Currently, the anthropogenic perturbation of the biogeochemical cycles remains unquantified due to the poor representation of lateral fluxes of carbon and nutrients in Earth system models (ESMs). This lateral transport of carbon and nutrients between terrestrial ecosystems is strongly affected by accelerated soil erosion rates. However, the quantification of global soil erosion by rainfall and runoff, and the resulting redistribution is missing. This study aims at developing new tools and methods to estimate global soil erosion and redistribution by presenting and evaluating a new large-scale coarse-resolution sediment budget model that is compatible with ESMs. This model can simulate spatial patterns and long-term trends of soil redistribution in floodplains and on hillslopes, resulting from external forces such as climate and land use change. We applied the model to the Rhine catchment using climate and land cover data from the Max Planck Institute Earth System Model (MPI-ESM) for the last millennium (here AD 850–2005). Validation is done using observed Holocene sediment storage data and observed scaling between sediment storage and catchment area. We find that the model reproduces the spatial distribution of floodplain sediment storage and the scaling behavior for floodplains and hillslopes as found in observations. After analyzing the dependence of the scaling behavior on the main parameters of the model, we argue that the scaling is an emergent feature of the model and mainly dependent on the underlying topography. Furthermore, we find that land use change is the main contributor to the change in sediment storage in the Rhine catchment during the last millennium. Land use change also explains most of the temporal variability in sediment storage in floodplains and on hillslopes.
Soil erosion by rainfall and the resulting soil redistribution in a landscape
play an important role in the cycling of soil carbon and nutrients in
ecosystems
Recent evidence has demonstrated that human activities, such as land use
change, have accelerated soil erosion rates globally
However, data on global soil erosion and redistribution are scarce to
non-existent. There exist several modeling approaches to estimate global
soil erosion rates
Consequently, the land components of Earth system models (ESMs), which are
the main tools to investigate the terrestrial carbon cycle and the carbon
flux between soil and the atmosphere, ignore the lateral carbon fluxes
associated with soil redistribution
The holistic understanding of the interaction and linkages between soil
erosion, deposition and transport can be addressed using the sediment budget
approach
There exist different spatial models of suspended sediment flux that also
consider the soil redistribution or sediment dynamics in a catchment
The overall aim of this study is to make a first step in quantifying large-scale soil erosion and redistribution rates and identifying their drivers in order to contribute to the representation of sediment dynamics and associated lateral fluxes of carbon and nutrients in ESMs. Therefore, we present and evaluate a new large-scale sediment budget model for the non-Alpine part of the Rhine catchment using the environment of ESMs. We use the model to quantify the spatial variability in floodplain and hillslope sediment storage for the Rhine catchment, and its dependence on climate change and land use change during the last millennium (here AD 850–2005). We also investigate the relationship between catchment area and sediment storage on hillslopes or in floodplains to derive a general validation test for our large-scale model. Finally, we discuss the main challenges in modeling large-scale, long-term soil erosion and redistribution, and future perspectives for application in ESMs.
The main purpose of the sediment budget model presented here is to estimate
large-scale, long-term floodplain and hillslope sediment storage and lateral
fluxes of sediment. The model should, therefore, be spatially explicit and
capable of estimating erosion, deposition and sediment transport processes.
For this purpose we will use a grid-cell-based approach. Compatibility of
this new model with ESMs is important for a future extension of the model to
include the carbon and nutrient cycling. Furthermore, it is essential to
distinguish between floodplain and hillslope systems due to the distinct
differences in sediment dynamics between these systems
Before we can define a model that satisfies the abovementioned conditions we have to make some basic assumptions. First, as it is difficult to disentangle the floodplains and hillslopes in available soil data sets, we assume that each grid cell contains both a hillslope and a floodplain reservoir. When estimating large-scale sediment storage with the aim of predicting the effects of soil redistribution on the biogeochemical cycles, the focus is to get the large-scale spatial patterns right, rather than accurate numbers for the sediment storage and fluxes. Second, we assume that the sediment deposition and transport behave differently between the floodplain and hillslope reservoirs on the timescale of the last millennium. Third, erosion is considered to mainly take place on hillslopes, where part of the eroded sediment is directly transported from hillslopes and deposited in the floodplains.
The underlying model framework (Fig. 1a) that consists of the erosion,
deposition and sediment transport modules is based on the sediment
mass-balance method. The change in sediment storage (
Here,
Model scheme
The specific rate is the inverse of the residence time (
The underlying RUSLE model stems from the original Universal Soil Loss
Equation (USLE) model developed by USDA (USA Department of Agriculture),
which is based on a large set of experiments on soil loss due to water
erosion from agricultural plots in the United States
In the adjusted RUSLE model, as presented above, the effects of the
slope length (
The effect of the land cover type on
After calculating erosion and deposition, the sediment is transported between
grid cells based on the multiple flow sediment routing scheme such as
presented by
The floodplain sediment storage rate (
For hillslopes the change in sediment storage is assumed to be equal to the
input rate (Eq. 10), because we assume that the stored hillslope sediment has
an infinite residence time on the timescale of the last millennium in
accordance with the study of
The modeling approach as presented by the equations above focuses on the net soil redistribution by separately modeling the main processes of soil redistribution, which are erosion, deposition and transport. In the following paragraphs we will show how this dynamical modeling approach performs when applied on the Rhine catchment.
The resolution of the sediment budget model is 5 arcmin. The main reason for choosing this particular model resolution is based on the assumption that this resolution is optimal when considering that each grid cell contains a floodplain and hillslope fraction. Here, a higher resolution could lead to cases where this assumption is not met. Also, the 5 arcmin resolution fits well with the resolution of the adjusted RUSLE model.
The sediment budget model uses climate and land cover data from simulations
of the Max Planck Institute Earth System Model (MPI-ESM) that have been
performed under the Coupled Model Intercomparison Project Phase 5 (CMIP5)
framework
Calculation of soil erosion according to the adjusted RUSLE model is mostly
based on the methods presented in the study of
Additionally, due to the overestimation of erosion rates by the adjusted
RUSLE model in the Alps, we defined a mean soil erosion rate of
20
We chose
The floodplain residence time is made to range between the median and maximum
residence time of floodplain sediment in the Rhine catchment of 260 and 1500
years, respectively. This is in accordance with the residence times derived
from observed sediment storage in the Rhine catchment. Furthermore,
The Rhine catchment
From observed Holocene sediment storage,
Here,
With the estimated scaling exponents (Eqs. 12 and 13)
Furthermore,
Simulation specifications for the application of the sediment budget model on the Rhine catchment. For each experiment with the sediment budget model, the type of simulation (equilibrium or transient), the time period, and the initial conditions on which the simulation is based are given. Furthermore, we also provide the number of simulations we made with the model for a certain type of simulation, and the experiment from MPI-ESM that we used to derive the input data to force the sediment budget model.
Finally,
In order to simulate sediment storage for a certain catchment, an initial state of that catchment has to be assumed. Here we assume the initial state to be the equilibrium state of a catchment, defined as the state of a catchment where the sediment input is equal to the sediment output, and thus the sediment yield at the outlet of the river is constant in time. External forces working on a catchment, such as land use activities or deglaciation, can bring the catchment out of equilibrium and into a transient state. In the case of the Rhine catchment the period directly after the Last Glaciation Maximum (LGM) could be of major importance due to strong erosion that was triggered by the retreating ice sheets. From today's observations on sediment yields or erosion rates we cannot determine when the Rhine catchment was in an equilibrium state. Additionally, there are no observations of sediment storage before the start of agricultural activities in the Rhine catchment. This poses a problem in simulating and interpreting present-day absolute values of sediment storage and yields with our sediment budget model.
In order to still be able to interpret the simulated results for the Rhine catchment, we will only focus on the change in sediment storage due to land use and climate change since AD 850. Considering mainly the changes induced by external forcing, it is not necessary to know whether the system was in an equilibrium or transient state at AD 850. Based on this reasoning, we use the environmental conditions of the period between AD 850 and 950 to determine the equilibrium state of the model.
In the rest of this study, we will refer to the period between AD 850 and 950 as the “default equilibrium state” that we define based on the mean environmental conditions between AD 850 and 950, while one should keep in mind that this is not the “real” equilibrium state of the catchment. The period AD 850–950 is used here as the equilibrium state due to reasons related to data availability, and because human impact in this time period is still small compared to present day.
Hence, our simulation setup structure is generally defined by an equilibrium simulation based on the mean climate and land cover conditions of the period between AD 850 and 950, followed by a transient simulation for the last millennium.
We performed three equilibrium simulations: one based on the mean climate and land cover conditions of the period AD 850–950, and the two others based on the mean climate and land cover conditions of the mid-Holocene period (6000 years ago) from the mid-Holocene experiment of the MPI-ESM (Table 1). The reason for performing an equilibrium simulation for the mid-Holocene period is to investigate how different initial conditions for climate and land cover influence the overall sediment storage change during the last millennium.
In the equilibrium simulations the erosion and deposition rates are kept
constant and the model is run with a yearly time step until the total
floodplain sediment storage of a catchment does not change by more than
1 t year
Summary of regression results of the scaling of sediment storage
at the end of the equilibrium and
transient simulations. Here we consider only the grid cells that correspond
to the observation points from
We performed five “default” transient simulations: two based on the mid-Holocene equilibrium states, and three based on the equilibrium state of AD 850–950. The different ensemble simulations were used to investigate the uncertainty in the resulting sediment storage due to the input data of MPI-ESM. Additionally, we also performed a climate change and land use change simulation based on the equilibrium state of AD 850–950 (Table 1). In the climate change simulation the land cover was fixed to the mean conditions of AD 850–950 during the whole period of the last millennium, while the climate was variable. In the land use change simulation the climate was fixed to the mean conditions of AD 850–950, while the land cover was variable (Table 1).
In order to validate the sediment budget model we tested whether the model can
reproduce the scaling relationships found by
When considering all the grid cells of the Rhine catchment we find a scaling
exponent for floodplain storage of
Scaling of floodplain
Summary of regression results of the scaling of sediment storage
after the equilibrium and transient simulations. Here we consider all grid
cells in the Rhine catchment area. The
Summary of regression results of the sensitivity analysis on
floodplain sediment storage scaling. Here we consider only the previously
mentioned selected grid cells in the Rhine catchment area.
Furthermore, when including all grid cells in the scaling approach, the spread
in the data increases, which is clear from the lower
Finally, we find that keeping either the climate or land cover constant
throughout the last millennium has very little impact on the scaling exponent
for floodplain storage. Here, the climate change simulation results in a
slightly higher and the land use change simulation in a slightly lower
scaling exponent. The different forcings have a stronger impact on the
scaling for hillslope storage, as hillslope storage is only dependent on
erosion and deposition rates. In the climate change simulation the scaling
exponent for hillslope storage increases by 3.8
With the above results we show that the scaling relationships are a general feature for the entire Rhine catchment and are independent of the selected observation points. As the Rhine catchment is a large catchment with a complex topography, this indicates that the scaling relationships might also be applicable for other large river catchments.
Summary of sediment storage
We also performed a sensitivity study to test the robustness of the scaling
relationships derived with the model. For this we investigated the dependence
of the scaling on the three main variables of the model, namely the
residence time, erosion and deposition. First, we investigated the dependence
of the scaling exponent for floodplain storage on the residence time. We
chose different median residence times for floodplain sediment in the Rhine
catchment, while keeping the maximum residence time fixed. Changing the
median residence time by a factor of 10, from 50 to 500 years, results in a
decrease of 21.8
Next, we investigated the dependence of the scaling exponents for floodplain
and hillslope storage on erosion. We changed the spatial variability in
erosion in the Rhine catchment by changing the spatial variability in the
For the deposition we find a minor effect on the scaling parameters, which can be neglected.
Overall we find that changing erosion and residence time does not change the basic property of the scaling, which is that floodplain storage increases in a non-linear way with catchment area while hillslope storage increases linearly with catchment area. As the residence time is determined by flow accumulation and flow accumulation determines the spatial variability in floodplain sediment storage, we expect that the scaling parameters for floodplain sediment storage are also mainly determined by flow accumulation. Erosion is mainly determined by the slope, and slope determines the spatial variability in hillslope sediment storage. Therefore, we expect that the slope determines the scaling parameters for hillslope sediment storage. Based on this we argue that the scaling for both floodplain and hillslope storage is an emergent property of the model and that the scaling parameters are controlled by the underlying topography.
We estimate an average soil erosion rate of
The average soil erosion rate for the last millennium results in a mean
floodplain and hillslope sediment storage change for the last millennium of
Furthermore,
Observed versus simulated sediment storage (Gt) for Rhine sub-catchments. The
sub-catchment area is given in km
We also analyzed the spatial variability in the simulated sediment storage in
floodplains and found that the model reproduces the spatial variability well
when compared to the observed values from
Observed vs. simulated
floodplain sediment storage for Rhine sub-catchments. The values are in
percent (actual storage divided by the sum times 100). Data on the observed
sediment storage are taken from
For hillslope sediment storage we find a similar spatial trend to that for the floodplain sediment storage, with some more variation between the minimum and maximum values (Table 6). Also here, the Mosel sub-catchment stores the most sediment. Furthermore, when comparing floodplain to hillslope sediment storage we find that the floodplain-to-hillslope ratio varies significantly between the various sub-catchments. The highest ratio of 0.48 is found for the Lower Rhine sub-catchment, while the lowest ratio of 0.14 is found for the Emscher sub-catchment. The ratios seem not to be correlated with slope or catchment area and can be assumed as independent features of the model.
The sediment budget model presented here has been developed to simulate
long-term trends and to determine the main drivers behind these trends.
Figure 5 shows the land use change and the 10-year mean precipitation
averaged over the Rhine catchment for the last millennium. There are two
interesting periods, AD 1350–1400 and 1750–1950, that show
increased precipitation amounts correlating with a sudden increase in land
use change (increase in crop and pasture). These periods lead to maxima in the
erosion time series of 2.8 and 4.3 t ha
Land cover and precipitation variability averaged over the Rhine catchment for the last millennium. The red line is the 10-year mean total precipitation for the Rhine catchment. The background colors are land cover types, starting from the darkest grey to the lightest: forest, bare soil, grass, crop and pasture. Land cover and precipitation data are from MPI-ESM.
We find the strongest increase in the sediment storage rate for floodplains
during the period AD 1750–1850, and for hillslopes during the period
AD 1850–1950. For hillslopes this maximum sediment storage rate corresponds
to a maximum increase in the deposition rate, which is a result of a maximum
increase in land use change. Land use change leads to a sediment
disconnectivity in the landscape, which prevents the sediment stored on
hillslopes of reaching the fluvial system on the timescale of the last
millennium. In contrast to hillslopes, the maximum sediment storage rate for
floodplains is a result of the interplay between deposition and sediment loss
from the catchment. In the period AD 1750–1850 land use change started to
increase in the Alpine region. This region did not experience such a strong
change in land use before AD 1750 compared to the downstream regions of the
catchment. During the period AD 1750–1850, the deposition to floodplains
increased significantly due to the increased erosion rates as a result of
land use change. As land use change started to impact the Alpine region,
steep slopes and short residence times led to a strong sediment flux
downstream. However, due to the long residence time of the areas located
downstream, the sediment loss from the entire catchment did not increase as much, leading to an increased
sediment storage in the floodplains. This is in accordance with the findings
of
Furthermore, if we disentangle the effects of land use and climate on the sediment storage in floodplains and on hillslopes, we find that land use change explains most of the change in sediment storage. For floodplains climate change also has a non-negligible impact on the temporal variability in sediment storage. For example, in the periods AD 1350–1400 and 1750–1950, the sediment storage rate is increased due to increased precipitation that lead to a strong sediment flux downstream. If the land use conditions of the period AD 850–950 are kept constant, the total change in sediment storage in floodplains and on hillslopes during the last millennium is 2.9 and 15.4 Gt, respectively. This is 4 and 2 times, respectively, less than the change in floodplain and hillslope sediment storage when land use change is variable (Fig. 7a and b). Here, the overall sediment storage still increases due to the overall increased trend in precipitation during the last millennium. If only the climate conditions are kept constant, the resulting change in sediment storage in floodplains and on hillslopes is 10 and 27.4 Gt, respectively.
As shown in the previous sections, the average
simulated erosion rate for the last
millennium of the Rhine catchment is overestimated when compared to the
average erosion rate for the Holocene from the study of
Simulated change in
Comparing our simulated erosion rates for present day with high-resolution
estimates from
Furthermore, using coarse-resolution data to calculate the
Additionally, the absence of the seasonality in the
Neglecting the support practice (
Also, biases in the adjusted RUSLE model, such as the unadjusted
Another large uncertainty in our sediment budget model, besides the biases in
erosion rates, is the choice of the equilibrium state. We find a decreasing
trend in the floodplain sediment storage in the transient simulation when
using the equilibrium state based on the mean conditions of 6000 BC. This can
be attributed to the different spatial distribution of erosion and the
average high erosion rate for the mid-Holocene of 7.8 t ha
The initial conditions determine the amount and spatial distribution of erosion in the catchment during the time that the model runs to equilibrium. Therefore, the equilibrium state that is then reached largely determines the spatial distribution, trend, and amount of the sediment storage during the transient period.
Furthermore, the different ensemble simulations for the period AD 1850–2005 do not differ strongly in precipitation and land cover/land use and therefore do not contribute much to the uncertainty in the overall erosion rates and sediment storage. This period is also too short to find significant effects on the sediment storage change using different ensemble simulations.
There are also some limitations to the model. The sediment yield cannot be accurately simulated for catchments where the initial state of the catchment is uncertain. However, with accurate data input on climate and land cover, the model can be made applicable for tropical catchments on the timescale of the last millennium, after adjusting the model parameters for these catchments. This is because we expect the effect of the last glaciation to be minimal on tropical catchments. In combination with few human activities during AD 850–950, assuming an equilibrium state for these catchments in this time period seems reasonable. This can be tested in a future application of the model on other large catchments.
Furthermore, a more concrete parameterization for the residence time and deposition of floodplain sediment, and a possible new parameterization for the residence time of hillslope sediment, could lead to an improvement of the model. Finally, more validation with long-term sediment storage from other catchments, especially tropical catchments, would be an important contribution in making the model applicable on the global scale.
In this study we introduced a new model to simulate long-term, large-scale soil erosion and redistribution based on the sediment mass-balance approach. The main objective here was to develop a sediment budget model that is compatible with Earth system models (ESMs) in order to simulate large-scale spatial patterns of soil erosion and redistribution for floodplains and hillslopes following climate change and land use change. We applied this sediment budget model on the Rhine catchment as a first attempt to investigate its behavior and validate the model with observed data on sediment storage and erosion rates.
We show that the model reproduces the scaling behavior between catchment area
and sediment storage found in observed data from
We find a mean soil erosion rate of
The simulated erosion rates result in a change in floodplain and hillslope
sediment storage during the last millennium of
In disentangling the contribution from climate change and land use change to the change in sediment storage during the last millennium for the Rhine catchment, we find that land use change contributes the most to the total change in sediment storage.
Furthermore, the model reproduces the overall spatial distribution of sediment storage in floodplains during the last millennium. However, there are some outliers, such as the Mosel sub-catchment, for which the model simulates too much sediment. This could be a result of biases in the erosion rates and the fact that our model is limited to the last millennium. We also found that the hillslope storage of the sub-catchments shows a similar spatial pattern to the floodplain storage.
When analyzing the time series of erosion and storage during the last
millennium we find that the model reproduces the timing of the maxima in
erosion rates as found in the study of
We conclude that our sediment budget model is a promising tool for estimating large-scale long-term sediment redistribution. An advantage of this model is its capability to use the framework of ESMs to predict trends in sediment storage and yields for the past, present and future.
The next steps in quantifying soil redistribution on the global scale are the application of the sediment budget model on other large catchments and validation of the model with existing data on net soil redistribution, sediment storage or yields. Furthermore, in order to make the soil redistribution model better applicable on a global scale and to prevent conflict with the underlying assumption of the simultaneous presence of floodplains and hillslopes in each grid box, the model needs to be made independent of grid resolution.
Finally, to have a complete picture of the net soil redistribution and the
feedbacks on the carbon and nutrient cycles, it is essential to also model
other types of soil erosion, such as wind erosion
We would like to thank Bertrand Guenet and Adrian Chappell for reviewing this manuscript. The article processing charges for this open-access publication were covered by the Max Planck Society. Julia Pongratz was supported by the German Research Foundation's Emmy Noether Programme (PO 1751/1-1). Edited by: A. Temme