Nazzareno Diodato

Pasquale Borrelli
email: pasquale.borrelli@unipv.it

Iñigo Gómara
email: i.gomara@uva.es

Gianni Bellocchi
email: gianni.bellocchi@inrae.fr

Sediment loss modelling framework for the Bradano River Basin, southern Italy, 1950-2020

Hazardous hydrological events cause soil erosion and it is essential to anticipate the potential environmental impacts of prevailing erosion processes that occur at different time-scales. Here, we present the modelling of net soil erosion rates for the Bradano River Basin (southern Italy), based on rainfall erosivity, surface overland flow and transport sub-models. A semi-empirical framework was developed, upscaling point rainfall values based on the Foster-Thornes approach in order to give an insight into monthly and annual soil losses over the period 1950-1958 and 1961 (calibration) and over a longer time-frame (1950-2020: reconstruction). In the 2765-km 2 study area, ~ 68% of the sediment mobilized within the basin reached the basin outlet (mean value for 1950-2020: ~ 366 Mg km -2 yr -1 ). A moderate declining trend in net erosion rates was observed after the 1980s, concurrent with the contraction of cropland in favour of natural vegetation and river channelization. Our results suggest that the parsimonious principle used here seems sufficiently robust to be suitable for applications in other Mediterranean landscapes.

Introduction

Accelerated soil erosion has substantial implications for nutrient and carbon cycling [START_REF] Ran | Effective soil erosion control represents a significant net carbon sequestration[END_REF], sustainable land productivity and socio-economic development [START_REF] Browning | Vulnerability to watershed erosion and coastal deposition in the tropics[END_REF]. Mediterranean areas are particularly affected by soil loss by water erosion and displacement of sediment (Diodato et al. 2021b). Already the empirical observations of the Italian High Renaissance polymath Leonardo da Vinci (1452-1519) in his Trattato sull'acqua ("Treatise on Water"), published in 1489, showed the interaction between rainfall and landscape in determining soil erosion [START_REF] Cardinali | Del moto e della misura dell'acqua -di Leonardo da Vinci Libro VI[END_REF].

In recent decades, important progress has been made in understanding, describing and modelling soil erosion at different spatial scales [START_REF] De Vente | Predicting soil erosion and sediment yield at regional scales: Where do we stand?[END_REF]). However, the timescale (from months to decades) has received less attention because monitoring of climate, hydrological and erosional processes are mostly not available for extended periods [START_REF] Kemp | The human impact on North American erosion, sediment transfer, and storage in a geologic context[END_REF]. A wide range of models are available to attempt to simulate the intricate dynamics in soil gross and net erosion [START_REF] Borrelli | Soil erosion modelling: a global review and statistical analysis[END_REF].

The Universal Soil Loss Equation (USLE) of [START_REF] Wischmeier | Predicting rainfall erosion losses: A guide to conservation planning[END_REF] and the Revised Universal Soil Loss Equation (RUSLE) were developed in the early 1990s [START_REF] Renard | RUSLE-revised universal soil loss equation[END_REF]. The latter is the most widely used model for assessing erosive soil degradation (e.g. [START_REF] Van Rompaey | Modelling mean annual sediment yield using a distributed approach[END_REF][START_REF] Pruski | Runoff and soil-loss responses to changes in precipitation: a computer simulation study[END_REF][START_REF] Jiang | Spatiotemporal dynamics of soil erosion risk for Anji County[END_REF]. Other useful models for predicting soil erosion dynamics include the Watershed Erosion Prediction Project (WEPP) by [START_REF] Guo | Improving and calibrating channel erosion simulation in the Water Erosion Prediction Project (WEPP) model[END_REF], the Water and Tillage Erosion Model and Sediment Delivery Model (WATEM/SEDEM) by [START_REF] Borrelli | A step towards a holistic assessment of soil degradation in Europe: coupling on-site erosion with sediment transfer and carbon fluxes[END_REF] and the Soil and Water Assessment Tool (SWAT) by [START_REF] Hussainzada | Effect of an improved agricultural irrigation scheme with a hydraulic structure for crop cultivation in arid northern Afghanistan using the Soil and Water Assessment Tool (SWAT)[END_REF]. Under the condition of scale invariance (over time) of topographic and lithological factors, soil losses mostly depend on the rainfall erosivity and vegetation cover. Thus, quantifying the effects of climate change-induced variations on erosivity and land use changes on soil protection is important to identify critical areas prone to soil erosion [START_REF] Gupta | Simulating climate change impact on soil erosion using RUSLE model -A case study in a watershed of mid-Himalayan landscape[END_REF]. For that, such complex approaches require many factors that are not always readily available for longterm estimates, and the application of such models can be challenging due to data availability issues [START_REF] Merritt | A review of erosion and sediment transport models[END_REF]. Consequently, these models may not fully capture the occurrence and co-evolution of natural phenomena mechanisms across various timescales [START_REF] Zhang | Preliminary research on the BP networks forecasting model of watershed runoff and sediment yielding[END_REF]. Despite these limitations, they can still serve as valuable tools in complementing empirical observations to support sustainable landscape management [START_REF] Arabameri | Credal decision tree based novel ensemble models for spatial assessment of gully erosion and sustainable management[END_REF]. Recent satellite development and data applications have also provided a better understanding of how natural and anthropic changes are evolving, and how they influence landscape dynamics. However, also in this case, only short time-series are available [START_REF] Cudahy | Satellite-derived mineral mapping and monitoring of weathering, deposition and erosion[END_REF]). To reconstruct inter-annual and inter-decadal variability in the evolution of landscape responses over several decades in historical times, a simpler approach using only monthly and daily rainfall amounts is preferable. Conceptual and regression-derived erosion models offer a parsimonious interpretation of the relationships between input data and basin-responses on the assumption of a homogeneous basin unit and can thus be more easily adopted (de Vente and Poesen 2005). However, parsimony is a prerequisite for model building and facilitates its use, not an indication that nature operates on the basis of parsimonious principles [START_REF] Mulligan | Modelling and model building[END_REF]. Semi-empirical models, based on simple physical concepts, are far more interesting from an interdisciplinary point of view because they can appeal to a wide range of scientists and end-users, who can communicate more easily than with physically-based models. In fact, this has stimulated the identification of concepts for the development of parsimonious modelling solutions for the assessment of sediment loss in river systems [START_REF] Gericke | Improving the estimation of erosionrelated suspended solid yields in mountainous, non-alpine river catchments[END_REF][START_REF] Diodato | Modelling the inter-annual variability of sediment yields: A case study for the upper Lech River[END_REF][START_REF] Diodato | Estimating long-term sediment export using a seasonal rainfall-dependent hydrological model in the Glonn River basin, Germany[END_REF][START_REF] Diodato | Climate-scale modelling of suspended sediment load in an Alpine catchment debris flow (Rio Cordon-northeastern Italy)[END_REF][START_REF] Diodato | Environmental drivers of dynamic soil erosion change in a Mediterranean fluvial landscape[END_REF][START_REF] Diodato | Reconstruction of seasonal net erosion in a Mediterranean landscape (Alento River Basin, Southern Italy) over the past five decades[END_REF].

In recent decades, geomorphological studies that have considered Basilicata Region, in southern Italy [START_REF] Pilogallo | Soil ecosystem services and sediment production: the Basilicata Region case study[END_REF], and in particular the Bradano basin, have focused on the long-term annual mean estimation of soil erosion [START_REF] Spilotro | Attività antropica e variazioni del bacino sedimentario relativo alla costa Ionica della Basilicata[END_REF][START_REF] Aiello | Remote sensing and GIS to assess soil erosion with RUSLE3D and USPED at river basin scale in southern Italy[END_REF]), yet leaving inter-annual dynamics unexplored. These temporal scales are important for the study of soil erosion because within them extreme events can occur and significantly alter the perception of erosive hazard that is hidden when only a mean value is estimated [START_REF] Kinnel | Event soil loss, runoff and the Universal Soil Loss Equation family of models: A review[END_REF].

Basilicata is one of the most hydrologically vulnerable regions in Italy [START_REF] Gostelow | Slope instability in historic hilltop towns of Basilicata, southern Italy[END_REF]. For instance, the Bradano River Basin (BRB) has been recently affected by extreme rainfall events, such as the one inducing the flood of 1 March 2011 (with 90 mm d -1 ), and those of an exceptional nature that occurred within about two months of each other: the event of 5-7 October and those of 1-2 December 2013. The first affected the province of Matera (in the south-east) and caused serious and widespread damage in many parts of its territory, including floods in the basins of Bradano and Basento rivers and occurrence of numerous landslides and soil erosion phenomena. The second occurred in early December, with violent rainstorms in the Metapontino area (in the lower part of the BRB), with rainfall accumulated between 1 and 2 December 2013 up to values above 150 mm, with peaks of 200 mm [START_REF] Manfreda | Le precipitazioni estreme in Basilicata[END_REF]. The latest floods with accelerated erosions occurred on 12 November 2019 and mainly affected the south-eastern part of the BRB around Matera.

However, rainfall-induced slope failures and erosion are not new phenomena in Basilicata. Already between the end of the 18 th century and the first half of the 19 th century, many lands of Basilicata were ploughed and cultivated, hundreds of hectares of woodland were cleared, and so often they were affected by remarkable erosive processes, as the contemporary historian Piero Bevilacqua wrote (Labella 2010, p. 17):

"le alture diboscate, e in primissimo luogo le terre di pendio, private della più o meno antica copertura forestale, erano sottoposte a intensi processi di erosione del suolo [con] smottamenti di terre e frane […] che investivano talora interi paesi posti a valle, colture, strade […]. Il diboscamento delle terre di altura produceva alterazioni di grande portata perché i torrenti, costretti a trascinare a valle massi e detriti" "the cleared hills, and in the first place the lands of slope, deprived of the more or less ancient covering forestry, were subjected to intense processes of soil erosion [with]

landslides […] which sometimes affected entire villages downstream, crops, roads […]. The deforestation of highlands produced far-reaching alterations because the streams, forced to drag downstream boulders and debris"

The winter floods overflowed and widened the riverbeds to form widespread swamps and marshes near the mouth of the rivers. In these dynamic and sensitive landscape systems driven by climatic, geomorphic and ecologic processes, and where magnitude of events is nested in longer-term environmental factors, the use of modelling to support the assessment of water erosion is a challenge [START_REF] Thomas | Landscape sensitivity in time and space -an introduction[END_REF]. With focus on the BRB, given the issue of assessing erosive sediment by complex models in recognition of the detailed input for the 1 3 historical period, we arranged a parsimonious erosion model adapted to the monthly and annual scales from the original algorithms of [START_REF] Foster | Runoff erosivity factor and variable slope length exponents for soil loss estimates[END_REF] and [START_REF] Thornes | The interaction of erosional and vegetational dynamics in land degradation: spatial outcomes[END_REF], because they provide an interpretation of empirically determined factors shaping active erosional landscapes in basin areas based on the parsimonious balance between driving and resisting forces in the sediment budget. In particular, the goal of this study was to develop a monthly based parsimonious erosion model, REgression-Derived Erosion Model -REDEM (BRB) for the BRB. The model aims to estimate soil erosion based on factors such as runoff, slope gradient, soil erodibility (driving forces) and vegetation cover (resistance force). By generating a long erosion time-series from 1950 to 2020, the study seeks to explore geomorphological processes in this Mediterranean river basin.

Material and methods

Study area

The study area covers 2765 km 2 , of which 2010 km 2 belong to the Basilicata region and the remaining 755 km 2 to the Apulia region. In the Italian context, this area is affected by moderate to strong soil erosion (Fig. 1a). The river Bradano (about 120 km long) starts from the Apennine chain on the northwest side of the river basin and reaches the Ionian Sea, with its mouth at Tavole Palatine (Fig. 1b). The basin has a mountainous morphology only in the north-western and northern areas, with altitudes between 700 and 1250 m a.m.s.l. The NW-SE strip of territory between Forenza (40° 52′ N, 15° 51′ E) and Spinazzola (40° 58′ N, 16° 05′ E) to the north, and Matera (40° 40 ′N, 16° 36′ E) and Montescaglioso (40° 33′ N, 16° 40′ E) to the south is characterised by hilly morphology with altitudes between 300 and 500 m a.m.s.l. The north-eastern sector of the basin includes part of the inner margin of the Altopiano delle Murge (Murge plateau), which has shares varying between 400 and 600 m a.m.s.l. The mean slope is about 12%, and 8% of the area has a slope of over 30% [START_REF] Canora | Quantitative assessment of the sensitivity to desertification in the Bradano River basin (Basilicata, southern Italy)[END_REF].

According to the classification plan of the Basilicata region (http:// www. brada nomet aponto. it/ Piano Class ifica. html), the landscape is dominated by arable nonirrigated lands. The utilised agricultural area (UAA) of over 218,000 ha accounts ~ 85% of the total farm areas, and the types of production are mainly wheat, olives, citrus and fruit crops. Cereal cultivation is the most widespread (~ 48% of the UAA), with durum wheat (a subsidised crop) playing a predominant role, accounting for ~ 95% of the cereal area. As far as olive growing is concerned, the area is particularly suited to this type of production, covering an area of ~ 16,000 ha (~ 7% of the UAA). In coastal areas, the agro-pedological nature of the land and the favourable climatic conditions allow the establishment of more profitable crops, such as fruits and vegetables (i.e. tomatoes, strawberries, oranges, lemons, tangerines, clementines, peaches and apricots), thanks also to a wellstructured irrigation network. The hills are characterised by patches of cultivated landscape. The percentage of surface area covered by woods is highly inhomogeneous in the municipalities that fall within the basin. Forests are mainly present at the highest elevations of the northwestern part of the basin, along the Apennine ridge. Pastures and meadows cover an area of ~ 19%, with sheep and goat farms widespread throughout the area (mainly the Murgian plateau), where significant livestock activities are mostly conducted on a pastoral basis. Towards the south, the natural vegetation becomes that typical of the Mediterranean maquis. Coniferous plantations are present inland and along the coast. Along the hydrographic network, hygrophilous vegetation is predominant [START_REF] Aiello | Remote sensing and GIS to assess soil erosion with RUSLE3D and USPED at river basin scale in southern Italy[END_REF].

The soils of the rough mountains are formed on a substratum of flyschoid sedimentary rocks, while the soils of the clay hills, which extend from the north of the central area to the south, in the immediate vicinity of the Ionian Sea, consist of fine-grained clay-silt marine deposits [START_REF] Canora | Quantitative assessment of the sensitivity to desertification in the Bradano River basin (Basilicata, southern Italy)[END_REF].

The climate is typically Mediterranean (Köppen-Geiger Csa), characterised by cool to mild, wet winters and warm to hot, dry summers. The winter season is mainly between October and February, when precipitation is dominated by the passage of synoptic low-pressure systems [START_REF] Hawcroft | How much Northern Hemisphere precipitation is associated with extratropical cyclones?[END_REF]). In the southern and coastal part of the basin, summers can often be similar to those of arid and semi-arid climates, where long periods with little rainfall are interrupted by heavy erosive convective precipitation (Fig. 2a). The spatial pattern of mean annual rainfall erosivity in the BRB ranges from 700 to 1200 MJ mm ha -1 h -1 yr -1 (Fig. 2b), and is concentrated in summer and early autumn, when the soil is more susceptible to erosion (Fig. 2a, red empty histogram). However, rainfall erosivity (i.e. the potential of rainfall to cause soil erosion) shows considerable inter-monthly variability and at same time a multi-modal distribution, with hazard values between summer and early autumn, when the soil begins to be free of vegetation. It also shows an intraseasonal cycle decoupled from the rainfall regime.

Data and conceptual scheme

Net erosion, also known as sediment yield, is the sum of sediment produced by all sources of soil erosion, including from splash erosion, overland flow and runoff, and stream channel areas, minus the amount of sediment deposited in these areas and in valley floodplains, which cross the outlet of a river basin (e.g. [START_REF] Toy | Soil erosion; prediction, measurement, and control[END_REF]. For this study, we have referred to the rainfall and net erosion data provided by the Regional Agency for Environmental Protection of Basilicata (ARPAB, Centro Funzionale Protezione Civile, http:// centr ofunz ional ebasi licata. it). For the BRB, net erosion data are available for the years 1950-1958 and 1961 (Annals Project of the former Hydrographic and Mareographic National Service, 1957-1972, https:// www. ispra mbien te. gov. it/ it/ proge tti/ carte lla-proge tti-incorso/ acque-inter ne-e-marino-costi ere-1/ proge tti-concl usi/ proge tto-annali), which were used for the calibration of the erosion model. The Irsina rainfall station (Fig. 2b), located at 548 m a.m.s.l., is the only one in the basin area that provides a continuous daily rainfall time-series for a long period, i.e. 1950-2020, which was used for model calibration and reconstruction of net erosion. Monthly data of vegetation cover are not available before 1981. Until 1980, the monthly vegetation cover percentage (VCP) was parameterized annually on a constant basis, with a monthly variation from January to December. The vegetation cover data up to 1980 were thus obtained by calibration of the model. Subsequently (until 2020), variable values were obtained over the BRB based on actual Normalized Difference Vegetation Index (NDVI) data from NOAA Climate Data Record (Vermote 2019), provided by Climate Explorer at a resolution of 0.1° (cell data over ~ 10 km • 10 km = 100 km 2 ). The annual NDVI values assigned to the BRB were the mean of the gridded data-points in (and around) the area of interest (i.e. 28 pixels). We had to transform NDVI values into VCP (%), since the model we developed -Eq. ( 1) -includes the exponential vegetation function of [START_REF] Thornes | The interaction of erosional and vegetational dynamics in land degradation: spatial outcomes[END_REF], which is based on VCP. Since NDVI and VCP were only available simultaneously for the year 1981, we had to develop a ratio between VCP and NDVI so that we could use it to estimate VCP over the entire period covered by NDVI. In 1981, the ratio between the VCP and NDVI was calculated for each month (from January to December): 80, 48, 50, 36, 53, 158, 179, 201, 153, 120, 115 and 122. These values likely reflect the agrarian landscape of previous years in Basilicata, which only saw significant transformations in the late 1970s [START_REF] Giambersio | La trasformazione del paesaggio agrario in Basilicata nel XX secolo[END_REF]. From 1982 onwards, this ratio was used to estimate the VCP by multiplying it by NDVI. Daily E-OBS (https:// www. ecad. eu/ downl oad/ ensem bles/ downl oad. php) gridded precipitation data at 0.25º horizontal resolution (cell data over ~ 25 km • 25 km ≈ 625 km 2 ) for the period 1950-2020 [START_REF] Cornes | An ensemble version of the E-OBS temperature and precipitation data sets[END_REF] were also considered in the study (i.e. areal mean of nine nodes at the crossing points of 12 pixels, four of which falling entirely within the basin).

These erosional features are thus taken into account in a hierarchical structure to discover the erosional phenomena in the present time. In this way, the temporal changes in water-driven soil erosion are influenced by both short-term convective storm events and longer-term environmental and climatic variations occurring at different time scales [START_REF] Thomas | Landscape sensitivity in time and space -an introduction[END_REF]). However, using the procedure originally developed by [START_REF] Wischmeier | Predicting rainfall erosion losses from cropland east of the Rocky Mountains: a guide for selection of practices for soil and water conservation[END_REF] to estimate mean annual erosion may not accurately capture soil loss from individual storms or monthly data [START_REF] Haan | Design hydrology and sedimentology for small catchments[END_REF]). To address this limitation, [START_REF] Foster | Runoff erosivity factor and variable slope length exponents for soil loss estimates[END_REF] suggested a modified approach suitable for individual storms or monthly data. In Italy, historical monitoring of rainfall and sediment yield provided the basis for adapting and calibrating the Foster-Thornes' algorithm into a semi-empirical erosion model, here called REDEM (REgression-Derived Erosion Model). In this model, the driving forces are simplified into rainfall and runoff proxies or indicators, representing splash and transport erosion, respectively. The model incorporates seasonal effects, considering the interaction between rainfall erosivity and the varying soil erodibility conditions during different seasons [START_REF] Diodato | Reconstruction of seasonal net erosion in a Mediterranean landscape (Alento River Basin, Southern Italy) over the past five decades[END_REF][START_REF] Diodato | Environmental drivers of dynamic soil erosion change in a Mediterranean fluvial landscape[END_REF].

The parameterization of the model was derived from physical and statistical considerations that were integrated with observed correlations, and included the upscaling issue through both the exponent of dx term in Eq. ( 2) and the exponential vegetation function of [START_REF] Thornes | The interaction of erosional and vegetational dynamics in land degradation: spatial outcomes[END_REF]. The gridded time-series of dx (0.25° spatial resolution) are too coarsely resolved to allow a reliable estimation of soil erosion from precipitation patterns. Here, we use basin-wide dx values, upscaled from the high-quality daily maximum rainfall data available monthly from a single station in the basin (monthly hourly data are not available). In particular, we applied a trigonometric approach, which is typically implemented to represent cyclical processes (including intraseasonal climatology), as documented for instance, in Diodato and Bellocchi (2007a, b) and Diodato et al. (2021a). For site-to-basin area upscaling, we refer to [START_REF] Diodato | Modeling and upscaling plot-scale soil erosion under Mediterranean climate variability[END_REF]. The mathematical formulation of the process studied, developed at a point-station, was thus designed to be representative over an area as large as a homogeneous basin unit, as follows:

where REDEM (BRB) is the modelled net erosion in Mg km -2 month -1 , A is a parameter of scale that depends on geographical characteristics of the basin; R S is the rainfallerosivity indicator associated more to splash erosion and rill erosion; R Q is the erosivity indicator linked more to overland flow and transport erosion; e -(0.07 • VCP) is the exponential Thornes's (1990) vegetation function, with the vegetation cover percentage (VCP) at contact with the surface; in fact, we can assume in first approximation that, surfaces hydraulically rough and covered from plants, reduce flow velocity and hence soil interril transport capacity [START_REF] Toy | Soil erosion; prediction, measurement, and control[END_REF]. This fraction (%) was set constant until 1980, and subsequently variable, until to 2020, accordingly with the NDVI actual data as described above.

As canopy cover reduces the erosivity of raindrop for detachment, it also reduces interrill sedimenttransport capacity. The last component of the model is the sediment delivery ratio (SDR), which is the sediment yield from the catchment area divided by the gross erosion (GE) of that same area. Expressed as a fraction, it represents the efficiency of the catchment in moving soil particles from areas of erosion to the (1)

REDEM (BRB) = A • R S + R Q • e -0.07•VCP • SDR
point where sediment yield is measured. Including SDR as an explicit variable in the model allows for the consideration of factors other than vegetation cover that influence runoff and its peak, such as basin shape, relieflength ratio, soil texture, the transport process and the gradient of the main channel slope (e.g. [START_REF] Van Rompaey | Modelling mean annual sediment yield using a distributed approach[END_REF]. Based on this understanding, rainfall power as the prevailing storm erosivity in summer and autumn is mainly captured by the R S term (unitless), while in winter and spring, runoff is mainly captured by the R Q term (unitless). In this way, soil erosion by water occurs more when the detachment of particles and their subsequent transport experience a greater driving force than the force that binds it into the vegetated slope. Within these processes, rain is used by nature as both a driving and resisting factor. Firstly, the erosive influence of rainfall increases with its amount, intensity and runoff; secondly, and in opposition to this influence, it is the protective effect of vegetation that also increases with the amount of rainfall.

Explaining the single terms, we obtained, arranging from Diodato and Aronica (2014):

where dx is the maximum daily rainfall (mm d -1 ) in each j month, the term in brackets is a site-to-basin scale transfer function including the unitless upscaling parameter ϑ , and the term in square brackets represents the periodic function including the unitless scale factor Ω , as well as the unitless position parameters and φ . These parameters are used to modulate the amplitude of intra-seasonal rainfall intensities, reflecting the distribution of maximum hourly rainfall over the year. This is in agreement with a multivariate analysis that explained how the inclusion of the effect of rainfall intensity increases sediment yield by ~ 24%, compared to the most notable single factor, i.e. rainfall duration [START_REF] Shojaei | Prediction of factors affecting activation of soil erosion by mathematical modeling at pedon scale under laboratory conditions[END_REF].

The following R Q term represents, instead, an erosivity indicator more associated with runoff-driven erosion:

where p is the amount of rainfall (mm) in each month j; the term in brackets is an indicator of soil humidity as a periodic function (with three empirical, unitless parameters α, β and ω) to modulate the intra-seasonal humidity after precipitation. This relies on [START_REF] Zhang | Runoff and soil loss characteristics on loess slopes covered with aeolian sand layers of different thicknesses under simulated rainfall[END_REF], who found that surface conditions on the loess slope significantly affected runoff and sediment yield processes, which is of great significance to further summarize the relationships between runoff and sediment yield, and to

(2) R S = 1 + dx ϑ • 1 -Ω • cos ⋅ 6.28 ⋅ j - φ -j (3) R Q = p • α + β • cos 6.28 ⋅ j ω -j
understand the variation in sediment yield associated with different rainstorms.

Based on [START_REF] Arnold | A continuous time water and sediment routing model for large basins[END_REF], the sediment delivery ratio (SDR) was estimated as (with ψ and η empirical parameters):

The concept is an analogue to the connectivity ratio (the amount of sediment reaching an outlet over the amount of sediment eroded), which characterises the efficiency of slope-channel transfer and depends on the transport capacity and slope-shape and drainage pattern (e.g. [START_REF] Quinton | Soil carbon losses by water erosion: experimentation and modeling at field and national scales in the UK[END_REF].

Once net erosion (NE) is estimated using Eq. ( 1), from simplifying the mass-balance equation that describes the variables that define NE [START_REF] Toy | Soil erosion; prediction, measurement, and control[END_REF], it follows: with deposition sediment within the basin (D) as: By replacing NE with Eq. ( 1), we obtained:

Model parameterization and evaluation

The modelling procedure was carried out on 120 monthly sediment data (included in the period 1950-1958 and 1961) by iteratively adding predictors and comparing the model predictions with the observational data. The parameters A in Eq. ( 1), ϑ, Ω, σ and φ in Eq. ( 2), α , β and ω in Eq. (3), and ψ and η in Eq. ( 4) were calibrated through a trial-and-error process. Previous studies with similar modelling approaches informed our calibration process (e.g. Diodato and Bellocchi 2019). The calibration aimed to establish a significant relationship between actual and predicted data, ensuring that the following criteria were met [START_REF] Diodato | The rise of climate-driven sediment discharge in the Amazonian River Basin[END_REF]):

i.e. maximizing the goodness-of-fit (R 2 , optimum 1), minimizing the mean absolute error (MAE, optimum 0) and minimizing the difference from the unity of the regression

(4) SDR = ψ • 0.78 + 0.22 • R Q η 1 + p 0.56 (5) NE + D = NE SDR (6) D = NE • 1 SDR -1 (7) D = A • R S + R Q • e -0.07•VCF • SDR • 1 SDR -1 (8) ⎧ ⎪ ⎨ ⎪ ⎩ R 2 = max MAE = min �b -1� = 0
slope (b, optimum 1) between actual and modelled data. An efficiency metric, the Nash-Sutcliffe index (-∞ < EF ≤ 1, optimal) was also calculated to assess model performance uncertainty, as EF > 0.6 indicates narrow parameter uncertainty [START_REF] Lim | Effects of calibration on L-THIA GIS runoff and pollutant estimation[END_REF]). The Durbin-Watson statistic was also performed to check for the presence of autocorrelated residuals, as strong temporal dependence can induce spurious correlations. Statistical analyses were spreadsheet-based with the support of software STAT GRA PHIC (http:// www. statp oint. net/ defau lt. aspx), CurveExpert Professional 1.6 (https:// www. curve expert. net), WESSA (https:// www. wessa. net/ tsa. wasp) and MATLAB® (https:// www. mathw orks. com/ produ cts/ matlab. html).

Results and discussion

Model parameterization and evaluation

A highly significant relationship (p < 0.01) was obtained between the available sediment data for the years 1950-1958 and 1961, and the corresponding predictions using the following calibrated parameter values: A = 2.19 in Eq. ( 1), ϑ = 2, Ω = 0.60, σ = 4 and φ = 19.6 in Eq. ( 2), α = 0.4, β = 0.2 and ω = 25 in Eq. ( 3), ψ = 0.5 and η = 1.3 in Eq. ( 4). Additionally, the calibrated monthly variation of the vegetation cover percentage (VCP) was as follows: 25% in January, 15% in February, 21% in March, 20% in April, 30% in May, 55% in June, 55% in July, 55% in August, 45% in September, 35% in October, 32% in November and 31% in December. These calibrated values reflect the distribution pattern of mean monthly values for the years 1950-1958 and 1961. It is worth noting that these values are slightly lower than those observed from 1981 to 2020, indicating a recent shift towards higher values in vegetation cover (Fig. 3). This shift is attributed to the influence of higher atmospheric temperatures and increased CO 2 concentrations, which have stimulated Mediterranean vegetation growth (e.g. [START_REF] Osborne | Modelling the recent historical impacts of atmospheric CO 2 and climate change on Mediterranean vegetation[END_REF].

Figure 4A reports the regression results (black line) of the calibrated model, Eq. ( 1), for 120 net erosion data-points (blank circles falling out of bounds showing 95% prediction limits for new observations-in light pink-were not considered), where negligible departures of the data-points from the 1:1 red line are observed. The observed monthly values vary between 0 and 927 Mg km -2 month -1 . The latter occurred in November 1959, when the annals of the former Hydrographic and Mareographic National Service registered a daily maximum rainfall equal to 116 mm d -1 with a cloudburst rainfall of 53 mm hr -1 . Figure 4B shows a distribution of the residuals compatible with a Gaussian pattern, indicating a free-skewed errors' distribution. The mean values of the predicted and observed values are not significantly different (pairwise Student-t p = 0.95). As the p-value of the Durbin-Watson (DW = 1.73) is greater than 0.05 (p = 0.86), there is no indication of serial autocorrelation in the residuals.

The R 2 -statistic indicates that the REDEM (BRB) explained 87% of net erosion variability. The mean absolute error (MAE), used to quantify the amount of error, was equal to 18 Mg km -2 month -1 , which is lower than the standard deviation of the residuals (27 Mg km -2 month -1 ). The Nash-Sutcliffe efficiency (EF), equal to 0.85, also indicates narrow parameter uncertainty. With the calibration dataset capturing a wide variability of net erosion values, the satisfactory model performance obtained (according to an array of performance metrics and test statistics) supports the robustness of the model against contrasting situations.

In determining whether the REDEM (BRB) can be simplified, we have fitted a multiple linear regression model to describe the relationship between net erosion and the four independent variables Rs, R Q , SDR and VCP of Eq. ( 1). The highest p-value (p = 0.0093), belonging to SDR, indicates that even this term is statistically significant, and that Eq. ( 1) cannot be simplified further, resulting a stable, interpretable and generally useful model [START_REF] Royston | Multivariable model -building: a pragmatic approach to regression anaylsis based on fractional polynomials for modelling continuous variables[END_REF].

In order to evaluate the time-scale invariance of the model, we have also aggregated net erosion on annual basis. Year-to-year fluctuations of actual net erosion values were largely reproduced by the time-integration of REDEM (BRB) for all the years available (Fig. 4C). The values are in agreement (R 2 = 0.91 and MAE = 60 Mg km -2 yr -1 ) and indicate the suitability of the annually integrated model for long-term assessments (standard deviation of the residuals equal to 89 Mg km -2 yr -1 ). The ability of the model to reproduce (1950-1958 and 1961) and determined from the Normalized Difference Vegetation Index for the period 1981-2020 1 3 year-to-year fluctuations and generate accurate estimates of annual net erosion reinforces its reliability for long-term assessments. By demonstrating the time-scale invariance of the model, we establish its applicability in studying the complex dynamics of sediment yield over extended periods.

However, due to the lack of direct measurements, validation of the soil erosion estimates was also carried out by testing the predictive ability of the model to estimate the mean annual silting of the reservoir. In particular, REDEM (BRB) estimates were compared to the sediment trapping data (dam silting) of the sub-basin subtended by the San Giuliano dam (~ 1669 km 2 , i.e. 55% of the entire Bradano basin; Fig. 1B, light brown area), as supplied by the interregional authority responsible for its management for the period 1977-2000 [START_REF] Spilotro | Attività antropica e variazioni del bacino sedimentario relativo alla costa Ionica della Basilicata[END_REF]. The comparison indicates that REDEM (BRB) estimates (316 Mg km -2 yr -1 ) can reliably quantify the amount of sediment yield at the mouth of Bradano River (silting at San Giuliano dam of 350 Mg km -2 yr -1 ). These features increase the robustness of this study, especially with regard to modelling, didactic simplicity and the environmental support role of the investigated landforms, despite its limitations. For instance, we do not have a way to validate the monthly values of the vegetation cover percentage until 1980. We obtained a mean annual vegetation cover of ~ 35%, which is reflected in published literature (e.g. [START_REF] Mancino | Rischio di erosione: telerilevamento e GIS per l'applicazione della Universal Soil Loss Equation (USLE)[END_REF][START_REF] Fuccella | Note di storia sul paesaggio agrario della Basilicata tra XIX e XXI secolo[END_REF], and the estimated monthly percentages of vegetation cover may not reflect the phenology of the arable crops at the scale of the basin. In fact, at this spatial unit, wooded areas coexist with agricultural and vegetable crops. Specifically to our study area, vegetable crops grown in coastal areas require preparatory tillage in spring, which may explain a more limited extension of the vegetation cover in April than winter months. Then, the factors limiting vegetation dynamics vary according to the type of stand characteristics of mountain and Mediterranean biomes. Our understanding is that for vegetation located in warm areas, a temperature increase, a decrease in soil water availability, or a combination of both, is expected to reduce vegetation cover in spring. However, atmospheric and soil effects are difficult to assess in order to understand variations in vegetation dynamics, due to the complex interactions between the water regime and soil nutrition, which act in conjunction with the thermal and precipitation regimes (e.g. [START_REF] Piedallu | Soil and climate differently impact NDVI patterns according to the season and the stand type[END_REF]. A posteriori, the satisfactory evaluation of the model (including the indirect evalaution against dam sediments) is a clue that our calibrated values of the vegetation cover percentage reliably reflect the monthly distribution of the vegetation cover. 1). The graph includes the regression line (black line), the 1:1 identity line (red line), the prediction limits for the new observations at 90% (area coloured in deep pink) and 95% (area coloured in light pink) confidence (out of which the only outlier value is marked as an empty circle and not considered for model calibration). Units are in Mg km -2 month -1 ; B Residuals between actual and modelled net erosion; C Scatterplot of observed and modelled values of integrated net erosion on an annual scale (Mg km -2 yr. -1 ), with 1:1 identity line and associated confidence limits. The data used to generate the graphs of this figure were derived from the Regional Agency for Environmental Protection of Basilicata (ARPAB, Civil Protection Functional Centre, http:// centr ofunz ional ebasi licata. it) and the former Hydrographic and Mareographic National Service for the years 1950-1958[START_REF] Sereni | Storia del paesaggio agrario Italiano Bari[END_REF](Annals project 1957-1972, https:// www. ispra mbien te. gov. it/ it/ proge tti/ carte lla-proge tti-in-corso/ acque-inter ne-e-marinocosti ere-1/ proge tti-concl usi/ proge tto-annali) 1 3

Scaling of the temporal and spatial domains

In relatively small mountain basins, geomorphological processes are characterised by nonlinear interactions between climate, land surface and fluvial responses at different spatial and temporal scales. For instance, sediment transport dynamics are nonlinear, as they can be strongly influenced by increased sediment availability after extreme events, such as downpours and floods, and by the complex dynamics of activation of sediment sources with different degrees of connectivity to the drainage at the basin scale [START_REF] Rainato | Three decades of monitoring in the Rio Cordon instrumented basin: sediment budget and temporal trend of sediment yield[END_REF].

A time-complexity approach in basin hydrological models must take into account the integration of fast-moving processes, such as the partitioning of precipitation into rainsplash and runoff [START_REF] Mulligan | Modelling and model building[END_REF]. Hydrological models are sensitive to the time step of the simulation, and then, in the representation of rainfall erosivity, only an indicator of the maximum hourly rainfall per month was taken, Eq. ( 2), to limit the large errors that can occur when aggregating intensity calculations in smaller steps. In this way, Eq. ( 2) is appropriate to account for the large variability from month to month, and between the same months in different years, in the amount of energy released in 1 to 24 h.

When the gross erosion has almost entirely originated, overland flow starts to prevail over splash erosion and the soil delivery ratio starts to detach the portion of the gross erosion that the tributaries introduce into the main hydrographic network until the outlet of the basin. It is observed that net erosion represents 68% of the eroded soil in the basin. Of the three relationships of R S , R Q and net erosion, R S has a higher correlation with net erosion.

As [START_REF] Mulligan | Modelling and model building[END_REF] pointed out, the hydrological processes illustrated above are strongly dominated by the spatial connectivity of runoff-producing elements. One attempt to incorporate upscaling in our model has been to account for both the VCP in the exponent of Eq. ( 1) and the SDR in Eq. ( 4).

The SDR has been modelled separately in a dynamic and hierarchical way based on the ratio between the runoff indicator (R Q ) and rainfall (p). In turn, the scaling of the SDR can be described as a simple power law of the linear regression of this ratio [START_REF] Mandelbrot | The Fractal Geometry of Nature[END_REF], and be sufficient to capture basin-wide behaviour. It denotes the interaction between hillslope and channel in terms of runoff and sediment-delivery rates in a given month. The basin-scale multi-year mean SDR value estimated from Eq. ( 4) was equal to 0.68, close to the experimental value of 0.65 [START_REF] Spilotro | Attività antropica e variazioni del bacino sedimentario relativo alla costa Ionica della Basilicata[END_REF], thus obtaining a reliable quantification of the sediment. These values are consistent with the low slope of the basin.

Model application: seasonal and long-term erosion patterns

For the BRB, the results obtained over the long-term of 70 years (1950-2020) of modelling, net erosion exhibit a value of about 366 ± 291 Mg km -2 yr -1 . The years with net erosion around 1000 Mg km -2 occurred in 1954, 1959, 1972, 1979 and 1994 with 939, 1103, 1181, 932 and 938 Mg km -2 , respectively. From the annual standard deviation (262 Mg km -2 yr -1 ), it is evident that there is a large inter-annual variability. A significant variation is also present in sediment transport on a monthly scale: in winter, the higher rate of annual sediment amount is delivered (39%), while 37% is delivered in autumn, and about 21% and 3%, in spring and summer, respectively. This is consistent with the soil types in the BRB, as the presence of arable land with seasonal cereal crops is more affected by erosion during the months without vegetation [START_REF] Aiello | Remote sensing and GIS to assess soil erosion with RUSLE3D and USPED at river basin scale in southern Italy[END_REF]. 1) and Eq. ( 7). In B, the red curve shows the 98 th percentile (Prc) of net erosion. The data used to generate the graphs were derived from the Regional Agency for Environmental Protection of Basilicata (ARPAB, Civil Protection Functional Centre, http:// centr ofunz ional ebasi licata. it) and the former Hydrographic and Mareographic National Service for the years 1950-1958[START_REF] Sereni | Storia del paesaggio agrario Italiano Bari[END_REF](Annals project 1957-1972, https:// www. ispra mbien te. gov. it/ it/ proge tti/ carte lla-proge tti-in-corso/ acque-inter ne-e-marino-costi ere-1/ proge tti-concl usi/ proge tto-annali)

In this way, the rationale behind Eq. ( 1) is that two main processes are relevant to produce net erosion in the BRB: the power of rainfall through erosive-storm events, Eq. ( 2), and the transport capacity of eroded material through runoff, Eq. ( 3). In summer and early autumn, the erosive-storm factor operates mainly on a local scale from raindrop splash erosive forces, when the hourly rainfall intensity is higher (Fig. 5A, red line). At this scale, storms cannot always carry sediment to the basin outlet, redistributing a larger ratio of sediment across the sub-basins. In the following stages, the gradual increase in the runoff rate in autumn and the moderate intensity of rainfall lead to a sharp increase in the runoff rate. During this period, cultivated land is active and subject to greater erosion risk. Long-lasting duration of winter and spring rains are usually associated with synoptic weather systems [START_REF] Hawcroft | How much Northern Hemisphere precipitation is associated with extratropical cyclones?[END_REF], with decreasing rainfall intensity compared to the previous period and a sequence of storms which, however, favours rilling and thus increased soil erosion. In this case, runoff-erosion is added to splash-erosion, and can act even under moderate rainfall conditions, since the soil is well wetted (Fig. 5A, black line), and then more sediment is delivered to main drainage network and in turn to the basin outlet (Fig. 5B, blue band).

In contrast to driving factors, vegetation exerts basinwide soil erosion control by dissipating the energy of rainfall [START_REF] Ribolzi | From shifting cultivation to teak plantation: effect on overland flow and sediment yield in a montane tropical catchment[END_REF]. In this way, vegetation patches trap sediment, particularly in summer and early autumn, playing an erosion-limiting role in about 50% along the BRB's main stream network (Fig. 5B, brown band), compared to 30% for other seasons. This seasonality may also be representative of gross erosion that is trapped, like re-sedimentation, from the landscape before the eroded soil reaches the main river for delivery to the dam (with a quite high roughness coefficient, ~ 0.1, [START_REF] Scarpino | Multitemporal SAR data and 2D hydrodynamic model flood scenario dynamics assessment[END_REF]. Figure 5B (red curve, right y-axis) also shows the seasonal pattern of the 98 th percentile of net erosion, which indicates rates five to ten times higher than the respective mean values (blue band, left y-axis), in winter, spring and autumn. This suggests that the extreme events, with return periods of about 50 years, can represent a damaging phenomenon in soil erosion processes. However, the decrease of net erosion does not occur in a linear, gradual trend (Fig. 6, black line) but, as shown by the change-point detected in 1986 by the Mann-Withney-Pettit test (p < 0.01), by a sudden shift that divides the time-series in two distinct segments : 1950-1986 and 1987-2020 (red arrow). According to this change-point, the first period is affected by an areal mean sediment loss of 458 Mg ha -2 yr -1 (± 334 standard deviation), compared to 266 Mg ha -2 yr -1 (± 198 standard deviation) in the second period. For both of these periods, the values of terrigenous input at river mouths clearly reflect the characteristics of climate conditions and vegetation cover, and secondarily of soil erodibility, highlighting in particular the considerable role in limiting sediment transport played by man-made and natural landscape elements. As net erosion decreases, gross erosion declines (Mann-Kendall test p = 0.02), but at a higher rate (data not shown), since net erosion is also influenced by a reduction of the soil delivery ratio. Considering the annual time-series of sediment loss by severity classes, it can be seen that in ~ 63% and ~ 27% of the years the eroded material was above the tolerable annual rates of 300 and 600 Mg km -2 yr -1 for poorly developed (< 0.5 m depth) and well developed (> 1 m depth) soils, respectively (OECD 2001).

In the long-term, the rainfall erosivity indicator, which is more associated with runoff erosion, appears to have affected the trend of sediment loss, especially after the change-point in 1986 (Fig. 6A, blue line), when this variable declined significantly (Mann-Kendall test: S = -725, Z = 3.59, p ~ 0.00). Although there is a possibility that the change-point detected in 1986 is related to the change of methodology in determining vegetation cover percentage (after 1980), this long-term decline in net erosion is consistent with the decrease in the width of the Basento Up channel (a river southwest of the Bradano River) in the period 1950-1996 and a flattening after that date (Fig. 6B, orange dashed line; de Musso et al. 2020).

According to de Musso et al. ( 2020), the Basento River channel narrowed strongly during the 20 th century, similar to other Italian rivers like the Bradano River, with the strongest phase from the 1950s to the 1990s (with a variation in width from -30 to -80%).

Periodic oscillations also occur, consistent with the fluctuating pattern of net erosion, when net erosion remains stable and high for almost the first four decades of the time-series, when continuous inter-annual oscillations attest to erosion rates above the critical sediment loss (Fig. 6C, black line).

The decade of the 1950s is characterised by very high rates of sediment loss, as confirmed by the Italian historian Emilio Sereni (1907Sereni ( -1977)), who considered indiscriminate deforestation to be the main cause of abnormal sediment production (Sereni 1961, p. 473): "… quale è riflesso nella degradazione dei terreni montani, di conseguenza di inconsulti disboscamenti […] e di una mancata politica di difesa del suolo, il cui aggravato difetto con particolare pericolosità si ripercorrevano in quegli anni anche al piano, con la frequenza e l'irruenza di nefaste alluvioni." "… which is reflected in the degradation of mountain soils, as a consequence of rash deforestation […] and a lack of soil defence policy, whose aggravated defect with particular danger was traced in those years also on the plain, with the frequency and impetuousness of harmful floods." Subsequently, we find a group of years after 1970 which show considerable erosion rates and are among the highest in the time-series. In January 1972, for instance, the BRB was affected by exceptionally heavy rainfall, which lasted 10 days. According to [START_REF] Manfreda | Le precipitazioni estreme in Basilicata[END_REF], the mean amount of rainfall in the lower part of the basin (Matera) was ~ 200 mm d -1 , with daily peaks of 310 mm in Calciano (40° 35′ N, 16° 12′ E) and 305 mm in Stigliano (40° 24′ N, 16° 14′ E). Inhabited centres were seriously damaged, roads and railways were disrupted, and the countryside was flooded by the overflow of the Basento and Cavone rivers [START_REF] Manfreda | Le precipitazioni estreme in Basilicata[END_REF]. In Montalbano Jonico (40° 17′ N, 16° 34′ E), the rains triggered a landslide that threatened several houses. After the 1980s, the simulated erosion rates underwent a remarkable pattern-change and decline, characterised by long period of drought interrupted by small groups of years with high erosion rates, often above the tolerance threshold of 300 Mg km -2 yr -1 for shallow soils (Fig. 6C, black line). This is in line with the observed climate anomalies (Fig. 7), as these years have seen a sharp reduction in the amount of rainfall during the winter period and, consequently, an increase in aridity that has triggered land degradation processes in the southeast of the basin [START_REF] Canora | Quantitative assessment of the sensitivity to desertification in the Bradano River basin (Basilicata, southern Italy)[END_REF].

Also, during the last erosion peak around 2012, two exceptional rainfall events were observed. The southeastern part of the Basilicata region, including the BRB municipalities, was the most affected by the rainstorms. The maximum amount of rainfall was recorded in the territory of Tursi (province of Matera in the southeast of the basin), where 152 mm of rain fell in 24 h. During the events of 5 and 7 October 2013, which affected the province of Matera, severe and widespread damage was observed in several parts of the province, causing the Bradano River to flood [START_REF] Manfreda | Le precipitazioni estreme in Basilicata[END_REF]. This indicates that the regulation of soil and water conservation Anomalies were calculated by subtracting their corresponding longterm annual or seasonal mean (1950-2020) from the time-series. Then, they were divided by their standard deviation. Right y-axis: number of days per year and per autumn (September-November) season when the mean areal precipitation is greater than 20 mm. The precipitation data used to generate the graph were derived from E-OBS v23.1e gridded dataset (https:// surfo bs. clima te. coper nicus. eu// dataa ccess/ access_ eobs. php# datafi les) via Climate Explorer measures on the spatio-temporal scale effects of the rainstorm-erosion processes in the BRB is at an unstable equilibrium, where events close to moderate-extreme storms can easily determine unsustainable conditions in soil loss in a long-term decline picture. This is the case of the period 2000-2020, when extreme autumn precipitation events and winter overland flow present higher values (Fig. 7). However, human intervention (e.g. channelization, arable land contraction) and the increase of natural vegetation appear to produce a counteracting effect [START_REF] Romano | Cambiamenti nell'uso del suolo: analisi e comparazione di mappe storiche e recenti[END_REF]. This is also in agreement with the decrease in landslides and floods in the period 1951-2000 found by [START_REF] Clarke | Hindcasting extreme events: the occurrence and expression of damaging floods and landslides in Southern Italy[END_REF] for the Basilicata region. It can also be assumed that the luxury of vegetation in recent years has been increased by the rise in average temperatures in all seasons of the year [START_REF] Diodato | Modelling NDVI responses to climate variability in Mediterranean terrestrial ecosystem[END_REF]. In this way, landscape changes have contributed to reducing the risk of soil erosion due to the positive effects of vegetation cover in confining the energy of precipitation. This decline in soil erosion hazard was also confirmed by [START_REF] Mancino | In-between forest expansion and cropland decline: a revised USLE model for soil erosion risk under land-use change in a Mediterranean region[END_REF], for the period 1990-2010, for which forests increased by 5.6% as an indirect response to land abandonment.

Conclusions and perspectives

Key findings and insights

The study focused on reconstructing sediment loss in the Bradano River Basin (BRB) from 1950 to 2020 to evaluate erosional processes in Mediterranean environments. By employing the REDEM (BRB) model, which utilises climatic and vegetation data, we were able to quantitatively assess net erosion. The model's performance was satisfactory, effectively capturing inter-annual variability and seasonal erosion patterns. Notably, vegetation emerged as a critical factor in controlling soil erosion by dissipating rainfall energy and trapping sediment, particularly during summer and early autumn. The study's findings have practical implications for land and water management, offering valuable insights for erosion control measures and reservoir management in the BRB. The identification of a change-point in erosion dynamics in c. 1986 emphasizes a shift in erosion dynamics, underscoring the importance of continuous monitoring and adaptive management strategies. Fur thermore, long-term assessments employing the annually integrated model can provide valuable information for watershed management and decision-making. To improve the model's predictive capabilities, future research should focus on refining it by incorporating additional variables such as land use changes, climate change projections and soil conservation practices. Rigorous monitoring and validation efforts under different scenarios are also necessary to assess the model's performance accurately. Additionally, applying the model to other river basins with similar characteristics can help evaluate its transferability and generalize its findings, extending its applicability beyond the BRB.

Significance of the study and recommendations

The significance of this study extends to supporting the implementation of landscape planning guidelines in Basilicata, specifically the "Guidelines for integrated landscape planning in Basilicata" (Linee guida per la progettazione integrata del paesaggio della Basilicata). These guidelines, based on the principles of the European Landscape Convention [START_REF] Giambersio | La trasformazione del paesaggio agrario in Basilicata nel XX secolo[END_REF], provide a framework for landscape planning methodologies at the regional level, defining a cognitive framework for the regional landscape and offering guidance for landscape recognition and design. By developing the REDEM (BRB) model and gaining insights into erosion patterns in the BRB, this study provides valuable information that can support the implementation of these guidelines. For future research, it is recommended to focus on incorporating additional variables such as land use changes, climate change projections and soil conservation practices to enhance the model's predictive capabilities. Rigorous monitoring and validation efforts under different scenarios are necessary to validate the model's estimates and assess its performance. Furthermore, applying the model to other river basins with similar characteristics can help evaluate its transferability and generalize its findings, expanding its applicability beyond the BRB. These advancements also set the stage for informed decision-making, sustainable land and water management practices, and the preservation of ecological processes [START_REF] Jiménez-Alfaro | Native plants for greening Mediterranean agroecosystems[END_REF]).

Fig. 1 A

 1 Fig. 1 A Map of the mean rate of soil loss in central and southern Europe; B hydrographic network of the Bradano River Basin with the basin outlet (red dot) at the hydrometric station of Tavole Palatine (40° 24′ N, 16° 49′ E), the sub-basin (light brown) subtended by the San Giuliano (40° 36′ N, 16° 29′ E) dam (green dot), and the reference pluviometric station (black dot) of Irsina (40° 45′ N, 16°

Fig. 2 A

 2 Fig. 2 A Monthly precipitation (solid bars) and rainfall erosivity (red blank bars) for Irsina station, and B spatial pattern of annual rainfall erosivity across the Bradano River Basin averaged over the period 2001-2011. In A, rainfall data from SCIA (Sistema nazionale per l'elaborazione e diffusione di dati climatici) dataset (http:// www. scia. ispra mbien te. it) for the period 1971-2010 were arranged by FAO LocClim software (https:// www. fao. org/ land-water/ land/ land-gover

Fig. 3

 3 Fig.3Comparison of the mean monthly vegetation cover in the Bradano River Basin, estimated in the calibration years(1950- 1958 and 1961) and determined from the Normalized Difference Vegetation Index for the period 1981-2020

Fig. 4 A

 4 Fig. 4 A Scatterplot of observed experimentally determined (observed) monthly net erosion (NE) at the outlet of Bradano River Basin in the years 1950-1958 and 1961, and data modelled with Eq. (1). The graph includes the regression line (black line), the 1:1 identity line (red line), the prediction limits for the new observations at 90% (area coloured in deep pink) and 95% (area coloured in light pink) confidence (out of which the only outlier value is marked as an empty circle and not considered for model calibration). Units are in Mg km -2 month -1 ; B Residuals between actual and modelled net erosion; C Scatterplot of observed and modelled values of integrated

Fig. 5 A

 5 Fig. 5 A Monthly means of soil humidity index (black curve) and rainfall hourly intensity index (orange curve), and B eroded sediment balance for the Bradano River Basin averaged over the period 1950-2020 estimated with Eq. (1) and Eq. (7). In B, the red curve shows the 98 th percentile (Prc) of net erosion. The data used to generate the graphs were derived from the Regional Agency for Environmental

Fig. 6 A

 6 Fig. 6 A Temporal evolution of erosivity indicator associated more to runoff erosion for the Bradano River Basin during the period 1950-2020 (blue line); B Temporal trend of river width (m) of Basento Up (orange dashed line); and C Annual sediment loss (Mg km. -2 ) resulting from Eq. (1) (black line). Y-axis of net erosion and runoff

Fig. 7

 7 Fig.7Left y-axis: time-series evolution of standardized winter (December-February) and annual precipitation anomalies (mm per standard deviation) averaged over the area(40-41° N, 15º-17º E). Anomalies were calculated by subtracting their corresponding longterm annual or seasonal mean (1950-2020) from the time-series. Then, they were divided by their standard deviation. Right y-axis: number of days per year and per autumn (September-November) season when the mean areal precipitation is greater than 20 mm. The precipitation data used to generate the graph were derived from E-OBS v23.1e gridded dataset (https:// surfo bs. clima te. coper nicus. eu// dataa ccess/ access_ eobs. php# datafi les) via Climate Explorer

Data availability Mean rate of soil loss in central and southern Europe: European Soil Data Centre (ESDAC, https:// esdac. jrc. ec. europa. eu/ themes/ rainf all-erosi vity-europe. Hydrographic network of the Bradano River Basin: Italian Institute for Environmental Protection and Research (http:// sgi2. ispra mbien te. it/ viewe rsgi2). Rainfall data from Irsina station: SCIA (Sistema nazionale per l'elaborazione e diffusione Code availability Codes can be available upon request to the authors.

Declarations

Competing interests The authors declare no competing interests.

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons. org/licenses/by/4.0/.

Supplementary Information

The online version contains supplementary material available at https:// doi. org/ 10. 1007/ s00704-023-04662-3.

Author contribution N. D. conceived the study, performed most of the analysis and drafted the manuscript with G. B., who wrote the final manuscript. P. B. and I. G. performed complementary analyses and contributed to the scientific discussions.

Funding Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. The authors performed this research as an investigator-driven study without financial support.

Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.


Karim Aissou
email: karim.aissou@umontpellier.fr

Muhammad Mumtaz

Nils Demazy

Gilles Pécastaings

Guillaume Fleury

Georges Hadziioannou

Periodic Bicontinuous Structures Formed on the Top Surface of Asymmetric Triblock Terpolymer Thick Films

Keywords: Solvent vapor annealing, ABC triblock terpolymer, self-assembly, asymmetric thick film, phase inversion process

The combination of the non-solvent induced phase separation (NIPS) process with a solvent vapor annealing (SVA) treatment is used to produce asymmetric and hydrophobic thick films having different long-range ordered network nanostructures, which are inaccessible via currently available membrane fabrication methods. We show that the disordered phase generated by NIPS on the material top surface can be transformed into a highly-ordered bicontinuous network nanostructure during the SVA process without disrupting the substructure morphology. For instance, by using a straightforward blending approach, either a triply periodic alternating diamond (D A ) structure or a core-shell perforated lamellar (PL) phase were demonstrated on the skin layer of fully hydrophobic poly(1,1dimethyl silacyclobutane)-block-polystyrene-block-poly(methyl methacrylate) (PDMSB-b-PS-b-PMMA) thick films. Such material fabrication method, enabling the formation of a sponge-like substructure topped by a network phase having an excellent long-range order, provides an appealing strategy to facilitate the manufacture of next-generation membranes at large scale since these bicontinuous morphologies obviate the need of the nanochannel alignment.

Asymmetric and isoporous block copolymer (BCP) membranes are promising materials to achieve a better figure of merit compared to the state of the art membranes as their unique architecture allows overcoming the ubiquitous permeability-selectivity trade-off. [START_REF] Mehta | Permeability and Selectivity Analysis for Ultrafiltration Membranes[END_REF][START_REF] Nunes | Block Copolymer Membranes for Aqueous Solution Applications[END_REF][START_REF] Abetz | Isoporous Block Copolymer Membranes[END_REF][START_REF] Zhang | Nanoporous Membranes Generated from Self-Assembled Block Polymer Precursors: Quo Vadis ?[END_REF] To produce such kind of high-performance materials, Peinemann et al. [START_REF] Peinemann | Asymmetric Superstructure Formed in a Block Copolymer via Phase Separation[END_REF] have used an elegant approach which combines the self-assembly of BCPs into an out-of-plane cylindrical nanostructure on the material top surface with the formation of a macroporous substructure generated by non-solvent induced phase separation (NIPS). However, a perfect-control of the nanopore formation is challenging to achieve with the SNIPS method (i.e., Self-assembly + NIPS) due to the fact that, at best, a kinetically trapped morphology derived from a micellization process is formed on the material skin layer when appropriate manufacturing conditions can be defined. [START_REF] Marques | Self-Assembly in Casting Solutions of Block Copolymer Membranes[END_REF][START_REF] Nunes | Ultraporous Films with Uniform Nanochannels by Block Copolymer Micelles Assembly[END_REF][START_REF] Nunes | Switchable pH-Responsive Polymeric Membranes Prepared via Block Copolymer Micelle Assembly[END_REF] Indeed, the complex exchange/migration of the non-solvent occurring during the porosity formation makes that isoporous membranes with pores extending over the top separation layer were solely demonstrated for specific amphiphilic AB-and ABC-type BCP systems since the hydrophilic block plays a crucial role in creating pores during the precipitation process. [START_REF] Phillip | Tuning Structure and Properties of Graded Triblock Terpolymer-Based Mesoporous and Hybrid Films[END_REF][START_REF] Qiu | Selective Separation of Similarly Sized Proteins with Tunable Nanoporous Block Copolymer Membranes[END_REF][START_REF] Gu | Tailoring Pore Size of Graded Mesoporous Block Copolymer Membranes: Moving from Ultrafiltration toward Nanofiltration[END_REF][START_REF] Hahn | Structure Formation of Integral-Asymmetric Membranes of Polystyrene-Block-Poly(ethylene Oxide)[END_REF][START_REF] Saleem | Block Copolymer Membranes from Polystyrene-B-Poly(solketal Methacrylate) (PS-b-PSMA) and Amphiphilic Polystyrene-b-Poly(glyceryl Methacrylate) (PS-B-PGMA)[END_REF][START_REF] Schöttner | Poly(2-Hydroxyethyl Methacrylate)-Based Amphiphilic Block Copolymers for High Water Flux Membranes and Ceramic Templates[END_REF] To produce innovative membranes with smart nanopores (e.g., thermo-, ion and/or pHresponsive channels), [START_REF] Clodt | Double Stimuli-Responsive Isoporous Membranes via Post-Modification of Ph-Sensitive Self-Assembled Diblock Copolymer Membranes[END_REF][START_REF] Schacher | Self-Supporting, Double Stimuli-Responsive Porous Membranes from Polystyrene-Block-poly(N,N-Dimethylaminoethyl Methacrylate) Diblock Copolymers[END_REF][START_REF] Jung | Formation of Integral Asymmetric Membranes of AB Diblock and ABC Triblock Copolymers by Phase Inversion[END_REF][START_REF] Ju | Stimuli-Responsive Smart Gating Membraneskarunakaran[END_REF] a large panoply of chemically distinct amphiphilic BCP materials has been generated by SNIPS. In addition, the self-assembly of blends of two chemically interacting amphiphilic BCPs was revealed to be a powerful strategy to achieve highly porous membranes with pore diameters as small as 1.5 nm. [START_REF] Yu | Self-Assembled Asymmetric Block Copolymer Membranes : Bridging the Gap from Ultrato Nanofiltration Angewandte[END_REF] However, so far, only few of these chemically distinct amphiphilic BCP membranes exhibit a dense top surface with long-range ordered nanopores.

The more challenging fabrication of fully hydrophobic BCP materials with an asymmetric structure or ordered pores over the whole film has been recently demonstrated by SNIPS [START_REF] Karunakaran | Nanostructured Double Hydrophobic Poly(styrene-B-Methyl Methacrylate) Block Copolymer Membrane Manufactured via a Phase Inversion Technique[END_REF] or a strategy related to SNIPS, [START_REF] Chisca | Artificial 3D Hierarchical and Isotropic Porous Polymeric Materials[END_REF] respectively. For the asymmetric material, although a complete pore formation was evidenced on the top layer during the SNIPS process, the resulting BCP morphology was arranged into a short-range ordered array with a broad pore size distribution, limiting the selectivity of the top separation layer. [START_REF] Karunakaran | Nanostructured Double Hydrophobic Poly(styrene-B-Methyl Methacrylate) Block Copolymer Membrane Manufactured via a Phase Inversion Technique[END_REF] In this work, we efficiently combine the NIPS process and the solvent vapor annealing (SVA) approach to demonstrate that fully hydrophobic triblock terpolymer thick films can also be manufactured with a sponge-like morphology topped by a long-range ordered nanostructure. We show that no-effort are required to pre-order the poly(1,1-dimethyl silacyclobutane)-block-polystyrene-block-poly(methyl methacrylate) (PDMSB-b-PS-b-PMMA) terpolymers on the material top surface during the NIPS process since the SVA treatment transforms the kinetically trapped poorly-ordered phase into a well-defined nanostructure. To obviate the need of alignment of the BCP nanodomains, we show that different network structures such as the alternating diamond (D A ) and perforated-lamellar (PL) phases can be readily produced on the top surface layer by using a simple blending strategy. As all the material architectures, consisting of a sponge-like substructure topped by a network structure having a high-areal density of well-defined continuous nanopathways, are highly-desired for the next generation-membranes, the NIPS-SVA process could be envisioned as a promising methodology towards the reproducible manufacturing in large scale of asymmetric and isoporous BCP membranes.

Results

The PDMSB-b-PS-b-PMMA used in this work was prepared by a sequential anionic polymerization, as described previously, [START_REF] Aissou | Highly Ordered Nanoring Arrays Formed by Templated Si-Containing Triblock Terpolymer Thin Films[END_REF] to achieve a perfect control of the molecular weight, M n , (34 kg.mol -1 ) with a narrow dispersity (Ð = 1.11) and a symmetric volume composition, , (ΦPDMSB = 0.32, ΦPS = 0.36, ΦPMMA = 0.32). This triblock terpolymer is nonfrustrated [START_REF] Bates | N Etwork Phases in Block Copolymer Melts[END_REF] since the Flory-Huggins interaction parameter, χPDMSB-PMMA, between the two end blocks (i.e., PDMSB and PMMA) is higher than the other pairs, χPDMSB-PS and χPS-PMMA (χPS-PMMA ≈ 0.04 < χPDMSB-PS ≈ 0.07 < χPDMSB-PMMA ≈ 0.2). [START_REF] Aissou | Highly Ordered Nanoring Arrays Formed by Templated Si-Containing Triblock Terpolymer Thin Films[END_REF][START_REF] Aissou | Sub-10 Nm Features Obtained from Directed Self-Assembly of Semicrystalline Polycarbosilane-Based Block Copolymer Thin Films[END_REF] Note that both (spin-coated) thin films and (drawn) asymmetric thick films made of this non-frustrated terpolymer exhibit a 39 nm period core-shell cylindrical structure having an in-plane orientation (i.e., an undesirable nanodomain orientation) when exposed to a chloroform (CHCl3) vapor (see Fig. S1). [START_REF] Chisca | Artificial 3D Hierarchical and Isotropic Porous Polymeric Materials[END_REF] A preferential swelling of the PDMDB domains under a CHCl3 stream makes that core-shell cylindrical structure differs from the bulk morphology since the SAXS profile of the thermally-annealed (24h, 180°C) PDMSB-b-PS-b-PMMA sample shows a first-order peak, q*, at 0.173 nm -1 and higher order peaks located at q/q* = 1, 2, 3, 4, 5, 6, 7, and 8, consistent with a lamellar phase having a period of 36.3 nm (see Fig. S2).

To alleviate the need for domain alignment, different highly-ordered network structures For short time durations of the SVA process (t < 1h), the characteristic D A (111) pattern is the most frequently observed on the free surface of the blended (25 % wt.) thick film. In contrast, the (310) and (311) motifs of the D A structure can be also encountered at the material-air interface when the time duration of the SVA process is increased. For instance, having a period of 27 nm. A hexagonal packing of perforations is commonly observed for the perforated layer structures in which the perforations are generally arranged into an AB or ABC stacking. [START_REF] Hamley | Hexagonal Mesophases between Lamellae and Cylinders in a Diblock Copolymer Melt[END_REF][START_REF] Hajduk | Stability of the Perforated Layer (PL) Phase in Diblock Copolymer Melts[END_REF][START_REF] Zhu | Dislocation-Controlled Perforated Layer Phase in a PEO-b-PS Diblock Copolymer[END_REF][START_REF] Ji | Kinetic Pathways of Lamellae to Gyroid Transition in Weakly Segregated Diblock Copolymers[END_REF] In contrast, a 27 nm period lamellar pattern without apparent perforations can be observed along the (101) plane (see Fig. 5c). The top view SEM images presented in For such PL structure having perforations stacked in ABAB… sequence, the (001) and (101) planes were also the most frequently observed at the material-air interface. Unfortunately, here the stacking sequence of the PMMA/PS perforations is unclear from the SEM images.

Conclusion

Bicontinuous network morphologies having an excellent long-range order were demonstrated on the skin layer of asymmetric and hydrophobic triblock terpolymer thick films manufactured by combining the conventional NIPS process with a SVA treatment used in advanced lithography application. Remarkably, an appealing triply periodic D A nanostructure of unprecedented complexity is achieved for the first time on a sponge-like microstructure. We believe this simple and scalable NIPS-SVA method, enabling the formation of appealing network nanostructures which differs from the common cylindrical morphology generated by SNIPS, can be viewed as a first step in the process of preparing newly-designed membranes. Indeed, porous nanochannels are also mandatory to manufacture a permeable membrane. To avoid any additional challenging etching process to remove the PMMA nanopathways, pH-responsive P2VP-containing triblock terpolymer membranes,

having either an open or closed state of the pores depending of the pH value, are currently being studied in our laboratory. nitrogen gas through the liquid solvent as described previously. [START_REF] Gotrik | Morphology Control in Block Copolymer Films Using Mixed Solvent Vapors[END_REF] This continuous flow system was used to control the CHCl3 vapor pressure in the chamber having a lid made of quartz by dilution with a separate N2 stream so that the solvent vapor consisted of 32 sccm CHCl3 vapor and 8 sccm N2 (total 40 sccm). As the in-situ measurement of the film thickness variation of an asymmetric thick film is not easy to achieve, the swelling ratio of a blended (25% wt.) PDMSB-b-PS-b-PMMA layer was estimated in thin configuration (initial thickness of 95 nm), using a Filmetrics spectroscopic white light reflectometer apparatus (see Fig. S8).

Methods

The blended layer, spin-coated (2 krpm) from a 2% wt. BCP solution in a mixture of tetrahydrofuran and propylene glycol monomethyl ether acetate (THF/PGMEA: 2/1), reached a plateau for a 70% thickness variation.

SEM and AFM

  were produced on the top surface layer by blending the PDMSB-b-PS-b-PMMA thick films with either 25 wt. % or 35 wt. % of PDMSB-b-PS chains ( PDMSB = 0.29, M n = 21.6 kg.mol-1 and Ð = 1.09). Importantly, blends of this triblock terpolymer with different amounts of a small PS homopolymer (hPS, 3 kg.mol -1 ) gave access to well-ordered cylindrical or spherical nanodomains on a denser sponge-like substructure. Here, the possible miscibility of PMMA domains with the small hPS chains, due to the low χPS-PMMA value, should be taken into account to explain the different phase behaviors of such blends.Blended PDMSB-b-PS-b-PMMA thick films were drawn into a silicon substrate from a 18 % wt. polymer solution in a di-solvent mixture of 1,4-dioxane and tetrahydrofuran (DOX/THF: 80/20 by weight) using a doctor's blade set at a gate height of 225 μm. After the thick film was casted, the di-solvent mixture was allowed to evaporate for 15s to form a dense top surface layer. The blended PDMSB-b-PS-b-PMMA thick films were then plunged in a water bath in order to induce the formation of a sponge-like substructure by NIPS. Note that a fluorine-rich reactive ion etching (RIE) plasma was performed to partially and preferentially remove PDMSB and PMMA domains, respectively, prior to take scanning electronic microcopy (SEM) images (plasma conditions are: 40 W, 17 sccm CF4 and 3 sccm O2, 180 mTorr, 45 s).The SEM image presented in Figure1ashows the resulting top surface morphology of a blended (25% wt.) PDMSB-b-PS-b-PMMA thick film generated by NIPS for a solvent evaporation time of 15s. In such conditions, the material top layer consists of dense regions formed by collapsed micelles (gray) which coexist with sub-100 nm diameter pores (black) randomly distributed across the surface. Conversely, a highly-ordered hexagonal nanoringlike array with a period of 38.5 nm is produced when the thick film is afterwards exposed to a CHCl3 vapor during 3h (see Fig.1b). This nanoring-like array pattern is consistent with the characteristic (111) crystallographic plane of an alternating diamond (D A , space group Fd3 ̅ m) structure oriented parallel to the air surface since it qualitatively resembles to the simulated cross-sectional view cut parallel to the D A (111) plane (see Fig.1binset) and to the D A (111) pattern recently observed in bulk from binary blends of polyisoprene-b-PS-b-poly(2-vinyl pyridine) (PI-b-PS-b-P2VP).[START_REF] Asai | Tricontinuous Double Diamond Network Structure from Binary Blends of ABC Triblock Terpolymers[END_REF] The presence of the D A (210) pattern as shown in Figure1cfurther confirms the formation of a D A structure, which consists of two chemically distinct (PDMSB and PMMA) and mutually interwoven networks embedded in a PS matrix (see Fig.S3). The D A (210) pattern presents wavy stripes ordered into a rectangular array with the lattice parameters a = 45 nm and b = 21 nm. The ratio a/b equal to 2.14 is quite similar to the one determined from the simulated (210) plane of the D A structure shown in Figure1cinset (a/b = 2.25).

Figure 1 : 2 .

 12 Figure 1: Top view SEM images of blended (25% wt.) PDMSB-b-PS-b-PMMA thick films manufactured by NIPS then exposed to a CHCl3 vapor during different times: (a) 0h and (b, c) 3h. The disordered phase generated by NIPS on the top surface membrane is transformed into a highly-ordered D A structure after the SVA treatment. Insets: Magnified SEM image showing (a) the dense regions formed by collapsed micelles after the NIPS process and (c) the D A (210) pattern. Additionally, simulated cross-sectional images of the D A structure cut parallel to (b) the (111) plane and (c) the (210) plane are presented. Scale bars: 100 nm.

Figure 2 :

 2 Figure 2: Cross-sectional SEM views of a blended (25% wt.) PDMSB-b-PS-b-PMMA thick film (t ~ 24 µm) generated by NIPS-SVA (3h, CHCl3) showing: (a) the full material on a Si substrate, (b) the D A structure formed within the material top layer, (c) the sponge-like substructure in the vicinity of the substrate, and (d) ordered D A grains delimited by red dashed lines in the sponge-like substructure. Inset: Magnified SEM view showing the complex D A structure. Scale bars: 0.5 µm.

  the atomic force microscopy (AFM) topographic and phase images taken from a blended (25 % wt.) PDMSB-b-PS-b-PMMA thick film exposed to a CHCl3 vapor for 3h then treated by a CF4/O2 RIE plasma show the typical wavy stripe pattern of the D A (310) plane oriented parallel to the air surface (see Fig. 3a-b).

Figure 3 :

 3 Figure 3: AFM (a) topographic and (b) phase views showing the D A (310) plane oriented parallel to the air surface of a blended (25% wt.) PDMSB-b-PS-b-PMMA thick film generated by NIPS-SVA (3h, CHCl3). (c) The 2D-FFT of the topographic image reveals that the wavy stripe pattern has c2mm symmetry. (d) Simulated cross-sectional image of the D A structure cut parallel to the (310) plane. Scale bars: 100 nm.

Figure 4 :

 4 Figure 4: AFM (a) topographic and (b) phase views showing the D A (311) plane oriented parallel to the air surface of a blended (25% wt.) PDMSB-b-PS-b-PMMA thick film generated by NIPS-SVA (3h, CHCl3). (c) The 2D-FFT of the topographic image indicates that the lozenge-like features are arranged in an oblique lattice. (d) Simulated cross-sectional image of the D A structure cut parallel to the (311) plane. Scale bars: 100 nm.

Figures 5d-e show

  Figures 5d-eshow the layered structure inside the material skin layer at different

Figure 5 :

 5 Figure 5: (a) Schematic representation of a bicontinuous PL structure having PMMA (red)/PS (blue) core-shell perforations. (b) and (c) Top view SEM images showing different PL planes oriented parallel to the air surface of a blended (35% wt.) PDMSB-b-PS-b-PMMA thick film generated by NIPS-SVA (3h, CHCl3). (d) and (e) Top view SEM images, at different magnifications, showing the PL phase inside the material skin layer. Scale bars: 200 nm.

Fabrication

  of asymmetric PDMSB-b-PS-b-PMMA-based thick films: 24 µm thick PDMSB-b-PS-b-PMMA thick films were drawn onto (1.5 x 2 cm²) silicon substrates by using a tape casting technique from a 18 % wt. terpolymer solution in a mixture of 1,4-dioxane and tetrahydrofuran (DOX/THF: 80/20 by weight). To manufacture asymmetric materials with a sponge-like substructure, solvents were allowed to evaporate during 15s to form a dense skin layer, and then the thick films were immersed into a water bath for 10 min. to precipitate the PDMSB-b-PS-b-PMMA terpolymer. A SVA treatment was subsequently performed to transform the kinetically trapped morphology formed on the material top surface into a selfassembled nanostructure. As the neat PDMSB-b-PS-b-PMMA terpolymer self-assembles into a core-shell cylindrical morphology when exposed to a CHCl3 vapor, the terpolymer solution was blended with either 25% wt. or 35% wt. of PDMSB-b-PS chains to achieve different bicontinuous network structures. Self-assembled PDMSB-b-PS-b-PMMA thick films: The self-assembly of unblended and blended PDMSB-b-PS-b-PMMA thick films was promoted by exposing the polymeric layers during different times to a continuous stream of CHCl3 vapor produced by bubbling

  Characterizations: Scanning electron microscopy (SEM, JEOL 7800) was used in Gentle Beam mode (GBSH) at an accelerating voltage of 1 kV to take PDMSB-b-PS-b-PMMA film images. Atomic force microscopy (AFM Dimension FastScan, Bruker) was used in tapping mode to characterize the surface morphology of blended and unblended PDMSB-b-PS-b-PMMA thick films. Silicon cantilevers (Fastscan-A) with a typical tip radius of 5 nm were used. The resonance frequency of the cantilevers was about 1.25 kHz. Prior to SEM and AFM measurements, PDMSB-b-PS-b-PMMA thick films were etched with a fluorine-rich plasma treatment in PE-100 chamber (RIE, Plasma Etch) to remove partially and preferentially the PDMSB and PMMA phases (plasma conditions: 40 W, 17 sccm CF4 and 3 sccm O2, 180 mTorr, and 45 s).Small Angle X-ray Scattering (SAXS):SAXS experiments were performed on the D2AM French-CRG Beamline at the European Synchrotron Radiation Facility (ESRF) in Grenoble, France. A XPAD 2D pixel detector was used for recording the 2D scattering images, and a 2400 mm sample-to-detector distance was chosen. The energy of the X-ray beam was 11 keV. The 2D images were radially averaged around the center of the primary beam to obtain the isotropic SAXS intensity profiles. The scattering pattern from a specimen of silver behenate was used for the calibration of the wavevector scale of the scattering curves. Finally, the data were normalized to the intensity of the incident beam to correct for primary beam intensity fluctuations.

Acknowledgements

This work was performed within the framework of the Equipex ELORPrintTec ANR-10-EQPX-28-01 with the support of the ANR JCJC AFM_Ring project, grant ANR-18-CE09-00xx of the French Agence Nationale de la Recherche. The ESRF is acknowledged for allocating beamtime at the D2AM French Beamline for the SAXS experiments.

Associated Content