The soil carbon erosion paradox reconciled

The acceleration of erosion, transport and burial of soil organic carbon (C) in response to agricultural expansion represents a significant perturbation of the terrestrial C cycle. Recent model advances now enable improved representation of the 10 relationships between sedimentary processes and C cycling and this has led to substantially revised assessments of changes in land C as a result of land cover and climate change. However, surprisingly a consensus on both the direction and magnitude of the erosion-induced land-atmosphere C exchange is still lacking. Here, we show that the apparent soil C erosion paradox, i.e., whether agricultural erosion results in a C sink or source, can be reconciled when comprehensively considering the range of temporal and spatial scales at which erosional effects on the C cycle operate. We developed a framework that describes 15 erosion-induced C sink and source terms across scales. We conclude that erosion is a source for atmospheric CO2 when considering only small temporal and spatial scales, while both sinks and sources appear when multi-scaled approaches are used. We emphasize the need for erosion control for the benefits it brings for the delivery of ecosystem services, but crossscale approaches are essential to accurately represent erosion effects on the global C cycle.


Introduction 20
Soil erosion has been identified as the biggest threat to global food security (Amundson et al., 2015). Reducing soil erosion to maintain or enhance soil fertility is therefore imperative to sustainably feed the growing and more demanding world population (Koch et al., 2013;Montgomery, 2007). Although there is no doubt that soil conservation practices reducing erosion result in healthier, more fertile soils, there is still a debate whether agricultural soil erosion represent a net C sink or source. Assuming that a substantial fraction of soil C mobilized on agricultural land is lost to the atmosphere, many researchers concluded that 25 agricultural erosion represents a source of atmospheric CO2, with estimates of up to 1 Pg C yr -1 (Lal, 2004). This realization led to the notion of a win-win situation whereby soil conservation practices that reduce soil erosion not only result in healthier soils, but that an additional and large C sink could be obtained by halting the large source term associated with pre-conservation agricultural soil erosion (Koch et al., 2013;Lal, 2003Lal, , 2019Ran et al., 2014Ran et al., , 2018Worrall et al., 2016). This notion was challenged by other studies that suggested a different pathway for the eroded C (Berhe et al., 2007;Harden et al., 1999;Van 30 Oost et al., 2007;Smith et al., 2001;Stallard, 1998). They proposed the concept of the geomorphic C pump that transfers C from the atmosphere to upland soils recovering from erosion to burial sites where C is protected from decomposition in lowmineralization contexts. Along this geomorphic conveyor belt, C originally fixed by plants is continuously displaced laterally along the Earth's surface where it can be stored in sedimentary environments such as colluvial and floodplain soils, lake and reservoir sediments and eventually the sea floor (i.e., the Land Ocean Aquatic Continuum or LOAC) (Regnier et al., 2013). 35 They argued that the combination of C recovery and sedimentation on land could capture vast quantities of atmospheric C of ca. 1 Pg C yr -1 and erosion therefore may represent a C sink (Berhe et al., 2007;Smith et al., 2005;Stallard, 1998). This soil C erosion source-sink paradox is an important knowledge gap because (i) erosion-induced C fluxes associated with agriculture operate at rates that are relevant for the global C budget (Aufdenkampe et al., 2011;Berhe et al., 2008;Chappell et al., 2016;Wang et al., 2017;Yue et al., 2016) and (ii) the expected future increases in food demand and climate erosivity will further 40 https://doi.org/10.5194/bg-2022-1 Preprint. Discussion started: 14 January 2022 c Author(s) 2022. CC BY 4.0 License. exacerbate erosion and its implications for the global C budget (Borrelli et al., 2017;Lugato et al., 2016). Here, we elucidate through a comprehensive and synthesizing literature review covering 74 studies (see methods) how the current source-sink paradox, i.e. whether agricultural soil erosion represents a sink or source for atmospheric C, can be reconciled. At the very center of this paradox is the fact that erosion-induced processes operate across temporal and spatial scales that determine the relationship between erosion and C loss versus stabilization processes. We conceptualize the effects of the contributing 45 erosional (sub-)processes across time and space using decay functions (see methods).

Transport in runoff and rivers
At very short timescales (seconds to days) erosion events shift a portion of the soil C from a protected state to an available state where it faster mineralizes to gaseous forms. More specifically, the breakdown of aggregates, either via raindrop impact or via transport in runoff or rivers, makes previously protected mineral associated organic matter (MAOM) and especially 50 particulate organic matter (POM) more readily available for microbial consumption because of reduced physical occlusion (Jacinthe et al., 2002(Jacinthe et al., , 2004Six et al., 2002) (Fig. 1). This facilitates the transformation of free MAOM and POM into more easily decomposable forms of C through desorption of MAOM from mineral surfaces and comminution and dissolution of POM-derived C (Bailey et al., 2019). Together, these processes, which can be observed during a single erosive event, result in an erosion-induced source term. Initial laboratory experiments focusing on the potential mineralization of C transported by 55 overland flow suggested that 13 to 37% of the transported C could be returned to the atmosphere in a matter of several weeks, thereby representing a large and almost instantaneous source term (Guenet et al., 2014;Jacinthe et al., 2002Jacinthe et al., , 2004. These high proportions of mineralizable C were related to the preferential erosion and translocation of labile C. Further experimental work and field observations based on in-situ measurements suggested that the net erosion-induced source term, i.e. relative to noneroded soils, was much smaller with fractional losses of only 4 ± 4.2 % (Van Hemelryck et al., 2010, 2011Polyakov and Lal, 60 2008;Wang et al., 2014a). In addition, at larger spatial scales the destabilization of eroded C during its transport in rivers and estuaries has to be considered and the oxidation of C during in-river transport can be substantial (Aufdenkampe et al., 2011;Wang et al., 2017;Worrall et al., 2016). During fluvial transport, fluid turbulence mixes and aerates water, and in combination with particle abrasion, this may enhance oxidation. The oxidation of particulate organic carbon mobilized by agricultural erosion during its transit time in the aquatic system is assumed to be large with estimates ranging between 0 and 50% 65 (Scheingross et al., 2019;Worrall et al., 2014). Based on this literature review, we estimate the loss terms for runoff and rivers, i.e. αrunoff and αriver, at -0.04 and -SDRx0.5, respectively, (where SDR is the fraction of the eroded C that reaches the river network). This outgassing is usually observed to occur quickly in the timeframe of several days to months. We therefore set the time constant for both processes (i.e. τrunoff and τriver) to 1 yr. Our literature review (Fig. 2) clearly shows that studies reporting erosion as a source term typically consider mobilization and transport processes at very short timescales (0.5 ± 0.7 70 yr). Thus, studies assuming that this short-term erosion-induced loss term is the dominant process concluded that agricultural erosion represents a large source of atmospheric CO2.

SOC recovery after erosion
In contrast, studies considering erosion as a sink for atmospheric C typically consider longer timescales at which the geomorphic C conveyor belt is operating. It is, the net outcome of the geomorphic C conveyor belt strongly depends on the C 75 sink mechanisms induced by erosion of upland soils (Manies et al., 2001;Van Oost et al., 2007;Stallard, 1998;Vandenbygaart et al., 2012). On eroding hillslopes, soils are truncated, and C depleted subsoil material is brought to the surface layers. This induces two competing processes occurring simultaneously: the decomposition of old subsoil C and the sequestration and stabilization of fresh C inputs from newly growing plants. It is, exposure of deep C by erosion of surface soil and associated changes in microclimatic conditions increase the rate of deep C decomposition (Bailey et al., 2019). Furthermore, the mixing 80 https://doi.org/10.5194/bg-2022-1 Preprint. Discussion started: 14 January 2022 c Author(s) 2022. CC BY 4.0 License.
of formerly deep C with labile C provides readily available energy sources for decomposers, which speeds up the decomposition rate of older, previously stable C, the so called priming effect (Fontaine et al., 2007). At the same time, new C formation from new vegetation inputs into the former subsoil may replace some or all of the eroded SOC. It is, erosion induced soil truncation facilitates the new formation of more stable MAOM by the adsorption of products from POM decomposition and DOC derived from plant material onto mineral surfaces of the former subsoil ( Fig. 1), thereby representing a net transfer 85 of C from the atmosphere to soils (Harden et al., 1999;Li et al., 2015;Liu et al., 2003;Wang et al., 2017). Observations covering a broad range of environmental conditions have shown that a substantial part of the eroded SOC in agricultural soils can be replaced by new C and dominates over the enhanced destabilization of deep C (Li et al., 2015;Liu et al., 2003;Van Oost et al., 2007;Wang et al., 2017). This leads to the counterintuitive situation where a system exhibiting lateral C loss due to erosion represents a net atmospheric sink. In contrast to the short-term source term described above, the underlying processes 90 leading to an erosion-induced sink term operate at a slower rate but occur at 70-90 % of the affected surface, whereas the source term is spatially restricted (Dlugoß et al., 2012). Thus, the sink-term is more difficult to isolate from the much larger background C fluxes between soil and atmosphere, particularly at short timescales. By using C isotopes and fallout radionuclides, in combination with space-for-time substitutions spanning several years to decades, studies have conclusively shown that a substantial part of the laterally eroded C can be effectively replaced (50 ± 43 %) (Li et al., 2015;Quine and van 95 Oost, 2007;Vandenbygaart et al., 2012), whereby this erosion-induced sink term was substantially larger than the source term related to erosion-induced C destabilization (Wang et al., 2017). Our literature review clearly shows that studies reporting C erosion recovery as a sink term typically consider these longer time-scales (91 ± 1098 yr) (Fig 2).
The C recovery potential of soils at the scale of eroding hillslopes, which is driving the C sink term of the geomorphic pump, is however in itself also time-dependent. In the initial phases after the start of an erosional disturbance, the soil is not yet in 100 equilibrium with the erosional disturbance and only a small fraction of the eroded C is replaced, which leads to only a small erosion-induced sink (Fig. 3). There is, however, a transient response where the C stocks at the eroding sites continue to decline until a new equilibrium is reached, i.e. when losses through decomposition and lateral erosion balance new C formation. At this point, the erosion loss term is part of a steady state flux where all the eroded C is atmospherically replaced and the sink term potential is maximized (Li et al., 2015). For example, for European cropland subjected to a recent erosional disturbance 105 of c. 2 decades associated with mechanized tillage, a sink-term representing only 26 % of the eroded C was found (Van Oost et al., 2007). In contrast, for cropland subjected to >100 yr of continued water erosion, replacement rates of 58-100 % were found (Dymond, 2010;Li et al., 2015;Naipal et al., 2020). Thus, both observation-and model-based studies support the notion that the fraction of the eroded C that is replaced, and hence the erosion-induced sink term, increases with the duration of the erosional disturbance (Fig. 3). This transient response of eroding landscapes to erosional disturbance is a key control on the 110 erosion-induced sink strength (Li et al., 2015;Van Oost et al., 2007;Wang et al., 2017), but is often overlooked in C budget assessments (e.g. Lugato et al., 2016Lugato et al., , 2018Worrall et al., 2014).
It is important to not, however, that at eroding sites, an erosion-induced decline in net primary production (NPP) may reduce soil C inputs and this may limit the sink term described above (Lal, 2019). Soil erosion reduces soil depth and modifies soil properties, which can have a detrimental effect on NPP through the decrease of the supply of water, nutrients and rooting space 115 ( Fig. 1). Model simulations (Fig. 3) show that NPP decline reduces the efficiency of the sink term and may eventually lead to a source rather than a sink under high erosion scenarios. Although there are documented cases where soil loss has contributed to the collapse of the soil system (e.g. Montgomery, 2007;Óskarsson et al., 2004), the available evidence from present-day agricultural land suggests that erosion-induced soil C input decline is not the dominant mechanism (Lugato et al., 2018), but rather, C stabilization in newly exposed subsoil results in efficient SOC recovery and the sink term is maintained over longer 120 timescales (Wang et al., 2017) (Fig. 3). This is most likely due to a small fraction (i.e. < 10%) of NPP is removed by erosion (Berhe et al., 2008). Based on the data available in literature, we estimate the fractional gain at steady state for the SOC recovery term (αrec) at 0.93, while the time constant (τrec) equals 167 yr (Fig. 3).

SOC burial
The erosion source-sink paradox is also related to an incomplete consideration of the multiple spatial scales at which C and 125 erosion processes interact. After mobilization, the eroded C is transported and a large amount of eroded sediment and C is redeposited in alluvial and colluvial soils while the remainder is stored in lake/reservoir deposits and ocean sediments (Aufdenkampe et al., 2011). At the global scale, colluvial and alluvial burial represent by far the largest stores of C burial (75 %) (Wang et al., 2017). Here, the eroded C is more efficiently protected from destabilization, relative to their origin, due to reaggregation, the formation of MAOM as well as the burial of autochthonous C (Fig. 1). However, high rates of post-130 depositional C losses in colluvial and alluvial soils have been observed with low C burial efficiencies of only 15-30 % at a centennial/millennial time scale; whereas C is preserved more efficiently in lake and ocean deposits with C burial efficiencies of 22-60 % (Van Oost et al., 2012;Wang et al., 2017). This leads to the counterintuitive situation where systems receiving lateral C inputs accumulate C but represent a source for atmospheric C. It has been observed that C destabilization in terrestrial burial stores is a very slow process, with half-lives of up to 300 yr (Van Oost et al., 2012), and C losses therefore lag C burial. 135 At decadal timescales, several studies reported no significant outgassing and hence a full protection of the buried C (Van Oost et al., 2007;VandenBygaart et al., 2015). This lag implies that there is a commitment to future climate as the result of both present and past agriculture and associated erosion and burial. Based on our literature review, we found a large variability in SOC burial response curves (αbur and τbur, Table 1), particularly for alluvial settings. This variability is most likely driven by climatic factors that regulate the hydrologic context, by local NPP and by differences in soil texture and geochemical 140 parameters. Nevertheless, we found a consistent pattern across burial sites with a median αbur and τbur of 0.58 and 0.0019 yr, respectively.

Discussion and conclusion
Using parameter values for α and τ for the different processes constrained by published estimates as presented above and summarized in Table 2 (Table 2), we developed a framework where the instantaneous source terms associated with runoff and 145 river transport are combined with the transient source/sink terms associated with oxidation during burial and SOC recovery on sites of erosion (Fig. 4). The model shows that C stocks in stores along the LOAC are not necessarily in equilibrium with the erosional disturbance and it is thus critical to consider the dynamic phases of both C recovery at sites of erosion and C destabilization in sedimentary environments. Furthermore, the time since agricultural disturbance and the residence times of C in sedimentary environments are critical factors to consider. Considering all these processes This reconciles the apparent 150 soil C erosion paradox by showing that both major source and sink terms for atmospheric C are simultaneously induced by erosion. The contrasting views that erosion represents a large sink or a source originate from a partial analysis and an incomplete consideration of the underlying processes that occur at vastly different spatial and temporal scales. When a comprehensive analysis is done by considering the complete trajectory of eroded C (i.e. the LOAC) at the appropriate timescales, the available evidence indicates that the sink and source terms are in the same order of magnitude. This implies 155 that the assertations of a very large effect of agricultural erosion on the global C budget, with a net C flux of up to 1 to 2 Pg C yr -1 (Berhe et al., 2007;Lal, 2004;Smith et al., 2005) are inconsistent with integrative assessments. Nevertheless, when considering the studies focusing on agricultural systems and accounting for all components of the geomorphic cascade, the available data suggests that the sink terms dominate and agricultural erosion represents a small sink in the order of 5 g C m -2 yr -1 , but a sink nonetheless ( Fig. 2 and Table 1) substrates and thus more data on low-input systems on marginal lands are urgently needed. While we emphasize the necessity 165 of programs to reduce soil losses because of the many benefits this brings for soil quality and delivery of ecosystems services, we urge to consider both C sink and source terms at appropriate scales when assessing the effect of erosion on the global C cycle.

Methods
We use the following model to describe system responses (Eq. 1): 170 where Rt is the erosion-induced C loss/gain at time t of process R, expressed as a fraction of the mobilized C, t is the time since the start of the erosional disturbance, α is the fractional C loss/gain at steady state and τ is the time constant that describes the pace at which the process is adjusting to the erosional disturbance. We compiled 74 studies that were available in the literature and that report on SOC erosion as a sink or source of atmospheric CO2. We used the search terms "soil erosion" & 175 "C sink"|"C source|C budget" in the Scopus database. This was complemented with review papers and references cited herein.
From these studies we extracted whether they report erosion as a sink, source or neutral (if no C flux direction is given). The data was complemented with the space and time scales considered as well as the C flux rates (lateral and vertical fluxes). The studies considered are shown in Table 1 Sci. Lett., 411, 281-289, doi:10.1016/j.epsl.2014.11.036, 2015  Lugato, E., Paustian, K., Panagos, P., Jones, A. and Borrelli, P.: Quantifying the erosion effect on current carbon budget of European agricultural soils at high spatial resolution, Glob. Chang. Biol., 22(5), 1976-1984, doi:10.1111/gcb.13198, 2016 Lugato, E., Smith, P., Borrelli, P., Panagos, P., Ballabio, C., Orgiazzi, A., Fernandez-Ugalde, O., Montanarella, L. and Jones, A.: Soil erosion is unlikely to drive a future carbon sink in Europe, Sci. Adv., 4(11), doi:10.1126/sciadv.aau3523, 2018.     (Quinton et al., 2010). Erosion rates were allowed to vary randomly between 0.1 415 and 0.2 mm yr-1 and soil C residence time for the top layer between 200 and 1000 yr. For the feedback scenario, we assumed a negative feedback that ranged randomly between 3 to 5% yield loss for each 10 cm of cumulative erosion (Bakker et al., 2004). The green boxplots represent oxidation in colluvial settings (bur, n=255, see Table 2). The thin cyan lines represent the non-linear regression models for five alluvial studies (n=273, see Table 2). The thick green and cyan lines represent the response curves for colluvial and alluvial burial using the median values for α and τ.    Figure 2 for key). Positive values for C strength denote a sink, while negative values denote a source. Methods are categorized as Data-or Model-based. Modelling studies using scenario analysis are reported as Mod/Scen and a range for the sink/source strength is given. Rec denotes the fraction (in %) of the eroded C that is replaced with atmospheric derived C.