Models for estimating daily rainfall erosivity in China

Highlights

• Three models estimating erosivity by daily rainfall are calibrated and validated.

• The models effectively estimate average annual, yearly and half-month erosivity.

• A model using daily and maximum 60-min amounts effectively predicts daily erosivity.

Summary

The rainfall erosivity factor (R) represents the multiplication of rainfall energy and maximum 30 min intensity by event (EI₃₀) and year. This rainfall erosivity index is widely used for empirical soil loss prediction. Its calculation, however, requires high temporal resolution rainfall data that are not readily available in many parts of the world. The purpose of this study was to parameterize models suitable for estimating erosivity from daily rainfall data, which are more widely available. One-minute resolution rainfall data recorded in sixteen stations over the eastern water erosion impacted regions of China were analyzed. The R-factor ranged from 781.9 to 8258.5 MJ mm ha⁻¹ h⁻¹ y⁻¹. A total of 5942 erosive events from one-minute resolution rainfall data of ten stations were used to parameterize three models, and 4949 erosive events from the other six stations were used for validation. A threshold of daily rainfall between days classified as erosive and non-erosive was suggested to be 9.7 mm based on these data. Two of the models (I and II) used power law functions that required only daily rainfall totals. Model I used different model coefficients in the cool season (Oct.–Apr.) and warm season (May–Sept.), and Model II was fitted with a sinusoidal curve of seasonal variation. Both Model I and Model II estimated the erosivity index for average annual, yearly, and half-month temporal scales reasonably well, with the symmetric mean absolute percentage error MAPE_sym ranging from 10.8% to 32.1%. Model II predicted slightly better than Model I. However, the prediction efficiency for the daily erosivity index was limited, with the symmetric mean absolute percentage error being 68.0% (Model I) and 65.7% (Model II) and Nash–Sutcliffe model efficiency being 0.55 (Model I) and 0.57 (Model II). Model III, which used the combination of daily rainfall amount and daily maximum 60-min rainfall, improved predictions significantly, and produced a Nash–Sutcliffe model efficiency for daily erosivity index prediction of 0.93. Thus daily rainfall data was generally sufficient for estimating annual average, yearly, and half-monthly time scales, while sub-daily data was needed when estimating daily erosivity values.

Introduction

The Universal Soil Loss Equation (USLE) and its revised versions (RUSLE, RULSE2) are the most widely used models for predicting soil erosion on agricultural fields (Wischmeier and Smith, 1965, Wischmeier and Smith, 1978, Renard et al., 1997, Foster, 2004). However, the most effective use of these models outside of the United States, where it was developed, requires that regional values for each factor be developed based on local data and conditions (Wischmeier, 1984). Computation of the R-factor involves the calculation and summation of rainfall erosivity for individual erosive storm events. An individual rainfall event was defined as a period of rainfall with at least six preceding and six succeeding non-precipitation hours. The erosivity for each individual event is the EI₃₀, which is the product of a storm’s kinetic energy (E) and its maximum 30-min rainfall intensity (I₃₀) (Wischmeier and Smith, 1958). It reflects the combined driving processes of detachment and transport by raindrops and runoff at the hillslope scale (Wischmeier, 1976). The EI₃₀ and R-factor equations developed by Wischmeier were based on more than 8000 plot years of measured soil erosion data in the eastern half of the United States (Wischmeier, 1959). Foster et al. (1982) evaluated 21 indices of rainfall-runoff erosivity factors for individual storms and found that these factors did not significantly improve soil loss prediction as compared with EI₃₀.

The method for calculating EI₃₀ requires hyetograph data for a storm, and the data series should have more than 20 years of record in order to include dry and wet climate periods (Wischmeier, 1976). Due to the limited availability of hyetograph data, statistical models have been developed that relate more commonly available data, such as daily (Richardson et al., 1983, Bullock et al., 1989, Yu and Rosewell, 1996a, Petkovsek and Mikos, 2004, Angulo-Martinez and Begueria, 2009), monthly (Renard and Freimund, 1994, Yu and Rosewell, 1996b, Ferro et al., 1999) and annual rainfall (Bonilla and Vidal, 2011, Lee and Heo, 2011), to erosivity calculated from hyetograph data. Three aspects of the R-factor are potentially useful for soil erosion estimations. One is the average annual rainfall erosivity for predicting average annual soil loss. The second is the seasonal distribution curve of rainfall erosivity, the most commonly used format being cumulative erosivity in 24 half-month intervals. This allows the model to reflect the interactions of the cropping system management and rainstorm distributions (Wischmeier and Smith, 1978). The third is event or daily rainfall erosivity, which is important in soil loss recurrence analysis and the non-point source pollution assessment (Knisel, 1980, Kinnell, 2000).

Models for calculating erosivity at all temporal scales using event or daily rainfall are attractive since they can satisfy the three usage requirements mentioned above. A power law function has been generally used for estimating erosion index EI₃₀ from event or daily rainfall amounts (Ateshian, 1974, Richardson et al., 1983). In early studies, event rainfall amount was used (Ateshian, 1974, Lombardi, 1979, Cooley, 1980). However, more long term series of daily rainfall amounts are available compared to event rainfall amount records. Richardson et al. (1983) first presented a statistically-based power law function for estimating erosion index EI₃₀ from daily rainfall amounts, which was evaluated in the eastern and central United States and proved to be an operational tool for erosion assessment (Haith and Merrill, 1987, Selker et al., 1990). In the development of the Richardson model, one event was assumed to occur within one day (Richardson et al., 1983). Elsenbeer et al. (1993) demonstrated the daily rainfall amount predicted the R factor as well as the event rainfall amount when the Richardson model was calibrated in the Amazon Basin.

However, it is recognized that daily rainfall is not always synonymous with event rainfall. A daily rainfall amount may include only one event, multiple events, or only part of an event (Richardson et al., 1983). Bagarello and D’Asaro (1994) demonstrated that daily rainfall in many cases in the Mediterranean area cannot be assumed as representative of the individual event, and a rule for grouping daily rainfall amounts was developed and tested. Monthly summations of the EI₃₀ index were used to develop the relationship (Yu and Rosewell, 1996a, Yu, 1998, Yu et al., 2001). When a storm spanned over midnight at the crossover between two months, the EI₃₀ value for that storm was partitioned to individual months in proportion the amount of rainfall in that month. A relationship between the EI₃₀ index for half month periods and the sum of estimated daily erosivity from daily rainfall amounts during the half month periods has been developed for China (Zhang et al., 2002). All of these models (Bagarello and D’Asaro, 1994, Yu and Rosewell, 1996a, Yu, 1998, Yu et al., 2001, Zhang et al., 2002, Zhu and Yu, 2015) were aimed at the average annual rainfall erosivity and its seasonal variations, while attention has not been paid to estimations of daily rainfall erosivity.

Daily erosivity has been defined in some work as the product of kinetic energy in a day and the maximum 30-min rainfall intensity during this day (Bullock et al., 1989, Capolongo et al., 2008) and R factor was the summation of all daily erosivity. No attempt was needed in these cases using the daily data to separate individual events, however, the R factor calculated in this way will be slightly different from the R values defined in the context of the USLE in Wischmeier and Smith (1958) because daily and event rainfall amounts are not synonymous (Bullock et al., 1989).

Based on simple power law form of the Richardson model, a sinusoidal or cosinusoidal function was subsequently introduced to describe the annual cycle of the coefficient of the power law function in order to represent seasonal differences in rainfall characteristics (Yu and Rosewell, 1996a, Yu, 1998, Yu et al., 2001, Capolongo et al., 2008, Zhu and Yu, 2015), which was considered to perform best among models included in a comparison study (Angulo-Martinez and Begueria, 2009). The China Meteorological Administration (CMA, 2003) requires that the maximum 60-min rainfall amount (P_60min)_d be compiled at government weather stations. We and others (Wang et al., 1995, Yin et al., 2007) hypothesize that the introduction of the index (P_60min)_d could improve the estimation of the EI₃₀ index over the use of only daily data, since the (P_60min)_d reflects the shorter interval intensity compared to the daily rainfall amount.

Previous research has focused on estimating annual average and seasonal scales of rainfall erovisity from readily available daily rainfall. The overall objective of this study was to calibrate and validate three relationships for estimating daily scale of erosivity from daily rainfall. The first two used power functions of only daily rainfall totals for estimating erosivity. One was fitted with different coefficients in warm and cool seasons, and the second used a sinusoidal relationship in order to represent seasonal differences in storm characteristics. The third relationship utilized daily rainfall totals and the daily maximum 60-min rainfall amount to estimate daily rainfall erosivity. We also investigated the relationship between daily and event rainfall amounts and statistically evaluated and determined the best value for delineating the threshold between erosive and non-erosive daily rainfall amounts.