The theoretical TCEV (Two Component Extreme Value) distribution was applied to interpret the sediment yield datasets available in Southern Italy. The analysis is based on hydrological data collected for twelve catchments located in Calabria and Basilicata. A hierarchical approach was used to obtain a regional parent distribution which was used to determine the return time for each event. The hierarchical approach proposed in this study includes two stages. The first stage served for calibration and made it possible to estimate the parameters of the theoretical TCEV distribution. More specifically, the hypothesis of homogeneity with regard to the skewness coefficient and the coefficient of variation was verified using the datasets related to nine catchments. The second stage consisted in verifying the goodness of the theoretical distribution on three independent datasets provided by three experimental catchments not involved in the calibration. Overall results show that, even if the TCEV distribution was conceived to estimate peak flow, its concept of “double component” can be extended to predict sediment yield on a regional scale.

Prediction of soil erosion and sediment yield, corresponding to a fixed return time, is necessary to adopt soil conservation strategies for reducing costs of on-site and off-site impacts in areas at risk.

In Southern Italy, high rates of soil erosion and sediment yield are well documented both on cultivated land (Porto and Walling, 2012) and in areas covered by forests (Porto et al., 2004). Over the last 60 years, predictions of sediment yield are based both on the use of traditional monitoring techniques, such as observations on experimental plots or catchments, and on different types of models that vary from empirical-parametric approaches, such as SEDD (Ferro and Porto, 2000) or revised versions of the USLE (Cinnirella et al., 1998) to more recent physically- based models, such as WEPP (Nearing et al., 1989), whose goal is to simulate both the detachment and transport of soil particles.

However, even if these models provide good estimates of long-term average values of sediment yield, they cannot make reliable predictions associated to a fixed return time especially if they are associated with extreme events.

A recent study (Porto and Callegari, 2019), carried out on three experimental catchments (W1, W2, and W3) located in Calabria (Southern Italy), demonstrated that a significant proportion of the annual sediment yield in these catchments is due to the extreme event occurred each year which produced more than 50 % of the total annual sediment yield with a very few exceptions.

Looking at the frequency distribution of these measurements of sediment
yield, the same authors showed that the empirical distribution of the
normalized variable

Gumbel's plot for the dataset of the normalized variable,

The authors concluded that the process can be represented by two Extreme
Value Type 1 (EV1) independent distributions, one for each component,
capable of associating each event with a corresponding return time

This approach is based on the TCEV (Two Component Extreme Value) model whose
ability was well demonstrated in predicting peak flow and critical rainfall
corresponding to a fixed return time (see Rossi et al., 1984; Ferro and
Porto, 1999, 2006). The TCEV distribution is based on the
assumption that in each historical sample of the observed variable

Therefore, the theoretical CDF of the TCEV law

The basic component is characterized by a high number of events and by
values of

In order to apply the model at a regional scale it is useful to introduce
the standardized variable

Introducing the dimensionless variable

For fixed return period

Considering the logical dependence of sediment yield on the magnitude of peak flow (see among the others Williams and Berndt, 1977), the aim of this work is to interpret the observed values of sediment yield using an approach based on the TCEV distribution.

The Italian Hydrographic Service (SIMI) has published long-term measurements of daily and monthly suspended sediment load (SSL) on many catchments throughout the country. In the present contribution, monthly measurements of SSL, which were collected on 11 rivers located in Calabria, and Basilicata, have been used for analysis. This step required also a preliminary aggregation of the data to generate the annual datasets of sediment yield (see Table 1 and Fig. 2 for details).

These datasets have been integrated by 3 long-term records of sediment yield obtained in three experimental catchments (W1, W2, and W3) located in Calabria (see Porto et al., 2004). In this case, the original measurements, collected at event scale, have been aggregated at annual scale to make them comparable with the previous datasets.

Location of the catchments investigated in this study.

More specifically, the 11 datasets were used to derive the growth curve (Eq. 3) for the entire region, here assumed as a unique homogeneous area, while the three catchments W1, W2, and W3 were used to test the validity of the Eq. (3) on independent datasets located in the same region.

In other words, the hierarchical approach proposed in this study consists of
two levels: (1) the first level aimed at calculating the 3 parameters
(

Details of stream gauges and rivers considered in this study.

The analysis carried out at the first level required the basic assumption
that the entire region can be considered homogeneous with respect to the skewness coefficient,

As explained above, in the first step of this analysis, the TCEV model
required the estimation of the regional parameters

The CDF of the empirical skewness related to the 9 samples and that
generated by the regional model are compared in Fig. 3. The
theoretical CDF was obtained using a Monte Carlo technique based on 20 000
synthetic series having a sample size

Comparison between the empirical CDF of the skewness coefficient calculated from the nine datasets and the regional CDF obtained from the theoretical distribution.

Comparison between empirical and theoretical CDF of the
variable

Comparison between empirical and theoretical CDFs of the
variable

Even if a perfect overlapping cannot be expected considering the limited number of datasets, Fig. 3 shows a certain ability of the TCEV distribution to reproduce the empirical skewness CDF.

The second step of the analysis is based on the assumption that the
investigated region should be divided into smaller homogeneous areas, named
sub-regions, in which the

The regional growth curve given by the Eq. (3) with the calibrated values of
the 4 parameters (

The visual inspection of the three graphs in Fig. 5 suggests that,
the model fits reasonably well the higher values (

Prediction of sediment yield generated by large events is very important in areas not covered by monitoring stations or for the areas with limited observational periods. Based on a previous contribution by Porto and Callegari (2019), the study presented herein reports a regional investigation carried out in Southern Italy aimed at evaluating the frequency distribution of sediment yield. The procedure applied in this contribution is based on the use of the TCEV model and its hierarchical approach to get reliable estimates of the regional parameters of the distribution. The choice is due to the ability of the TCEV distribution to reproduce the skewed empirical distributions of sediment yield observed in many historical datasets and to generate estimates of sediment yield associated with a fixed return time. Overall, the study demonstrated that even if the TCEV distribution was conceived to provide estimates of peak flow, its basic assumptions and its hierarchical procedure can be used to predict sediment yield at regional scale.

Data collected by the Italian Hydrographic Service (SIMI) can be downloaded from the website

All authors setup the research, analyzed the results and participated in writing the paper.

The authors declare that they have no conflict of interest.

This article is part of the special issue “Land use and climate change impacts on erosion and sediment transport”. It is a result of the ICCE Symposium 2018 – Climate Change Impacts on Sediment Dynamics: Measurement, Modelling and Management, Moscow, Russia, 27–31 August 2018.

The study has been finalized in the frame of the Erasmus

This research has been supported by the European Project SETOF (grant no. 598403-EPP-1-2018-1-RS-EPPKA2-CBHE-JP).