Can the models keep up with the data? Possibilities of soil and soil surface assessment techniques in the context of process based soil erosion models – A Review

Climate change, accompanied by intensified extreme weather events, results in changes in intensity, frequency and magnitude of soil erosion. These unclear future developments make adaption and improvement of soil erosion modelling approaches all the more important. Hypothesizing that models cannot keep up with the data, this review gives an overview of 44 process based soil erosion models, their strengths and weaknesses and discusses their potential for further development with respect to new and improved soil and soil erosion assessment techniques. We found valuable tools in areas, as remote 15 sensing, tracing or machine learning, to gain temporal and spatial distributed high resolution parameterization and process descriptions which could lead to a more holistic modelling approach. Most process based models are so far not capable to implement cross-scale erosional processes or profit from the available resolution on a temporal and spatial scale. We conclude that models need further development regarding their process understanding, adaptability in respect to scale as well as their parameterization and calibration. The challenge is the development of models which are able to simulate soil erosion 20 processes as close to reality as possible, as user-friendly as possible and as complex as it needs to be. https://doi.org/10.5194/soil-2021-85 Preprint. Discussion started: 20 August 2021 c © Author(s) 2021. CC BY 4.0 License.


Introduction
Soil, a natural resource with essential functions to the ecosystem, has experienced extensive degradation over the past decades (Swinton et al., 2007;Evans et al., 2019). Soil degradation is caused by a combination of spatial and temporal 25 highly variable factors of natural and anthropogenic origin. Natural processes such as soil nutrient depletion, salinization and soil erosion are intensified by anthropogenic influences, such as agricultural mismanagement, overgrazing, overexploitation and environmental pollution (Jie et al., 2002;Baumgart et al., 2017). Soil erosion can lead to extensive soil loss and eventually to the exposure of the underlying bedrock (Evans et al., 2019). Due to its complexity, the determination of influencing parameters is challenging (Phinzi and Ngetar, 2019). Soil erosion represents a decisive process for degrading 30 agricultural land and with this crop yield on a global scale (Bakker et al., 2004;Zhang et al., 2004;Zhao et al., 2016). Climate change, accompanied by an increase in frequency and magnitude of weather extremes, leads to spatially differentiated changes in extent, intensity and frequency of soil erosion (Nearing et al., 2005;Routschek et al., 2014;Li and Fang, 2016;Guo et al., 2019). A variety of studies such as Boardman et al. (1990), Favis-Mortlock and Boardman (1995), Michael et al. (2005), Klik and Eitzinger (2010), Nunes et al. (2013) and Hu et al. (2020b) focusses on estimating climatic 35 impact on erosional processes. According to them, the impact of climate change on soil erosion varies greatly depending on the region. One approach to better estimate these impacts, suggests to link climate change models with soil erosion models working on a high temporal resolution (Li and Fang, 2016).
Climate change having its direct impact on soil erosion, also triggers indirect drivers, such as anthropogenic activity, changes in crop management or land use changes, which can affect soil erosion even more strongly (Li and Fang, 2016;Guo et al., 40 2019). While soil erosion on arable land is generally higher than on non-arable land (Cerdan et al., 2010), it largely depends on land management practices. Consequently, adapted land management is an important step towards the sustainable use of soils (Mullan et al., 2012;Routschek et al., 2014). The protection and conservation of soils has become a major social challenge worldwide and represents an important field of research (Govers et al., 2007). To support soil protection efforts and recovery strategies, precise assessments of erosion rates and information on erosion and sedimentation processes are of 45 crucial importance (Boardman and Poesen, 2006;Evans et al., 2019).
Research on this topic started early in the last century, with first modelling approaches in the 1940s by Zingg (1940) (quoted in Wischmeier and Smith, 1965) and the development of an empirical based soil erosion model, the universal soil-loss equation (USLE) by Wischmeier and Smith (1965). Since then many soil erosion and sedimentation models have been developed and many authors have reviewed them, providing an overview of the variety of existing models. Amongst others, 50 they point out the following limiting factors for process based soil erosion models: - High data demand and model complexity (Pandey et al., 2016) -The risk of equifinality (Govers, 2010;Batista et al., 2019) -Temporal unchanging soil and surface input parameters (Merritt et al., 2003;Pandey et al., 2016) -Spatial homogenous soil input parameters for areas of similar properties (Pandey et al., 2016;Merritt et al., 2003) 55 -Scarce data availability (Schindewolf et al., 2013) -Only a selective process description (e.g. leaving out gully erosion, rill-interill interaction or rill initiation) (Aksoy and Kavvas, 2005;Hajigholizadeh et al., 2018) For a more holistic understanding of soil erosion and an impact reduction by applying adapted management strategies, models need to integrate the current understanding of soil erosion processes from splash to gully erosion (Parsons, 2019;Li 60 and Fang, 2016). The continuous development and improvement of measurement techniques for soil erosion and soil properties, lead to spatially and temporally highly resolved information at different scales (Li et al., 2017). In this context, it is of great interest to consider how far they can contribute to the improvement and further development of soil erosion https://doi.org/10.5194/soil-2021-85 Preprint. Discussion started: 20 August 2021 c Author(s) 2021. CC BY 4.0 License. models. Based on these considerations we work with the hypothesis that models cannot keep up with the data, in the context of which, we consider the 65 i) State-of-the-art -Are current process based soil erosion models insufficient in terms of parameterization and modern process description at high spatial and temporal scales?
-What are the opportunities and limitations offered by today's data assessment techniques?
ii) What to do next? 70 -Can today's potential in data assessment overcome shortcomings and improve existing models?
-Can soil erosion process descriptions be delineated from modern erosion measurement techniques and be integrated into the models?
-Can these data possibilities make the models more accurate and improve them in terms of parameterization and validation? 75 This review intends to offer scientists an overview of potentials and shortcomings of process based soil erosion models, especially regarding their capabilities of implementing data from new and improved measurement techniques. Along this interface, we want to identify the relevant factors for verification and advancement of these models based on today's possibilities of data generation and processing to overcome limitations and to improve soil erosion modelling.

Soil erosion assessmentstate of research
Today, a large number of soil erosion models exist and a wide range of methods for measuring soil erosion processes by water have been developed. A brief summary on process based soil erosion models is provided, taking the spatial and 145 temporal frame, the limitations, capabilities and the type of considered erosion process, into account. An overview of soil erosion assessment techniques follows, focusing on their type of assessment and the temporal and spatial scale they can be applied to.

Process based soil erosion models
Models as simplifications of reality can, by definition never represent the processes of the real world in its entirety. Soil 150 erosion modelling started with the development of first empirical based models in the middle of the last century (Wischmeier and Smith, 1965;Wischmeier and Smith, 1978;Renard et al., 1991) and where, with the improvement of computing power and data availability, followed by process based or physically based soil erosion models (Schmidt, 1991;De Roo and Offermans, 1995). The latter, while being more complex regarding their input data, computing requirement, calibration necessity and being less user-friendly, offer due to physical based descriptions of soil erosion and sediment transport a more 155 accurate understanding and reproduction of the occurring processes (Hajigholizadeh et al., 2018). Process based models therefor enable a better extrapolation and transferability of the results than empirical based models (Merritt et al., 2003;Lane et al., 2001;Li et al., 2017;Pandey et al., 2016;Vente et al., 2013;Schindewolf et al., 2013). Furthermore, they allow an isolated consideration of individual components of soil erosion processes as well as a better understanding of the relationship between cause and impact within soil erosion research (Scherer, 2008). 160 Soil erosion models can be further distinguished along different aspects, as their considered temporal (continual/event-based) and spatial (field/catchment/regional) scale, or their distribution of erosion patterns (lumped/spatially distributed) (Karydas et al., 2012). Water erosion, as a discontinuous process, is mainly driven by single extreme rainfall events (Edwards and Owens, 1991), making the event-based simulation an important aspect. Spatially distributed models enable spatially distributed predictions, as ranking erosion prone areas, sediment dynamics within a catchment and acceptable simulations of 165 outlet transport rates (Batista et al., 2021).  Considering that many process based soil erosion models have been developed in the end of the 20th century ( fig. 1), the 170 question arises which of the once limiting factors might be outdated and can be remedied with the help of new measurement techniques and temporal and spatial high resolution data as well as new possibilities regarding processing and computing power. Taking different perspectives into account, several authors have reviewed soil erosion models in recent years (Merritt et al., 2003;Aksoy and Kavvas, 2005;Jetten and Favis-Mortlock, 2006;Pandey et al., 2016;Hajigholizadeh et al., 2018;Guo et al., 2019;Baartman et al., 2020), considering the following aspects:  While process based models exist, which are more frequently used than others (e.g. LISEM), researchers continue to develop soil erosion models, to create approaches that have advantages in one or the other way (e.g. being more accurate to simulate 200 a specific process or being more simplified) (Hajigholizadeh et al., 2018). As models are conceptualized for different purposes as well as spatial and temporal scales (Karydas et al., 2012), they vary widely regarding their complexity, data demand, temporal and spatial representation of process mapping as well as input and output parameters (Pandey et al., 2016).
As simplifications of reality, the all-achieving model does not exist jet, which results in a constantly rising and meanwhile confusing amount of models with a range of different strengths and weaknesses, as listed in tab. 1. 205 In their study on 16 European erosion models Jetten and Favis-Mortlock (2006) review them next to others with respect to their process representation. They emphasize the problem, that different models are calibrated for special spatial and temporal scales, and in general assume continuous temporal soil and surface input parameters, which lead to falsified process description. The models e.g. EGEM, EPIC, GLEAMS, GUEST or PERFECT are developed to simulate erosion on the field to small catchment scale. Restrictions such as these are often accompanied by the practical aspect of data availability 210 (Pandey et al., 2016), a factor with decreasing importance due to the increasing possibility of collecting high resolution data on a large spatial and temporal scale. Aksoy and Kavvas (2005)  in implementing the process description of rill-interrill interaction in soil erosion models. Various models, e.g. ANSWERS, WEPP, PERFECT, LISEM, EUROSEM or KINEROS2, lack the ability to simulate gully erosion processes, making the application in large gully prone areas unfeasible (Hajigholizadeh et al., 2018). The prediction quality of a model is heavily 215 influenced by its input data and its parameterization, which concludes appropriate data collection from multiple sources, accurate model parameterization and temporal and spatial high resolution input data as important aspects for model improvement (Batista et al., 2021;Pandey et al., 2016).

Techniques on soil erosion measurement
Measurement techniques to assess soil properties and soil erosion are constantly advancing in terms of their spatial and 220 temporal resolution (Li et al., 2017). In the context of reviewing those, most researchers focus on a selection of similar technological approaches but do not take a holistic overview on assessment techniques into account (e.g. Padarian et al., 2020;Castillo et al., 2012). Li et al. (2017) i.e. compare the selected methods of runoff plot, radionuclide tracers and erosion pins for soil erosion assessment. Taking just a few methods into account, they predict a future trend towards merging different methods for more quantitative and precise approaches. Rodrigo-Comino (2018), includes 91 publications in his 225 review on soil erosion assessment methods. To gain an improved understanding of processes and connectivity, he as well recommends a combined application of methods, working on different temporal and spatial scales. Figure 2 gives an overview of assessment techniques used in soil erosion research, compiled according to types of assessment and ordered by their applicability on a temporal scale.

Tracer
Authors as Guzmán et al. (2013) and Guan et al. (2017) review different tracing approaches, as also listed in fig. 2 namely the fallout radionuclides of both anthropogenic and natural origin as e.g. Caesium-137 ( 137 Cs), Beryllium-7 ( 7 Be) or Lead-235 210 ( 210 Pb ex) . These tracers are capable of reconstructing sedimentation histories on different temporal scales, from a few months up to approximately 100 years (Mabit et al., 2008;Alewell et al., 2017;Guan et al., 2017). While 137 Cs is most suitable for the measurement of medium-term soil erosion on slope scales (Baumgart et al., 2017), combining soil erosion modelling with both 7 Be and soil measurements can help to improve the understanding of soil relocation processes https://doi.org/10.5194/soil-2021-85 Preprint. Discussion started: 20 August 2021 c Author(s) 2021. CC BY 4.0 License. (Deumlich et al., 2017). Joining 7 Be with high resolution unmanned aerial vehicle (UAV) photogrammetry shows useful to 240 quantitative assess surface change detection in a spectrum of up to 2 mm resolution (Baumgart et al., 2017), offering high resolution cross-scale measurement of different erosion processes. Rare earth elements, which can be of natural origin or artificially added, are useful for studying both rill and interill detachment and deposition processes from the plot up to the catchment scale. Using the magnetic properties of the soil, natural or artificially incorporated, magnetic tracers enable the reconstruction of sediment sources on different temporal and spatial scales. Sediment fingerprinting takes the chemical, 245 biological or physical properties of soil into account, comparing a given composition at one area with those elsewhere (Guan et al., 2017;Guzmán et al., 2013). Combining different tracing and soil erosion monitoring approaches on different temporal and nested spatial scales, can be used to identify sediment sources, and their change of spatial and temporal distribution in a catchment over time (Guan et al., 2017).
To better understand the influence of spatial variability in water erosion, Guzmán et al. (2013)  approach is the thermal tracing (Lima et al., 2015;Tauro and Grimaldi, 2016). Thanks to an increase in resolution, portability and a reduction in cost, today infrared thermography offers a fast, effective and accurate opportunity to monitor flow velocity via thermal tracer on a high temporal and spatial resolution (Lima et al., 2015;Lin et al., 2018).

Remote Sensing
While remote sensing shows already useful in combination with tracing approaches, it can also stand alone as a valuable tool 260 in soil erosion and soil property assessment. In this context, satellite sensors provide a vast range of spatial resolutions, spectral bands and revisiting times. They show great potential for soil erosion measurements due to the method's robustness, the large spatial scales and the data availability especially in remote regions, they furthermore are becoming affordable and display low time expenditure of data assessment (Sepuru and Dube, 2018). Data by e.g. Sentinel 1, Sentinel 2 or Landsat 8 offer a great spectrum of information on i.e. soil organic carbon, soil total nitrogen, clay content of the soil or the 265 Normalized Difference Vegetation Index (NDVI), with resolutions up to 10 m (Septianugraha et al., 2019;Zhou et al., 2020;Gholizadeh et al., 2018). While valuable to identify erosion and its consequences on the medium to large scale (Vrieling, 2006) and showing usefulness for empirical models working on large areas (Aiello et al., 2015), satellite data has not yet established itself in combination with process based soil erosion models, mostly used on smaller, slope to catchment, scales.
Methods on aerial and terrestrial photogrammetry and aerial and terrestrial LiDAR or laser scanning (ALS and TLS) are very 270 valuable in soil erosion research and become even more efficient with further development and improvement in computing power (Guo et al., 2016;Neugirg et al., 2015;Glendell et al., 2017). They allow, remote sensing with high temporal and spatial resolution. The photogrammetric technique Structure from Motion (SfM) via UAV offers a powerful and achievable method for measuring soil erosion, also in terrain difficult to access . Thanks to their high spatial and temporal resolution, photogrammetry and LiDAR can be used to measure on-going soil erosion processes quasi continuous 275 during artificial and natural rainfall events. On the one hand the data can be used to e.g. validate measured soil loss on an artificial plot while on the other hand they give valuable insight on the continuous process of soil erosion (Guo et  UAVs equipped with cameras, as a cost-effective and flexible tool (Pineux et al., 2017), offer the assessment of spatially distributed soil surface changes over different temporal and spatial scales and with resolutions in the low millimetre range 285 (Kaiser et al., 2018). These datasets and the quantification of soil loss help to assess and understand the water erosion mechanisms and the spatial and temporal dimension of the soil erosion processes taking place on the slope to catchment scale (Cândido et al., 2020;Eltner et al., 2018). LiDAR, despite the higher time and cost expenditure, proves a feasible tool for change detection , helping to improve the understanding of soil erosion forms, as soil crusts (Hu et al., 2020a) or rill characteristics (Vinci et al., 2015). Jiang et al. (2020) monitor rilling on an artificial plot via LiDAR and SfM. 290 They promote the use of close range photogrammetry, achieving even higher accuracies than by the use of TLS. Meinen and Robinson (2020) see great potential in UAV SfM-MVS (multi-view stereo) for validation and calibration of soil erosion models. Photogrammetric approaches and LiDAR, allow a spatial and temporal high resolution cross-scale understanding of on-going processes and their development from the microplot to the catchment scale, offering cross-scale validation opportunities and new and accurate process understanding by water induced soil erosion to process based soil erosion 295 models. Hu et al. (2020a) use LiDAR to quantify results of interrill erosion processes. They describe LiDAR as a promising technology for generating microtopography soil parameters, which can be linked to high resolution photogrammetric derived Digital Elevation Model (DEM). Photogrammetry and TLS as non-invasive, high accuracy, high mobility and in the case of photogrammetry low cost techniques allow the assessment of soil properties as e.g. roughness (Thomsen et al., 2015;Kaiser 300 et al., 2018;Li et al., 2020b;Gilliot et al., 2017) or soil moisture (Kemppinen et al., 2018). Soil spectra measured via remote sensing are an important step for in-situ assessment of soil properties at real time (Ge et al., 2011). Remote sensing enables the spatially distributed assessment of soil properties on a high temporal resolution, which can be of great value for the parameterization of physically based soil erosion models. Thomsen et al. (2015) already point out that the possibilities offered by SfM and TLS regarding the survey of roughness exceed the integration opportunities of process based soil erosion 305 models such as LISEM. This supports the hypothesis that the models cannot keep up with the available data and that the latter need to be further developed for an appropriate inclusion of the novel possibilities.

Machine Learning
Machine learning (ML) approaches as artificial neural networks (ANN) offer cost and time efficient ways for spatially distributed assessment of soil parameters (Alexakis et al., 2019) and erosion forms, as e.g. gully erosion (Arabameri et al., 310 2020a;Arabameri et al., 2020b). Different authors have used different ML approaches to map the susceptibility of gully erosion and the factors controlling it (Lei et al., 2020;Pourghasemi et al., 2020). In this context Pourghasemi et al. (2020) found the Random Forest approach the most reliable to understand such controlling factors. While techniques have been developed to use ML (e.g. linear equation model or decision tree) based on visual data to predict soil properties (i.e. soil bulk density), those approaches seem only to be applicable for approximate in situ measurements, filling the gaps of laboratory 315 assessed data (Bondi et al., 2018). Deep learning, as ANN can offer new opportunities to model soil spectral data (Padarian et al., 2019). Open source algorithms combined with proximally and remotely assessed soil data enable the use of ML approaches to analyse soil data (Padarian et al., 2020). While there is great potential in ML approaches for soil erosion prediction and management (Vu Dinh et al., 2021), there also exists the risk of equifinality, gaining plausible results for the wrong reason (Padarian et al., 2020). While these techniques offer new possibilities they so far show most useful on regional 320 scales with large data availability (Zhang et al., 2018b) and up to now have not found their way in improving process based soil erosion models. https://doi.org/10.5194/soil-2021-85 Preprint. Discussion started: 20 August 2021 c Author(s) 2021. CC BY 4.0 License.

Challenges and opportunities of process based soil erosion modelling in the context of novel data acquisition methods
Limits set by computing power are constantly shifting and creating new possibilities. In addition, the required time and cost 325 for the collection of high resolution data is decreasing and new opportunities arise. In the development of soil erosion monitoring, measuring approaches have become more precise and thus small scale monitoring techniques were supplemented by those applicable to large, regional scales (Li et al., 2017). Due to improved and novel assessment technologies, possibilities for process based soil erosion models constantly increase. In the following the necessity for model adaption and further development, regarding the aspects of parameterization and calibration, process description, scale and 330 resolution as well as complexity and equifinality will be discussed.

Parameterization and calibration
Being time and resource consuming and accompanied by a high parameterization requirement, expecting input parameters on e.g. topographic data, soil data, tillage practices and crop management, process based soil erosion models, are considered rather complex, making them more difficult in their handling than empirical models (Merritt et al., 2003;Pandey et al., 2016;335 Hajigholizadeh et al., 2018). To reduce assessment time and complexity and to increase user-friendliness, the input parameters are often assumed homogeneously distributed for the whole field or catchment (e.g. CREAMS). Nether the less new assessment techniques especially in the field of remote sensing can extremely facilitate the procurement of highly resolved parameters on both temporal and spatial scales, enabling distributed input data in both time and space Jester and Klik, 2005;Kaiser et al., 2015). Time-varying input data for process based models as the RUNOFF model, 340 are important to gain more accurate results (Aksoy and Kavvas, 2005), while also their flexibility in space proves to be of great value (Guo et al., 2019).
Even parameters such as roughness, which over the past, for the lack of other possibilities, were determined empirically, can increasingly be derived, by remote sensing, as shown for the models LISEM (Thomsen et al., 2015) or EROSION3D . Due to its high resolution, SfM enables the spatially distributed assessment of roughness on a large scale (Eltner 345 et al., 2018). Besides novel methods in the field of topographic reconstruction and ML, advances in the area of image velocimetry as mentioned before, bare great potential for an automatic measurement technique, offering new possibilities for the parameterization of process based soil erosion models (Lima et al., 2015;Lin et al., 2018).
Since they represent reality in a simplified way, models cannot include all influencing factors. Model developers therefore decide to include certain processes as close to reality as possible and to neglect others in order to avoid overly complex 350 models. This results in a large number of models with different strengths and weaknesses. Regarding the precipitation, there are models, as EROSION3D, taking the temporally variable intensity of the rainfall event into account (Pandey et al., 2016) while others, e.g. PERFECT, ignore this impact using the same intensity for every time step (Merritt et al., 2003). An aspect widely neglected by process based models is the influence of wind-driven rain on soil erosion. This influence of the wind can be immense with up to 30 % more erosion, emphasizing the need for assessing and integrating high resolution data on 355 near surface wind speed and direction in soil erosion modelling (Marzen et al., 2017;Schmidt et al., 2017). Recent advances in time-lapse SfM photogrammetry allow for the assessment of surface changes during a rainfall event with a temporal resolution of several seconds . Such data, combined with surface wind speed and direction, can offer new possibilities for the further development of process based soil erosion models. While up to a certain degree, the model's accuracy improves with the number of input parameters, in general more input parameters lead to an increasing model 360 complexity. A balancing act of process based models is the over-parameterization: the more parameters are included in a model, the greater the risk of having a stochastically fitting model that however fails to map the processes actually taking place (Pandey et al., 2016;Vente et al., 2013;Jetten et al., 2003). In the case that parameters cannot be assessed directly, the calibration of the models helps to determine these parameters and thus to achieve the best possible agreement between measured and modelled output (Merritt et al., 2003;Pandey et al., 365 2016). One or multiple parameters are calibrated against an available dataset to minimize the prediction error (Batista et al., 2019). While Guo et al. (2019) see improvement in generating more extensive calibration data for soil erosion models (e.g.

MEFIDIS)
, regarding the GSSHA model Pandey et al. (2016) on the other hand propose, less dependency on model calibration all together. Based on high resolution data, a better process understanding can help reduce the necessity of model calibration. Further model development as improving the parameter validation and calibration for models e.g. SHETRAN, 370 MEFIDIS, GLEAMS and WESP can already help reduce the risk of equifinalitygaining a statistical right answer for the wrong reason (Guo et al., 2019;Batista et al., 2019;Pandey et al., 2016).

Soil erosion processes
The soil erosion processes, as splash, interrill, rill and gully erosion, show high variability in their process description (Batista et al., 2019) and are represented differently well depending on the model. Models as ANSWERS miss the sediment 375 transport by rainfall (splash erosion) (Hajigholizadeh et al., 2018), while others such as EUROSEM simulate splash erosion, but only until interrill erosion starts (Aksoy and Kavvas, 2005). Different soil erosion models are developed for different scales and therefore vary regarding their process description (Batista et al., 2019). Models for small scales depict splash erosion and interrill erosion especially well, where there are models developed for larger scales, focusing on gully erosion.
Due to the complexity of the occurring and transforming soil erosion processes, many models make simplified assumptions. 380 The KINEROS model for example does not differentiate between interrill and rill erosion (Aksoy and Kavvas, 2005), while WEPP simulates interrill erosion and concentrated runoff within rills, but does not take the transition from one to another into account (Merritt et al., 2003).
While most process based soil erosion models are capable of modelling runoff and soil erosion within existing rills as well as in interrill areas, they miss the ability to depict spontaneous rill formation (Pandey et al., 2016). Existing rill erosion models, 385 such as RillGROW 2 by Favis-Mortlock et al. (2000), can map the hydraulic processes inside a rill, but are unable to model its initiation (Wirtz et al., 2010;Pandey et al., 2016). An approach on a WEPP-based soil erosion model by Wu et al. (2018) simulates erosion and rill evolution on the hillslope scale. However even this model is not capable to model every occurring rill formation and has difficulties in locating the bifurcation and merging of rills. The embedding of the initiation and development of rills in soil erosion models is an important future step to gain more precise modelling results (Wu and Chen, 390 2020).
To this goal, a new and improved process understanding, gained by repeated and accurate rill erosion assessment (Di Stefano et al., 2017) and detailed information about their origin, geometry and frequency (Merritt et al., 2003) is an important step in the understanding and modelling of rills. Advances in time-lapse SfM photogrammetry allow for the assessment of surface changes during a rainfall event with a temporal resolution of several seconds . Such approaches, as well 395 as information gained by rare earth elements on rill-interrill erosion processes, might enable an enhanced temporal and spatial high resolution process understanding (Zhang et al., 2018a). Information that can help develop and integrate a topographic threshold concept, as suggested by Nouwakpo et al. (2016) to implement the transition from interrill to rill erosion in process based soil erosion models. Different assessment techniques offer opportunities for an enhanced understanding of soil erosion processes and especially the cross-scale transition from one process to another. 400 Gully erosion as an important driver of land degradation is in many cases neglected by process based soil erosion models (Pandey et al., 2016;Lei et al., 2020). There are certain landscapes, as the loess plateau in China or areas in Iran, where annual sediment loss due to gully erosion exceeds that of slope erosion by far, making it a severe environmental problem (Cai et al., 2019;Arabameri et al., 2020b). For these gully-prone areas, as well as for cross-scale and large scale soil erosion modelling the incorporation of gully erosion processes in process based soil erosion models is of great importance (Li and 405 https://doi.org/10.5194/soil-2021-85 Preprint. Discussion started: 20 August 2021 c Author(s) 2021. CC BY 4.0 License. Fang, 2016;Cai et al., 2019). Various ML approaches are used for the susceptibility mapping of gully erosion (Arabameri et al., 2020a), which could be a helpful extension for the detection of gully initiation in process based models.
Often unattended by these models, is the simulation of nutrients and chemical paths as shown by the models: AGNPS (Adu and Kumarasamy, 2018), CASCA2D, DWSM, EGEM, EROSION2D/3D, KINEROS, MEFIDIS, PERFECT, PERSERA, RUNOFF, SHESED, WATEM or the WEPP (Pandey et al., 2016). Nether the less as soil erosion is to great parts an 410 agricultural challenge such discharge presents an important modelling aspect (Tao et al., 2020). For a better understanding of soil relocation processes, including nutrients and chemical paths, and to implement them in soil erosion models, Deumlich et al. (2017) propose to combine soil erosion models, with the tracer technique 7 Be as well as soil measurements.
Considering that changing climate leads to an increase in extreme weather events, it is important to gain a holistic understanding of processes and feedback mechanisms (Vereecken et al., 2016;Guo et al., 2019). Guo et al. (2019) 415 recommend to implement such aspects and to further develop soil erosion models in respect to changing climate scenarios.
Bringing together knowledge of different disciplines Li and Fang (2016) propose combining climate, land use and soil erosion models to achieve a both multi-scenario as well as multi-model framework for an improved simulation of soil erosion influenced by climate change, associated land use changes and adopted management strategies.

Scale and resolution 420
Process based soil erosion models deliver the best results in the observation scale they were parameterized and validated for (Batista et al., 2019;Govers, 2010;Hajigholizadeh et al., 2018;Cerdà et al., 2013;Vente et al., 2013). The governing equations are usually derived on the basis of small scales and then transferred to larger scales, which can lead to poor validation results (Hajigholizadeh et al., 2018). Most models are developed for the field scale (e.g. GUEST or RillGROW), the field and small catchment scale (e.g. CREAMS, EGEM, EPIC, EROSION3D, EUROSEM, GLEAMS, OPUS, PEPP-425 HILLFLOW, PERFECT and WATEM) or the catchment scale (e.g. TOPMODEL) (Pandey et al., 2016). By changing the considered scale, both prevailing erosional process as well as the complexity of these processes alter (Govers, 2010;Merritt et al., 2003). Taking the role of scale into account is important to understand the dominant processes and their influence on erosional rates (Vente and Poesen, 2005). With improving technology, large scale, high resolution data is available, enabling a validated extension of the spatial modelling scales (Baartman et al., 2020). 430 To gain reliable and accurate results, the resolution and quality of the different input data is of importance to the model performance (Merritt et al., 2003;Alewell et al., 2019). The impact of the cell size on the soil erosion simulation varies with the model choice. The LISEM model for example proves more adaptable to changes in spatial and temporal resolution than EROSION3D, where the choice for the right solution shows to be more complex and requires a higher modelling experience (Starkloff and Stolte, 2014). Varying the DEM cell size in either direction, can lead to a different focus on operating 435 processes and connectivity (Baartman et al., 2020). Due to new and further developed assessment techniques, data with higher temporal and spatial resolution arise, offering new opportunities and challenges for modelling approaches. Changes in resolution can lead to changes in the representation of hydrology or topography and therefore affect soil erosion predictions (Zhang et al., 2008;Cochrane and Flanagan, 2005). An increasing resolution can expose non-erosive processes, as e.g.
swelling and shrinking, which may mask the actual erosional processes (Kaiser et al., 2018). Therefore an holistic 440 understanding of soil erosion processes, including its scale, is inevitable (Cerdà et al., 2013). Remote sensing data can enable temporal and spatial high resolution change detection and process mapping on different magnitudes (Balaguer-Puig et al., 2018;Cândido et al., 2020), offering such information for soil erosion modelling.

Model complexity and equifinality
One downside of process based compared to empirical soil erosion models is the model complexity. Nether the less, there 445 are little to no alternatives if the model is to be transferable and offer spatially differentiated and event-based predictions https://doi.org/10.5194/soil-2021-85 Preprint. Discussion started: 20 August 2021 c Author(s) 2021. CC BY 4.0 License. (Hessel et al., 2006). Complex models are not automatically the better choice (Jetten et al., 2003). An increase in complexity is not necessarily reflected in improved modelling (Govers, 2010), but enhances the dependency of modelling results on the modeller's experience (Merritt et al., 2003). With rising complexity process based models forfeit user-friendliness (Batista et al., 2019). Model development therefore is a balancing act between complex models that represent reality as accurate as 450 possible and user-friendly models developed for a wide range of users.
The large number of input data not only results in a high model complexity but also in a large number of degrees of freedom (Govers, 2010). Varying parameter combinations can lead to equally sufficient model outputs (Batista et al., 2019), misjudging the relationship between observed and predicted erosion (Evans and Brazier, 2005). Even though the model adequately simulates the sediment yield at the systems outlet, it not necessarily implicates a correct process description or a 455 correct spatial distribution of erosion and deposition (Starkloff et al., 2018). This points out another challenge of process based soil erosion models, the risk of achieving the correct outcome for the wrong reasons (Govers, 2010). Even though the model is working poorly in identifying spatially distributed erosion hotspots or representing internal dynamics it might still offer a realistic prediction of the overall simulation outcome in respect to soil loss and runoff at the systems outlet (Favis-Mortlock, 2010;. Modellers should be aware that equifinality is an inevitable consequence of model 460 calibration (Batista et al., 2019), which might even lead to misdirected management and recovery strategies . Spatially and temporally distributed data, as high-resolution surface change detection, can be used for validation and thus help reducing the risk of equifinality.

Connectivity
The complexity and multitude of processes taking place within a catchment, affects the sediment and water transfer 465 throughout the system. To address management strategies and mitigation measurements, it is inevitable to gain a holistic overview of the system's connectivity, shifting the perspective away from the single slope to the connected system and taking a variety of spatial scales into account. Such knowledge leads to a better understanding of the influences of human built structures and natural landforms on the continuity of water and sediment transfer throughout the system as well as the cause of off-site damages (Cavalli et al., 2019;Biddulph et al., 2017). Models, being simplifications of reality, often neglect 470 the delayed reaction of the sediment yield and the impact of sediment connectivity . Supplementary to erosion rate assessment, the mapping and modelling of sediment transport and runoff throughout the system, is of major importance as it has great influence on off-site damage (Boardman et al., 2019). Regarding accurate modelling results the aspects of sediment sources and connectivity might be even more important than the model parameterization (Uber et al., 2020). 475 High rainfall intensity leads to large amounts of sediment yield, which increases the impact of connectivity. Stronger events result in better simulated sediment connectivity (Baartman et al., 2020). Including connectivity analysis into soil erosion models, the parameterization of the landscape and rainfall characteristics are decisive (Uber et al., 2020). For a best-fit of sediment transfer to its outlet, Mahoney et al. (2020) stress the need of coupling erosion, sediment routing and connectivity formula. The GeoWEPP-C model, based on the GeoWEPP, offers an approach of integrating process based soil erosion 480 modelling and modelling of lateral sediment connectivity. While this model presents an opportunity to combine these different aspects, it still needs major improvement before applicable to the practice (Poeppl et al., 2019). To gain insights on the development of connectivity on short to long terms Baartman et al. (2020) propose a continuous monitoring and modelling of runoff and sediment transfer. GIS-based indices offer an approach to overcome the extensive field work and large amount of input data necessary to partly quantify relevant connectivity factors (Najafi et al., 2021). Even though 485 connectivity is up to now just to some extents assessable, new high resolution remote sensing data (e.g. DEMs), help measuring connectivity aspects at least partway and enable the development of connectivity indices (Heckmann et al., 2018), which can be of interest to process based soil erosion modelling. https://doi.org/10.5194/soil-2021-85 Preprint. Discussion started: 20 August 2021 c Author(s) 2021. CC BY 4.0 License.

Conclusion and outlook
Climate change accompanied by local changes in extreme weather events, as droughts, rising temperature, high rainstorm 490 intensity and temporal precipitation shifts also leads to changes in soil erosion rates. A major influence on soil erosion in modern times is human-driven land use changes. Unclear future developments only make an adaption of assessment techniques and modelling approaches all the more important. Regarding heavy local rainstorm events, resulting in intensified local soil erosion, assessment and modelling on the sub-daily scale is of great importance (Mullan et al., 2012). This review gives an overview of 44 process based soil erosion models, their strengths and their shortcomings. Potential of their further 495 development is based on new opportunities, which assessment techniques offer the soil erosion research today.
Hypothesizing, that models cannot keep up with the data, we found several weaknesses that can be improved or even eliminated, utilizing up to date assessment techniques of soil erosion research. Future research should focus on incorporating improved, new as well as spatial distributed input data and an updated process description. Evaluating the scale dependent boundaries of processes, researchers should strive to include the initial development of rills and enable cross-scale modelling 500 from the micro-plot to the regional scale. Huge potential could be found by remote sensing, to further develop process descriptions, assess parameters as topography, roughness or flow velocity with high temporal and spatial resolution, or to work across scale. Techniques, with low cost, low time expenditure and high resolution, show potential to gain adequate data from the micro to the macro scale. Further of interest are ML approaches and tracing techniques. They for once pave the way to respond to different processes on different scales (splash-, sheet-, rill-, gully erosion, transport and deposition). ML and 505 automated assessment systems, could even offer opportunities on a completely new level, enabling the development of fully automated modelling approaches in the future.
Over the years many soil erosion models have been developed, resulting today in a large amount of process based models with different strengths and weaknesses. Even though the models are not capable to include the different erosional processes or make use of the newly available resolution or temporal and spatial scale, the question arises if we need jet another model 510 or if we could further develop and improve existing approaches. These models should be adapted to our possibilities and needs, to meet the current data availability and achieve a more holistic process understanding. The goal should be to achieve a realistic but user-friendly model, minimizing challenges as equifinality and offering an improved understanding of soil erosion processes and influences.

Authors contribution 515
L. Epple conceptualized and prepared the manuscript with supervision of A. Eltner and A. Kaiser and the reviewing and editing from all co-authors.