- Email: [email protected]
Sensitivity analysis of kinetic energy-intensity relationships and maximum rainfall intensities on rainfall erosivity using a long-term precipitation dataset
Journal of Hydrology 527 (2015) 788–793
Contents lists available at ScienceDirect
Journal of Hydrology journal homepage: www.elsevier.com/locate/jhydrol
Sensitivity analysis of kinetic energy-intensity relationships and maximum rainfall intensities on rainfall erosivity using a long-term precipitation dataset Gabriel P. Lobo a, Carlos A. Bonilla a,b,⇑ a b
Departamento de Ingeniería Hidráulica y Ambiental, Pontificia Universidad Católica de Chile, Av. Vicuña Mackenna 4860, Macul, Santiago, Chile Centro de Desarrollo Urbano Sustentable CEDEUS, El Comendador 1916, Providencia, Santiago, Chile
a r t i c l e
i n f o
Article history: Received 5 January 2015 Received in revised form 30 March 2015 Accepted 23 May 2015 Available online 27 May 2015 This manuscript was handled by Konstantine P. Georgakakos, Editor-in-Chief, with the assistance of Joanna Crowe Curran, Associate Editor Keywords: Kinetic energy-intensity relationships Rainfall erosivity Rainfall kinetic energy Water erosion
s u m m a r y This paper analyses and compares rainfall erosivity values that were computed with five different kinetic energy-intensity (KE-I) relationships using the 0.5-h and 1-h maximum rainfall intensities (I30 and I60, respectively). The KE-I relationships included three exponential equations (Brown and Foster, 1987 (BF); McGregor et al., 1995 (MG); van Dijk et al., 2002 (VD)), a logarithmic equation (Wischmeier and Smith, 1958 (WS)) and a linear equation (Hudson, 1961 (HU)). The KE-I relationships were used to compute rainfall erosivity from pluviographic records of 30 sites that are located in central Chile. A total of 415 years of data were used, and more than 18,000 storms were identified. The results showed that among the exponential equations, the MG relationship yielded erosivity results that were statistically identical to the VD and the BF relationships. However, when comparing the VD and the BF relationships, significant differences in erosivity were found, which showed that the exponential equation is highly sensitive to changes in its regression parameters and is therefore site-specific. Among all of the relationships, the WS logarithmic equation yielded the largest erosivity estimates; however, they were statistically equal to the estimates made with the MG and the VD relationships but were not statistically equal to estimates predicted by the BF relationship. In contrast, in comparison to the other equations, the HU linear relationship yielded significantly smaller erosivity values. Conversely, regardless of the KE-I relationship and the site, computing erosivity using I60 provided erosivity estimates that are 10% smaller than those obtained using I30. The relative size of the erosivity estimates is due to the relative values of I60 and I30; on average I60 was 10% smaller than I30 at the study sites. Finally, because the rainfall erosivity estimates at the study sites were highly affected by the type of KE-I relationship, these results demonstrate that selecting an appropriate KE-I relationship is crucial for accurately estimating erosivity. These differences were augmented because of the typically low rainfall intensities at the study sites. Under this condition, the differences between the KE-I relationships were greatest. However, with higher rainfall intensities, all of the KE-I relationships provide similar kinetic energy estimates, which makes the selection of the KE-I relationship less important than the use of a reliable I30 value for computing rainfall erosivity. Ó 2015 Elsevier B.V. All rights reserved.
1. Introduction Rainfall kinetic energy is a commonly used climatic parameter for the prediction of soil erosion by water (Roswell, 1986; Lobo et al., 2015). This parameter has often been used as an indicator of rainfall erosivity, which is the capability of rainfall to detach soil particles (van Dijk et al., 2002). Widely used indices of erosivity,
⇑ Corresponding author at: Departamento de Ingeniería Hidráulica y Ambiental, Pontificia Universidad Católica de Chile, Av. Vicuña Mackenna 4860, Macul, Santiago, Chile. E-mail address: [email protected] (C.A. Bonilla). http://dx.doi.org/10.1016/j.jhydrol.2015.05.045 0022-1694/Ó 2015 Elsevier B.V. All rights reserved.
such the relationships proposed by Hudson (1961), Govers (1991) and the R-factor of the Revised Universal Soil Loss Equation (RUSLE) (Renard et al., 1997), include rainfall kinetic energy. In these relationships the kinetic energy is not linearly related to the soil loss. This is mainly caused by the typical small size of raindrops in low-intensity rainfall events; small raindrops are less efficient at detaching soil than larger raindrops (Salles and Poesen, 2000). On the other hand, high rainfall intensities are more likely to produce saturation and ponding, which may increase the efficiency of detachment (Torri et al., 1987). In the case of the RUSLE equation, the erosivity of each individual storm was defined as the kinetic energy of the storm multiplied by the
G.P. Lobo, C.A. Bonilla / Journal of Hydrology 527 (2015) 788–793
maximum 0.5-h rainfall intensity (I30), while erosivity was defined as the average of the annual summation of each storm’s erosivity (Renard et al., 1997). Thus, estimating rainfall erosivity using this definition requires having a reliable measure of the rainfall kinetic energy and sub-hourly rainfall measurements. Several methods have been developed to measure and estimate rainfall kinetic energy (Abd Elbasit et al., 2011). Estimating kinetic energy from rainfall intensity records by using empirical kinetic energy-rainfall intensity (KE-I) relationships is the most widely used method. Many types of mathematical formulations that are derived from measured precipitation intensity and calculated kinetic energy data have been proposed to describe KE-I relationships (Salles et al., 2002). Wischmeier and Smith (1958) proposed the following logarithmic relationship:
KE ¼ a þ blogðIÞ
ð1Þ
where KE is the kinetic energy of rain that is falling with intensity I, and a and b are constants that are derived from a nonlinear regression using actual data. This relationship was calibrated with data from 60 sites in 31 eastern states in the USA (Wischmeier, 1959) and was used in the Universal Soil Loss Equation (USLE) (Wischmeier and Smith, 1978). On the other hand, Hudson (1961) proposed the following linear relationship:
KE ¼ a1 ðb cI1 Þ
ð2Þ
where a, b and c are regression parameters. This equation was calibrated for subtropical climates in Zimbabwe and was adopted in the Soil Loss Estimator Model for Southern Africa (SLEMSA) (Elwell, 1978). This linear equation also proved to be valid for rainfall data that were collected in Miami (Kinnell, 1973). Later, Kinnell (1981) developed this exponential equation:
KE ¼ emax ð1 aebI Þ
ð3Þ
where emax is the maximum kinetic energy content of the rainfall, and a and b are regression parameters. This relationship provides kinetic energy values that are similar to those of the logarithmic equation, however it should be preferred because, unlike the logarithmic equation, it is a continuous equation with a physical meaning. The exponential equation was calibrated by Brown and Foster (1987) and incorporated in the RUSLE model. However, the equation used in RUSLE2 was that developed by McGregor et al. (1995), which is based on Eq. (3) but was calibrated for more sites that were located in Mississippi (Foster, 2008). Even though all of these equations are, to some degree, based on drop size distribution and drop velocity (Fox, 2004), there is no consensus regarding which equation best represents rainfall kinetic energy (Shamshad et al., 2008). In addition, their regression parameters have proven to be different and highly dependent on geographic location (Fornis et al., 2005), which limits their use on sites that are different from those that were used to build and calibrate them. Therefore, when using these equations to compute rainfall erosivity in sites where no kinetic energy records are available, it is important to consider that erosivity estimates will vary depending on the selected KE-I equation. Similarly, if there are no readily available sub-hourly rainfall records to compute the I30 values, which is a typical condition in many countries all over the world (Yin et al., 2007), the erosivity estimates may vary according to the I30 estimation method. These methods include using Intensity–Duration–Frequency (IDF) curves (Wenzel, 1982) and Bell’s equation (Bell, 1969), which provide different I30 estimates. Erosivity estimates are highly sensitive to I30 (Catari et al., 2011); thus choosing the appropriate estimation method is crucial to compute a reliable erosivity value. Therefore, the objective of this study was to perform a sensitivity analysis of the various
789
KE-I relationships and I30 estimation methods on rainfall erosivity using a long-term precipitation dataset from central Chile. 2. Materials and methods 2.1. Study sites and rainfall data Hourly pluviographic records were used to compute rainfall erosivity values at 30 sites that are located in central Chile. These records were obtained from the meteorological stations that are shown in Fig. 1, which are distributed between latitudes 32°040 S and 39°470 S. The stations are part of two national rain gauge networks that are managed by the Dirección General de Aguas (DGA) and the Sistema Nacional de Calidad del Aire (SINCA). As shown in Table 1, the amount of data per station ranged from 3 to 28 years and totaled 418 years and 18,012 storms. Depending on the station, the rainfall data were recorded between 1970 and 2013. Annual data were missing at some stations. The climate in this portion of Chile is mainly semi-arid, and the rainfall is usually of a frontal nature (Escobar and Aceituno, 1998), with intensities that rarely exceed 5.5 mm/h (Table 1). Additionally, precipitation amounts increase with latitude, and rainfall is highly erosive in some areas because of prolonged storms, especially in the southern sites of the study area (Bonilla and Vidal, 2011; Lobo et al., 2015). 2.2. KE-I relationships Five KE-I relationships were used to compute rainfall erosivity at the study sites (Table 2). These relationships consisted of three types of equations, one logarithmic, one linear, and three exponential and were developed by Wischmeier and Smith (1958), Hudson (1961), Brown and Foster (1987), McGregor et al. (1995) and van Dijk et al. (2002), respectively. The equations are shown in Table 2 and are plotted against rainfall intensity in Fig. 2. As shown in the figure, the differences among the equations decrease with increasing rainfall intensity. The differences among the equations are especially large at low rainfall intensities (<5 mm h1), which is the typical condition in central Chile (Table 1). This is particularly important in the case of Hudson’s equation, which was developed for subtropical climates with high rainfall intensities (Nel and Sumner, 2007) and not for a semi-arid climate with low rainfall intensities. Nevertheless, this equation was included in this comparison to assess its applicability under a different climate condition. 2.3. Estimation of I30 Estimating erosivity requires computing I30 for each storm. Unfortunately, as in many other places in the world, this parameter is not usually recorded in Chile. Therefore, I30 values were estimated using the Intensity–Duration–Frequency (IDF) curve that was developed by Wenzel (1982), which is based on the 1-h rainfall records as follows:
I¼
K Dn þ b
ð4Þ
where I is the storm’s mean intensity (mm h1) for duration D (h), and K, n and b are regression parameters. To fit the parameters, the intensities for durations of 1–6 h were computed for each storm, and a non-linear regression was used. Then, I30 was computed for each storm using Eq. (4) with the fitted parameters. Table 1 shows the average I30 that were estimated with this method, which are 8–14% larger than the 1-h maximum intensities, I60, depending on the station. The similarities between the I30 and I60
790
G.P. Lobo, C.A. Bonilla / Journal of Hydrology 527 (2015) 788–793
Fig. 1. Spatial distribution of the meteorological stations that were used in the study.
Table 1 Location and rainfall characteristics of the meteorological stations that were used in this study. Station
Latitude
Longitude
Elevation (m.a.s.l.)
Years of hourly rainfall records
Annual rainfall depth (mm)
Average rainfall intensity (mm h1)
I60 (mm h1)
I30 (mm h1)
Pedernal Sobrante Los Vientos Rancagua Quillota Lliu Lliu Pirque Melipilla Rengo Popeta C. Las Nieves Potrero Grande Fundo Peral Colorado Melozal Ancoa Bullileo Chillan Viejo Coihueco Caracol Diguillin Quilaco Cerro el Padre El Vergel Contulmo Traiguén Manzanar Pueblo Nuevo Freire Sendos Pucón
32°050 S 32°140 S 32°500 S 32°500 S 32°540 S 33°060 S 33°400 S 33°410 S 34°250 S 34°260 S 34°300 S 35°110 S 35°240 S 35°380 S 35°460 S 35°540 S 36°170 S 36°380 S 36°390 S 36°390 S 36°520 S 37°410 S 37°470 S 37°490 S 38°010 S 38°150 S 38°280 S 38°440 S 38°580 S 39°170 S
70°480 W 70°470 W 70°600 W 70°600 W 71°130 W 71°130 W 70°350 W 71°120 W 70°520 W 70°470 W 70°430 W 71°060 W 71°470 W 71°160 W 71°470 W 71°170 W 71°250 W 72°060 W 71°480 W 71°230 W 71°390 W 71°600 W 71°520 W 72°390 W 73°140 W 72°400 W 71°420 W 72°340 W 72°370 W 71°570 W
1100 810 130 170 130 260 670 170 310 400 700 460 110 420 110 430 600 125 300 620 670 225 400 75 25 170 790 100 100 230
21 21 4 10 10 14 2 18 23 6 22 21 13 24 22 22 22 9 8 6 28 28 17 5 4 5 17 4 3 9
40 46 27 171 35 139 183 136 169 152 287 316 353 532 227 532 1236 511 709 972 770 786 1067 307 236 506 831 444 316 1042
0.3 0.3 0.4 1.2 0.3 0.5 0.5 0.4 0.5 0.5 0.5 0.7 0.5 0.8 0.5 0.9 1.1 0.7 0.9 1.0 0.9 0.8 0.9 0.5 0.4 0.5 0.8 0.5 0.5 0.7
2.5 2.0 2.6 4.5 2.6 3.5 2.3 2.7 2.5 3.1 3.1 3.7 2.7 4.0 2.6 4.0 5.0 3.0 3.1 4.2 3.9 3.6 3.8 2.4 3.2 2.4 3.3 2.2 2.8 2.9
2.8 2.3 2.9 5.0 3.0 4.0 2.6 3.1 2.9 3.5 3.5 4.1 3.1 4.5 3.0 4.5 5.5 3.6 3.5 4.6 4.3 4.2 4.3 2.8 3.8 2.8 3.8 2.6 3.3 3.3
values are explained by the frontal nature of the storms in central Chile, which makes their intensities fairly constant. This condition differs from the storms that were used to calibrate the KE-I relationships that were analyzed in this study, which were mostly of a
convective nature. Because there are other methods for estimating I30, a sensitivity analysis was performed to quantify the effect of variations of I30 on erosivity. For this purpose, erosivity was also computed using the measured I60 instead of the estimated I30.
791
G.P. Lobo, C.A. Bonilla / Journal of Hydrology 527 (2015) 788–793 Table 2 Kinetic energy-rainfall intensity relationships that were used in this study. The kinetic energy, e, has units of MJ ha1, and the rainfall intensity, i, is expressed in mm h1. Equation 0:119 þ 0:0873 logðiÞ i 6 76 e¼ 0:283 i > 76 0 i64 e¼ 1 0:2986ð1 4:29i Þ i > 4 e ¼ 0:29½1 0:72 expð0:05iÞ e ¼ 0:29½1 0:72 expð0:082iÞ e ¼ 0:283½1 0:52 expð0:042iÞ
Author
Abbreviation
Wischmeier and Smith (1958) Hudson (1961)
WS HU
Brown and Foster (1987) McGregor et al. (1995) van Dijk et al. (2002)
BF MG VD
Table 3 Rainfall erosivities computed with the five KE-I relationships. McGregor
van Dijk
Brown and Foster
Wischmeier and Smith
Hudson
127a 69a 64a 349a 114a 549a 267a 250a 274a 272a 617a 819a 396a 1273a 395a 1271a 3250a 854a 937a 1823a 1389a 1085a 1441a 587a 579a 488a 923a 492a 614a 983a
175b 95b 90b 452b 157b 734b 366b 342b 377b 375b 844b 1103b 543b 1715b 532b 1714b 4329b 1141b 1266b 2499b 1879b 1460b 1943b 786b 778b 665b 1238b 665b 832b 1329b
42c 10c 10c 205c 33c 296c 70c 77c 68c 85c 217c 378c 113c 607c 145c 618c 1753c 374c 395c 672c 593c 422c 589c 254c 241c 122c 339c 132c 186c 270c
(MJ ha1 mm h1 yr1) Pedernal Sobrante Los Vientos Rancagua Quillota Lliu Lliu Pirque Melipilla Rengo Popeta C. Las Nieves Potrero Grande Fundo Peral Colorado Melozal Ancoa Bullileo Chillán Viejo Colhueco Caracol Diguillin Quilaco Cerro el Padre El Vergel Contulmo Traiguen Manzanar Pueblo Nuevo Freire Sendos Pucón
148ab 78ab 73ab 407ab 132ab 647ab 308ab 290ab 316ab 316ab 718ab 959ab 458ab 1493ab 458ab 1492ab 3822ab 994ab 1094ab 2129ab 1623ab 1259ab 1678ab 683ab 674ab 560ab 1067ab 564ab 709ab 1129ab
169ab 96ab 88ab 430ab 154ab 695ab 363ab 335ab 373ab 365ab 815b 1055b 534ab 1635b 524ab 1631b 4100b 1113b 1222b 2394b 1804b 1428b 1886b 765ab 762ab 668b 1226b 673b 825b 1336b
Means with different letters in the same row indicate significant differences between the erosivities according to the Kruskal–Wallis test. I30 was computed using an IDF curve according to Wenzel (1982).
Fig. 2. Graphical output comparing the kinetic energy estimates with different energy-intensity relationships. The kinetic energy computed using Hudson’s relationship is assumed to be 0 for rainfall intensities <5 mm h1 to avoid negative energy estimates.
2.4. Comparison method The five KE-I relationships were used to compute the rainfall erosivity for every site using I30 and I60. The erosivity estimates were compared among the five KE-I relationships by using the Kruskal–Wallis test because rainfall properties usually are not normally distributed (Zhang et al., 2008). The test was applied to the erosivity results of the five KE-I relationships using the I30 and I60 values. 3. Results and discussion Table 3 shows the rainfall erosivity (MJ ha1 mm h1 yr1) that was computed for the 30 sites using the different KE-I relationships (MJ ha1) and I30 (mm h1). Based on the statistical analysis, comparable rainfall erosivities were computed for every site when using the McGregor (MG) and the van Dijk (VD) relationships and when using the MG and the Brown and Foster (BF) relationships. At low erosivity values (<600 MJ ha1 mm h1 yr1), the three exponential relationships provided statistically equal erosivity estimates, but the differences increased as the erosivity values increased. These results are consistent with Fig. 3, where the erosivity values for all of the stations are plotted against their annual rainfall amounts. At low rainfall amounts, the erosivity
Fig. 3. Erosivity estimates computed using five KE-I relationships as a function of the annual rainfall for all of the sites. Each point shows the rainfall erosivity and the annual rainfall depth at a given site.
values computed with the VD, MG and BF relationships are close to each other. However, at higher rainfall amounts, the differences in erosivity increase, especially between the VD and BF relationships. On average, a 25% difference was observed between the
792
G.P. Lobo, C.A. Bonilla / Journal of Hydrology 527 (2015) 788–793
erosivity values that were computed using the VD and BF relationships, which makes their erosivity values significantly different at high rainfall amounts. As shown in Fig. 3, the erosivity values computed with the MG relationship are always in-between the values of the other exponential equations. The differences in erosivity between the MG and the BF relationships and between the MG and VD relationships are no larger than 15% and do not produce significantly different erosivity values (Table 3). The three exponential KE-I relationships derive from the same equation that was developed by Kinnell (1981) but were calibrated for different locations. Thus, the differences in erosivity, especially between the estimates that were obtained using the VD and the BF relationships, demonstrate that the exponential equation is highly sensitive to changes in the regression parameters and is therefore site-specific, as shown by van Dijk et al. (2002). The WS equation provided statistically equivalent erosivity values to those that were computed with the MG and VD equations but not with the BF equation (Table 3). As shown in Fig. 3, this is because the erosivity values that were obtained using the WS, VD and MG relationships are close for every station, regardless of the rainfall amount. However, the WS equation predicted larger erosivity estimates than the other KE-I relationships, because as shown in Fig. 2, it provided the highest KE for the range of intensities that were analyzed in this study (<5.5 mm/h). On average, the differences in the erosivity estimates when using the WS and the VD relationships and when using the WS and the MG relationships are 3%, and 14%, respectively. The differences in erosivity values are larger when using the WS and the BF relationships, and the average difference is 36%. The Hudson (HU) relationship provided significantly different erosivity values when compared to the erosivity estimates that were computed using the remaining KE-I relationships for every site (Table 3). This relationship predicted significantly smaller erosivity values than the other equations. The largest differences in erosivity were observed when using the HU and the WS relationships; using the HU relationship provided erosivity estimates that are up to three times smaller than those computed with the WS relationship (Fig. 3). These differences in erosivity show that using the HU relationship under inadequate climatic conditions affects its erosivity results. This equation should be only used in subtropical climates where the rainfall intensities are greater than 5 mm/h, as recommended in the study of Nel and Sumner (2007). Central Chile has a semi-arid climate and low-intensity frontal storms, which is not a suitable condition for using the HU relationship. Fig. 4 compares the erosivity values that were computed using I30 and I60 for all of the sites and the five KE-I relationships that were compared in this study. A single linear regression was used for every KE-I relationship and site, with an R2 of 0.99. As shown by the regression, using I60 instead of I30 makes the erosivity values approximately 10% smaller regardless of the KE-I relationship and site. The I60 records are on average 10% smaller than the estimated I30, and because the erosivity for each individual storm (MJ ha1 mm h1) was computed as the storm kinetic energy multiplied by its respective I30, a 10% variation in I30 accounts for a 10% change in erosivity (MJ ha1 mm h1 yr1). Therefore, if other methods were used to estimate I30 from I60, such as Bell’s equation or other IDF curves, the erosivity estimates would vary proportionally to the variation in I30. Moreover, the proportional differences in the erosivities among the equations remain the same regardless of the I30 estimation method. As shown in Table 1, the mean rainfall intensities in central Chile are usually in the range of 5.5 mm/h or less because of the predominate frontal systems. The largest differences among the KE-I relationships occur in this range (Fig. 2); thus the erosivity values are significantly different at almost every site, depending
Fig. 4. Comparison between the erosivity results that were obtained using I30 and I60 for all of the sites and the five KE-I relationships that were analyzed in this study. The linear regression was obtained using all of the KE-I relationships and sites.
on the KE-I relationship. Therefore, in sites with predominating low-intensity storms, it is critical to choose a KE-I relationship that can be adapted to the local conditions when estimating rainfall erosivity. On the other hand, in frontal storms the I30 values are usually very close to the I60 values, and therefore using different methods for estimating I30 from the I60 values will not produce a substantial difference in erosivity estimates. Nevertheless, in sites where rainfall intensities are usually higher, the type of KE-I relationship will not have a considerable impact on rainfall erosivity because these equations predict similar energy values at high rainfall intensities (Fig. 2). Therefore, the main source of variability when computing erosivity with high rainfall intensities is related to the I30 estimation method rather than the KE-I relationship because rainfall erosivity is directly proportional to I30. 4. Conclusions This study demonstrates that the rainfall erosivity estimates can be highly dependent on the KE-I relationship that is used to compute them. The erosivity estimates that were obtained using the three exponential KE-I relationships were significantly different, which proves that this type of equation is highly sensitive to changes in its regression parameters. Thus, these equations should be calibrated based on local precipitation data to generate reliable erosivity estimates. This recommendation applies especially if rainfall intensities are low because the differences in kinetic energy among the exponential equations increase with decreasing intensity. Significant differences were also found when comparing the erosivity values that were computed with the exponential and the logarithmic equations. The logarithmic equation predicted higher kinetic energy estimates than the exponential equations at low rainfall intensities, which is the typical rainfall condition in central Chile. In contrast, the linear equation predicted the lowest erosivity values, which are up to three times smaller than those estimated using the logarithmic equation. The linear equation was fitted for subtropical climates with high rainfall intensities, which is not the case in central Chile, where rainfall intensities are usually
G.P. Lobo, C.A. Bonilla / Journal of Hydrology 527 (2015) 788–793
low and the climate is semi-arid. This proves that it is crucial to verify whether similar climatic conditions exist between the local sites and those that were used to build the KE-I relationships. The results also show that computing the erosivity at the study sites using I60 instead of I30 produced a 10% reduction in the erosivity estimates. On average I60 is 10% smaller than I30 for every site, and because erosivity is defined as the kinetic energy of the storms multiplied by their respective I30, a 10% variation in I30 accounts for a 10% change in erosivity. The small difference between I30 and I60 at the study sites is explained by the frontal systems in central Chile, which produce fairly constant rainfall intensities. Because of this, the method that was used to estimate I30 from I60 values did not have a significant impact on the estimation of rainfall erosivity at the study sites. The opposite situation occurred at sites with moderate or larger differences between I30 and I60. Finally, the erosivity values may vary significantly depending on the KE-I relationship that is used to compute them. Because large differences were found among the exponential, logarithmic and linear KE-I relationships that were analyzed in this study at low rainfall intensities, it is crucial to select a proper KE-I relationship that can be adapted to local conditions, especially at sites with low-intensity storms. Nevertheless, at higher rainfall intensities, the kinetic energy-intensity relationships provided similar kinetic energy estimates, which makes the type of relationship less important. Therefore, the largest source of variability when estimating rainfall erosivity in areas with high rainfall intensities is the I30 estimation method, rather than the KE-I relationship.
Acknowledgments This research was supported by funding from the National Commission for Scientific and Technological Research – Chile CONICYT/FONDECYT/Regular 1130928. The rainfall data were provided by the General Directorate of Water Resources (DGA), Government of Chile.
References Abd Elbasit, A.A.M., Yasuda, H., Salmi, A., 2011. Application of piezoelectric transducers in simulated rainfall erosivity assessment. Hydrol. Sci. J. 56 (1), 187–194. Bell, F.C., 1969. Generalized rainfall duration-frequency relationships. J. Hydraulics Div. 95 (1), 311–327. Bonilla, C.A., Vidal, K.L., 2011. Rainfall erosivity in Central Chile. J. Hydrol. 410 (1–2), 126–133. Brown, L.C., Foster, G.R., 1987. Storm erosivity using idealized intensity distributions. Trans. Am. Soc. Agric. Eng. 30, 379–386.
793
Catari, G., Latron, J., Gallart, F., 2011. Assessing the sources of uncertainty associated with the calculation of rainfall kinetic energy and erosivity – application to the Upper Llobregat Basin, NE Spain. Hydrol. Earth Syst. Sci. 15, 679–688. Elwell, H.A., 1978. Modeling soil losses in Southern Africa. J. Agric. Eng. Res. 23, 117–127. Escobar, F., Aceituno, P., 1998. Influencia del fenómeno ENSO sobre la precipitación nival en el sector andino de Chile central durante el invierno. Bulletin de l’Institut Français Détudes Andines 27 (3), 753–759 (In Spanish). Fornis, R.L., Vermeulen, H.R., Nieuwenhuis, J.D., 2005. Kinetic energy–rainfall relationships for Central Cebu, Philippines for soil erosion. J. Hydrol. 300, 20–32. Foster, G.R., 2008. Revised universal soil loss equation Version 2 (RUSLE2). USDAARS, Washington, D.C. Fox, N.I., 2004. TECHNICAL NOTE: The representation of rainfall drop-size distribution and kinetic energy. Hydrol. Earth Syst. Sci. 8 (5), 1001–1007. Govers, G., 1991. Spatial and temporal variations in splash detachment: a field study. Catena 20 (Suppl.), 15–24. Hudson, N.W., 1961. An introduction to the mechanics of soil erosion under conditions of sub-tropical rainfall. Rhodesia Sci. Assoc. Proc. 49, 14–25. Kinnell, P.I.A., 1973. The problem of assessing the erosive power of rainfall from meteorological observations. Soil Sci. Soc. Am. J. 37, 617–621. Kinnell, P.I.A., 1981. Rainfall-kinetic energy relationships for soil loss prediction. Soil Sci. Soc. Am. J. 45, 153–155. Lobo, G.P., Frankenberger, J.R., Flanagan, D.C., Bonilla, C.A., 2015. Evaluation and improvement of the CLIGEN model for storm and rainfall erosivity generation in Central Chile. Catena 127, 206–213. McGregor, K.C., Bingner, R.L., Bowie, A.J., Foster, G.R., 1995. Erosivity index values for northern Mississippi. Trans. Am. Soc. Agric. Eng. 38 (4), 1039–1047. Nel, W., Sumner, P.D., 2007. Intensity, energy and erosivity attributes of rainstorms in the KwaZulu-Natal Drakensberg, South Africa. South Afr. J. Sci. 103, 398–403. Renard, K.G., Foster, G.R., Weesies, G.A., McCool, D.K., Yoder, D.C., 1997. Predicting Soil Erosion by Water: A Guide to Conservation Planning with the Revised Universal Soil Loss Equation (RUSLE). USDA Agriculture Handbook No. 703.Washington DC. Rosewell, C.J., 1986. Rainfall kinetic energy in Eastern Australia. J. Clim. Appl. Meteorol. 25, 1695–1701. Salles, C., Poesen, J., 2000. Rain properties controlling soil splash detachment. Hydrol. Processes 14, 271–282. Salles, C., Poesen, J., Sempere-Torres, D., 2002. Kinetic energy of rain and its functional relationship with intensity. J. Hydrol. 257, 256–270. Shamshad, a., Azhari, M.N., Isa, M.H., Hussin, W.M.a.W., Parida, B.P. (2008). Development of an appropriate procedure for estimation of RUSLE EI30 index and preparation of erosivity maps for Pulau Penang in Peninsular Malaysia. Catena, 72, 423–432. Torri, D., Sfalanga, M., Del Sette, M., 1897. Splash detachment: runoff depth and soil cohesion. Catena 14, 149–155. van Dijk, A.I.J., Bruijnzeel, L.A., Rosewell, C.J., 2002. Rainfall intensity – kinetic energy relationships: a critical literature appraisal. J. Hydrol. 261, 1–23. Wenzel, H., 1982. Rainfall for urban stormwater design. In: Urban storm water hydrology. (7th ed., Vol. 7, pp. 35–67). Washington DC: American Geophysical Union. Wischmeier, W.H., 1959. A rainfall erosion index for a universal soil-loss equation. Soil Sci. Soc. Am. J. 23 (3), 246–249. Wischmeier, W.H., Smith, D.D., 1958. Rainfall energy and its relation to soil loss. Trans. Am. Geophy. Union 39, 285–291. Wischmeier, W.H., Smith, D.D., 1978. Predicting rainfall erosion. USDA Agriculture Handbook No. 537. Washington D.C. Yin, S., Xie, Y., Nearing, M.A., Wang, C., 2007. Estimation of rainfall erosivity using 5to 60-minute fixed-interval rainfall data from China. Catena 70 (3), 306–312. Zhang, Y., Liu, B., Wang, Z., Zhu, Q., 2008. Evaluation of CLIGEN for storm generation on the semiarid Loess Plateau in China. Catena 73 (1), 1–9.
Contents lists available at ScienceDirect
Journal of Hydrology journal homepage: www.elsevier.com/locate/jhydrol
Sensitivity analysis of kinetic energy-intensity relationships and maximum rainfall intensities on rainfall erosivity using a long-term precipitation dataset Gabriel P. Lobo a, Carlos A. Bonilla a,b,⇑ a b
Departamento de Ingeniería Hidráulica y Ambiental, Pontificia Universidad Católica de Chile, Av. Vicuña Mackenna 4860, Macul, Santiago, Chile Centro de Desarrollo Urbano Sustentable CEDEUS, El Comendador 1916, Providencia, Santiago, Chile
a r t i c l e
i n f o
Article history: Received 5 January 2015 Received in revised form 30 March 2015 Accepted 23 May 2015 Available online 27 May 2015 This manuscript was handled by Konstantine P. Georgakakos, Editor-in-Chief, with the assistance of Joanna Crowe Curran, Associate Editor Keywords: Kinetic energy-intensity relationships Rainfall erosivity Rainfall kinetic energy Water erosion
s u m m a r y This paper analyses and compares rainfall erosivity values that were computed with five different kinetic energy-intensity (KE-I) relationships using the 0.5-h and 1-h maximum rainfall intensities (I30 and I60, respectively). The KE-I relationships included three exponential equations (Brown and Foster, 1987 (BF); McGregor et al., 1995 (MG); van Dijk et al., 2002 (VD)), a logarithmic equation (Wischmeier and Smith, 1958 (WS)) and a linear equation (Hudson, 1961 (HU)). The KE-I relationships were used to compute rainfall erosivity from pluviographic records of 30 sites that are located in central Chile. A total of 415 years of data were used, and more than 18,000 storms were identified. The results showed that among the exponential equations, the MG relationship yielded erosivity results that were statistically identical to the VD and the BF relationships. However, when comparing the VD and the BF relationships, significant differences in erosivity were found, which showed that the exponential equation is highly sensitive to changes in its regression parameters and is therefore site-specific. Among all of the relationships, the WS logarithmic equation yielded the largest erosivity estimates; however, they were statistically equal to the estimates made with the MG and the VD relationships but were not statistically equal to estimates predicted by the BF relationship. In contrast, in comparison to the other equations, the HU linear relationship yielded significantly smaller erosivity values. Conversely, regardless of the KE-I relationship and the site, computing erosivity using I60 provided erosivity estimates that are 10% smaller than those obtained using I30. The relative size of the erosivity estimates is due to the relative values of I60 and I30; on average I60 was 10% smaller than I30 at the study sites. Finally, because the rainfall erosivity estimates at the study sites were highly affected by the type of KE-I relationship, these results demonstrate that selecting an appropriate KE-I relationship is crucial for accurately estimating erosivity. These differences were augmented because of the typically low rainfall intensities at the study sites. Under this condition, the differences between the KE-I relationships were greatest. However, with higher rainfall intensities, all of the KE-I relationships provide similar kinetic energy estimates, which makes the selection of the KE-I relationship less important than the use of a reliable I30 value for computing rainfall erosivity. Ó 2015 Elsevier B.V. All rights reserved.
1. Introduction Rainfall kinetic energy is a commonly used climatic parameter for the prediction of soil erosion by water (Roswell, 1986; Lobo et al., 2015). This parameter has often been used as an indicator of rainfall erosivity, which is the capability of rainfall to detach soil particles (van Dijk et al., 2002). Widely used indices of erosivity,
⇑ Corresponding author at: Departamento de Ingeniería Hidráulica y Ambiental, Pontificia Universidad Católica de Chile, Av. Vicuña Mackenna 4860, Macul, Santiago, Chile. E-mail address: [email protected] (C.A. Bonilla). http://dx.doi.org/10.1016/j.jhydrol.2015.05.045 0022-1694/Ó 2015 Elsevier B.V. All rights reserved.
such the relationships proposed by Hudson (1961), Govers (1991) and the R-factor of the Revised Universal Soil Loss Equation (RUSLE) (Renard et al., 1997), include rainfall kinetic energy. In these relationships the kinetic energy is not linearly related to the soil loss. This is mainly caused by the typical small size of raindrops in low-intensity rainfall events; small raindrops are less efficient at detaching soil than larger raindrops (Salles and Poesen, 2000). On the other hand, high rainfall intensities are more likely to produce saturation and ponding, which may increase the efficiency of detachment (Torri et al., 1987). In the case of the RUSLE equation, the erosivity of each individual storm was defined as the kinetic energy of the storm multiplied by the
G.P. Lobo, C.A. Bonilla / Journal of Hydrology 527 (2015) 788–793
maximum 0.5-h rainfall intensity (I30), while erosivity was defined as the average of the annual summation of each storm’s erosivity (Renard et al., 1997). Thus, estimating rainfall erosivity using this definition requires having a reliable measure of the rainfall kinetic energy and sub-hourly rainfall measurements. Several methods have been developed to measure and estimate rainfall kinetic energy (Abd Elbasit et al., 2011). Estimating kinetic energy from rainfall intensity records by using empirical kinetic energy-rainfall intensity (KE-I) relationships is the most widely used method. Many types of mathematical formulations that are derived from measured precipitation intensity and calculated kinetic energy data have been proposed to describe KE-I relationships (Salles et al., 2002). Wischmeier and Smith (1958) proposed the following logarithmic relationship:
KE ¼ a þ blogðIÞ
ð1Þ
where KE is the kinetic energy of rain that is falling with intensity I, and a and b are constants that are derived from a nonlinear regression using actual data. This relationship was calibrated with data from 60 sites in 31 eastern states in the USA (Wischmeier, 1959) and was used in the Universal Soil Loss Equation (USLE) (Wischmeier and Smith, 1978). On the other hand, Hudson (1961) proposed the following linear relationship:
KE ¼ a1 ðb cI1 Þ
ð2Þ
where a, b and c are regression parameters. This equation was calibrated for subtropical climates in Zimbabwe and was adopted in the Soil Loss Estimator Model for Southern Africa (SLEMSA) (Elwell, 1978). This linear equation also proved to be valid for rainfall data that were collected in Miami (Kinnell, 1973). Later, Kinnell (1981) developed this exponential equation:
KE ¼ emax ð1 aebI Þ
ð3Þ
where emax is the maximum kinetic energy content of the rainfall, and a and b are regression parameters. This relationship provides kinetic energy values that are similar to those of the logarithmic equation, however it should be preferred because, unlike the logarithmic equation, it is a continuous equation with a physical meaning. The exponential equation was calibrated by Brown and Foster (1987) and incorporated in the RUSLE model. However, the equation used in RUSLE2 was that developed by McGregor et al. (1995), which is based on Eq. (3) but was calibrated for more sites that were located in Mississippi (Foster, 2008). Even though all of these equations are, to some degree, based on drop size distribution and drop velocity (Fox, 2004), there is no consensus regarding which equation best represents rainfall kinetic energy (Shamshad et al., 2008). In addition, their regression parameters have proven to be different and highly dependent on geographic location (Fornis et al., 2005), which limits their use on sites that are different from those that were used to build and calibrate them. Therefore, when using these equations to compute rainfall erosivity in sites where no kinetic energy records are available, it is important to consider that erosivity estimates will vary depending on the selected KE-I equation. Similarly, if there are no readily available sub-hourly rainfall records to compute the I30 values, which is a typical condition in many countries all over the world (Yin et al., 2007), the erosivity estimates may vary according to the I30 estimation method. These methods include using Intensity–Duration–Frequency (IDF) curves (Wenzel, 1982) and Bell’s equation (Bell, 1969), which provide different I30 estimates. Erosivity estimates are highly sensitive to I30 (Catari et al., 2011); thus choosing the appropriate estimation method is crucial to compute a reliable erosivity value. Therefore, the objective of this study was to perform a sensitivity analysis of the various
789
KE-I relationships and I30 estimation methods on rainfall erosivity using a long-term precipitation dataset from central Chile. 2. Materials and methods 2.1. Study sites and rainfall data Hourly pluviographic records were used to compute rainfall erosivity values at 30 sites that are located in central Chile. These records were obtained from the meteorological stations that are shown in Fig. 1, which are distributed between latitudes 32°040 S and 39°470 S. The stations are part of two national rain gauge networks that are managed by the Dirección General de Aguas (DGA) and the Sistema Nacional de Calidad del Aire (SINCA). As shown in Table 1, the amount of data per station ranged from 3 to 28 years and totaled 418 years and 18,012 storms. Depending on the station, the rainfall data were recorded between 1970 and 2013. Annual data were missing at some stations. The climate in this portion of Chile is mainly semi-arid, and the rainfall is usually of a frontal nature (Escobar and Aceituno, 1998), with intensities that rarely exceed 5.5 mm/h (Table 1). Additionally, precipitation amounts increase with latitude, and rainfall is highly erosive in some areas because of prolonged storms, especially in the southern sites of the study area (Bonilla and Vidal, 2011; Lobo et al., 2015). 2.2. KE-I relationships Five KE-I relationships were used to compute rainfall erosivity at the study sites (Table 2). These relationships consisted of three types of equations, one logarithmic, one linear, and three exponential and were developed by Wischmeier and Smith (1958), Hudson (1961), Brown and Foster (1987), McGregor et al. (1995) and van Dijk et al. (2002), respectively. The equations are shown in Table 2 and are plotted against rainfall intensity in Fig. 2. As shown in the figure, the differences among the equations decrease with increasing rainfall intensity. The differences among the equations are especially large at low rainfall intensities (<5 mm h1), which is the typical condition in central Chile (Table 1). This is particularly important in the case of Hudson’s equation, which was developed for subtropical climates with high rainfall intensities (Nel and Sumner, 2007) and not for a semi-arid climate with low rainfall intensities. Nevertheless, this equation was included in this comparison to assess its applicability under a different climate condition. 2.3. Estimation of I30 Estimating erosivity requires computing I30 for each storm. Unfortunately, as in many other places in the world, this parameter is not usually recorded in Chile. Therefore, I30 values were estimated using the Intensity–Duration–Frequency (IDF) curve that was developed by Wenzel (1982), which is based on the 1-h rainfall records as follows:
I¼
K Dn þ b
ð4Þ
where I is the storm’s mean intensity (mm h1) for duration D (h), and K, n and b are regression parameters. To fit the parameters, the intensities for durations of 1–6 h were computed for each storm, and a non-linear regression was used. Then, I30 was computed for each storm using Eq. (4) with the fitted parameters. Table 1 shows the average I30 that were estimated with this method, which are 8–14% larger than the 1-h maximum intensities, I60, depending on the station. The similarities between the I30 and I60
790
G.P. Lobo, C.A. Bonilla / Journal of Hydrology 527 (2015) 788–793
Fig. 1. Spatial distribution of the meteorological stations that were used in the study.
Table 1 Location and rainfall characteristics of the meteorological stations that were used in this study. Station
Latitude
Longitude
Elevation (m.a.s.l.)
Years of hourly rainfall records
Annual rainfall depth (mm)
Average rainfall intensity (mm h1)
I60 (mm h1)
I30 (mm h1)
Pedernal Sobrante Los Vientos Rancagua Quillota Lliu Lliu Pirque Melipilla Rengo Popeta C. Las Nieves Potrero Grande Fundo Peral Colorado Melozal Ancoa Bullileo Chillan Viejo Coihueco Caracol Diguillin Quilaco Cerro el Padre El Vergel Contulmo Traiguén Manzanar Pueblo Nuevo Freire Sendos Pucón
32°050 S 32°140 S 32°500 S 32°500 S 32°540 S 33°060 S 33°400 S 33°410 S 34°250 S 34°260 S 34°300 S 35°110 S 35°240 S 35°380 S 35°460 S 35°540 S 36°170 S 36°380 S 36°390 S 36°390 S 36°520 S 37°410 S 37°470 S 37°490 S 38°010 S 38°150 S 38°280 S 38°440 S 38°580 S 39°170 S
70°480 W 70°470 W 70°600 W 70°600 W 71°130 W 71°130 W 70°350 W 71°120 W 70°520 W 70°470 W 70°430 W 71°060 W 71°470 W 71°160 W 71°470 W 71°170 W 71°250 W 72°060 W 71°480 W 71°230 W 71°390 W 71°600 W 71°520 W 72°390 W 73°140 W 72°400 W 71°420 W 72°340 W 72°370 W 71°570 W
1100 810 130 170 130 260 670 170 310 400 700 460 110 420 110 430 600 125 300 620 670 225 400 75 25 170 790 100 100 230
21 21 4 10 10 14 2 18 23 6 22 21 13 24 22 22 22 9 8 6 28 28 17 5 4 5 17 4 3 9
40 46 27 171 35 139 183 136 169 152 287 316 353 532 227 532 1236 511 709 972 770 786 1067 307 236 506 831 444 316 1042
0.3 0.3 0.4 1.2 0.3 0.5 0.5 0.4 0.5 0.5 0.5 0.7 0.5 0.8 0.5 0.9 1.1 0.7 0.9 1.0 0.9 0.8 0.9 0.5 0.4 0.5 0.8 0.5 0.5 0.7
2.5 2.0 2.6 4.5 2.6 3.5 2.3 2.7 2.5 3.1 3.1 3.7 2.7 4.0 2.6 4.0 5.0 3.0 3.1 4.2 3.9 3.6 3.8 2.4 3.2 2.4 3.3 2.2 2.8 2.9
2.8 2.3 2.9 5.0 3.0 4.0 2.6 3.1 2.9 3.5 3.5 4.1 3.1 4.5 3.0 4.5 5.5 3.6 3.5 4.6 4.3 4.2 4.3 2.8 3.8 2.8 3.8 2.6 3.3 3.3
values are explained by the frontal nature of the storms in central Chile, which makes their intensities fairly constant. This condition differs from the storms that were used to calibrate the KE-I relationships that were analyzed in this study, which were mostly of a
convective nature. Because there are other methods for estimating I30, a sensitivity analysis was performed to quantify the effect of variations of I30 on erosivity. For this purpose, erosivity was also computed using the measured I60 instead of the estimated I30.
791
G.P. Lobo, C.A. Bonilla / Journal of Hydrology 527 (2015) 788–793 Table 2 Kinetic energy-rainfall intensity relationships that were used in this study. The kinetic energy, e, has units of MJ ha1, and the rainfall intensity, i, is expressed in mm h1. Equation 0:119 þ 0:0873 logðiÞ i 6 76 e¼ 0:283 i > 76 0 i64 e¼ 1 0:2986ð1 4:29i Þ i > 4 e ¼ 0:29½1 0:72 expð0:05iÞ e ¼ 0:29½1 0:72 expð0:082iÞ e ¼ 0:283½1 0:52 expð0:042iÞ
Author
Abbreviation
Wischmeier and Smith (1958) Hudson (1961)
WS HU
Brown and Foster (1987) McGregor et al. (1995) van Dijk et al. (2002)
BF MG VD
Table 3 Rainfall erosivities computed with the five KE-I relationships. McGregor
van Dijk
Brown and Foster
Wischmeier and Smith
Hudson
127a 69a 64a 349a 114a 549a 267a 250a 274a 272a 617a 819a 396a 1273a 395a 1271a 3250a 854a 937a 1823a 1389a 1085a 1441a 587a 579a 488a 923a 492a 614a 983a
175b 95b 90b 452b 157b 734b 366b 342b 377b 375b 844b 1103b 543b 1715b 532b 1714b 4329b 1141b 1266b 2499b 1879b 1460b 1943b 786b 778b 665b 1238b 665b 832b 1329b
42c 10c 10c 205c 33c 296c 70c 77c 68c 85c 217c 378c 113c 607c 145c 618c 1753c 374c 395c 672c 593c 422c 589c 254c 241c 122c 339c 132c 186c 270c
(MJ ha1 mm h1 yr1) Pedernal Sobrante Los Vientos Rancagua Quillota Lliu Lliu Pirque Melipilla Rengo Popeta C. Las Nieves Potrero Grande Fundo Peral Colorado Melozal Ancoa Bullileo Chillán Viejo Colhueco Caracol Diguillin Quilaco Cerro el Padre El Vergel Contulmo Traiguen Manzanar Pueblo Nuevo Freire Sendos Pucón
148ab 78ab 73ab 407ab 132ab 647ab 308ab 290ab 316ab 316ab 718ab 959ab 458ab 1493ab 458ab 1492ab 3822ab 994ab 1094ab 2129ab 1623ab 1259ab 1678ab 683ab 674ab 560ab 1067ab 564ab 709ab 1129ab
169ab 96ab 88ab 430ab 154ab 695ab 363ab 335ab 373ab 365ab 815b 1055b 534ab 1635b 524ab 1631b 4100b 1113b 1222b 2394b 1804b 1428b 1886b 765ab 762ab 668b 1226b 673b 825b 1336b
Means with different letters in the same row indicate significant differences between the erosivities according to the Kruskal–Wallis test. I30 was computed using an IDF curve according to Wenzel (1982).
Fig. 2. Graphical output comparing the kinetic energy estimates with different energy-intensity relationships. The kinetic energy computed using Hudson’s relationship is assumed to be 0 for rainfall intensities <5 mm h1 to avoid negative energy estimates.
2.4. Comparison method The five KE-I relationships were used to compute the rainfall erosivity for every site using I30 and I60. The erosivity estimates were compared among the five KE-I relationships by using the Kruskal–Wallis test because rainfall properties usually are not normally distributed (Zhang et al., 2008). The test was applied to the erosivity results of the five KE-I relationships using the I30 and I60 values. 3. Results and discussion Table 3 shows the rainfall erosivity (MJ ha1 mm h1 yr1) that was computed for the 30 sites using the different KE-I relationships (MJ ha1) and I30 (mm h1). Based on the statistical analysis, comparable rainfall erosivities were computed for every site when using the McGregor (MG) and the van Dijk (VD) relationships and when using the MG and the Brown and Foster (BF) relationships. At low erosivity values (<600 MJ ha1 mm h1 yr1), the three exponential relationships provided statistically equal erosivity estimates, but the differences increased as the erosivity values increased. These results are consistent with Fig. 3, where the erosivity values for all of the stations are plotted against their annual rainfall amounts. At low rainfall amounts, the erosivity
Fig. 3. Erosivity estimates computed using five KE-I relationships as a function of the annual rainfall for all of the sites. Each point shows the rainfall erosivity and the annual rainfall depth at a given site.
values computed with the VD, MG and BF relationships are close to each other. However, at higher rainfall amounts, the differences in erosivity increase, especially between the VD and BF relationships. On average, a 25% difference was observed between the
792
G.P. Lobo, C.A. Bonilla / Journal of Hydrology 527 (2015) 788–793
erosivity values that were computed using the VD and BF relationships, which makes their erosivity values significantly different at high rainfall amounts. As shown in Fig. 3, the erosivity values computed with the MG relationship are always in-between the values of the other exponential equations. The differences in erosivity between the MG and the BF relationships and between the MG and VD relationships are no larger than 15% and do not produce significantly different erosivity values (Table 3). The three exponential KE-I relationships derive from the same equation that was developed by Kinnell (1981) but were calibrated for different locations. Thus, the differences in erosivity, especially between the estimates that were obtained using the VD and the BF relationships, demonstrate that the exponential equation is highly sensitive to changes in the regression parameters and is therefore site-specific, as shown by van Dijk et al. (2002). The WS equation provided statistically equivalent erosivity values to those that were computed with the MG and VD equations but not with the BF equation (Table 3). As shown in Fig. 3, this is because the erosivity values that were obtained using the WS, VD and MG relationships are close for every station, regardless of the rainfall amount. However, the WS equation predicted larger erosivity estimates than the other KE-I relationships, because as shown in Fig. 2, it provided the highest KE for the range of intensities that were analyzed in this study (<5.5 mm/h). On average, the differences in the erosivity estimates when using the WS and the VD relationships and when using the WS and the MG relationships are 3%, and 14%, respectively. The differences in erosivity values are larger when using the WS and the BF relationships, and the average difference is 36%. The Hudson (HU) relationship provided significantly different erosivity values when compared to the erosivity estimates that were computed using the remaining KE-I relationships for every site (Table 3). This relationship predicted significantly smaller erosivity values than the other equations. The largest differences in erosivity were observed when using the HU and the WS relationships; using the HU relationship provided erosivity estimates that are up to three times smaller than those computed with the WS relationship (Fig. 3). These differences in erosivity show that using the HU relationship under inadequate climatic conditions affects its erosivity results. This equation should be only used in subtropical climates where the rainfall intensities are greater than 5 mm/h, as recommended in the study of Nel and Sumner (2007). Central Chile has a semi-arid climate and low-intensity frontal storms, which is not a suitable condition for using the HU relationship. Fig. 4 compares the erosivity values that were computed using I30 and I60 for all of the sites and the five KE-I relationships that were compared in this study. A single linear regression was used for every KE-I relationship and site, with an R2 of 0.99. As shown by the regression, using I60 instead of I30 makes the erosivity values approximately 10% smaller regardless of the KE-I relationship and site. The I60 records are on average 10% smaller than the estimated I30, and because the erosivity for each individual storm (MJ ha1 mm h1) was computed as the storm kinetic energy multiplied by its respective I30, a 10% variation in I30 accounts for a 10% change in erosivity (MJ ha1 mm h1 yr1). Therefore, if other methods were used to estimate I30 from I60, such as Bell’s equation or other IDF curves, the erosivity estimates would vary proportionally to the variation in I30. Moreover, the proportional differences in the erosivities among the equations remain the same regardless of the I30 estimation method. As shown in Table 1, the mean rainfall intensities in central Chile are usually in the range of 5.5 mm/h or less because of the predominate frontal systems. The largest differences among the KE-I relationships occur in this range (Fig. 2); thus the erosivity values are significantly different at almost every site, depending
Fig. 4. Comparison between the erosivity results that were obtained using I30 and I60 for all of the sites and the five KE-I relationships that were analyzed in this study. The linear regression was obtained using all of the KE-I relationships and sites.
on the KE-I relationship. Therefore, in sites with predominating low-intensity storms, it is critical to choose a KE-I relationship that can be adapted to the local conditions when estimating rainfall erosivity. On the other hand, in frontal storms the I30 values are usually very close to the I60 values, and therefore using different methods for estimating I30 from the I60 values will not produce a substantial difference in erosivity estimates. Nevertheless, in sites where rainfall intensities are usually higher, the type of KE-I relationship will not have a considerable impact on rainfall erosivity because these equations predict similar energy values at high rainfall intensities (Fig. 2). Therefore, the main source of variability when computing erosivity with high rainfall intensities is related to the I30 estimation method rather than the KE-I relationship because rainfall erosivity is directly proportional to I30. 4. Conclusions This study demonstrates that the rainfall erosivity estimates can be highly dependent on the KE-I relationship that is used to compute them. The erosivity estimates that were obtained using the three exponential KE-I relationships were significantly different, which proves that this type of equation is highly sensitive to changes in its regression parameters. Thus, these equations should be calibrated based on local precipitation data to generate reliable erosivity estimates. This recommendation applies especially if rainfall intensities are low because the differences in kinetic energy among the exponential equations increase with decreasing intensity. Significant differences were also found when comparing the erosivity values that were computed with the exponential and the logarithmic equations. The logarithmic equation predicted higher kinetic energy estimates than the exponential equations at low rainfall intensities, which is the typical rainfall condition in central Chile. In contrast, the linear equation predicted the lowest erosivity values, which are up to three times smaller than those estimated using the logarithmic equation. The linear equation was fitted for subtropical climates with high rainfall intensities, which is not the case in central Chile, where rainfall intensities are usually
G.P. Lobo, C.A. Bonilla / Journal of Hydrology 527 (2015) 788–793
low and the climate is semi-arid. This proves that it is crucial to verify whether similar climatic conditions exist between the local sites and those that were used to build the KE-I relationships. The results also show that computing the erosivity at the study sites using I60 instead of I30 produced a 10% reduction in the erosivity estimates. On average I60 is 10% smaller than I30 for every site, and because erosivity is defined as the kinetic energy of the storms multiplied by their respective I30, a 10% variation in I30 accounts for a 10% change in erosivity. The small difference between I30 and I60 at the study sites is explained by the frontal systems in central Chile, which produce fairly constant rainfall intensities. Because of this, the method that was used to estimate I30 from I60 values did not have a significant impact on the estimation of rainfall erosivity at the study sites. The opposite situation occurred at sites with moderate or larger differences between I30 and I60. Finally, the erosivity values may vary significantly depending on the KE-I relationship that is used to compute them. Because large differences were found among the exponential, logarithmic and linear KE-I relationships that were analyzed in this study at low rainfall intensities, it is crucial to select a proper KE-I relationship that can be adapted to local conditions, especially at sites with low-intensity storms. Nevertheless, at higher rainfall intensities, the kinetic energy-intensity relationships provided similar kinetic energy estimates, which makes the type of relationship less important. Therefore, the largest source of variability when estimating rainfall erosivity in areas with high rainfall intensities is the I30 estimation method, rather than the KE-I relationship.
Acknowledgments This research was supported by funding from the National Commission for Scientific and Technological Research – Chile CONICYT/FONDECYT/Regular 1130928. The rainfall data were provided by the General Directorate of Water Resources (DGA), Government of Chile.
References Abd Elbasit, A.A.M., Yasuda, H., Salmi, A., 2011. Application of piezoelectric transducers in simulated rainfall erosivity assessment. Hydrol. Sci. J. 56 (1), 187–194. Bell, F.C., 1969. Generalized rainfall duration-frequency relationships. J. Hydraulics Div. 95 (1), 311–327. Bonilla, C.A., Vidal, K.L., 2011. Rainfall erosivity in Central Chile. J. Hydrol. 410 (1–2), 126–133. Brown, L.C., Foster, G.R., 1987. Storm erosivity using idealized intensity distributions. Trans. Am. Soc. Agric. Eng. 30, 379–386.
793
Catari, G., Latron, J., Gallart, F., 2011. Assessing the sources of uncertainty associated with the calculation of rainfall kinetic energy and erosivity – application to the Upper Llobregat Basin, NE Spain. Hydrol. Earth Syst. Sci. 15, 679–688. Elwell, H.A., 1978. Modeling soil losses in Southern Africa. J. Agric. Eng. Res. 23, 117–127. Escobar, F., Aceituno, P., 1998. Influencia del fenómeno ENSO sobre la precipitación nival en el sector andino de Chile central durante el invierno. Bulletin de l’Institut Français Détudes Andines 27 (3), 753–759 (In Spanish). Fornis, R.L., Vermeulen, H.R., Nieuwenhuis, J.D., 2005. Kinetic energy–rainfall relationships for Central Cebu, Philippines for soil erosion. J. Hydrol. 300, 20–32. Foster, G.R., 2008. Revised universal soil loss equation Version 2 (RUSLE2). USDAARS, Washington, D.C. Fox, N.I., 2004. TECHNICAL NOTE: The representation of rainfall drop-size distribution and kinetic energy. Hydrol. Earth Syst. Sci. 8 (5), 1001–1007. Govers, G., 1991. Spatial and temporal variations in splash detachment: a field study. Catena 20 (Suppl.), 15–24. Hudson, N.W., 1961. An introduction to the mechanics of soil erosion under conditions of sub-tropical rainfall. Rhodesia Sci. Assoc. Proc. 49, 14–25. Kinnell, P.I.A., 1973. The problem of assessing the erosive power of rainfall from meteorological observations. Soil Sci. Soc. Am. J. 37, 617–621. Kinnell, P.I.A., 1981. Rainfall-kinetic energy relationships for soil loss prediction. Soil Sci. Soc. Am. J. 45, 153–155. Lobo, G.P., Frankenberger, J.R., Flanagan, D.C., Bonilla, C.A., 2015. Evaluation and improvement of the CLIGEN model for storm and rainfall erosivity generation in Central Chile. Catena 127, 206–213. McGregor, K.C., Bingner, R.L., Bowie, A.J., Foster, G.R., 1995. Erosivity index values for northern Mississippi. Trans. Am. Soc. Agric. Eng. 38 (4), 1039–1047. Nel, W., Sumner, P.D., 2007. Intensity, energy and erosivity attributes of rainstorms in the KwaZulu-Natal Drakensberg, South Africa. South Afr. J. Sci. 103, 398–403. Renard, K.G., Foster, G.R., Weesies, G.A., McCool, D.K., Yoder, D.C., 1997. Predicting Soil Erosion by Water: A Guide to Conservation Planning with the Revised Universal Soil Loss Equation (RUSLE). USDA Agriculture Handbook No. 703.Washington DC. Rosewell, C.J., 1986. Rainfall kinetic energy in Eastern Australia. J. Clim. Appl. Meteorol. 25, 1695–1701. Salles, C., Poesen, J., 2000. Rain properties controlling soil splash detachment. Hydrol. Processes 14, 271–282. Salles, C., Poesen, J., Sempere-Torres, D., 2002. Kinetic energy of rain and its functional relationship with intensity. J. Hydrol. 257, 256–270. Shamshad, a., Azhari, M.N., Isa, M.H., Hussin, W.M.a.W., Parida, B.P. (2008). Development of an appropriate procedure for estimation of RUSLE EI30 index and preparation of erosivity maps for Pulau Penang in Peninsular Malaysia. Catena, 72, 423–432. Torri, D., Sfalanga, M., Del Sette, M., 1897. Splash detachment: runoff depth and soil cohesion. Catena 14, 149–155. van Dijk, A.I.J., Bruijnzeel, L.A., Rosewell, C.J., 2002. Rainfall intensity – kinetic energy relationships: a critical literature appraisal. J. Hydrol. 261, 1–23. Wenzel, H., 1982. Rainfall for urban stormwater design. In: Urban storm water hydrology. (7th ed., Vol. 7, pp. 35–67). Washington DC: American Geophysical Union. Wischmeier, W.H., 1959. A rainfall erosion index for a universal soil-loss equation. Soil Sci. Soc. Am. J. 23 (3), 246–249. Wischmeier, W.H., Smith, D.D., 1958. Rainfall energy and its relation to soil loss. Trans. Am. Geophy. Union 39, 285–291. Wischmeier, W.H., Smith, D.D., 1978. Predicting rainfall erosion. USDA Agriculture Handbook No. 537. Washington D.C. Yin, S., Xie, Y., Nearing, M.A., Wang, C., 2007. Estimation of rainfall erosivity using 5to 60-minute fixed-interval rainfall data from China. Catena 70 (3), 306–312. Zhang, Y., Liu, B., Wang, Z., Zhu, Q., 2008. Evaluation of CLIGEN for storm generation on the semiarid Loess Plateau in China. Catena 73 (1), 1–9.