Rainfall Erosivity and Its Estimation: Conventional and Machine Learning Methods

Rainfall erosivity concerns the ability of rainfall to cause erosion on the surface of the earth. The difficulty in modeling the distribution, the size, and the terminal velocity of raindrops in relation to the detachment of soil particles led to the use of more tractable rainfall indices. Thus, in the universal soil loss equation (USLE), the coefficient of rainfall erosivity, R, was introduced. This coefficient is based on the product of the rainfall kinetic energy of a storm and its maximum 30-minute intensity. An important problem in the application of USLE and its revisions in various parts of the world concerns the computation of R, which requires pluviograph records with a length of at least 20 years. For this reason, empirical equations have been developed that are based on coarser rainfall data, such as daily, monthly, or yearly, which are available on larger spatial and temporal extents. However, the lack of denser data is dealt more effectively by means of machine learning methods. Computational systems for this purpose were recently developed based on feed-forward neural networks, yielding significantly better results

Calculation of Sediment Transport Capacity of Flowing Water in Rivers with Machine Learning

Sediment Transport and Morphodynamic

Extending the Applicability of the Meyer–Peter and Müller Bed Load Transport Formula

The present paper deals with the applicability of the Meyer–Peter and Müller (MPM) bed load transport formula. The performance of the formula is examined on data collected in a particular location of Nestos River in Thrace, Greece, in comparison to a proposed Εnhanced MPM (EMPM) formula and to two typical machine learning methods, namely Random Forests (RF) and Gaussian Processes Regression (GPR). The EMPM contains new adjustment parameters allowing calibration. The EMPM clearly outperforms MPM and, also, it turns out to be quite competitive in comparison to the machine learning schemes. Calibrations are repeated with suitably smoothed measurement data and, in this case, EMPM outperforms MPM, RF and GPR. Data smoothing for the present problem is discussed in view of a special nearest neighbor smoothing process, which is introduced in combination with nonlinear regression

A New Approach to the Optimization of Looped Water Distribution Networks with Velocity Constraints

The optimal design of a looped water distribution system is a problem that is addressed frequently in the literature. Usually, the flow velocity in the pipes is not taken into account. Nevertheless, in real-life applications, there are velocity restrictions that must be considered for the proper function of water distribution systems. An algorithm has been presented recently for the optimal design of such systems, relying entirely on the hydraulic characteristics of the system, and not involving any parameters to be adjusted. This paper presents a new suitably designed algorithm that retained the features of the original algorithm and handled the problem of velocity restrictions without recourse to penalty functions. The new algorithm was tested and compared with others that used penalty functions to handle the velocity constraints. The results demonstrated its efficiency, reliability, and better performance

Temporal and Elevation Trend Detection of Rainfall Erosivity Density in Greece

This paper presents certain characteristics of trends in rainfall erosivity density (ED), that have not been so far investigated in depth in the current literature. Raw pluviograph data were acquired from the Greek National Bank of Hydrological and Meteorological Information for 108 stations. Precipitation time series values were cleared from noise and errors, and the ratio of missing values was computed. Erosive rainfalls were identified, their return period was determined using intensity–duration–frequency (IDF) curves and erosivity values were computed. A Monte Carlo method was utilized to assess the impact of missing values ratio to the computation of annual erosivity (R) and ED values. It was found that the R values are underestimated in a linear way, while ED is more robust against the presence of missing precipitation values. Indicatively, the R values are underestimated by 49%, when only 50% of the erosive rainfall events are used, while at the same time the estimation error of ED is 20%. Using predefined quality criteria for coverage and time length, a subset of stations was selected. Their annual ED values, as well as the samples' autocorrelation and partial autocorrelation functions were computed, in order to investigate the presence of stochastic trends. Subsequently, Kendall's Tau was used in order to yield a measure of the monotonic relationship between annual ED values and time. Finally, the hypothesis that ED values are affected by elevation was tested. In conclusion: (a) It is suggested to compute ED for the assessment of erosivity in Greece instead of the direct computation of R; (b) stationarity of ED was found for the majority of the selected stations, in contrast to reported precipitation trends for the same time period; and (c) the hypothesis that ED values are not correlated to elevation could not be rejected

Robustness Spatiotemporal Clustering and Trend Detection of Rainfall Erosivity Density in Greece

Soil erosion is affected by rainfall, among other factors, and it is likely to increase in the future due to climate change impacts, resulting in higher rainfall intensities. This paper evaluates the impact of the missing values ratio on the computation of the rainfall erosivity factor, R, and erosivity density, ED. The paper also investigates the temporal trends and defines regions of Greece with a similar monthly distribution of ED using an unsupervised method. Preprocessed and free from noise and errors rainfall data from 108 stations across Greece were extracted from the Greek National Bank of Hydrological and Meteorological Information. The rainfall data were analyzed and erosive rainfalls were identified, their return period was determined using intensity−duration−frequency curves and R and ED values were computed. The impact of missing data in the computation of annual values of R and ED was investigated using a Monte Carlo simulation. The findings indicated that missing rainfall data resulted in a linear underestimation of R, while ED is more robust. The trends in ED timeseries were evaluated using the Kendall’s Tau test and their autocorrelation and partial autocorrelation were computed for a small subset of stations using criteria based on the quality of data. Furthermore, cluster analysis was applied to a larger subset of stations to define regions of Greece with similar monthly distribution of ED. The findings of this study indicate that: (a) ED should be preferred for the assessment of erosivity in Greece over the direct computation of R, (b) ED timeseries are found to be stationary for the majority of the selected stations, in contrast to reported precipitation trends for the same time period, (c) Greece is divided into three clusters/areas of stations with distinct monthly distributions of ED

Estimating Current and Future Rainfall Erosivity in Greece Using Regional Climate Models and Spatial Quantile Regression Forests

A future variation of precipitation characteristics, due to climate change, will affect the ability of rainfall to precipitate soil loss. In this paper, the monthly and annual values of rainfall erosivity (R) in Greece are calculated, for the historical period 1971–2000, using precipitation records that suffer from a significant volume of missing values. In order to overcome the data limitations, an intermediate step is applied using the calculation of monthly erosivity density, which is more robust to the presence of missing values. Spatial Quantile Regression Forests, a data driven algorithm that imitates kriging without the need of strict statistical assumptions, was utilized and validated, in order to create maps of R and its uncertainty using error propagation. The monthly average precipitation for the historical period 1971–2000 estimated by five (5) Global Circulation Models-Regional Climatic Models were validated against observed values and the one with the best performance was used to estimate projected changes of R in Greece for the future time period 2011–2100 and two different greenhouse gases concentration scenarios. The main findings of this study are: (a) the mean annual R in Greece is 1039 MJ·mm/ha/h/y, with a range between 405.1 and 3160.2 MJ·mm/ha/h/y. The highest values are calculated at the mountain range of Pindos and the lowest at central Greece; (b) the monthly R maps adhere to the spatiotemporal characteristics of precipitation depth and intensities over the country; (c) the projected R values, as an average over Greece, follow the projected changes of precipitation of climatic models, but not in a spatially homogenous way