics, and insensitive to the influences of anthropogenic activities or recent stochastic events (Brown et al., 1995;von Blanckenburg, 2006;Granger et al., 2013;Granger and Schaller, 2014;Dosseto and Schaller, 2016). At both regional and global scales, suspended sediment yields and cosmogenic nuclides have been widely used for analysing short-and long-term erosion rates, respectively. Suspended sediment analysis has been employed for many decades, initiated 80 by major investment in a nationwide monitoring programmes (e.g. USGS) and subsequently replicated in many other countries. Exploration of the valuable data provided by programmes has revealed insights into the relationships between climatic and anthropogenic drivers and sediment yields. For example, Langbein and Schumm (1958) used a limited dataset on sediment yields to identify a non-linear relationship between sediment yields and effective mean annual precipitation (MAP) across various biomes in the USA, with a peak in the semi-arid rainfall regimes. They considered both precipitation 85 and vegetation cover to play important roles. Specifically, they suggested that at low MAP, there is also little vegetation, so erosion increases commensurately with rainfall via Hortonian overland flow. However, with sufficient rainfall, vegetation cover may increase and slow erosion rate because of increased interception, higher infiltration, and correspondingly higher evapotranspiration or subsurface storm flow (Dunne and Leopold, 1978). Thus, humid regions have lower sediment yields than semi-arid landscapes. Subsequently, Walling and Kleo (1979) extended this analysis to include data from around the 90 globe and therefore including regions with higher MAP than the USA. Their results show that for basins smaller than 10,000 km 2 , sediment yield peaks in semi-arid regions, but also in Mediterranean and tropical monsoon climate zones, with a strong seasonal rainfall pattern and intense precipitation that can exceed the protection capacity of vegetation cover. In addition to climatic controls, land surface processes are strongly influenced by anthropogenic activities through construction, mining, timber harvesting, and conversion of natural vegetation to agriculture (crop and pasture), the last of which is the most 95 dominant in terms of area (Hooke, 2000). Global analyses of short-term erosion rates from suspended sediment records suggest that a change to agricultural land cover has enhanced erosion rates by one to two orders of magnitude (Dedkov and Mozzherin, 1996;Montgomery, 2007;Wilkinson and McElroy, 2007;Kemp et al., 2020). Regarding long-term erosion rates, a non-linear relationship between MAP and erosion rate was developed by (Mishra et al.,100 2019) on the basis of a global compilation of 10 Be measurements (n = 1,790). Whilst significant scatter is observed in the data, they identify a general increase in erosion rate to a local maximum MAP at ~ 1,000 mm, followed by a slight reduction up to MAP of ~ 2,200 mm and then return to increasing values for higher MAP. The relationship is explained by the interrelated influences of precipitation and vegetation cover as suggested for short-term studies (e.g. Langbein and Schumm, 1958), although their pattern of erosion rate change with MAP is quite different. 105 In addition to these climate/vegetation controls, glaciers and wildfires exert important influences on long-term erosion rates.
Glaciers shape the land surface directly through the stripping of rock underneath basal ice, and through freeze-thaw and weathering processes on the margins of ice (Harel et al., 2016;Cook et al., 2020). Glacial erosion, for example, has been shown to increase long-term erosion rates in temperate and cold regions, especially within mid-and high-latitudes (Portenga 110 and Bierman, 2011;Harel et al., 2016). Wildfires, on the other hand, are more prevalent during dry periods and the occurrence is modified by variation of temperature and wind regimes (Pierce et al., 2004;Han et al., 2020). Wildfires burn the vegetation cover and deposit loose material on the hillslope, destroy root system underground, decrease the infiltration rate, and provide the material for transportation (Cannon et al., 1998;Pierce et al., 2004). Burned areas are more susceptible to debris flow and landslides, which transports sediments from hillslopes to river channels, and increase the erosion rate of 115 drainage basins over longer timescales (Cannon et al., 1998;Meyer et al., 2001).

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This study aims to understand the geographic expression of long-and short-term erosion rates around the globe and explore the climatic and other potential controls on erosion rates across spatial and temporal scales. We specifically address the https://doi.org/10.5194/esurf-2021-7 Preprint. Discussion started: 24 February 2021 c Author(s) 2021. CC BY 4.0 License.
following questions: 1) What is the overall pattern of long-and short-term erosion rates across climate regimes? 2) To what extent do long-term erosion rates reflect glacial processes in mid-and high-latitude regions? 3) Is the previously observed non-linear relationship between precipitation and erosion rate applicable to both short and long timescales? 4) Do human 135 activities outweigh other controls over short-term erosion rates? 5) How do basin topography and topology affect erosion rates?
To answer these questions, we compiled drainage basin erosion rates estimated from in situ 10 Be data (long-term) and suspended sediment yields from gauging stations (short-term). We then stratified the erosion rates using two commonly used 140 climate classifications, Köppen-Geiger and Aridity Index, and analysed the relationships between erosion rates and potential controls, including climate, topography, and anthropogenic activity. We compared erosion rates around the globe with and without these controls to quantitatively assess their influence on erosion rates between timescales.

Methods
We compiled long-and short-term drainage basin erosion rates from existing databases and published literature. All data 145 were stratified by the Köppen-Geiger climate classification and Aridity Index classification to examine relationships with climate. We also used ice extent at the last glacial maximum (LGM; Ray and Adams, 2001), MAP for the USA (calculated from CPC US Unified Precipitation data), mean slope gradient and total relief of river channels (extracted and calculated from Global Longitudinal Profiles database, GLoPro; Chen et al., 2019), and global agricultural regions (Foley et al., 2005).

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Long-term erosion rates were obtained from the Open Cosmogenic Isotope and Luminescence Database (OCTOPUS), which includes basin-averaged erosion rates derived from cosmogenic nuclides ( 10 Be and 26 Al) and luminescence measurements in fluvial sediments . This database classifies data based on the methods, regions, and degree of completeness. To gain the highest reliability and consistency, we only included 10 Be-derived erosion rates of CRN (cosmogenic radionuclide) International and CRN Australia categories from the database, resulting in a total of 3,074 data 155 points ( Fig. 1). For each data point, we extracted the erosion rate, coordinates, and drainage basin area.

Figure 1: Global map of drainage basin erosion rate locations. Long-term erosion rates were obtained from OCTOPUS (Open Cosmogenic Isotope and Luminescence Database, red), estimated by 10 Be in the fluvial sediments. Short-term erosion rates were compiled from published literature (green) and USGS (blue), determined by suspended sediment yield of gauging stations. Coastline is from Nature Earth (https://www.naturalearthdata.com) in the Pseudo Plate Carree map projection.
Short-term erosion rates were compiled from the published literature and the USGS (National Water Information System, https://waterdata.usgs.gov/nwis), based on estimations from suspended sediment yields at gauging stations. From the 165 published literature, we compiled sediment yields (t ha -1 y -1 ) or erosion rates (mm ky -1 ) at each data point. To convert erosion rates from sediment yields, we assumed sediment density to be 1.6 g cm -3 (= 1.6 t m -3 ). Using this density, sediments with the depth of 0.1 mm across 1 ha area weight 1.6 t. A sediment yield of 1 t ha -1 y -1 , for example, is equivalent to an erosion rate of 0.0625 mm y -1 (or 62.5 mm ky -1 ). If the coordinates of the gauging stations were not provided, we acquired the point coordinates from Google Maps. If data from the same gauging station were reported in multiple literature sources, we only 170 included the erosion rate with the most recent data record. For the USGS data, two criteria were set for choosing gauging station data: 1) the monitoring time period needed to be > 5 years, and 2) the basin area < 2,500 km 2 (to avoid basins representing more than one climate zone). Note that some of the gauging stations meeting these criteria may be on the same river. We extracted the daily sediment discharge (t d -1 ), converted this into sediment yield (t ha -1 y -1 ) by summing the daily data and dividing by the number of years and basin area. The sediment yield was then converted into an erosion rate. In total, 175 we obtained 1,521 short-term erosion rates; 1,073 from the published literature and 448 from USGS ( Fig. 1), with corresponding station coordinates and drainage basin areas (Supplement).
includes five main zones (Tropical, Arid, Temperature, Cold, and Polar) and 29 sub-zones. We classified data on the basis of the main Köppen-Geiger zones to provide sufficient data points in each category, and we excluded Polar because there are too few data. The Aridity Index (AI) is a quantitative metric for representing water balance and is calculated by dividing MAP by mean annual potential evapotranspiration from the Global Aridity and PET Database (Trabucco and Zomer, 2009).
There are numerous environmental controls on erosion rates around the globe, among them glacial processes during the ice ages (Portenga and Bierman, 2011;Harel et al., 2016), topography (e.g. Portenga and Bierman, 2011), and human activities (e.g. Covault et al., 2013). To explore the influence on erosion rates of these three broad drivers, we considered the extent of 190 ice coverage at the LGM, the slope gradient and relief of river channels, and the spatial pattern of agricultural regions.
Previous studies typically used MAP to examine climatic controls on erosion rates (e.g. Langbein and Schumm, 1958;Walling and Kleo, 1979). Thus, in addition to classifying erosion rates by climate zones, we also used MAP across the continental USA for further analysis.

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The extent of glacial processes at the ice ages was determined from Ray and Adams (2001), which provides the global vegetation map at the LGM (25,000-15,000 BP) based on fossil and sedimentary information, and expert consultation. Since the timescale of 10 Be-derived erosion rates is in the range of 10 3 -10 5 years, the data cover several ice ages. However, we used coverage of the last ice age as the most reliable estimate of glacial influences. The glacial regions at the LGM were defined as the following five categories in the data source: Tundra, Steppe-tundra, Polar and alpine desert, Alpine tundra, 200 and Ice sheet and other permanent ice.
The topographic parameters used here include the mean slope gradient and total relief of river longitudinal profiles extracted from the GLoPro database (Chen et al., 2019). GLoPro includes river longitudinal profiles around the globe which were extracted from NASA's 30 m Shuttle Radar Topography Mission Digital Elevation Model (SRTM-DEM). The rivers in the 205 database are the mainstem rivers (the longest rivers) of basins or sub-basins that do not cross Köppen-Geiger climate subzones. The recorded topographic data include the concavity, elevation, flow distance, and drainage area of each river profile.
To extract river profiles from the database for comparing topographic parameters with erosion rates, we chose a subjective distance threshold as 150 m between river profiles and erosion rate sampling points (i.e. selecting river profiles which are within 150 m to the closest erosion rate points), and calculated the mean slope gradient and total relief of river longitudinal 210 profiles.
Anthropogenically impacted regions were determined from Foley et al. (2005), which provides global maps of croplands, and pastures and rangelands classified by the relative percentages of areas within these land uses. These maps were modified https://doi.org/10.5194/esurf-2021-7 Preprint. Discussion started: 24 February 2021 c Author(s) 2021. CC BY 4.0 License.
from previous studies (Ramankutty and Foley, 1999;Asner et al., 2004), in which they classified land use types from 215 satellite images using GIS analysis. We conservatively defined anthropogenic regions with higher than 50% area of croplands or pastures and rangelands.
MAP across the continental USA was obtained from CPC US Unified Precipitation data (https://www.esrl.noaa.gov/psd) produced by National Oceanic and Atmospheric Administration Physical Sciences Laboratory (NOAA PSL). The data is in 220 raster format with 0.25-degree resolution (~ 28 km at the equator), including daily precipitation rates from 1948 to 2006 (59 years). We summed the daily data of each grid in each year to convert daily data into yearly data and calculated the precipitation rates for all locations where we have erosion rates.
To analyse the statistical difference of erosion rates between climate zones, timescales, and environmental controls, we 225 conducted the Kruskal-Wallis nonparametric hypothesis test by the built-in function, kruskalwallis, in MATLAB R2018a.

Climate influence on long-and short-term erosion rates
Using both Köppen-Geiger and Aridity Index climate classifications, short-term erosion rates are significantly higher (P < 0.05) than long-term rates in all climate zones, except for the Cold K-G zone (Fig. 2, Table 1a). Within the Aridity Index 230 categories, there is a general pattern of an increasing difference between long-and short-term erosion rates with higher aridity. However, these differences are only significant for the Arid and Semi-arid categories (P < 0.05, Fig. 2b, Table 1b).
For the long-term erosion rates, Tropical and Arid K-G zones have significantly (P < 0.01) lower erosion rates (medians = 29.7 and 32.2 mm kyr -1 , respectively) than Temperate and Cold zones (medians = 92.9 and 92.5 mm kyr -1 , respectively, Fig.  235 2a, Table 1a). Within the Aridity Index categories, long-term erosion rates are significantly lower in the dryland regions (i.e. Hyper-arid, Arid, and Semi-arid group of categories) compared to the non-dryland regions (i.e. Dry sub-humid and Humid group of categories, P < 0.01) (Fig. 2b), and there are no differences within them (P > 0.05, Table 1b). The maximum longterm erosion rates are exhibited in the Temperate and Cold K-G categories and in the Dry sub-humid AI category.   = 3,074) and short-term (n = 1,521) erosion rates 250 between climate zones of Köppen-Geiger climate classification (a) and Aridity Index classification (b), and between long-and short-term erosion rates of each climate zone. Bold numbers indicate P-values < 0.05. The number of data points for each climate zone is listed in Fig. 2.

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To make our analysis comparable to other studies, we also analysed long-term erosion rates against MAP for all data points within the continental USA. The result shows a similar pattern of erosion rates as those analysed by Aridity Index, with the https://doi.org/10.5194/esurf-2021-7 Preprint. Discussion started: 24 February 2021 c Author(s) 2021. CC BY 4.0 License.
highest erosion rates exhibited in the Dry sub-humid category (MAP ~ 600 mm, Fig. 3a) but also followed by a dip around 1,250 mm and a subsequent increase again in erosion rates in extremely humid regions, where MAP is higher than 1,300 mm. 260 Figure 3: The relationships between mean annual precipitation (MAP) and long-(a) and short-term (b) erosion rates in the USA. The precipitation data were acquired from CPC US Unified Precipitation data. Points are colour coded by Aridity Index categories. Black curve in panel a is LOWESS regression, showing that long-term erosion rates peak at regions with precipitation about 600 mm and more than 1,300 mm. In contrast, no clear pattern is indicated for short-term erosion rates.

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Within the short-term erosion rates, there is no dependency on climate according to either climate classifications (P > 0.05), except in the Cold zone of K-G classification, where there were significantly lower erosion rates compared to other climate zones (P < 0.01, Fig. 2a, b, Table 1). The medians of short-term erosion rates in all climates are generally between 90 and 150 mm kyr -1 , whereas the Cold K-G zone is only 37.5 mm kyr -1 , and the Hyper-arid AI category is as high as 643.8 mm 270 kyr -1 (note that the result of Hyper-arid category may not be robust because of limited available data). Similarly, there is no apparent relationship between short-term erosion rates and MAP across the continental USA (Fig. 3b).

Influence of glaciation on long-term erosion rates
To explore the influence of past glaciations on long-term erosion rates, we compared data for those locations that are currently in the Temperate K-G zone and were previously in glacial and pro-glacial zones during the Pleistocene (e.g. north-275 western Europe, part of the Andes, the Himalayas, and New Zealand) against the Temperate sites that were not glaciated (Fig.   4). We find that long-term erosion rates for formerly glaciated regions of the Temperature zone are approximately 5 times higher than in non-glaciated regions (medians = 202.3 and 41.4 mm kyr -1 , respectively, P < 0.01). This result accentuates the role of glaciers in stripping surfaces across the landscape resulting in higher long-term erosion rates.

Anthropogenic influences on short-term erosion rates
To examine the anthropogenic influences on short-term erosion rates, we compared the erosion rates in "croplands", and "pastures and rangelands", with erosion rates in regions with no such evidence of anthropogenic disturbance. Short-term erosion rates in "croplands", and "pastures and rangelands" are 1.4 times higher than regions without these anthropogenic 290 influences (78.3 mm kyr -1 , P < 0.05, Fig. 5). However, there was no significant difference in erosion rates between these anthropogenically impacted land use types (104.2 and 114.0 mm kyr -1 , respectively, P > 0.05).

Influence of basin characteristics
Finally, we explored the influences of spatial scale and topography on erosion rates. Across the whole datasets, for both 300 long-and short-term erosion rates, there is no clear relationship with basin area (Fig. 6). To investigate this further, we grouped the erosion rates in three bins of basin area, < 500 km 2 , 500-2,500 km 2 , and ≥ 2,500 km 2 . The area thresholds were chosen to achieve a similar number of observations within each bin and climate category. We then calculated the ratio of short-to long-term median erosion rates (RS/L). We found a negative relationship between RS/L and basin area for each K-G climate zone, except the Cold zone (Fig. 7). Generally, short-term erosion rates are several times higher than long-term rates 305 in small basins, whilst in large basins, long-term rates tend to be more similar or even higher than short-term rates. In addition, long-term erosion rates are positively related to the slope gradient and total relief of the river channels (R 2 = 0.29 and 0.24, respectively), whilst for short-term erosion rates, the influences of these topographic parameters are unclear (Fig.   8).

Discussion
Drainage basin erosion influences landscape evolution and has been studied widely to estimate its spatial and temporal changes and identify its environmental controls. The dominant controls on erosion rates between locations and over different 330 timescales may vary and climate influence on erosion rates is complex and hard to isolate (Aalto et al., 2006;von Blanckenburg, 2006;Li and Fang, 2016). Climate controls glacial and hydrological processes, which shape the land surface, and it covaries with other factors, such as topography (e.g. orographic precipitation), geology (e.g. weathering and erodibility of lithology), and vegetation cover (Aalto et al., 2006;von Blanckenburg, 2006;Collins and Bras, 2008;Li and Fang, 2016;Chen et al., 2019;Mishra et al., 2019;Sorensen and Yanites, 2019). 335 Previous studies have shown that, in some regions, short-term erosion rates are higher than long-term rates because of recent human activities (Clapp et al., 2000;Gellis et al., 2004;von Blanckenburg, 2006;Kemp et al., 2020) or climatic change https://doi.org/10.5194/esurf-2021-7 Preprint. Discussion started: 24 February 2021 c Author(s) 2021. CC BY 4.0 License. (Clapp et al., 2000;Gellis et al., 2004;Bierman et al., 2005;Wittmann et al., 2011). In contrast, other regions show higher long-term erosion rates, which were interpreted to be a result of the result of incorporating more high-magnitude, low-340 frequency, events (e.g. wildfires, landslides), but are not detectable within short erosion records (Kirchner et al., 2001;Schaller et al., 2001;Covault et al., 2013). Signals are further complicated by spatial variations of erosion rates within basins that may not be detected at the basin outlet due to the buffering capacity associated with sediment sequestration along channels and behind dams, which is more common in large basins (Milliman and Syvitski, 1992;Walling and Fang, 2003;Wilkinson and McElroy, 2007;Wittmann et al., 2011). 345 Here we compiled long-and short-term drainage basin erosion rates around the globe and analysed the relationships between erosion rates and potential climatic and environmental controls. We demonstrated that precipitation, former glacial processes, and topography influence long-term erosion rates, whilst anthropogenic activities dominate short-term erosion rates. In addition, drainage basin area influences the difference between short-and long-term erosion rates, as does aridity. 350

Influence of climate on long-term erosion rates
A key finding from this meta-analysis using a large, globally distributed dataset, is that there is a non-linear relationship between long-term erosion rates and climate (Fig. 3a) which broadly corroborates early theoretical work on short-term erosion rates ( Fig. 9; Langbein and Schumm, 1958;Walling and Kleo, 1979) and subsequent modelling work (Collins and Bras, 2008). Our result is based on a robust scatterplot smoothing method (LOWESS). Based on a small number of data 355 points, Langbein and Schumm (1958) proposed that sediment yields (as a proxy for erosion rates) in the USA peak in semiarid regions due to the combination of rainfall (high enough) and vegetation cover (low enough) that results in optimum conditions for erosion (Fig. 9). Following their work, Walling and Kleo (1979) analysed sediment yields from around the globe and in regions with higher humidity. Their result shows that in addition to semi-arid regions, there are also peaks in sediment yield in humid climates, where the precipitation is subject to highly seasonal variability (Fig. 9). These previous 360 studies can be considered useful theoretical frameworks for interpreting erosion-climate relationships as the data points are limited and the curves fitted are subjective. Mishra et al. (2019), broadly corroborated this result with compiled global 10 Be data by showing a non-linear relationship between long-term erosion rate and precipitation which, however, differs in its peaks and dips relative to the others (Fig. 9).

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Using 3,074 data points, our study shows that there is a relationship between climate and erosion rates that likely results from the interplay between rainfall and vegetation cover (Langbein and Schumm, 1958;Walling and Kleo, 1979;Mishra et al., 2019). Our results show a peak in erosion rates in the Dry sub-humid regions (MAP ~ 600 mm), a dip in the humid regions (MAP ~ 1,250 mm) and then an increase in erosion rates again in the very humid regions (MAP > 1,300 mm). The patterns in Fig. 3a support with an extensive dataset the idea that the interplay between rainfall and vegetation represent an 375 important expression of climate that controls erosion rates globally. In arid regions, rainfall is too low to induce any significant erosion despite the lack of vegetation cover (Molnar et al., 2006). In dry sub-humid regions, the rainfall is high enough and the vegetation cover low enough to result in high erosion rates. In humid regions, the substantive vegetation cover hinders the effectiveness of high precipitation, but as rainfall continues to increase, the highly erosive energy of precipitation exceeds the protective capability of vegetation and results in higher erosion rates again (Collins and Bras, 2008). 380 One major finding of our study is that the systematic relationship between erosion and climate only holds for long-term erosion rates (Fig. 3a), and not for short-term rates (Fig. 3b). We propose that this difference is due to the overwhelming influence of anthropogenic activities on the land surface that masks the inherent climatic influence.

Influence of glaciation on long-term erosion rates
Prior studies argued that in mid-and high-latitude regions, long-term erosion rates tend to be higher than low-latitude 385 regions because glacial processes during ice ages stripped away the underlying land surface and increased physical weathering through freeze-thaw processes (Schaller et al., 2002;Portenga and Bierman, 2011;Harel et al., 2016;Cook et al., 2020). These processes would yield young exposure ages directly after glacial retreat, after which the rates might not be expected to change much in the absence of glacial processes. Since cosmogenic radionuclide-derived erosion rates span the https://doi.org/10.5194/esurf-2021-7 Preprint. Discussion started: 24 February 2021 c Author(s) 2021. CC BY 4.0 License.
period of glaciation up to the present, they average over the relatively fast and high erosion by glaciers and the subsequent 390 low erosion period. We quantified the role of glaciers in producing such high long-term erosion rates through our comparison of formerly glaciated versus non-glaciated areas within temperate regions (Fig. 4). This analysis showed five times higher erosion rates for the formerly glaciated locations within the same Temperate K-G climate zone, which is consistent with previous studies (Schaller et al., 2002;Portenga and Bierman, 2011;Harel et al., 2016). This result is consistent with the relatively low ratio of short-to long-term erosion for the Humid AI category (Fig. 2b), which likely arises 395 in part because the Humid class includes 46% of the total number of formerly glaciated sites included in our analysis.
Overall, our results suggest that post-glacial erosion rates within temperate areas were much lower due to widespread vegetation cover and thick soils, and the long-term average mostly reflects the result of glacial erosion.

Anthropogenic influence on short-term erosion rates
Human activities have increased short-term erosion rates by an estimated one to two orders of magnitude (Milliman and 400 Syvitski, 1992;Dedkov and Mozzherin, 1996;Montgomery, 2007;Wilkinson and McElroy, 2007;Kemp et al., 2020), suggesting that human influences on sediment yields outweigh natural processes (Hooke, 2000;Wilkinson and McElroy, 2007;Kemp et al., 2020). Among the many human activities expressed on surface erosion around the globe, agriculture has one of the highest impacts on the land surface because it directly alters both vegetation through replacement of forest canopies with low-interception coverage crops, and soils through replacement of natural profiles containing developed 405 organic layers with homogenised profiles that undergo cycles of tillage and surface compaction (Hooke, 2000). This anthropogenic disruption of vegetation and soils should create higher susceptibility to erosion by rainsplash, runoff, and wind (Dedkov and Mozzherin, 1996;Wilkinson and McElroy, 2007;Kemp et al., 2020). The eroded material would then contribute to stream channels, where it would be measured as elevated sediment flux compared to pre-historic levels.

410
Our analysis showed that short-term erosion rates are higher than the long-term rates in all climate categories, except for the K-G Cold zone (Fig. 2). The short-term erosion rates within this zone, mainly concentrated in Canada, Eastern Europe, and Russia, are significantly lower than other climate zones (Fig. 2a, Table 1), which we suggest is because most of these regions are covered by contiguous boreal forest that protects the land surface from erosion. Moreover, once we classified short-term erosion rates by land-use categories, we found that erosion in croplands and pastures and rangelands is similar, but these 415 rates are significantly higher than erosion rates for classes without anthropogenic influences (Fig. 5). These results demonstrate that human activities significantly increase short-term erosion rates, that they are consistently detectable around the globe, and that these influences outweigh natural controls including climate and topography (Fig. 2, 3b, 8c, d, Table 1).
We note that short-term erosion rates are likely to change in the future due to both changes in human land use and due to the regional expression of climate change. For example, milder winters and less snow cover in higher latitudes may promote 420 more land management activities such as forestry, agriculture, and road building, all of which could rapidly increase shortterm erosion rates (Serreze et al., 2000). Even though the prevailing agriculture types between climate zones are different https://doi.org/10.5194/esurf-2021-7 Preprint. Discussion started: 24 February 2021 c Author(s) 2021. CC BY 4.0 License. and may have different impacts on erosion, our results strongly point to the overwhelming impact of agriculture and related activities on short-term erosion rates, corroborating previous work (Dedkov and Mozzherin, 1996;Montgomery, 2007;Wilkinson and McElroy, 2007;Kemp et al., 2020). 425 However, it is worth noting that the difference in short-term erosion rates between anthropogenic and non-anthropogenic regions shown here is smaller than was shown in previous studies (Dedkov and Mozzherin, 1996;Montgomery, 2007;Wilkinson and McElroy, 2007;Kemp et al., 2020). For example, Dedkov and Mozzherin (1996) estimated that anthropogenic activities increase sediment yields by a factor of 3.5 in large rivers and 8 in small rivers. We speculate that 430 one of the main reasons for this discrepancy is that here we may be underestimating the amount of area that is influenced by anthropogenic activity, based on our defined threshold of > 50% agricultural area. Another possibility is that our analysis may be including more short-term erosion rates sampled in anthropogenically impacted regions, where substantial soil and water conservation efforts in upstream basins, as well as engineering structures (e.g. dams) that trap sediment may result in artificially lower sediment yields (Walling and Webb, 1996;Hooke, 2000;Walling and Fang, 2003;Syvitski et al., 2005;435 Wilkinson and McElroy, 2007;Singer and Dunne, 2006;Singer and Aalto, 2009).

Physiographic controls on basin-averaged erosion rates
Although drainage basin area is commonly used (in combination with slope) as a proxy for erosion (i.e. stream power incision law), we found no clear relationship between basin area and long-term or short-term erosion rates within our compiled global dataset (Fig. 6), consistent with other studies (e.g. Summerfield and Hulton, 1994;Kirchner et al., 2001;440 DiBiase et al., 2010). There are several factors that potentially obscure any systematic relationship between basin area and erosion including sampling location within the basin, tectonic setting, and underlying lithology. Cosmogenic radionuclidederived erosion rates assume a uniform average erosion rate within the upstream contributing area, so sampling location matters. Samples taken in lower order streams (upper parts of basins) reflect more hillslope and debris flow erosion (Stock and Dietrich, 2003), whereas downstream samples reflect more fluvial erosion, but may be biased by floodplain storage of 445 sediment, violating the detachment-limited assumption within area-erosion relationships . Tectonic setting controls the topographic relief of the basin, where active margins have higher relief and steepness than passive margins, promoting higher erosion rates and lower deposition (Ahnert, 1984;Milliman and Meade, 1983;Walling and Webb, 1996;. Underlying lithology also affects erosion rates, yielding lower exhumation for basins with harder basement rocks for the same drainage area (Hurst et al., 2013). Finally, climate influences the development of soils 450 and vegetation cover, as well as orographic gradients, all of which in turn affect erosion, irrespective of basin area (Dedkov and Mozzherin, 1996;Walling and Webb, 1996;Willett, 1999;Collins and Bras, 2010;Milliman and Farnsworth, 2011).
When we classified erosion rates by basin area, we found a negative relationship between RS/L (the ratio of short-to long-shown that in large basins (e.g. Amazon River), the differences between long-and short-term erosion rates are less discernible compared to small basins, due to the sediment buffering capacity of large drainage basins (Wittmann et al., 2011;Covault et al., 2013). Buffering capacity, or the degree of sediment transport delay from the source area to the basin outlet in response to the variations of environmental controls, is determined by the balance between sediment supply (affected by erosion rate and river transport capacity) and the accommodation of deposition, such as riverbed or flood plain (Wittmann et 460 al., 2011;Covault et al., 2013). Large basins usually have higher buffering capacity, since they tend to have longer river channels and larger flood plains; therefore, short-term variations of sediment supply from the uplands may be diluted within the basin (i.e. the increased sediments may deposit temporarily when transported along the river channel), and harder to be detected at the downstream sections (Jerolmack and Paola, 2010).

465
The RS/L values are insensitive to basin area within Arid catchments (Fig. 7). We argue that this is because arid regions have a distinctive hydrological regime, where storms tend to have shorter duration, smaller spatial coverage, and high spatial variability, which generate partial area runoff (Yair et al., 1978;Singer and Michaelides, 2017;Michaelides et al., 2018).
Arid regions also experience transmission losses within porous river channels, resulting in a breakdown in the relationship between basin area and streamflow, compared to the positive relationship found in humid regions (Knighton and Nanson, 470 1997;Tooth, 2000;Jaeger et al., 2017;Singer and Michaelides, 2014). These characteristic features of arid zone hydrology reduce the influence of basin area on hydrological processes, including sediment transportation, leading to weaker influence of buffering capacity of drainage basins in arid regions. In the Temperature and Cold zones, the RS/L values are generally lower than the other two categories (i.e. long-term erosion rates are more similar to short-term rates, or even higher) because glacial processes during past ice ages led to increased long-term rates (Section 4.2). In addition to glacial processes, wildfires, 475 landslides and volcanic events that exhibit high magnitude and low frequency, may also lead to higher long-term erosion rates in humid climate zones (Kirchner et al., 2001;Schaller et al., 2001;Covault et al., 2013) as the higher soil coverage can generate large amounts of sediment. The rarity of these large magnitude events means that they are not usually captured in short-term records. The increased timescale of 10 Be-derived erosion rates provides a higher probability that extreme erosion events are included in the data record. 480 Drainage basin steepness is considered a critical control on erosion rates (e.g. Summerfield and Hulton, 1994;Granger et al., 1996;Portenga and Bierman, 2011), which is also fundamental to the stream power incision law. Drainage basins with higher steepness tend to produce higher velocity of runoff because of the downslope vector of potential energy, which increase the shear stress of water flow and thus produce higher erosion that shapes land surface and transports sediments 485 downstream (Knighton, 1998;Whipple and Tucker, 1999). In addition, steep drainage basins are often located in tectonicactive regions, with low strength of bedrock (because of joints and faults developments), high frequency of landslides (Binnie et al., 2007;Grin et al., 2018), and high precipitation rates caused by orographic effects (Willett, 1999;Roe et al., 2002), all of which would tend to increase erosion rates. Our analyses show positive relationships between slope gradient https://doi.org/10.5194/esurf-2021-7 Preprint. Discussion started: 24 February 2021 c Author(s) 2021. CC BY 4.0 License. and total relief of river channels and long-term erosion rates (Fig. 8a, b), suggesting that both climatic and topographic 490 factors control long-term erosion rates despite no clear relationship between short-term erosion rates and these topographic controls (Fig. 8c, d). Short-term erosion rates are dominated by anthropogenic activities. Agriculture, a key anthropogenic influence on erosion, tends to cluster in downstream parts of drainage basins with gentler slopes (Wilkinson and McElroy, 2007). In upstream sections of drainage basins, anthropogenic activities that accelerate erosion (e.g. deforestation) may be ameliorated (from a sediment yield perspective) by soil and water conservation efforts (Montgomery, 2007), and/or by the 495 trapping of sediment within reservoirs (Walling and Webb, 1996;Walling and Fang, 2003;Syvitski et al., 2005). Thus, sediment yields may differ substantially from upstream to downstream within the same basin, depending on the locations of these anthropogenic activities within the landscape. Therefore, human-induced sediment yields may generate unclear relationships between short-term erosion rates and steepness of drainage basins.

Conclusions 500
By compiling and analysing erosion rates from globally distributed sites, we demonstrate a few key differences in long-and short-term rates and their dominant controls: 1) short-term erosion rates are significantly higher than long-term erosion rates in all climate zones except in the K-G Cold zone; 2) long-term erosion rates are higher in mid-and high-latitude regions (and in K-G Cold zone), which were enhanced by glacial processes during past ice ages; 3) only long-term erosion rates are strongly related to climate and topography, while short-term rates do not exhibit any relationship to climatic or topographic 505 factors; 4) short-term rates seem to be dominated by human activities which mask natural controls; 5) a key finding is that a non-linear relationship exists between long-term erosion rates and climate, reflecting the balance between precipitation and vegetation cover; however, this relationship does not hold for the short-term erosion rates as proposed by former studies (Langbein and Schumm, 1958;Walling and Kleo, 1979); 6) short-term erosion rates are generally several times higher than long-term rates in small basins, showing that human-induced erosion is more detectable in small basins with lower sediment 510 buffering capacity; 7) on the contrary, long-term erosion rates tend to be similar or even higher than short-term rates in large basins. The latter can be explained by former glacial processes and high-magnitude, low frequency natural events such as wildfires, mass movements, and volcanic activity (Kirchner et al., 2001;Schaller et al., 2001;Covault et al., 2013). Based on these findings we suggest that erosion rates around the world, regardless of climate zone, are likely to change in the future in response to both climate change and anthropogenic influences, which are growing in prevalence globally. 515