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Soil erosion induced by rainfall is mainly due to the rainfall impact besides the consequent surface runoff. Rainfall kinetic energy is the most used variable to represent its erosivity. The latter represents the weathering attitude to erode soil and is a fundamental variable of the erosion process. Consequently, precise measurements of rainfall erosivity have to perform to develop a reliable prediction model of the erosive phenomenon. Currently, impact energy can be reliably measured only by disdrometers. These instruments measure the Drop Size Distribution (DSD) which, joined with the raindrop falling velocity, allow to calculate, by integration, the impact kinetic energy. However, disdrometers are expensive tools that imply to collect and process a remarkable amount of data, and for these reasons, they are not suitable for land large scale use. Without direct measurements, the rainfall impact energy is currently estimated using only the rainfall intensity, widely detected by the recording rain-gauge network operating all over the country. Recently, an innovative method to measure the rainfall energy, subject of a patent, has been proposed. This method is based on the simultaneous detection, in a given time interval, of the rainfall intensity and the number of raindrops that hit a specific surface. In this paper a theoretical analysis aimed at improving the reliability of this rainfall energy measurement is firstly presented. The developed analysis accounts for the detection of a further variable deriving from the momentum distribution. Then, the reliability of the proposed approach was tested using 44,695 DSDs recorded in Palermo in the period 2006-2014. Using the proposed approach, the reliability of the rainfall energy measurement can significantly improve.

Water soil erosion is a process of detachment and transport of soil particles due to rainfall and runoff and causes the landform modeling on earthʹs surface. The acceleration of soil erosion process through anthropogenic perturbation has severe impacts on soil which becomes qualitatively poor for crop establishment and growth. Planning soil conservation strategies requires prediction technologies of soil loss over a long‐time period. The Universal Soil Loss Equation (USLE), and its revised versions, are widely tested and applied in different environments throughout the world. At present, the USLE continues to be the most applied model for estimating soil loss and still represents the best compromise between applicability in terms of required input data and reliability of the obtainable soil loss estimates. Recent studies proposed to modify the climatic factor of USLE to give explicit consideration of runoff since this choice is expected to improve both interpretation of soil erosion processes and soil loss predictions. In this paper modified versions of the Universal Soil Loss Equation, which recognize that runoff is a primary independent factor in modeling rainfall erosion and use a general definition of the rainfall‐runoff erosivity factor including the power of both event runoff coefficient QR and event rainfall erosivity index EI30 of the USLE, were reviewed. The parameterization of the USLE‐MM and the USLE‐MB models useful to estimate the soil loss of given return period was also developed.

Trabajo presentado en TERRAenVISION Environmental Issues Today: Scientific Solutions for Societal Issues, celebrado en Barcelona (España) del 27 de enero al 2 de febrero de 2018, This contribution results from international collaborative efforts of different research groups around the Mediterranean basin focusing on soil conservation and water management. We will present the most complete database of runoff and soil erosion information and analyze the records from 68 locations, including more than 22458 detail events between 1985-2015. Soil conservation and water planning are two of the most challenging problems around the Mediterranean basin due to climate conditions and human activity. We believe that future advances on understanding soil degradation by water should be developed under global approaches. In this contribution, we will present an analysis of atmospheric conditions, expressed by weather types and the resulted rainfall, runoff, and erosion and sediment yield around the Mediterranean basin. The weather types compile daily information about the different air masses responsible for rainfall, runoff and eventually erosion and sediment yield, and their analyses let us know the synchrony of the response at different sites around the Mediterranean basin. The analyses of the global dataset display different spatial patterns for rainfall, runoff, and sediment yield, related to different atmospheric patterns. This research will be a valuable tool for understanding the evolution of these environmental variables, and therefore it will allow future planning to design regional water management and soil conservation measures

Nel presente lavoro viene valutata la potenzialità di accoppiare la USLE con il contenuto d’acqua del suolo pre-evento o il deflusso stimato, per migliorare l’accuratezza della stima della perdita di suolo a scala di singolo evento erosivo. A tale scopo sono stati utilizzati due approcci per i quali la perdita di suolo e il fattore di erosività sono legati da una legge di potenza. Il primo è il modello USLE-MM con deflusso stimato da un modello afflussi deflussi, SCRRM, che importa dati di contenuto d’acqua. Il secondo approccio è quello del modello SM4E che utilizza i dati di contenuto d’acqua pre-evento per correggere il fattore di erosività della pioggia. I due modelli sono stati testati usando le misure effettuate sulle parcelle di 22 m realizzate alle stazioni sperimentali di Masse e Sparacia. I risultati mostrano che la USLE-MM, che impiega misure di deflusso, conduce alle migliori stime della perdita di suolo. In atto, la simulazione del deflusso o l’uso del contenuto idrico del suolo conducono a una performance del modello peggiore di quella riscontrabile con la USLE originaria. Ulteriori indagini dovranno essere effettuate per migliorare la previsione del deflusso a scala di parcella, facendo anche ricorso a un database di misure più esteso.

Soil erosion by water, and the consequent loss of a non-renewable resource, is a relevant environmental issue which has economic, ecologic, and social repercussions. In the context of the European Green Deal, the increasing awareness of soil Ecosystem Services is leading to give the due relevance to this problem. Notwithstanding the recent soil conservation strategies adopted by the Common Agricultural Policy had positive effects, the concern regarding this topic is drastically increasing for the normalization of extraordinary rainfall events due to climate change. Recent events occurred in Europe demonstrated that landscape protection is often inadequate and interventions to prevent damages due to hydrogeological instability are scarce. The determination of a “tolerable” soil loss TSL is useful to establish a quantitative standard to measure the effectiveness of strategies and techniques to control soil erosion. However, soil conservation strategies/works designed by the mean annual value of the climatic variable, as the rainfall erosivity factor R, are not appropriate for some erosive events which produce intolerable sediment yield values. Therefore, the adoption of an adequate TSL, which could help to ensure the protection of soil functions and a sustainable soil use, should be a primary goal to reach for policy makers. In this paper, a new method to define the tolerable soil loss is proposed. This approach is based on the statistical analysis of the measured annual values of R and leads to the determination of the cover and management factor for which the maximum tolerable soil loss is equal to the annual soil loss of given return period. The analysis demonstrated that to limit soil erosion to the tolerable soil loss, interventions to change land use, reduce field length or apply support practices can be carried out.

Rills caused by runoff concentration on erodible hillslopes generally have very irregular longitudinal profiles and cross-section shapes. Rill erosion directly depends on the hydraulics of flow within the rills which may differ greatly from that in larger and regular channels like streams or rivers. At first, in this paper, a review of the two different approaches to estimate rill flow velocity, based on flow regime and flow resistance laws, is presented. Recent advances in measurements of rill geometry by the three-dimensional photo-reconstruction (3D-PR) technique, which allows one to obtain a Digital Terrain Model (DTM) by low-altitude aerial and terrestrial photogrammetry, are also discussed. Indeed, information on rill geometry is also necessary to estimate flow velocity and depth using flow resistance equations. Then, the results of related laboratory and field investigations carried out from 1984 to 2022 are reported. In particular, the review was developed considering the studies conducted investigating the different components of rill flow resistance due to grain resistance, morphological resistance (step-pool), and sediment transport. Moreover, a brief mention of the slope threshold, equal to 18%, determining differences in hydraulic and sediment transport variables, is done. Also, an analysis is developed to demonstrate that a theoretical rill flow resistance law has been erroneously presented as an example of spurious correlation. Finally, some research needs on rill flow hydraulics are highlighted.

The relevant erosive effects of extraordinary rainfall events due to climate change require establishing soil conservation strategies to prevent damages due to hydrogeological instability. The “tolerable” soil loss, i.e., the maximum soil loss compatible with sustainable soil use, represents a quantitative target to establish the effectiveness of actions to control soil erosion. In this paper, a new approach to defining the condition corresponding to a tolerable soil loss is proposed. At first, using the statistical analysis of the measured annual values of the rainfall erosivity factor, the cover and management factor CT, for which the maximum tolerable soil loss is equal to the annual soil loss of given return period T, is defined. Then, for the Sicilian region, a relationship between the CT factor obtained for T = 1000 years and the mean annual value of the rainfall erosivity factor, R, is established. For a given value C of the cover and management factor, this relationship allows for the establishment of the corresponding mean annual rainfall erosivity factor, named Rland-use. The result C ≤ CT for T = 1000 years is obtained for areas with R ≤ Rland-use, and the compliance with soil loss tolerance is then assured. Conversely, for areas characterized by R > Rland-use, the reduction of C to a value less than CT for T = 1000 years is required to obtain a tolerable soil loss condition. Finally, for the Sicilian region, the overlay between the C spatial distribution for arable lands (mainly cereals and legumes) and areas covered by vineyards, derived from the land use map, and the CT spatial distribution allowed to define areas in which tolerable soil loss conditions occur or soil conservation strategies are required.

The applicability of a theoretical rill flow resistance equation, based on the integration of a power velocity distribution, was tested using measurements carried out in mobile and fixed bed rills, shaped on plots having different slopes (9, 14, 15, 18, 22, 24, 25 and 26%) and soil textures (clay fractions ranging from 32.7% to 73% and silt of 19.9–30.9%), and flume measurements available in the literature. The Darcy–Weisbach friction factor resulted dependent on the slope, Froude number, Reynolds number and clay and silt percentages, used as variables representative of soil transportability and detachability, respectively. This theoretical approach was applied to two different databases distinguished by the slope threshold of 18%. The results showed that for both steep (≥18%) and gentle (

Flow velocity is one of the most important hydrodynamic variables for both channelized (rill and gullies) and interrill erosive phenomena. The dye tracer technique to measure surface flow velocity Vs is based on the measurement of the travel time of a tracer needed to cover a known distance. The measured Vs must be corrected to obtain the mean flow velocity V using a factor αv=V/Vs which is generally empirically deduced. The Vs measurement can be influenced by the method applied to time the travel of the dye-tracer and αv can vary in different flow conditions. Experiments were performed by a fixed bed small flume simulating a rill channel for two roughness conditions (sieved soil, gravel). The comparison between a chronometer-based (CB) and video-based (VB) technique to measure Vs was carried out. For each slope-discharge combination, 20 measurements of Vs, characterized by a sample mean Vm, were carried out. For both techniques, the frequency distributions of Vs/Vm resulted independent of slope and discharge. For a given technique, all measurements resulted normally distributed, with a mean equal to one, and featured by a low variability. Therefore, Vm was considered representative of surface flow velocity. Regardless of roughness, the Vm values obtained by the two techniques were very close and characterized by a good measurement precision. The developed analysis on αv highlighted that it is not correlated with Reynolds number for turbulent flow regime. Moreover, αv is correlated neither with the Froude number nor with channel slope. However, the analysis of the empirical frequency distributions of the correction factor demonstrated a slope effect. For each technique (CB, VB)-roughness (soil, gravel) combination, a constant correction factor was statistically representative even if resulted in less accurate V estimations compared to those yielded by the slope-specific correction factor.

Rills caused by run-off concentration on erodible hillslopes have very irregular profiles and cross-section shapes. Rill erosion directly depends on the hydraulics of flow in the rills, which may differ greatly from hydraulics of flow in larger and regular channels. In this paper, a recently theoretically deduced rill flow resistance equation, based on a power–velocity profile, was tested experimentally on plots of varying slopes (ranging from 9% to 26%) in which mobile and fixed bed rills were incised. Initially, measurements of flow velocity, water depth, cross-section area, wetted perimeter, and bed slope, carried out in 320 reaches of mobile bed rills and in 165 reaches of fixed rills, were used for calibrating the theoretical flow resistance equation. Then the relationship between the velocity profile parameter Γ, the channel slope, and the flow Froude number was separately calibrated for the mobile bed rills and for the fixed ones. The measurements carried out in both conditions (fixed and mobile bed rills) confirmed that the Darcy–Weisbach friction factor can be accurately estimated using the proposed theoretical approach. For mobile bed rills, the data were supportive of the slope independence hypothesis of velocity, due to the feedback mechanism, stated by Govers. The feedback mechanism was able to produce quasicritical flow conditions. For fixed bed rills, obtained by fixing the rill channel, by a glue, at the end of the experimental run with a mobile bed rill, the slope independence of the flow velocity measurements was also detected. Therefore, an experimental run carried out by a rill bed fixed after modelling flow action is useful to detect the feedback mechanism. Finally, the analysis showed that, for the investigated conditions, the effect of sediment transport on the flow resistance law can be considered negligible respect to the grain roughness effect.

Recent research recognized that the slope of 18% can be used to distinguish between the ‘gentle slope’ case and that of ‘steep slope’ for the detected differences in hydraulic variables (flow depth, velocity, Reynolds number, Froude number) and those representatives of sediment transport (flow transport capacity, actual sediment load). In this paper, using previous measurements carried out in mobile bed rills and flume experiments characterized by steep slopes (i.e., slope greater than or equal to 18%), a theoretical rill flow resistance equation to estimate the Darcy-Weisbach friction factor is tested. The main aim is to deduce a relationship between the velocity profile parameter Γ, the channel slope, the Reynolds number, the Froude number and the textural classes using a data base characterized by a wide range of hydraulic conditions, plot or flume slope (18%–84%) and textural classes (clay ranging from 3% to 71%). The obtained relationship is also tested using 47 experimental runs carried out in the present investigation with mobile bed rills incised in a 18%—sloping plot with a clay loam soil and literature data. The analysis demonstrated that: (1) the soil texture affects the estimate of the Γ parameter and the theoretical flow resistance law (Equation 25), (2) the proposed Equation (25) fits well the independent measurements of the testing data base, (3) the estimate of the Darcy-Weisbach friction factor is affected by the soil particle detachability and transportability and (4) the Darcy-Weisbach friction factor is linearly related to the rill slope.

In this paper a recently theoretically deduced rill flow resistance equation, based on a power-velocity profile, was tested experimentally on plots of varying slopes and soil texture in which mobile bed rills are incised. Measurements of flow velocity, water depth, cross section area, wetted perimeter and bed slope conducted in rill reaches incised on experimental plots, having different slope values (9, 14, 22, 24 and 26%) and soil texture (clay fraction ranging from 42 to 73%), and literature data were used to calibrate the flow resistance equation. In particular, the relationship between the velocity profile parameter Γ, the channel slope, the flow Froude number and texture fractions was firstly calibrated using 147 rill reach data. Then this relationship was tested using 126 measurements carried out with soils having different texture (percentage of clay ranging from 9.6 to 73%) and slopes (6.9%–26%). The measurements allowed to establish that a) the Darcy-Weisbach friction factor can be accurately estimated using the proposed theoretical approach, and b) the data were supportive of the soil texture influence on rill velocity and flow resistance.

In this paper, a new flow resistance equation for rill flow was deduced applying dimensional analysis and self‐similarity theory. At first, the incomplete self‐similarity hypothesis was used for establishing the flow velocity distribution whose integration gives the theoretical expression of the Darcy–Weisbach friction factor. Then the deduced theoretical resistance equation was tested by some measurements of flow velocity, water depth, cross section area, wetted perimeter, and bed slope carried out in 106 reaches of some rills shaped on an experimental plot. A relationship between the velocity profile, the channel slope, and the flow Froude number was also established. The analysis showed that the Darcy–Weisbach friction factor can be accurately estimated by the proposed theoretical approach based on a power–velocity profile.

Many field investigations have clearly shown that rare and severe events control total soil erosion occurring over a long time period with up to 92% of total soil erosion over a 7‐year period resulting from just three daily events. Therefore, soil conservation strategies should be developed taking into account large events rather than long‐term average erosion. From an engineering point of view, establishing the soil loss of a given return period is needed. This can be obtained by the frequency analysis of soil loss measurements or by suitable soil erosion models. The USLE‐M modified and USLE‐M based are two empirical Universal Soil Loss Equation‐Modified (USLE‐M) type models which were developed using runoff and soil loss measurements collected at the Sparacia (South Italy) station. According to USLE‐M type models, the return period of the estimated soil loss coincides with that of the rainfall‐runoff erosivity index. In this investigation, using the maximum annual values of event soil loss measured on bare plots at Sparacia, this hypothesis was recognized to be not valid. To overcame this limit, a parameterization method which imposes the coincidence of the two return periods was applied. The models, which were parameterized by the maximum annual values of event soil loss, produced only moderate improvements in the prediction of the soil loss of given return period as compared with their previously published versions, which were parameterized by all available measurements. This result induced to hypothesize that parameterization of the USLE‐MM and the USLE‐MB models useful to estimate the soil loss of given return period in other sites can be also performed with all available data, not only with the maximum annual event soil losses which would require a larger number of recording years to obtain a suitable sample size. However, the developed database should span a wide soil loss measurement range. In general, at Sparacia both USLE‐MM and USLE‐MB were able to yield accurate predictions for return period ranging from 4 to 20 years.

In this paper a recently theoretically deduced flow resistance equation, based on a power-velocity profile, was tested using data collected for overland flow under simulated rainfall carried out in plots with vegetation. The available data were obtained exploring a wide range of rainfall intensities (from 60 to 181 mm h−1) and slopes (from 3.6 to 39.6%), and with four different types of vegetation. The database, including measurements of flow velocity, water depth, cross sectional flow area, wetted perimeter and bed slope, was divided in four datasets (one for each vegetation type), which allowed the calibration of the relationship between the velocity profile parameter Γ, the slope steepness, the flow Froude number, and the rainfall Reynolds number. The effect of rainfall intensity and different types of vegetation on flow resistance was investigated. The results showed that the theoretically deduced flow resistance equation allowed an accurate estimate of the Darcy-Weisbach friction factor for overland flow under simulated rainfall and in presence of vegetation. The developed analysis also suggested that flow resistance increases with rainfall intensity for laminar overland flow. The available data demonstrated that a quasi-independence between slope and mean velocity occurred. Finally, a single flow resistance equation resulted applicable to all investigated vegetation types and this equation was affected by flow regime represented by flow Reynolds number.

At first, in this paper a general definition of the event rainfall-runoff erosivity factor for the USLE-based models, REFe = (QR)b1(EI30)b2, in which QR is the event runoff coefficient, EI30 is the single-storm erosion index and b1 and b2 are coefficients, was introduced. The rainfall-runoff erosivity factors of the USLE (b1 = 0, b2 = 1), USLE-M (b1 = b2 = 1), USLE-MB (b1 ≠ 1, b2 = 1), USLE-MR (b1 = 1, b2 ≠ 1), USLE-MM (b1 = b2 ≠ 1) and USLE-M2 (b1 ≠ b2 ≠ 1) can be defined using REFe. Then, the different expressions of REFe were simultaneously tested against a dataset of normalized bare plot soil losses, AeN, collected at the Sparacia (south Italy) site. As expected, the poorest AeN predictions were obtained with the USLE. A distinction was made among the four power-type models since the fitting to the data was poor with the USLE-MR as compared with the other three models. Estimating two distinct exponents (one for EI30 and another for QR, USLE-M2) instead of a single exponent (USLE-MB, USLE-MR, USLE-MM) did not appreciably improve soil loss prediction. The USLE-MB and the USLE-MM were the best performing models.

Improving Universal Soil Loss Equation (USLE)‐based models has large interest because simple and reliable analytical tools are necessary in the perspective of a sustainable land management. At first, in this paper, a general definition of the event rainfall‐ runoff erosivity factor for the USLE‐based models, REFₑ = (QR)ᵇ¹(EI₃₀)ᵇ², in which QR is the event runoff coefficient, EI₃₀ is the single‐storm erosion index, and b₁ and b₂ are coefficients, was introduced. The rainfall‐runoff erosivity factors of the USLE (b₁ = 0 and b₂ = 1), USLE‐M (b₁ = b₂ = 1), USLE‐MB (b₁ ≠ 1 and b₂ = 1), USLE‐MR (b₁ = 1 and b₂ ≠ 1), USLE‐MM (b₁ = b₂ ≠ 1), and USLE‐M2 (b₁ ≠ b₂ ≠ 1) can be defined using REFₑ. Then the different expressions of REFₑ were simultaneously tested against a data set of normalized bare plot soil losses, AₑN, collected at the Sparacia (south Italy) site. As expected, the poorest AₑN predictions were obtained with the USLE. The observed tendency of this model to overestimate small AₑN values and underestimate high AₑN values was reduced by introducing in the soil loss prediction model both QR and an exponent for the erosivity term. The fitting to the data was poor with the USLE‐MR as compared with the USLE‐MB and the USLE‐MM. Estimating two distinct exponents (USLE‐M2) instead of a single exponent (USLE‐MB, USLE‐MR, and USLE‐MM) did not appreciably improve soil loss prediction. The USLE‐MB and the USLE‐MM were recognized to be the best performing models among the possible alternatives, and they performed similarly with reference to both the complete data set and different sub‐data sets, only including small, intermediate, and severe erosion events. In conclusion, including the runoff coefficient in the soil loss prediction model is important to improve the quality of the predictions, but a great importance has to be paid to the mathematical structure of the model.

Flow velocity controls hillslope soil erosion and is a key hydrodynamic variable involved in sediment transport and deposition processes. The dye-tracer technique is one of the most applied methods for measuring velocity of shallow interrill and rill flow. The technique is based on the injection of a tracer in a specific point and the measurement of its speed to travel the known distance from the injection point to a given channel section. The dye-tracer technique requires that the measured surface flow velocity has to be corrected to obtain the mean flow velocity using a correction factor which is generally empirically deduced. The technique has two sources of uncertainties: i) the method applied for measuring the travel time of the dye-tracer and ii) the estimate of the correction factor, which is the ratio between the mean flow velocity and the surface velocity, in different flow conditions. In this paper the results of a wide experimental investigation, carried out using a fixed bed small flume simulating a rill channel, are presented. At first, the comparison between a chronometer-based (CB) and video-based (VB) technique was carried out for establishing the influence of the travel time measuring technique. For each experimental run, which was characterized by a sample of 20 measurements carried out with the same values of slope and discharge, the developed analysis showed that the empirical frequency distribution of the ratio between the single measurement and the sample mean (i.e., the average of 20 measurements) is more uniform for the VB technique than for the CB one. In any case, this sample mean was representative of surface flow velocity for both the CB and the VB technique. Furthermore, the mean value obtained by the CB measurements lightly underestimated (−1.7%) the corresponding mean obtained by the VB technique. Finally, the effects of slope (0.1–8.7%), flow Reynolds number (3462–10040), Froude number (1.44–5.17) on the correction factor are presented. The analysis demonstrated that the correction factor is independent of flow Reynolds number while a relationship with a Froude number, obtained by surface velocity measurement, or channel slope can be established.

Soil erosion is a key process to understand the land degradation, and modelling of soil erosion will help to understand the process and to foresee its impacts. The applicability of the Universal Soil Loss Equation (USLE) at event scale is affected by the fact that USLE rainfall erosivity factor does not take into account runoff explicitly. USLE-M and USLE-MM, including the effect of runoff in the event rainfall– runoff erosivity factor, are characterized by a better capacity to predict event soil loss. The specific objectives of this paper were (i) to determine the suitable parameterization of USLE, USLE-M and USLE-MM by using the dataseries of Sparacia experimental site and (ii) to evaluate their performances at both event and annual scale. The measurements allowed to establish the relationships for calculating the factors of USLE, USLE-M and USLE-MM usable at the Sparacia experimental area. At first, for slope-length values greater than 33 m, the calibration of USLE model at event scale pointed out that sediment delivery processes, that is processes involving deposition of the transported eroded soil particles, occur. The analysis showed that USLE and USLE-M tend to overestimate low event soil losses, while for USLE-MM, this tendency is less pronounced. However, the USLE-MM performed better than USLE and USLE-M and was able to reproduce better than other two models the highest soil loss values that are the most interesting from a practical point of view. The results obtained at annual scale were generally consistent with those obtained at event scale.

Planning soil conservation strategies requires predictive techniques at event scale because a large percentage of soil loss over a long-time period is due to relatively few large storms. Considering runoff is expected to improve soil loss predictions and allows relation of the process-oriented approach with the empirical one, furthermore, the effects of detachment and transport on soil erosion processes can be distinguished by a runoff component. In this paper, the empirical model USLE-MB (USLE-M based), including a rainfall-runoff erosivity factor in which the event rainfall erosivity index EI30 of the Universal Soil Loss Equation (USLE) multiplies the runoff coefficient QR raised to an exponent b1>1 is tested by the measurements carried out for the Masse (10 plots) and Sparacia (22 plots) experimental stations in Italy. For the Masse experimental station, an exponent b1>1 was also estimated by tests carried out by a nozzle-type rainfall simulator. For each experimental site in fallow conditions, the effect of the sample size of the plot soil loss measurements on the estimate of the b1 coefficient was also studied by the extraction of a fixed number N of randomly obtained pairs of the normalized soil loss and runoff coefficient. The analysis showed that the variability of b1 with N is low and that 350 pairs are sufficient to obtain a stable estimate of b1. A total of 1,262 soil loss data were used to parameterize the model both locally and considering the two sites simultaneously. The b1 exponent varied between the two sites (1.298–1.520), but using a common exponent (1.386) was possible. Using a common b1 exponent for the two experimental areas increases the practical interest for the model and allows the estimation of a baseline component of the soil erodibility factor, which is representative of the at-site soil intrinsic and quasi-static properties. Development of a single USLE-MB model appears possible, and sampling other sites is advisable to develop a single USLE-MB model for general use.

Water flow on hillslope soil surface supplies energy which is required to detach soil particles, to transport and deposit sediments, therefore flow velocity is a key variable related to hillslope hydrodinamics of soil erosion processes. Among the different methods available for measuring velocity of shallow interrill and rill flow, the trace technique is widely used. Trace technique is applied by adding a material (salt, magnetic material, water isotope, floating object) and then measuring the speed of the material to travel a known distance from the injection point. When flow velocity is measured using a dye-tracing method, the mean velocity is calculated by multiplying the measured surface velocity of the leading edge of the tracer plume by a correction factor which was generally empirically deduced. The main uncertainty of the dye-tracing technique stands in the estimate of this correction factor, which is the ratio between the mean flow velocity and the surface velocity. The main goal of this paper is establishing a theoretical relationship for calculating the correction factor by using a power velocity profile. At first, the developed analysis demonstrated that the correction factor only depends on the exponent of the power velocity distribution (Eq. (5) ). Then, this theoretical expression of the correction factor was applied using the velocity profiles measured by Baiamonte and Ferro for the condition of sediment-free flow in motion on a rough bed and by Coleman for a sediment-laden flow moving on a smooth flume. Using the correction factor values calculated by the velocity measurements carried out for the sediment-free flow in motion on a rough bed, the relationship between the correction factor and roughness height was established. In agreement with a previous study by Ali et al., for a sediment-free flow the correction factor increases with roughness height. Finally, the velocity profile measurements carried out for a sediment-laden flow in motion on a smooth bed were used to state the effect of sediment load on the correction factor. This last analysis allowed to conclude, in agreement with Li and Abrahams and Zhang et al., that the correction factor decreases when the sediment load increases.

In this paper, 1017 rainfall events from 2008 to 2017 are used to identify the rainfall threshold that produces upland erosion at the Masse (central Italy) and Sparacia (southern Italy) experimental stations. The rainfall events are classified into three classes: non-erosive, interrill-only and rill. The threshold values for separating as correctly as possible the erosive rains (case I) and the rill rains (case II) are derived solely from the hyetograph. Each threshold value is obtained by imposing that the long-term erosivity of the events above the threshold is equal to the long-term erosivity of all erosive events (case I) or only rill events (case II). The performances of selective criteria based on 31 threshold variables are compared, and those most effective in separating erosive and rill events are identified. The identification of the best criterion depends on the aim of the analysis. It could be required to provide the greatest accuracy for separating erosive and rill events or the lowest error in the prediction of long-term erosivity. In general, the results clearly show that the best variables are those that quantify the characteristics of rainfall patterns, such as rain showers (periods of continuous rain) and the deviations in the rain records over a truncation level. These results are especially significant for the operational estimation of rainfall erosivity and for identifying the trigger of the erosion process and rill development by using only a hyetograph. This is obtained by relatively simple field measurements and is also widely available on a global scale. The most effective variables are potentially usable in water erosion prediction models as proxies of variables that are more rarely available and/or more difficult to measure.

The modified Universal Soil Loss Equation (USLE-M) was empirically deduced by a statistical analysis of the original data set of soil loss measurements used to derive the Universal Soil Loss Equation (USLE). The USLE-M, including the effect of runoffin the event rainfall-runofferosivity factor, is characterized by a better capacity to predict event soil loss. At first, in this paper, using the soil erosion representative variables of USLE-M and the reference condition adopted in the USLE, the dimensional analysis and the self-similarity theory are applied to theoretically deduce a multiplicative equation similar to the USLE-M. Then using the database of the Sparacia experimental site, the ability to predict event soil loss by the USLE-M and modified USLE-M (USLE-MM) models are tested. The analysis demonstrates that the relationships used to predict the topographic factors of USLE-MM can be applied in areas different from the one of its original derivation. Finally, the analysis shows that, overall, USLE-MM [Nash-Sutcliffe index (NSEI) = 0.80; root mean square error (RMSE) = 10.3] performed slightly better than USLE-M (NSEI = 0.75; RMSE = 11.4) whereas the soil loss prediction accuracy especially improved for the relatively low and the highest values. In fact, for event soil loss per unit area (Ae) < 10 Mgha-1 the RMSE was equal to 7.1 for USLE-M and 4.4 for USLE-MM, and for Ae > 100 Mgha-1 the maximum factor of difference between predicted and measured soil losses was equal to 1.8 for USLE-M and 1.2 for USLE-MM.

Many process-oriented erosion prediction models reproduce rill erosion as affected by site-specific parameters, as for example, rill erodibility, and thus, their practical application requires the measurement of these parameters or their estimate. The aim of this paper was establishing a method for indirectly measuring field rill erodibility. A simple mathematical approach based on a known soil detachment equation and accounting for the rill erosion dynamic process is applied. Field measurements carried out for seven natural rainfall events occurring at the plots of the Sparacia experimental station, southern Italy, are used for indirectly measuring the rill erodibility of the investigated soil. This method needs only the knowledge of the geometric characteristics of the rills at the end of the erosion event and the event duration. The method was also tested by using the Water Erosion Prediction Project database, and this analysis showed that a reliable value of rill erodibility can be obtained by the proposed Equation 18. The proposed method has the following advantages: (i) to be applicable at field scale, being more realistic than the laboratory scale because the soil structure is not destroyed, and (ii) to avoid the disadvantages of field experiments such as the cumbersome experimental set-up and the large volume of water inflow needed

In order to measure soil loss in equipped plots the estimate of the weight of solid material intercepted at their lower end is required. At the experimental area of Sparacia, Sicily, the runoff produced by an erosive event is collected within storage tanks with a capacity of about 1m3. In this paper, the use of a new sampler is proposed to measure easily the weight of solid material eroded from an experimental plot and collected into a storage tank. The sampler is a cylinder having a closing valve at the bottom. Two different series of runs were carried out both to test the reliability of the sampler and to establish a sampling procedure, respectively. An analysis of various sampling configurations usable in the field differentiated by the number and location of sampling verticals in the tank cross-section was finally carried out. The results of the present investigation are that the concentration measurement by the sampler was more accurate than that obtained by other methods involving a collection tank, agitation and sampling of the suspension. This sampler is cheap and usable in combination with a quick field sampling procedure which is particularly advisable when the number of plots equipped at an experimental area is large. The sampler was tested using a clay soil contained within cylinders and a cubic tank, but it appeared also to be usable with coarser sediment than clay and in combination with tanks having a different shape.

In this paper, the physical model concept by Nearing (1998. Catena 32: 15–22) was assessed. Soil loss data collected on plots of different widths (2–8 m), lengths (11–44 m) and steepnesses (14.9–26.0%), equipped in south and central Italy, were used. Differences in width between plots of given length and steepness determined a lower data correlation and more deviation of the fitted regression line from the identity one. A coefficient of determination between measured, M , and predicted, P , soil losses of 0.77 was representative of the best-case prediction scenario, according to Nearing (1998). The relative differences, Rdiff = ( P − M ) / ( P + M ), decreased in absolute value as M increased only for erosion rates approximately > 1 kg m − 2 . An alternative applicative criterion of the physical model concept, based on the | P − M | difference, was valid for the entire range of measured soil losses. In conclusion, the physical model should be defined in terms of perfect planimetrical equivalence. The best applicative criterion of the physical model concept may vary with the considered dataset, which practically implies the need to further test this concept with other datasets.

Producción Científica, Rainfall is the key factor to understand soil erosion processes, mechanisms, and rates. Most research was conducted to determine rainfall characteristics and their relationship with soil erosion (erosivity) but there is little information about how atmospheric patterns control soil losses, and this is important to enable sustainable environmental planning and risk prevention. We investigated the temporal and spatial variability of the relationships of rainfall, runoff, and sediment yield with atmospheric patterns (weather types, WTs) in the western Mediterranean basin. For this purpose, we analyzed a large database of rainfall events collected between 1985 and 2015 in 46 experimental plots and catchments with the aim to: (i) evaluate seasonal differences in the contribution of rainfall, runoff, and sediment yield produced by the WTs; and (ii) to analyze the seasonal efficiency of the different WTs (relation frequency and magnitude) related to rainfall, runoff, and sediment yield. The results indicate two different temporal patterns: the first weather type exhibits (during the cold period: autumn and winter) westerly flows that produce the highest rainfall, runoff, and sediment yield values throughout the territory; the second weather type exhibits easterly flows that predominate during the warm period (spring and summer) and it is located on the Mediterranean coast of the Iberian Peninsula. However, the cyclonic situations present high frequency throughout the whole year with a large influence extended around the western Mediterranean basin. Contrary, the anticyclonic situations, despite of its high frequency, do not contribute significantly to the total rainfall, runoff, and sediment (showing the lowest efficiency) because of atmospheric stability that currently characterize this atmospheric pattern. Our approach helps to better understand the relationship of WTs on the seasonal and spatial variability of rainfall, runoff and sediment yield with a regional scale based on the large dataset and number of soil erosion experimental stations., Ministerio de Economía y Competitividad - FEDER (CGL2014 52135-C3-3-R; ESP2017-89463-C3-3-R; CGL2014-59946-R; CGL2015-65569-R; CGL2015-64284- C2-2-R; CGL2015-64284-C2-1-R; CGL2016-78075-P; GL2008-02879/BTE; LEDDRA 243857; RECARE-FP7; CGL2017-83866-C3-1-R y PCIN-2017- 061/AEI), Ministerio de Economía y Competitividad (FJCI-2017-33652), Organización para la Cooperación y el Desarrollo Económicos (TAD/CRP JA00088807), Junta de Castilla y León - FEDER (CLU-2018-04)