PreprintPDF Available

Translating deposition rates into erosion rates with landscape evolution modelling

Authors:
Preprints and early-stage research may not have been peer reviewed yet.

Abstract and Figures

Soil erosion is one of the main threats to agricultural food production due to the loss of fertile soil. Determination of erosion rates is essential to quantify the degree of land degradation, but it is inherently challenging to determine temporally dynamic erosion rates over agricultural time scales. Optically Stimulated Luminescence (OSL) dating can provide temporally-resolved deposition rates by determining the last moment of daylight exposure of buried colluvial deposits. However, these deposition rates may differ substantially from the actual hillslope erosion rates. In this study, OSL-based deposition rates were converted to hillslope erosion rates through inverse modelling with soil-landscape evolution model ChronoLorica. This model integrates geochronological tracers into the simulations of soil mixing and redistribution. The model was applied to a kettle hole catchment in north-eastern Germany, which has been affected by tillage erosion over the last 5000 years. The initial shape of the landscape and the land use history are well-constrained, enabling accurate simulations of the landscape evolution that incorporate uncertainties in the model inputs. The calibrated model reveals an increase in erosion rates of almost to orders of magnitude from pre-historic ard ploughing up to recent intensive land management. The simulated rates match well with independent age controls from the same catchment. Uncertainty in the reconstructed initial landscape and land use histories had a minor influence of 12–16 % on the simulated rates. The simulations showed that the deposition rates were on average 1.5 higher than the erosion rates due to the ratio of erosional and depositional area. Recent artificial drainage and land reclamation have increased deposition rates up to five times the erosion rates, emphasizing the need of cautious interpretation of deposition rates as erosion proxies. This study demonstrates the suitability of ChronoLorica for upscaling experimental geochronological data to better understand landscape evolution in agricultural settings.
Content may be subject to copyright.
1
Translating deposition rates into erosion rates with landscape
evolution modelling
Willem Marijn van der Meij1
1Institute of Geography, University of Cologne, Zülpicher Straße 45, 50674 Cologne, Germany
Correspondence to: W. Marijn van der Meij (m.vandermeij@uni-koeln.de)
5
Abstract. Soil erosion is one of the main threats to agricultural food production due to the loss of fertile soil. Determination
of erosion rates is essential to quantify the degree of land degradation, but it is inherently challenging to determine
temporally dynamic erosion rates over agricultural time scales. Optically Stimulated Luminescence (OSL) dating can
10
provide temporally-resolved deposition rates by determining the last moment of daylight exposure of buried colluvial
deposits. However, these deposition rates may differ substantially from the actual hillslope erosion rates.
In this study, OSL-based deposition rates were converted to hillslope erosion rates through inverse modelling with soil-
landscape evolution model ChronoLorica. This model integrates geochronological tracers into the simulations of soil mixing
and redistribution. The model was applied to a kettle hole catchment in north-eastern Germany, which has been affected by
15
tillage erosion over the last 5000 years. The initial shape of the landscape and the land use history are well-constrained,
enabling accurate simulations of the landscape evolution that incorporate uncertainties in the model inputs.
The calibrated model reveals an increase in erosion rates of almost two orders of magnitude from pre-historic ard ploughing
up to recent intensive land management. The simulated rates match well with independent age controls from the same
catchment. Uncertainty in the reconstructed initial landscape and land use histories had a minor influence of 12-16% on the
20
simulated rates. The simulations showed that the deposition rates were on average 1.5 higher than the erosion rates due to the
ratio of erosional and depositional area. Recent artificial drainage and land reclamation have increased deposition rates up to
five times the erosion rates, emphasizing the need of cautious interpretation of deposition rates as erosion proxies. This study
demonstrates the suitability of ChronoLorica for upscaling experimental geochronological data to better understand
landscape evolution in agricultural settings.
25
1 Introduction
Soil erosion is one of the main threats to agricultural land and food provision, because it reduces agricultural productivity by
loss of fertile soil (Rhodes, 2014). Soil erosion is not only a problem of recent times. Already in the prehistoric, the first land
use activities, such as deforestation and manual hoeing, triggered soil loss by removing the protective vegetative cover and
loosening up the soil (Dreibrodt et al., 2010; Vanwalleghem et al., 2017). With developments in agricultural practices and an
30
increase in food demand, agricultural activity and consequently soil erosion increased over time. In current intensively
https://doi.org/10.5194/egusphere-2024-1036
Preprint. Discussion started: 18 April 2024
c
Author(s) 2024. CC BY 4.0 License.
2
managed landscapes, where land use is heavily mechanized, averaged rates of soil loss can exceed 15 t ha-1 a-1 (Nearing et
al., 2017).
Prehistoric erosion rates are often magnitudes smaller than current-day erosion rates, but over the long agricultural use of
many fields, may have contributed substantially to the overall land degradation. It is inherently challenging to resolve
35
temporally dynamic erosion rates over agricultural time scales, especially in systems where erosion types and rates have
changed over time (Loba et al., 2022). Geochronometers such as radionuclides can provide erosion rates that are averaged
over timescales that depend on their half-lives, such as cosmogenic nuclides (Granger and Schaller, 2014), or on the moment
of introduction in the landscape, such as fallout radionuclides (Mabit et al., 2008; Puela et al., 2023). Other
geochronometers, such as radiocarbon dating or optically stimulated luminescence (OSL) dating do have the ability to
40
provide temporally resolved rates by dating layers from different depths. However, these techniques provide deposition rates
instead of erosion rates, as they rely on deposited or buried material. These deposition rates can act as proxies for erosion
rates, but will also be affected by other factors, such as the ratio between erosional and depositional area, the
sedimentological connectivity of the hillslope and the capacity to store sediments in depositional locations. Deposition rates
can therefore deviate substantially from the actual erosion rates, which could lead to erroneous evaluation of land
45
degradation.
In this work, deposition rates determined with OSL dating will be translated into erosion rates using inverse landscape
evolution modelling. OSL dating measures the built-up luminescent signal in soil minerals (often quartz or feldspar), that
accumulates due to ionizing radiation in the subsurface and incoming cosmic radiation. The luminescence signal resets when
the soil particle is exposed to daylight. The luminescence is thus a proxy for the duration of burial (Murray and Roberts,
50
1997). Advances in numerical soil-landscape evolution models enable the tracing of geochronometers such as OSL particles
and radionuclides with simulated mixing and transport processes over decadal to millennial timescale (ChronoLorica, Van
der Meij et al., 2023). Through inverse modelling, hillslope erosion rates could be derived from the depositional ages
determined with OSL. Such a modelling exercise requires detailed information on the major erosion processes that occur in
the landscape, the initial shape of the terrain and erosion and land use history during the evolution of the landscape (Tucker
55
and Hancock, 2010; Perron and Fagherazzi, 2012; Finke et al., 2015). These initial and boundary conditions come with
uncertainty, especially when they have to be reconstructed beyond timespans where observations are available. This
uncertainty should be quantified and incorporated in simulations of soil and landscape evolution to better convey our
confidence in the model results (Perron and Fagherazzi, 2012; Minasny et al., 2015). Through comparison with independent
data and age controls, the validity of the calibrated parameters and their uncertainty can be tested (Temme et al., 2017).
60
The objectives of this paper are to test 1) whether luminescence-based deposition rates can be translated into erosion rates
using a soil-landscape evolution model, 2) how these rates are affected by uncertainties in initial and boundary conditions,
and 3) how the reconstructed rates compare to rates derived from other geochronological methods.
https://doi.org/10.5194/egusphere-2024-1036
Preprint. Discussion started: 18 April 2024
c
Author(s) 2024. CC BY 4.0 License.
3
2 Study area
The study area is the agricultural landscape laboratory CarboZALF-D (Figure 1, Sommer et al., 2016). This site is located in
65
the young morainic landscape in northeastern Germany, which formed after the last glacial retreat in the Weichselian around
19 ka ago (Lüthgens et al., 2011). The parent material is illitic, calcareous glacial till. Annual rainfall is around 480 mm and
annual mean temperature is 8.7 °C. The first agricultural practices started around ~5 ka ago, with intensification in the last
1000 years (Kappler et al., 2018; Van der Meij et al., 2019; Öttl et al., 2023).
70
Figure 1: Map of the study area CarboZALF-D, showing the locations where the geochronological samples and soil descriptions
were taken. They grey shaded areas indicate where colluvium and peat are currently present.
CarboZALF-D is a closed kettle hole catchment, meaning that almost all eroded sediments are stored in the central
depression, providing unique opportunities for studying erosion processes and landscape reconstruction. This includes a
75
reconstruction of the palaeotopography before anthropogenic erosion using truncation of soil profiles (Van der Meij et al.,
2017), determination of deposition rates and patterns using optically stimulated luminescence (Van der Meij et al., 2019),
determination of short-term and long-term erosion rates using 239+240Pu and meteoric and in-situ 10Be (Calitri et al., 2019),
https://doi.org/10.5194/egusphere-2024-1036
Preprint. Discussion started: 18 April 2024
c
Author(s) 2024. CC BY 4.0 License.
4
and determination of recent erosion rates using 137Cs (Aldana Jague et al., 2016). Altogether, this resulted in a large
geochronological dataset covering different spatial and temporal scales (Figure 1).
80
2.1 Landscape evolution at CarboZALF-D
CarboZALF-D underwent a complex landscape evolution (Van der Meij et al., 2019). Two distinct layers of colluvium could
be identified. The first layer, with ages from 5 ka up to 300 a, was deposited at the fringes of the colluvium, but did not reach
into the central kettle hole. This area was probably too wet for agricultural practices such as tillage, as identified by the peaty
layer that is still present under the colluvium. Following drainage at the start of the 19th century to increase agricultural
85
acreage, the central depression became accessible for agricultural practices. Continued erosion in the catchment, including
re-erosion of the old colluvium, led to the deposition of a younger layer of colluvium in the central depression, covering the
old colluvium at the fringes. With modernization of agricultural tools and increased tractive power, recent erosion rates far
exceed the (pre-)historical erosion rates (Sommer et al., 2008). The CarboZALF-D catchment is split by a railroad
constructed around 1900 CE. The southwestern part of the catchment is relatively flat and most soil profiles are still intact
90
(Van der Meij et al., 2017). Therefore, the assumption in this paper is that that part didnt contribute substantially to the
build-up of the colluvium in the central depression. It was therefore left out of the analysis.
Table 1: Overview of land management history at CarboZALF-D. Periods of different plough uses with corresponding mixing
depths and their uncertainties are indicated. Modified from Van der Meij et al. (2019).
Management type
Introduction year of
management type
Mixing depth (cm)
Corresponding tillage
parameter
Ard plough
3700-3200 BCE
5-7
TIpot_1
Medieval mouldboard plough
200-900 CE
8-15
TIpot_2
Early modern mouldboard plough
1795-1800 CE
15-17
TIpot_3
Contemporary mouldboard plough
1954-1965 CE
25-30
Current mouldboard plough
1989 CE
20
Artificial drainage
1787-1826 CE
-
-
2.2 The erosion processes
95
In the young morainic landscape of northeastern Germany, tillage is currently the dominant erosion process and played a
substantial role in the past as well (Aldana Jague et al., 2016; Van der Meij et al., 2019; Wilken et al., 2020; Öttl et al.,
2023). This is best expressed in the erosion and deposition patterns, with most intensive erosion on convex hillslopes and
deposition in concave positions (De Alba et al., 2004), which are observed in current agricultural landscapes and long-term
(>240 a) forested landscapes (Van der Meij et al., 2017; Calitri et al., 2020, 2021). These findings indicate that diffusive soil
100
transport, caused by tillage erosion, has been the dominant erosion process in the study area. Therefore, and to facilitate the
modelling exercise, tillage is considered the sole erosion process in this study.
https://doi.org/10.5194/egusphere-2024-1036
Preprint. Discussion started: 18 April 2024
c
Author(s) 2024. CC BY 4.0 License.
5
3 Methods
3.1 ChronoLorica
3.1.1 Model architecture
105
Soil-landscape evolution model ChronoLorica was used for simulating the landscape evolution (Van der Meij et al., 2023;
Van der Meij and Temme, 2022). ChronoLorica is based on soil-landscape evolution model Lorica (Temme and
Vanwalleghem, 2016), with the addition of a geochronological module. This module couples the soil and landscape forming
processes to the redistribution of different geochronometers, in this case particle ages that are analogous to OSL ages. The
landscape surface is represented by a raster-based elevation model. Below each raster cell there is a pre-defined number of
110
soil layers. Inside each layer, the model keeps track of five texture classes (gravel, sand, silt, clay, fine clay). Changes in the
mass of the soil constituents due to additions or removals is converted into a change in layer thickness and consequently
elevation of the surface through the bulk density. In these simulations, a constant bulk density of 1500 kg m-3 was used,
because pedotransfer functions that are usually used to calculate the bulk density underestimate the bulk density of glacial
till. A more detailed description of the model architecture can be found in Temme and Vanwalleghem (2016) and Van der
115
Meij et al. (2023).
The three-dimensional representation of the soil landscape enables the simulation of depth functions of particle ages and
radionuclides, which facilitates comparison with measured age-depth functions. This is not possible with most other
landscape evolution models that only consider two-dimensional landscape surfaces.
3.1.2 Process descriptions
120
In ChronoLorica, tillage is simulated as a two-part process. The first part addresses the soil mixing. Over the range of the
plough depth pd [m], soil layers are completely homogenized. This includes the mineral soil, organic components, stocks of
radionuclides and particles with OSL ages.
The second part addresses soil translocation by tillage. Tillage erosion and deposition follows a linear diffusion equation
(Eq. (1)). The transport of tilled material to a lower-lying neighbour (TIlocal, [m]) is a function of the potential tillage
125
parameter TIpot [-], local slope and plough depth. TIpot is distributed over all lower-lying neighbouring cells, proportional to
their slopes to the power of a convergence factor p [-] (Holmgren, 1994). Then it is multiplied with the slope gradient Λlocal
[m m-1] and the plough depth.
 

  (1)
This formulation was used instead of the conventional diffusion Equation from Govers et al. (1994), because it explicitly
130
considers the effect of plough depth on tillage redistribution. In Govers et al. (1994), this is encapsulated in the tillage
constant ktil. Both equations are equivalent and can be transformed into each other through a bulk density value.
https://doi.org/10.5194/egusphere-2024-1036
Preprint. Discussion started: 18 April 2024
c
Author(s) 2024. CC BY 4.0 License.
6
ChronoLorica’s particle age module keeps track of the location of a small number of OSL particles throughout the
simulations. The fate of the OSL particles is coupled to the sand fraction in the model, which is the fraction that is commonly
selected for OSL dating. The age of the OSL particles is increased with one for every simulation year. The age of particles
135
present in the surficial bleaching layer of predetermined depth is reset every simulation year. The transport and bleaching of
OSL particle ages are modelled as a stochastic process. The probability that a particle is transported as consequence of
mixing or erosion processes is equal to the mass of transported sand [kg] divided by the total mass of sand in the source layer
[kg].
3.1.3 Parametrization
140
The parent material of the soils was based on average parent material properties from CarboZALF-D soils (sand 53%, silt
34%, clay 13%). The initial topography was derived from reconstructions based on soil profile truncations and colluvial
additions to the current landscape (reconstruction 2c, Van der Meij et al., 2017). The initial soil profiles were 2 meters deep,
consisting of 40 layers of 5 cm. The amount of OSL particles was set to ~150 grains per layer and the bleaching depth was
set to 5 mm. Simulations were 5000 years, through which plough depth and tillage intensity changed based on values in
145
Table 1 and the calibrated tillage intensities (Section 3.2). To mimic the two-stage landscape evolution at CarboZALF-D, the
central kettle hole, with the size of the current peat extent, was only included in the last ~200 years, following the artificial
drainage. Model output was provided every 100 years during most of the simulations and every 10 years after the artificial
drainage.
3.2 Inverse modelling
150
The unknown parameter in the tillage equation (Eq. (1)) is the potential tillage parameter TIpot. This parameter was calibrated
using the OSL dates from Van der Meij et al. (2019) through inverse modelling. These OSL samples were taken from five
different locations in the colluvial depression (Figure 1). Samples taken from the soil buried below the colluvium and from
the plough layer were excluded, leaving 27 OSL samples. To account for changes in TIpot in time, the periods of different
management types were aggregated to three periods with each their own potential (but unknown) tillage rate (Table 1). For
155
each period, the average introduction year and plough depth were used in the inverse modelling (Figure 2). The first period is
the ard plough period, from the start of the simulations (3000 BCE) until 550 CE, with seven OSL dates covering this
timeframe. The second period is the Medieval mouldboard plough, lasting until 1800 CE. There are no OSL dates that fall in
this period, probably because sediments from this period located on the fringes of the depression have been re-eroded when
the central depression was reclaimed. It was still possible to calibrate a TIpot for this period based on the total amount of
160
sediments that was required for filling the central depression without eroding the fringes beyond where the OSL dates from
period 1 were located. The final period lasted until the end of the simulations and represents the use of the modern
mouldboard plough. For this period there were 20 OSL dates.
https://doi.org/10.5194/egusphere-2024-1036
Preprint. Discussion started: 18 April 2024
c
Author(s) 2024. CC BY 4.0 License.
7
Figure 2: Workflow for the inverse modelling and uncertainty analysis in this study.
165
For each OSL sample, the equivalent layer at the same location and same depth in the simulated soil landscape was
identified and the mode of its age distribution was derived. For samples for which there was no equivalent layer, for example
due to too thinly simulated colluvium, a dummy age of two times the simulation time was used to ensure that such an error
was penalized heavily. The three TIpots were calibrated by minimizing the absolute difference between the modes of the
measured and simulated age distributions.
170
3.3 Uncertainty from initial and boundary conditions
The initial and boundary conditions come with uncertainties, as is evidenced by the interpolation uncertainty of interpolated
soil and colluvium thickness reported in Van der Meij et al. (2017) and the ranges of introduction years and plough depths in
Table 1. This uncertainty was accounted for in the reconstruction of erosion rates by doing a sensitivity analysis after the
model calibration (Figure 2). For the initial topography, 10 realizations of interpolated soil and colluvium thickness were
175
made using Sequential Gaussian Simulation with the gstat package version 2.1-1 (Pebesma and Gräler, 2023), which
randomly samples unique initial landscapes within the interpolation uncertainty. For the boundary conditions, 20 land use
histories with corresponding plough depths were randomly sampled from the values in Table 1, assuming uniform
distributions for each range of values. The combination of the different initial topographies and land use histories produced
200 unique model runs, from which the average and 2-sigma error ranges of rates of landscape change are presented in the
180
remainder of this paper.
https://doi.org/10.5194/egusphere-2024-1036
Preprint. Discussion started: 18 April 2024
c
Author(s) 2024. CC BY 4.0 License.
8
3.4 Evaluation
The simulated topographical changes and erosion and deposition rates from ChronoLorica were evaluated with different
geochronological and erosion datasets. The simulated spatial patterns of erosion and deposition in the calibrated model run
were compared with reconstructed elevation changes from Van der Meij et al. (2017). The simulated erosion and deposition
185
rates resulting from the sensitivity analysis were compared with rates derived from OSL, 10Be, 137Cs, 239+240Pu and 14C data
(Aldana Jague et al., 2016; Calitri et al., 2019; Van der Meij et al., 2019).
4 Results
4.1 Model calibration
Figure 3 shows the measured and calibrated age-depth profiles for all sampling locations. The calibrated depth-profiles
190
follow the measured profiles, although some profiles are overall younger than simulated (P3, BP5), whereas other profiles
are overall older than simulated (BP8). The thickness of the colluvium is simulated thinner than observed for the fringe
positions P2 and P3, while it is simulated similar or thicker for the locations in the central depression.
Figure 3: Depth plots showing the modes of the measured and simulated ages of the calibration run with the lowest error. The
195
horizontal dashed lines indicate the observed levels of the fossil surface below the colluvium and the current soil surface.
https://doi.org/10.5194/egusphere-2024-1036
Preprint. Discussion started: 18 April 2024
c
Author(s) 2024. CC BY 4.0 License.
9
The calibrated tillage parameters show an increase through time and thus agricultural intensification, with 0.13 for the period
of the ard plough, 0.16 for the period of the Medieval mouldboard plough and 0.38 for the period of the modern mouldboard
plough. When including the differences in ploughing depth in these periods (Table 1), which also affect tillage erosion rates
(Eq. (1)), the intensity of tillage erosion and deposition for both historical periods were 8% and 19% of the contemporary
200
tillage intensity.
Since OSL particle tracing operates as a stochastic process, the distribution and ages of particles will be different between
runs. To assess the impact of this on the calibration, a simulation was repeatedly performed with the same parameter set.
This resulted in a relative error of 0.2% in the calibration error, and had no discernible effect on the overall calibration
outcomes.
205
4.2 Reconstructed and simulated elevation changes
The simulated elevation changes with ChronoLorica resemble the reconstructed elevation changes by Van der Meij et al.
(2017) (Figure 4A, B). The extent of the central colluvium is smaller in the simulated elevation changes, while the size of
depositional areas on the hillslope is slightly larger. The differences between the reconstructed and simulated elevation
changes (Figure 4C) indicate that the simulations predicted slightly more erosion (mean error (ME) = 0.03 m), less
210
deposition (ME = -0.15 m), and overall less elevation change in the catchment (ME = -0.04 m compared to the
reconstructions.
Figure 4: Elevation changes derived from A) reconstructions with field data (Van der Meij et al., 2017), B) the calibrated
simulations and C) the difference between both maps (simulated minus reconstructed). Contour lines indicate elevation differences
215
of 0 m.
4.3 Erosion and deposition rates
The simulated erosion and deposition rates vary by two orders of magnitude over time (Figure 5A). The catchment-averaged
rates (dashed lines) show the same trend as the 95th percentile of elevation change (solid lines), but are on average 3-4 times
https://doi.org/10.5194/egusphere-2024-1036
Preprint. Discussion started: 18 April 2024
c
Author(s) 2024. CC BY 4.0 License.
10
lower. Both erosion and deposition rates start relatively high at the start of the simulations and drop an order of magnitude
220
during the period of ard ploughing. The transition to the period of the Medieval mouldboard plough shows an increase of the
rates. The rates in the period of the modern mouldboard plough are again much higher, ranging up to 1 cm per year for the
95th percentile of the simulated rates. The uncertainty of the erosion and deposition rates is relatively constant through time,
except during the switch from one plough regime to the next, which is especially evident for the uncertain transition from ard
to Medieval mouldboard period. The simulated variation in erosion rates is 12-16% due to uncertain initial and boundary
225
conditions. Uncertainties from these sources contribute in almost equal amounts to the overall uncertainty in rates of
landscape change, but do show different temporal patterns (Figure 5B). Uncertainty derived from the initial conditions is
highest at the start and diminishes throughout the simulations as the tillage process smoothes different landscapes to similar
end products. Uncertainties from boundary conditions start at lower levels and diminish throughout a ploughing period, but
increase again during shifts in management regime.
230
Rates derived from the experimental geochronological data follow the same trends as the simulated rates. In-situ and
meteoric 10Be show rates in and below the lower regions of the simulation. The catchment-averaged rates derived with 137Cs
is in the same order of magnitude as recent simulated catchment-averaged erosion and deposition rates. Rates derived with
OSL and 239+240Pu lean towards the higher end of the simulated rates.
With the exception of the first ~1000 years, catchment-averaged deposition rates are 1-1.5 times higher than erosion rates
235
(Figure 5C). In the last ~220 years, following the drainage and cultivation of the central depression, deposition rates were up
to five times as high as the erosion rates.
https://doi.org/10.5194/egusphere-2024-1036
Preprint. Discussion started: 18 April 2024
c
Author(s) 2024. CC BY 4.0 License.
11
Figure 5: A) Compilation of simulated and measured erosion and deposition rates. Simulated rates are provided in the blue
[erosion] and orange [deposition] bands and lines, for the catchment-averaged rates (dashed lines) and the 95th percentile of
240
erosion and deposition rates to represent severe erosion and deposition locations (solid lines). Experimental data is provided with
either rectangles representing their representative periods and corresponding rates with uncertainty, or as point information.
Closed rectangles and symbols represent erosion rates, while open rectangles and symbols represent deposition rates. All provided
uncertainties are 2-sigma intervals, except for 137Cs (80% interval). For 239+240Pu and OSL, uncertainties are not provided, because
they are not provided or they obscure the rest of the Figure. B) Variation in erosion rates coming from uncertainties in initial
245
conditions and boundary conditions, expressed as the standard deviation in catchment-averaged erosion rates. C) Ratio between
deposition and erosion rates, for catchment-averaged and 95th-percentile rates, provided with mean and 2-sigma uncertainty.
Numbers larger than 1 indicate higher deposition rates.
https://doi.org/10.5194/egusphere-2024-1036
Preprint. Discussion started: 18 April 2024
c
Author(s) 2024. CC BY 4.0 License.
12
5 Discussion
5.1 Calibration on spatial data
250
The OSL data gathered from five locations in the depression were used to calibrate temporally varying potential tillage
constants (Figure 3). The measured and modelled age-depth plots are not identical, but do follow the same trends and have
ages in the same ranges. While calibration using data from a single location might yield a more precise calibration line, it
would be based on a smaller dataset and overlook spatial variations in the deposition process. Utilizing spatial calibration
data provided a sufficient number of calibration points for the calibration of the tillage constants while also considering
255
spatial patterns of deposition, which are complex for this kettle hole catchment (Van der Meij et al., 2019).
The match between simulated and reconstructed elevation changes indicates that the calibrated model simulates the
landscape evolution fairly well (Figure 4). The small overestimation of erosion and larger underestimation of deposition
indicate a possible unconsidered source of sediments in the depression, such as a part of the catchment located beyond the
railroad track. However, this discrepancy can also be a result of uncertainties in the reconstruction of elevation changes and
260
the simulations. When considering root mean squared errors (RMSE) of reconstructed versus simulated elevation changes,
the run with calibrated potential tillage parameters of 0.14 and 0.4 for periods 2 and 3 would yield the lowest error. These
values are consistent with the calibrated parameters using the OSL datings (0.13 and 0.38 respectively), and provide another
line of evidence for the plausibility of the calibrated parameters.
TIpot functions in the same fashion as the parameter B in the Equation of the tillage constant ktil from Govers et al. (1994).
265
Through the bulk density and plough depth, the calibrated TIpot can be converted to ktil. Öttl et al. (2023) made an extensive
compilation of experimental ktil values from different machineries and plough types and placed them along a timeline of
agricultural use over the last 1000 years for the region around CarboZALF-D. The values from this study fall in the lower
range of the compiled values, and the value for the ard plough (11.7 kg m-1) is even under the lowest reported value. This
could be explained by much less intense land reworking in the prehistoric times than in more recent uses of the ard plough.
270
The value for the Medieval mouldboard period (27.6 kg m-1) is above the lowest reported values for the first reported
mouldboard uses. Calibration of this period was complicated due to the lack of OSL dates falling in this time period, and
therefore the calibrated parameter should be considered with care. The values for the modern mouldboard plough match
better with the compilation of tillage constants, where the values for the period around 1800 (91.2 kg m-1) is similar to the
median reported value and the value for the recent period with heavy machinery (156.8 kg m-1) is above the 25th percentile.
275
Overall, the calibrated values for the last 200 years match well with the compilation of Öttl et al. (2023) and provide local
estimates for tillage constants for future tillage erosion studies.
5.2 Effect of uncertainties
Uncertainty in reconstructed initial and boundary conditions and model formulation will propagate through the model
simulations and affect the accuracy of the model outcomes (Perron and Fagherazzi, 2012; Temme et al., 2017). This
280
https://doi.org/10.5194/egusphere-2024-1036
Preprint. Discussion started: 18 April 2024
c
Author(s) 2024. CC BY 4.0 License.
13
uncertainty propagation is often neglected due to limited information on the level of uncertainty associated with the model
inputs. The CarboZALF-D area provides a unique setting for assessing the effects of uncertain initial and boundary
conditions on model output, as these initial and boundary conditions including uncertainty are well-constrained, the
landscape evolution is complex but only subject to one main process and there is independent data for verifying the
calculated erosion and deposition rates. The relative standard deviations of the simulated erosion and deposition rates range
285
between 12 and 16%. Variations in initial and boundary conditions contribute in equal amounts to the overall uncertainty in
erosion rates in the catchment, but do so show different temporal patterns (Figure 5B). The effect of uncertainty in the initial
landscape on the variation in erosion rates is mainly visible at the start of the simulations, after which it diminishes to a
steady low level. Uncertainty in the boundary conditions affects variation in erosion rates at the start of the simulations and
after shifts in plough regime. This suggests that, over the entire simulation period, the overall landscape change is only
290
affected to a small degree by the uncertainty in the inputs.
These simulations did not consider uncertainties in model parameters, although these also can affect model outputs (Skinner
et al., 2018). The uncertainty in the tillage parameters could potentially be quantified by considering uncertainty in initial
and boundary conditions during the calibration, but this would require an unrealistic number of simulations and runtime.
This study required about 160 model runs for the full calibration using fixed initial and boundary conditions, each run taking
295
approximately three hours. Considering the uncertainties in the inputs would require 200 times more simulations,
corresponding to ~11 CPU years at the time of writing.
5.3 Comparison of erosion and deposition rates
The inverse modelling provided spatial and temporal variations in erosion rates, based on the deposition rates derived from
OSL dating (Figure 5A). Pre-industrial catchment-averaged erosion rates were in the order of 1 t ha-1 a-1, resembling natural
300
soil production rates and erosion rates under present-day conservation agriculture and exceed erosion rates under natural
vegetation (Alewell et al., 2015; Minasny et al., 2015; Nearing et al., 2017). Erosion rates under the modern mouldboard
plough are almost an order of magnitude higher (5-10 t ha-1 a-1), with local extreme erosion rates ranging up to 100 t ha-1 a-1.
T