Introduction
Soil is the interface between earth, air and water and hosts most of the
biosphere. As soil formation is an extremely slow process, soil can be
considered essentially as a non-renewable resource. Soil is recognized as a
strategic non-renewable resource that, in addition to the specific relevant
environmental role, assumes also that of a strategic policy framework for
competitiveness. Therefore, specific policies and actions designed to limit
the consumption of soil are required in order to create, where possible, a
barrier to stop the worrying phenomenon of progressive depletion of the
resource with a consequent acceleration of erosion and geological
instability. The prerequisite for the effective protection of the territory
is to monitor processes at different spatial and temporal scales and use the
obtained database to formulate, calibrate and validate predictive models
needed to define the “risk areas” and to quantify this risk. Usually, these
models must be properly calibrated and validated over the territory in which
they are used, making use of databases and studies carried out on a local
scale (Bagarello et al., 2011, 2014; Butzen et al., 2014; Cerdà, 1998; Di
Stefano et al., 2005; Kinnell, 2010; Leh et al., 2013; Morgan and Nearing,
2000; Porto et al., 2014; Vrieling et al., 2014).
Regarding soil erosion, the Universal Soil Loss Equation, USLE (Wischmeier
and Smith, 1978) is the most used empirical model for the estimation of the
long-term average annual soil loss of a plot associated with sheet and rill
erosion. The USLE estimates the soil loss using six factors that are
associated with climate, soil, topography, vegetation and soil management.
The USLE is considered the best compromise between applicability in terms of
required input data and reliability of the soil loss estimates (Risse et al.,
1993). It was originally formulated to estimate the soil loss in rural areas
of the USA, and then extended in the Revised USLE, RUSLE (Renard et al.,
1997) and further modifications (RUSLE1, RUSLE2, Foster et al., 2003). The
RUSLE conserves the same mathematical structure of the USLE, the revision
being limited to the estimating procedure of some of the involved factors.
Currently, the USLE/RUSLE is widely applied in Europe and in many other
Mediterranean countries for practical purposes (e.g., Larson et al., 1997;
Huang, 1998; Rejman et al., 1999; Bagarello and Ferro, 2004; Morgan, 2005;
Parsons et al., 2006; Bagarello et al., 2008, 2010, 2011, 2012; Ligonja and
Shrestha, 2013). The process-based models characterized by low computational
efforts fail to produce better results than the USLE/RUSLE model (Tiwari et
al., 2000). Consequently the USLE/RUSLE model is often used for purposes for
which it was not designed (Kinnell, 2010). In particular, it is widely used
in watershed models even at the event temporal scale. However, it was found
in the scientific literature (Todisco et al., 2009; Bagarello et al., 2008;
Risse et al., 1993) that the USLE/RUSLE model, and similarly (Tiwari et al.,
2000) process-oriented models (e.g., Water Erosion Prediction Project, WEEP,
Flanagan et al., 1995), tends to overestimate (underestimate) soil losses for
low (high) erosive events. Foster et al. (1982) noted that the USLE model is
somewhat unsatisfactory for estimating soil loss from individual storms, and
observed that including rainfall amount, rainfall intensity and runoff amount
in the erosivity factor provided better performance. Foster et al. (1982)
also noted that erosivity factors with separate terms for rainfall and runoff
erosivity were more appropriate. Successively, Kinnell (1997) suggested that
the sediment concentration for individual rainfall event is dependent on the
event rainfall erosivity index per unit rainfall depth and developed the
so-called USLE-M model, including direct measures of the runoff in the event
rainfall–runoff erosivity factor (Kinnell and Risse, 1998; Kinnell, 2007,
2010; Bagarello et al., 2011). Bagarello et al. (2010), by using soil loss
and runoff data for a relatively high number of simultaneously operating
plots of different length (11–44 m) established at the experimental station
of Sparacia in southern Italy (clay soil), developed a modified version of
the USLE-M, named USLE-MM, in which the event rainfall–runoff erosivity
factor is raised to a power greater than 1. The USLE-MM was found to
perform better than both the USLE and the USLE-M at Sparacia site (Bagarello
et al., 2008, 2010, 2014), and it was also successfully applied at the Masse
station in central Italy, silty–clay–loam soil (Todisco et al., 2009;
Bagarello et al., 2013).
Even if including runoff in the USLE/RUSLE model improves its accuracy, it
should be highlighted that the measurement of the event runoff is not
straightforward. At experimental stations, the surface runoff is generally
collected into specific storage tanks allowing the estimation of the event runoff
by measuring the amount of water in the tanks after the end of each rainfall
event (Todisco et al., 2012a)
However, this procedure is time consuming and expensive, and it requires
specific measurement campaigns. Otherwise, the water amount collected in the
tanks could be measured by hydrometric gauges that, unfortunately, require
strong maintenance and are not easy to be realized. It should be also
underlined that by using the measured runoff, the same quantity (runoff) is
used both for estimating the event soil losses (given by the product of
runoff and the bulk sediment concentration in the tanks) and in the
rainfall–runoff erosivity factor thus introducing a conceptual issue in the
model determination procedure.
Summary statistics of the 22 m long plot data available at the Masse
site.
Plot size
s
L S
Ne
he
Re
Nm
Qe,i
Ae,i
μ
CV
μ
CV
μ
CV
μ
CV
22 × 8
16
2.04
62
35.4
65.2
81.8
102.6
113
3.6
136.6
4.1
221.5
22 × 4
16
2.04
53
33.2
66.6
75.1
110.0
98
2.4
145.7
2.8
260.7
s, slope steepness ( %); L S, USLE topographic factors;
Ne, number of events per plot scheme; he, event
rainfall depth (mm); Re, event rainfall erosivity factor
(MJ mm ha-1 h-1); Nm, number of measurements per plot
scheme; Qe,i, plot event runoff volume (mm); Ae,i, plot event soil
loss (Mg ha-1); μ, mean; CV, coefficient of variation
(%).
In the absence of direct measurements, runoff can be estimated through
rainfall–runoff modeling. This usually needs a specific calibration of
the parameters (and structure) to provide satisfactory results which are not
easily applied at the plot scale. Therefore, notwithstanding the USLE-M
and USLE-MM models have a noticeable practical interest, these models are
difficult to be applied over large areas mainly for the need to also predict
event runoff (Bagarello et al., 2014). The same issue can be found in other
existing USLE-derived models, such as MUSLE (Williams, 1975; Williams and Berndt,
1977), EPIC (Williams et al., 1984a,b) and APEX (Williams et al., 2008),
which explicitly consider the runoff characteristics, even with a certain detail,
for the estimation of soil losses. Efforts have been recently made in order
to incorporate reliable and parsimonious methods for the runoff estimation in
the USLE-derived models. However, it is evident that a poor estimation of
event runoff will produce a low-accuracy forecast of the soil loss. Gao et
al. (2012) coupled a modified SCS-CN (Soil Conservation Service curve
number) and RUSLE model for runoff and soil loss simulation at plot scale in
the Loess Plateau. In RUSLE2, runoff prediction for storm events is obtained
using the SCS-CN method with empirical equations that vary the values of CN
in association with both soil moisture and rainfall intensity (Kinnell,
2014). Todisco et al. (2012b) evaluated the efficiency of the MISDc model
(Modello idrologico semidistribuito in continuo, Brocca et al., 2011a),
coupled with an USLE-derived model, for the estimation of surface runoff and
soil loss at the event timescale at Masse experimental station. The model
performance is found to be promising, but it was underlined that the
antecedent soil moisture proved to be a good alternative with respect to
runoff for correcting the rainfall–runoff erosivity factor in the USLE-MM
model. These preliminary results open interesting scenarios for improving the
capability of USLE-derived models in predicting the unit soil loss at the
event scale. Indeed, measuring in situ soil moisture is much easier
(e.g., by using Time Domain Reflectometry, Brocca et al., 2014a) and less
expensive than estimating surface runoff. Moreover, the recent widespread
availability of satellite-derived soil moisture data (e.g., Wagner et al.,
2013) might allow one to easily apply over large areas a modified USLE/RUSLE
model incorporating this information. In summary, it could be highly
beneficial to find a procedure for incorporating soil moisture in the
erosivity factor rather than runoff coefficient as in previous investigations
(e.g., Kinnell, 2010; Bagarello et al., 2014).
The main objective of this study is to investigate the use of
satellite-derived and modeled soil moisture data for improving the
prediction of unit soil loss through a modification of USLE-based models.
Specifically, it is expected that modeled soil moisture data will provide
better performance, but they require continuous meteorological observations
not always available. Satellite data, even though with an expected lower
accuracy, have the enormous advantage of being available on a global scale, thus
allowing model application everywhere. The Masse experimental area
(Umbria, central Italy) is used as a case study in which rainfall, air
temperature, soil losses and runoff are measured at the event timescale for
different bare plots in the period 2008–2013. The satellite soil moisture
product is obtained from the Advanced SCATterometer (ASCAT) through the
TUWien algorithm (Wagner et al., 2013). Moreover, modeled soil moisture data
obtained from the soil water balance model (SWBM) developed by Brocca et
al. (2014b) are also considered. The specific objective of this study is to
evaluate the opportunity of coupling soil moisture and rainfall data for
correcting the erosivity index of the USLE model. For comparison, the results are
evaluated against those obtained by the standard USLE/RUSLE and USLE-M-based
models in previous investigations (Todisco et al., 2012b).
Materials
The Masse experimental station and the soil loss database
The Masse experimental station for soil erosion measurements (Fig. 1) of the
Department of Agricultural, Food and Environmental Sciences, Perugia
University, is located 20 km south of Perugia, in the region of Umbria
(central Italy).
The soil is Typic Haplustept (Soil Survey Staff, 2006) with a
silty–clay–loam texture (clay = 34 %, silt = 59 % and
sand = 7 %). The soil has a polyhedral angle structure and the gravel
content is negligible. The Ap horizon has a depth of approximately 0.40 m.
The meteorological data are monitored by a weather station located within the
experimental site and are recorded at a time resolution of 5 min. The station
includes plots of different length λ = 11 and 22 m and width w=2, 4 and 8 m. All plots are oriented parallel to a 16 % slope and are
maintained in a cultivated fallow by obliterating the rills at the end of
each erosive event. The total runoff amount and the soil loss per unit area
are measured in each plot after an erosive event, defined as an event
yielding a measurable soil loss. The Masse database was therefore developed
by considering, for each event, the simultaneous measurements of plot runoff,
Qe,i, and soil loss, Ae,i, and of the rainfall data required to
derive the erosivity factor, Re, according to Wischmeier and
Smith (1978), with a mean interval time of 6 h (Bagarello and Ferro, 2004;
Mannocchi et al., 2008; Todisco, 2014). The study area and the experimental
schemes, installations and procedures are already described more in depth in
Bagarello et al. (2011) and Todisco et al. (2012a).
For the purposes of this investigation, only the data collected on the
λ=22 m plots (two plots with w= 4 m and two plots with w=8 m) were considered. A total of 63 erosive events were monitored in the
years from 2008 to 2013. Over 70 % of them (45 events) occurred during
the wet period (from October to May). In the 22 m × 8 m
experimental schemes, 62 events yielded a measurable runoff, corresponding to
113 plot measurements. In the 22 m × 4 m schemes, 58 events were
erosive, corresponding to 98 plot measurements. The plot data used in this
investigation are summarized in Table 1.
View of the Masse experimental station for monitoring water soil
loss at plot scale in Umbria (central Italy).
![]()
Soil moisture from satellite data
The satellite soil moisture product adopted in this study was obtained from
the ASCAT radar scatterometer onboard the Metop satellites. ASCAT measures
radar backscatter at the C-band (5.255 GHz) in VV polarization. Specifically,
the product delivered through the “Satellite Application Facility on Support
to Operational Hydrology and Water Management (H-SAF)” project is used.
Global coverage over Europe is achieved in ∼ 1.5 days, while in Italy
measurements are available about once a day. The spatial resolution of the
soil moisture product is 25 km with a sampling distance of 12.5 km. The
surface soil moisture product is calculated from the backscatter measurements
through a time-series-based change detection approach (Wagner et al., 1999,
2013). The soil moisture product obtained is expressed in terms of degree of
saturation, from 0 % (dry) and 100 % (wet). The product obtained
provides knowledge of soil moisture for a very thin surface layer (about
2 cm), whereas a root-zone soil moisture product would be required for the
prediction of soil losses. Even though an exact quantification of the depth
of the root zone is not possible, in this study we considered that a layer
depth of 15 cm is required. Therefore, the Soil Water Index (SWI) method
(Wagner et al., 1999) was employed to convert surface soil moisture
observations into a root-zone soil moisture product (i.e., the SWI). This
method relies on the estimation of a single parameter, the characteristic
time length, T, that was obtained by calibration. The reader is referred to
Wagner et al. (1999) for more details on the SWI approach. Lastly, the data
were converted in volumetric units (m3 m-3) through a linear
rescaling approach (Brocca et al., 2011b) for matching the range of
variability of satellite and modeled soil moisture data provided by the
SWBM. The ASCAT data for the pixel closest to the Masse study area were used.
The ASCAT soil moisture product was already validated in central Italy
through the comparison with in situ observations by Brocca et al. (2010,
2011b). The obtained accuracy (RMSE) was found to range between 0.03 and
0.07 m3 m-3.
Methods
Soil Moisture for Erosion model
A USLE-derived model to predict the unit event soil loss was formulated,
parameterized and tested with the use of soil moisture in the rainfall–runoff
erosivity factor. The model was derived from the USLE:
A=R⋅K⋅L⋅S⋅C⋅P,
where A is the mean annual soil loss (Mg ha-1 yr-1) over the
long term (e.g., 20 years), R (MJ mm ha-1 h-1 yr-1) is
the rainfall–runoff erosivity factor, and K (Mg h MJ-1 mm-1) is
the soil erodibility factor. L and S are the topographic factors
depending on the slope length and gradient, C is the crop management
factor, and P is the soil conservation practice factor. L, S, C, and P are
dimensionless factors. Equation (1) with the erosivity factor calculated for
the single erosive event, Re (MJ mm ha-1 h-1), is
also used to determine the plot soil loss at the event temporal scale,
Ae (Mg ha-1), and the corresponding unit value,
Aue, as follows:
Aue=AeL⋅S⋅C⋅P=Re⋅K.
Equation (2) estimates the average event soil losses fairly well, but it
tends to overestimate the lowest and underestimate the highest values
(Kinnell, 2010). The reason for this is found in the lack of explicit
consideration of runoff. Indeed, although the rainfall erosivity and the soil
erodibility are responsible for the detachment of soil particles, it is the
runoff that transports the detached particles causing the soil loss.
Therefore the USLE model has been further modified to account for the
relationship between soil loss and runoff. Two well-known examples are the
USLE-M (Kinnell and Risse, 1998) and the USLE-MM (Bagarello et al., 2008)
models, in which the event rainfall–runoff erosivity factor is given by the
product of Re and the runoff coefficient Qr=Qe / he, with Qe (mm) being the event runoff
and he (mm) the rainfall depth, as follows:
Aue=Ku⋅Qr⋅Reα
with α=1 in the USLE-M and α > 1 in the USLE-MM
and where Ku varies in accordance with the selected model.
In this study, the Eq. (3) was modified using soil moisture, θ, in
place of the runoff coefficient, Qr, in the rainfall–runoff
erosivity factor. The following model was finally formulated and named Soil
Moisture for Erosion (SM4E) model:
Aue=Kuθ⋅θ⋅Reα.
With α=1, the SM4E model is linear; that is, Aue
increases linearly with the erosivity factor corrected with the soil water
content, θ⋅Re. With α > 1, the
SM4E model is a power law; that is, the Aue, is proportional to
the power of θ⋅Re.
Equation (4) was parameterized and tested using soil moisture data estimated
by a soil water balance model (SWBM), θ=θest, and
derived from satellite observations θ=θsat.
Soil water balance model
The soil water balance model (SWBM, Brocca et al., 2008, 2014b) was used to
estimate the temporal evolution of soil moisture from standard meteorological
data. SWBM considers the surface soil layer as a spatially lumped system, for
which the continuous time variation of soil moisture is derived from the
application of the soil water balance equation, taking into account the
infiltration, evapotranspiration and drainage processes. The infiltration
rate is estimated using the Green–Ampt equation. The empirical relation of
Blaney and Criddle, as modified by Doorenbos and Pruitt (1977), is used to
determine the potential evapotranspiration, from which the evapotranspiration
rate is computed. The drainage rate is derived with the relation proposed by
Famiglietti and Wood (1994). The model requires rainfall and air temperature
data as input and incorporates five parameters that are optimized as
described later in the paper. Further details on SWBM, with the full list of
equations, are given in Brocca et al. (2014b).
Time series of satellite-derived and estimated (through the SWBM)
soil moisture at the beginning of 63 erosive events in the study period
2008–2013.
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The soil water balance model was extensively validated with actual soil
moisture measurements in different studies already published in the
scientific literature (Brocca et al., 2008, 2013, 2014b; Lacava et al.,
2012). Specifically, in Brocca et al. (2013) the model was validated exactly
in the same study area by obtaining reliable and satisfactory results. Based
on previous studies, the accuracy (RMSE) of SWBM was found to range between
0.02 and 0.04 m3 m-3 when compared with in situ measurements. On
this basis, we believe the soil water balance model is an appropriate tool
for obtaining reliable soil moisture estimates.
Calibration and testing
The SM4E model, Eq. (4), and the SWBM model require calibration. The measured
soil loss data at the different plots of the Masse experimental station were
used for this purpose. Specifically, only the 22 m long plots were
considered. The average value of the unit soil loss, Aue, was
then computed by using Eq. (2) in which, specifically, Ae is the
mean of the plot measures; C and P equal values that are assumed equal to 1 as
bare plots were used; the topographic factors, L and S, were calculated
(see Table 1) according to the relations proposed by Wischmeier and Smith
(1978), Eq. (5) and by Nearing (1997), Eq. (6).
L=λ22.13m,
where λ (m) is the plot length and m is an exponent. In the USLE,
m is equal to 0.5 if slope steepness, s, is greater than or equal to
5 %.
S=-1.5+171+exp(2.3-6.1sinβ),
where β is the slope angle.
For the analysis, the database of erosive events was split to define a
calibration and a validation set of events: the 63 events were arranged in
descending order with respect to the Aue values and alternatively
assigned to the calibration (n=32 events) or the validation set (m=31 events). The calibration set was used to optimize the five
parameters of the SWBM, the characteristic time length of the SWI method, and
the two coefficients (Kuθ and α) of the SM4E models. The
parameters were defined maximizing the coefficient of determination R2,
of the regression between the measured Aue and the erosivity
factor θ⋅Re, with θ=θest and
θ=θsat. For the power model
(α> 1), R2 is computed by a linear regression on a
logarithmic scale, while for the linear model (α=1), as the
regression line is forced to pass through the origin, R2 is computed on
a linear scale as
R2=1-∑j=1nAue,j-Aue,est,j2∑j=1nAue,j2,
where Aue,est,j is the estimated value of Aue for
the jth erosive event (i.e., the soil loss that would result from the
regression models), and n is the number of erosive events in the calibration
subset. The validation set was used to test the accuracy and robustness of
the regression models SM4E, which was evaluated by the RMSE between the
measured and the estimated Aue values.
The effectiveness of the event soil loss models was also compared with that
of the USLE-derived models with a simulated runoff coefficient in the
erosivity factor (Kinnell, 2015; Todisco et al., 2012b). In particular
Todisco et al. (2012b) coupled the USLE models with a continuous
rainfall–runoff model, MISDc (Brocca et al., 2011a), for the estimation of the
runoff volumes. MISDc incorporates a limited number of parameters and it is
characterized by low computational efforts. The input data required are only
rainfall and air temperature. Besides runoff, the model simulates also the
temporal evolution of soil moisture.
In this paper, the analysis performed in Todisco et al. (2012b) was extended
to the current 63 erosive events. The MISDc model was parameterized,
maximizing the Nash–Sutcliffe efficiency index between the estimates
Qe,est and the corresponding observed Qe values of
the set of calibration events. A regression analysis was also performed
between the observed Aue and the erosivity indices
Re, Qr,est⋅Re and (Qr,est⋅Re)α. The accuracy of the regression models in soil
loss estimation was evaluated by RMSE between the estimates
(Aue,est) and the measurements (Aue) of the set of
validation events.
Results and discussion
Soil moisture estimation through modeled and satellite data
Based on the procedure mentioned above, the parameter values of the SWBM and
of the SM4E models were obtained by maximizing the R2 value between the
observed and estimated Aue values in the calibration events.
Figure 2 shows the temporal evolution of the modeled and satellite soil
moisture data at the beginning of the 63 erosive events that occurred during the
2008–2013 study period.
Even though the parameters of the SWBM and of the SWI method were calibrated
for reproducing soil losses, and not for making the two soil moisture
data sets match each other, a very good agreement among the soil moisture time
series is evident. Indeed, a very low RMSE = 0.03 m3 m-3
was obtained, even for the validation sets. These results confirm the
capability of the ASCAT-derived soil moisture product to provide high-quality
measurements in central Italy (Brocca et al., 2010, 2011b), even though the
spatial mismatch between satellite and ground data is significant. As has
already been shown in the scientific literature, these unexpected good
results must be attributed to the statistical properties of soil moisture
spatial patterns. Indeed, the temporal dynamics of soil moisture field is
often very similar across a wide range of scales – a phenomenon usually
referred to as “temporal stability” (e.g., Brocca et al., 2011b, 2014a).
Therefore, local point measurements can be used for obtaining an estimate of
soil moisture over large areas (Brocca et al., 2009) and, vice versa, coarse-scale soil moisture measurements can be properly used for small-scale
applications (Brocca et al., 2012).
Regression models between measured soil loss Aue and
the erosivity indices θ Re and QrRe
of the calibration subset. Linear models (a), (b),
(c): SM4E model and satellite soil moisture (a); SM4E model
and estimated soil moisture (b); USLE-M model and estimated runoff
coefficient (c). Power models (d), (e),
(f): SM4E model and satellite soil moisture (d); SM4E model
and estimated soil moisture (e); USLE-MM model and estimated runoff
coefficient (f).
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Calibration parameters and validation root mean square error for the
SM4E models (Eq. 4).
Erosivity factor
All the events
Wet period events
RMSE (Mg ha-1)
Ku,θ
α
RMSE (Mg ha-1)
Ku,θ
α
θsat Re
3.07
0.178
–
1.10
0.174
–
(θsat Re)α
3.04
0.007
1.70
1.15
0.042
1.14
θest Re
2.85
0.180
–
1.63
0.270
–
(θest Re)α
2.80
0.006
1.78
1.26
0.043
1.29
RMSE: root mean square error; Ku: scale factor; α: exponent
for the erosivity factor.
Estimation of SM4E model parameters
The scatterplots in Fig. 3 show the regressions between the soil loss and the
erosivity factor θ Re with α≥1 both with
θ=θsat (Fig. 3a and d) and θ=θest (Fig. 3b and e) for the set of calibration events. The
linear SM4E models (α=1) are very similar in the scale factors
Ku,θ= 0.178 and 0.180. The coefficient of determination using
satellite soil moisture data θ=θsat, R2=0.358,
is higher than that obtained with the simulated soil moisture data θ=θest, R2=0.325. Also the power SM4E models are similar
both in the scale factors equal to 0.007 and 0.006, and in the exponent
α equal to 1.69 and 1.77 for the modeled and satellite data,
respectively. The coefficient of determination is slightly higher for the
θ=θest (R2=0.501), than for θ=θsat (R2=0.462), and in any case much higher than the
linear models. The parameters for the SM4E models are given in Table 2 (all
the events). The white dots in Fig. 3 represent the events that occurred
during the dry period (from June to September), which will be commented on
later in the paper. The erosivity index θRe performs better
when raised at an exponent α > 1, making it possible
to obtain higher coefficients of determination R2.
Soil losses estimated by SM4E models
The calibrated SM4E models were then tested with the validation set to
estimate the soil loss, Aue,est, by using the corresponding
satellite soil moisture retrievals, θ=θsat, or the
modeled ones, θ=θest, and event rainfall data. The
results are given in Fig. 4, by showing the dispersion of the
(Aue, Aue,est) pairs around the 1:1 line for the
linear model (Fig. 4a and b) and the power model (Fig. 4d and e). The results
in terms of RMSE are derived and given in Table 2 (all the events). With
satellite soil moisture, θ=θsat, the RMSE obtained
with the linear SM4E model is equal to 3.07 Mg ha-1 (R2 = 0.329)
and decreases slightly to RMSE = 3.04 Mg ha-1 (R2 = 0.371)
when the power model is used. The errors decrease, even if not
substantially, using estimated soil moisture θ = θest,
with RMSE = 2.85 Mg ha-1 (R2 = 0.401)
and RMSE = 2.80 Mg ha-1 (R2 = 0.338) with linear
and power models respectively. The better performance of SM4E when using
modeled data is due to the expected better accuracy of SWBM (∼ 0.03 m3 m-3)
with respect to satellite data (∼ 0.05 m3 m-3).
Moreover, the linear and the power models are compared in terms of confidence
intervals of the regression coefficients. The uncertainty is estimated as the
percentage of the size of the 90 % confidence interval with regard to the
corresponding coefficient value. The results show that the uncertainty in the
estimation of coefficients is similar (100 %). This result is expected,
given that the data set used is the same. The lowest uncertainty (60 %) is
estimated for the exponent of the power model when the erosivity factor
(θ Re)α is used. Furthermore, for
model comparison, two criteria, namely Akaike information criterion (AIC,
Akaike, 1974) and Bayesian information criterion (BIC, Burnham and Anderson,
2002), are used. According to these criteria the best model provides the
lowest AIC and BIC values. The results show that the power model performs
better than linear model.
The power model provides AIC values of 30.14 and 32.56 respectively for
θ=θest and θ=θsat, which are
lower than the corresponding values, 85.41 and 83.80, derived from the
linear model, thus denoting a statistically significant better accuracy.
Similarly, the BIC values for the power model, 26.47 and 28.89, are lower
than the corresponding values, 83.63 and 82.02, derived from the linear
model. Moreover, according to Nagin and Roeder (2001), the difference
between the BIC values, 57.15 and 53.12, obtained respectively for θ=θest and θ=θsat, can be considered
significant, being greater than 10. The models using (θ Re)α
as erosivity factor (both satellite and simulated
θ) appear to work quite well. We note that the SM4E model
incorporating satellite-derived soil moisture data might effectively and
easily be applied over large areas for the estimation of event water soil
loss.
Comparison with the previous studies at Masse site
The results provide a clear indication that the power models perform better
than the linear models. They also show that the coefficients of determination
of the USLE-derived models that include simulated or satellite-retrieved soil
moisture in the erosivity factor (SM4E models) never exceed the value of 0.5.
This is lower than that obtained by the USLE-M and USLE-MM (R2=0.82),
which include direct measurements of the runoff in the event rainfall–runoff
factor (Todisco et al., 2012b). However, the benchmark for a correct
assessment of the accuracy of the SM4E models is the performance of the
USLE-derived models that include predicted runoff coefficient, Qr,est,
in the event rainfall–runoff factor such as that analyzed by Todisco et
al. (2012b). This analysis was extended to the current database. As stated
earlier the runoff volumes were estimated from the calibrated rainfall–runoff
model MISDc. A paired t test shows that there are no significant (α=0.05)
differences between the observed and the estimated runoff samples in
both the calibration and in the validation sets. Furthermore MISDc provides
fairly accurate event runoff estimates with a Nash and Sutcliffe efficiency
index, NSE = 0.416 between the Qe,est and the observed
Qe of the calibration events and an RMSE = 2.56 mm and
NSE = 0.450 between the validation events.
The regressions models between the soil loss and the erosivity factor
Qr,est Re with α ≥ 1 (Fig. 3c and f)
for the set of calibration events were derived and shown in the scatterplots
of Fig. 3. The coefficient of determination using (Qr,est⋅Re)α, R2=0.304, is higher than that obtained with
the corresponding linear model, R2=0.255. The erosivity index
Qr,estRe performs better when raised to an exponent
α > 1, making it possible to obtain higher coefficients
of determination R2. In all cases the coefficient of determination is
slightly lower than that obtained for the corresponding SM4E models.
Testing of the Aue vs. θ Re and
the Aue vs. QrRe models with the
validation subset. Linear models (a), (b), (c):
SM4E model and satellite soil moisture (a); SM4E model and estimated
soil moisture (b); USLE-M model and estimated runoff coefficient
(c). Power models (d), (e), (f): SM4E
model and satellite soil moisture (d); SM4E model and estimated soil
moisture (e); USLE-MM model and estimated runoff coefficient
(f).
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Comparison of the results obtained by the power SM4E model with
both satellite and estimated soil moisture, the USLE-MM including predicted
runoff, and the original USLE, in terms of root mean square error (RMSE)
and coefficient of determination (R2).
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Comparison of the results obtained by the power SM4E model with
both satellite and estimated soil moisture, the USLE-MM including predicted
runoff, and the original USLE, in terms of deviations between estimated,
Aue,est, and observed, Aue, soil losses. The values
of the estimated runoff and of the mean soil moisture computed as the mean
between the estimated and the satellite-retrieved values are also given.
![]()
Furthermore both the AIC and BIC criteria show that the power model provides
lower values, 40.80 and 37.13, than the linear model, 88.57 and 86.78, thus
denoting a statistically significant better accuracy. As seen earlier,
according to Nagin and Roeder (2001), the difference between the BIC values
obtained, 49.65, can be considered significant. Moreover, the AIC and BIC
values associated with the USLE-derived models with simulated runoff in the
erosivity factors are always higher than those provided by the SM4E models,
which prove to be more efficient. The accuracy of the calibrated models in
estimating the event plot soil loss, Aue,est, was tested with
the validation values of Re and Qe,est. The results are
given in Fig. 4, by showing the dispersion of the (Aue,
Aue,est) pairs around the 1:1 line for the linear model (Fig. 4c)
and the power model (Fig. 4f). The results in terms of RMSE obtained with
the linear model are equal to 2.96 Mg ha-1 and remain almost constant when
the power model is used. The errors are higher, even if only slightly, than
those obtained with the linear SM4E and between those obtained with the two
power SM4E models tested. Figure 5 also shows the comparison between the
results obtained in terms of RMSE and R2 in this study with Eq. (4),
the results obtained by extending the analysis performed in
Todisco et al. (2012b) to the current 63 erosive events, and the results
obtained with the USLE model. Only the results of the power models compared
with the USLE are shown in Fig. 5 since the power models have proven to be
better than the linear models both in this study and in Todisco et
al. (2012b). The accuracy in the estimation of the soil loss by the USLE-MM
model that includes the predicted runoff coefficient in the event
rainfall–runoff factor quantified in an RMSE = 2.96 Mg ha-1 is
higher than that obtained with (θest⋅Re)α
and slightly lower than that derived obtained with
(θsat⋅Re)α (Fig. 5). The worst
performance is that of the USLE model with an RMSE = 3.28 Mg ha-1,
while the lowest coefficient of determination is
obtained for the USLE-MM with estimated runoff (R2 = 0.185). It is
interesting to notice that the accuracy in estimating the event soil loss of
the models with erosivity factor that includes the simulated runoff
coefficient, i.e., (Qr,est⋅Re)α, is overcome
surpassed by at least one model that uses the antecedent soil moisture
θ in the erosivity index. In Fig. 6, the deviations between observed
and predicted soil loss values are also given with the corresponding runoff
coefficient and the mean soil moisture (average of θest and
θsat) values. On the one hand, it is evident that the
introduction of both the soil moisture and the predicted runoff coefficient
data significantly reduces the overestimation issues of the USLE model. The
correction is also effective when USLE highly overestimates soil
losses, e.g., in May 2009 and August 2013. On the other hand, when USLE
underestimates the measured values, the use of soil moisture and predicted
runoff coefficient slightly increases the deviations (June and September
2010, July 2011 and August 2012). Also given in Fig. 6 is the mean absolute
error (MAE), which confirms the ranking of the best performing models
and clearly shows that the soil moisture is an effective alternative to
estimated runoff in the prediction of the event soil loss.
Model performance in wet and dry periods
As stated earlier, the white dots in Figs. 3 and 4 represent the events that
occurred during the dry period (from June to September). It is evident that
for these events the estimated soil losses are distant from the regression
line and the 1:1 line, thus reducing the value of R2 and RMSE. In
Fig. 6 the highest deviations between the observed and estimated values occur
in the dry period events. This is likely due to the particular
characteristics of summer rainfall events in central Europe (Todisco et al.,
2012b; Todisco, 2014). Summer rainfall events are generally isolated and
characterized by high intensity associated with low antecedent soil moisture
but elevated soil losses. Therefore, even with a high Re, the
erosivity factor θRe is reduced since both
θsat and θest assume typically low values.
As a representative example, the event characterized by the highest soil loss
(Aue=19.14 Mg ha-1, July 2012) is associated with the
lowest pre-event soil moisture, both satellite-derived (θsat=0.09 m3 m-3) and simulated (θest=0.05 m3 m-3).
This issue affects the Qr Re
erosivity factor too, if Qr is derived from runoff simulated by
standard rainfall–runoff models in which runoff increases with antecedent
soil moisture conditions (Todisco et al., 2012b). In the dry period, high
surface runoff is observed, despite low θ values, due to the
development of superficial crusts creating a shield that is responsible for
low infiltration and high runoff. This aspect is particularly significant for
bare soil as in the plots considered in this study.
Given the above consideration, another analysis was performed excluding the
dry period's events from the database. Among the 45 remaining events, 23 are
used to calibrate the models and 22 to validate the results. In this case, as
expected, the performances of all the equations analyzed generally increase
(Table 2). In particular, for the calibration subset, R2=0.247 and
R2= 0.496 are obtained for the erosivity factor
(θsat Re)α for α=1 and
α > 1, respectively. The
(θest Re)α factor gives R2=0.605
and R2=0.715 for α=1 and α > 1,
respectively. Therefore, particularly the performance of the regression
significantly increases in terms of R2 especially when modeled data are
used.
In validation, RMSE = 1.10 Mg ha-1 (1.15 Mg ha-1) is
obtained with satellite soil moisture with the linear (power) model; by using
modeled soil moisture, the linear model gives
RMSE = 1.63 Mg ha-1, while the power model gives
RMSE = 1.26 Mg ha-1 (see Table 2). In comparison, the USLE model
provides an RMSE = 1.99 Mg ha-1; thus the modified-USLE model
moisture data – the SM4E models – improved the performance of the USLE when
satellite (modeled) data were considered.
Conclusions
The attempt made in the paper is to use the pre-event soil moisture to
account for the spatial variation in runoff within the area for which the
soil loss estimates are required. More specifically the analysis was focused
on the evaluation of the effectiveness of the Soil Moisture for Erosion
model (SM4E), which is derived by coupling modeled or satellite-derived
soil moisture with the USLE model, in predicting event unit soil loss at the
plot scale in a silty–clay–loam soil in central Italy. To this end, the
Masse experimental station database for the measurement of event soil losses
at plot scale was used.
The formulations analyzed are the USLE-derived equations, called SM4E models,
in which the event erosivity factor, Re, is corrected by the
antecedent soil moisture, θ, and powered to an exponent
α ≥ 1 (α=1: linear model; α > 1: power model).
Both satellite measurements from the ASCAT sensor (θ = θsat)
and modeled values through the SWBM (θ = θest)
were tested. The results showed that including direct
consideration of antecedent soil moisture in the event rainfall–runoff
erosivity factor of the USLE enhanced the capacity of the model to account
for variations in event soil losses.
The accuracy of the original USLE model was lower than that obtained by
incorporating satellite and modeled soil moisture data. The most accurate
model is that with the modeled soil moisture data when the entire the
database is used and with the satellite-retrieved soil moisture data when
only the wet period events are considered. It was in fact also verified that
much of the inaccuracy of the tested models is due to summer rainfall
events, probably because of the particular characteristics that the soil
assumes in the dry period (superficial crusts causing higher runoff): in
these cases, high soil losses are observed in association with low soil
moisture values, and, hence, the model performance decreases. As expected,
by excluding the summer events, the performance of all the analyzed
equations increases. This aspect is particularly important, as it highlights
the conditions in which the developed models fail to reproduce soil losses
and that deserves further investigation. More specifically, the
incorporation of the mechanism for the formation of superficial crusts in
the developed soil water balance model will be the subject of future
investigations.
We highlight that the obtained results open interesting scenarios in the
overview of the studies aimed at defining USLE-derived models that could
improve the unit soil loss estimation at the event scale. In particular, the
choice of using soil moisture data to correct the rainfall–runoff erosivity
factor takes on great importance for the practice. Indeed, soil moisture is
a relatively simple measurement, and different techniques are available for
providing accurate measurements at the field scale. Moreover, remote sensing
soil moisture data are also widely available on a global scale. Through
satellite data, there is the potential of applying the developed
USLE-derived model for large-scale monitoring and quantification of the soil
erosion process.