Drop size distributions and kinetic energy rates in variable intensity rainfall

Transcription

1 WATER RESOURCES RESEARCH, VOL. 45,, doi: /2009wr007927, 2009 Drop size distributions and kinetic energy rates in variable intensity rainfall S. Assouline 1 Received 1 March 2009; revised 2 July 2009; accepted 6 August 2009; published 13 November [1] Rainfall kinetic energy is a key factor in soil erosion processes. It is determined by rainfall intensity, related drop size distribution (DSD), and the drops terminal velocity. Temporal variability in rainfall intensity is reflected in the DSD and affects the rainfall kinetic energy during the event. Smith et al. (2009) reported on 1-min interval rainfall intensity and corresponding DSD variability during a storm on 22 July 2006 at Princeton, New Jersey. They reported also on DSD characteristics of heavy convective rainfall events during the whole summer. It is shown that (1) a similar relationship between the mean drop size and the rainfall intensity characterized the local rainfall at both the seasonal and the single-storm scale, and (2) using the mean drop size as a scaling factor of the DSD removes the rainfall intensity dependence also at the intrastorm scale, providing a powerful tool to deal with temporal variability of rainfall rates during rainfall events. For a given storm characterized by a specific temporal variability of rates, three different ways of evaluating kinetic energy per unit mass or time were applied. By comparison to estimates accounting for rainfall temporal variability and related full DSDs, representing the storm by mean intensity and drop diameter tends to overestimate kinetic energy for low intensities and underestimate it for the higher ones. The relative error for the kinetic energy per unit of mass is ±45% and shifts from negative to positive sign for I > 25 mm/h. For the kinetic energy per unit of time, the relative error ranges from 100% to +210% and changes sign from negative to positive for I > 45 mm/h. When temporal variation of intensity is accounted for but drops are characterized by their mean values instead of the full DSD, kinetic energy is underestimated by 20% on average. Consequently, accounting for temporal variability in rainfall intensity during a storm has a notable impact on the erosive power of the rainfall. Citation: Assouline, S. (2009), Drop size distributions and kinetic energy rates in variable intensity rainfall, Water Resour. Res., 45,, doi: /2009wr Introduction [2] Strong temporal variability in intensity is ubiquitous in rainfall, especially in systems that produce heavy rains. As an illustration (Figure 1), a convective storm of 30 min during the rainy season of summer 2006 at Princeton, New Jersey, was characterized by rainfall intensities ranging from 0 to 120 mm/h [Smith et al., 2009]. For that event, 40% of the total rainfall amount was delivered in a short period of 7 min of intense rain (between the 20th to the 27th min). [3] Temporal variability in rainfall intensity affects infiltration and runoff processes and the temporal resolution required to improve their prediction is soil-type-dependent [Agnese and Bagarello, 1997; Wainwright and Parsons, 2002; Assouline et al., 2007]. Temporal variability in rainfall intensity affects also erosion processes [Frauenfeld and Truman, 2004]. Interill erosion is the outcome of the 1 Department of Environmental Physics and Irrigation, Institute of Soil, Water, and Environmental Sciences, ARO, Bet Dagan, Israel. Copyright 2009 by the American Geophysical Union /09/2009WR balance between soil resistance to degradation and the erosive power of the raindrops, generally represented by the transfer of raindrops kinetic energy to the soil surface [Cruse and Larson, 1977; Gilley and Finkner, 1985; Nearing and Bradford, 1985]. For a given soil, the resistance to degradation is a function of the soil bulk density and the water content, or capillary suction [Cruse and Larson, 1977]. Temporal variability of wetting rates reflects on the dynamics of the capillary head at the soil surface [Assouline et al., 2007] and thus affect the soil surface reaction to raindrops impacts. The erosive power of a rainfall is determined mainly by its intensity, raindrop size distribution, and terminal velocity of the drops at the soil surface [Kinnell, 1973; Mualem and Assouline, 1986]. When relevant, wind-driven rain splash could also have additional effects [Pedersen and Hasholt, 1995; Erpul et al., 2003]. The drop size distribution (DSD) is related to the rainfall intensity, inducing a strong relationship between rainfall kinetic energy and intensity [Park et al., 1983; Kinnell, 1981; Mualem and Assouline, 1986; Assouline and Mualem, 1989; Steiner and Smith, 2000]. In the case of bare soils, expenditure of raindrops kinetic energy to the soil surface increases its bulk density, which in turn, affects the water regime in the soil profile [Assouline, 2004; Augeard et al., 1of7

2 ASSOULINE: KINETIC ENERGY RATES IN VARIABLE INTENSITY RAINFALL Figure 1. The temporal variability in rainfall intensity during the storm of 22 July 2006 at Princeton, New Jersey [Smith et al., 2009]. 2008] and affects the soil resistance to further degradation. Therefore, temporal variability in rainfall intensity during a storm could have a significant impact on both the erosive power of the rainfall and the ability of the soil to resist erosion. [4] Rainfall DSDs are the outcome of breakup and coalescence processes occurring during the raindrop free fall from the 0 C level to the ground, and consequently depict skewed bell-shape distributions. Different appropriate mathematical models are applied to describe the DSD in terms of probability density functions: lognormal distribution [Park et al., 1983; Feingold and Levin, 1986; Quimpo and Brohi, 1986], gamma function [Takeuchi, 1978; Ulbrich, 1983; Willis, 1984; Narayana Rao et al., 2006; Smith et al., 2009], and Weibull distribution [Best, 1950b; Mualem and Assouline, 1986; Assouline and Mualem, 1989]. The Weibull distribution in the study of Assouline and Mualem [1989] was derived from a uniform random fragmentation model [Tenchov and Yanev, 1986] assuming that the probability for a drop breakup is proportional to its volume, as suggested by the experimental results of Low and List [1982]. [5] Rainfall DSDs vary with rainfall intensity [Laws and Parsons, 1943; Marshall and Palmer, 1948; Joss and Waldvogel, 1967; Waldvogel, 1974]. However, the dependence on rainfall intensity can be removed by appropriate scaling, leading to the definition of a unique DSD for given rainfall type and site characteristics [Sekhon and Srivastava, 1971; Willis, 1984; Assouline and Mualem, 1989; Sempere Torres et al., 1994]. The scaling factor is a power law of the rainfall intensity [Sempere Torres et al., 1994]. Since the mean drop size of the DSD can be expressed as a power function of rainfall intensity, the scaling factor can be the mean drop size of the DSD [Feingold and Levin, 1986; Willis and Tattelman, 1989; Assouline and Mualem, 1989]. By adopting the theoretical power of 3 to transform drop diameter into volume, Assouline and Mualem [1989] have shown that the scaled Weibull distribution becomes largely independent of site and rainfall characteristics, leading to a kind of universal or general distribution, in agreement with the suggestion of Sekhon and Srivastava [Willis, 1984, p. 1650]. [6] Insights into the rainfall process, and the investigation of the relationship between DSD and rainfall intensity are based on multiyear data collection from various geographical regions and rainfall types. These data sets regroup information from several storms, measured at different periods and at various temporal resolutions, and using different methods and devices. For the first time, the study of Smith et al. [2009] provided data on temporal variability of rainfall intensity and the corresponding DSDs at 1-min intervals, at both the seasonal and the single-storm scale at the same location. This offered the opportunity to look into the nature of the relationship between convective rainfall characteristics at these two interesting scales at a given location and during the same season. The objectives of this study are (1) to characterize the relationship between the DSD and the rainfall intensity at the intrastorm scale and to compare it to that representing the seasonal one, (2) to check the applicability of the concept of the scaled DSD to the structure of a single storm, and (3) to evaluate the impact of temporal resolution in rainfall intensity and corresponding DSD data on the rate of transfer of rainfall kinetic energy to the soil surface. 2. Theoretical Background [7] The DSD is expressed in terms of the probability function of the Weibull distribution, F(d, I) [Assouline and Mualem, 1989]: Fd; ð I Þ ¼ 1 exp½ aðþd I n Š; ð1þ where d represents the raindrop diameter, I represents the rainfall intensity, and a(i) and n are the distribution parameters. The first moment of the distribution defines the mean diameter, d G (I): d G ðþ¼a I ðþ I n 1 G 1 þ n 1 ; ð2þ with G denoting the gamma function. Using d G as the scaling factor, the scaled diameter, d*, with d* = d d G, leads to the scaled form of equation (1): with F d* ¼ 1 exp gd * n ; ð3þ g ¼ G n 1 þ n 1 : ð4þ If one assumes that a drop volume, v, is related to its diameter via v / d 3, the resulting universal/general DSD is obtained: F d* ¼ 1 exp 0:71 v * ; ð5þ where v* / d* 3. The empirical expression for d G (I) suggested by Assouline and Mualem [1989] accounts for the observed decrease in d G at very high rainfall intensities: d G ðþ¼ai I b e ci ; where a, b, and c are regional parameters representing rainfall type and site characteristics. ð6þ 2of7

3 ASSOULINE: KINETIC ENERGY RATES IN VARIABLE INTENSITY RAINFALL [8] The rainfall kinetic energy, E, per unit mass, M, is expressed by I ðþ¼1 2 Z dmax o fðd; IÞV 2 ðdþdx; where d max is the maximum raindrop diameter, f(d, I) is the probability density function corresponding to F(d, I), V(d)is the terminal velocity of a drop of diameter d, and x is the variable of integration. In this study, the relationship V(d) suggested by Best [1950a], as it was fitted by Mualem and Assouline [1986], is applied: n h VðdÞ ¼ V max 1 exp ðd=e Þ b ð7þ io ; ð8þ with V max = 9.5 m/s, e = 1.77 mm, and b = [9] The kinetic energy per unit time, (I), is ðþ¼i I ðþ: I For a given storm characterized by a specific temporal variability I(t), three different ways of evaluating (t) or (t) can be applied. The mean storm intensity value, I m, can be used to estimate the corresponding mean diameter, d m, via equation (6). Consequently, the mean kinetic energy per unit mass of rain,, for the whole event can be estimated as ð9þ ¼ 1 2 V 2 ðd m Þ: ð10þ Alternatively, the mean diameter, d G (t), corresponding to I(t) (equation (6)), can be used to estimate the mean h i(t): ðþ¼ t 1 2 V 2 ½d G ðþ t Š: ð11þ Finally, a more accurate representation of (t) can be achieved by considering the full DSD at each sampling interval during the storm: Z dmax ðþ t ðþ¼1 t 2 o fd; ½ It ðþšv 2 ðdþdx: The corresponding (t) can be computed accordingly: ¼ I m ; ðþ¼it t ðþ¼it t ðþ: t ðþ; t ð12þ ð13þ ð14þ ð15þ Equations (11), (12), (14), and (15) address directly the temporal variability in I and will reflect it in terms of the kinetic energy rates (t), while equations (10) and (13) lump it into a mean constant value I m, and therefore lead to constant kinetic energy rates for the entire rainfall event. 3. Methodology [10] Smith et al. [2009] studied the temporal variability of rainfall intensity of heavy convective rainstorms, defined as events for which peak 1-min rainfall intensity exceeded 25 mm/h. Twenty-five events were recorded during summer 2006 in Princeton, New Jersey. Corresponding DSDs were also measured by means of a disdrometer [Joss and Waldvogel, 1967; Steiner and Smith, 2000]. In this study, we focus on two aspects: (1) the maximum rain intensity at 1-min interval and its related mean diameter for the 25 rainfall events, as reported in Table 1 of Smith et al. [2009], and (2) the DSD corresponding to each 1-min interval rainfall intensity of the storm on 22 July 2006 from 2025 to 2055 UTC, as they were characterized by the distribution parameters depicted in Figure 3 of Smith et al. [2009]. These DSDs were represented by a gamma probability density function, f(d, t), of the drop diameter, d, with time, t [Smith et al., 2009, equation (1)]: fðd; tþ ¼ N 0 ðþd t mðþ t exp½ LðÞd t Š; ð16þ where N 0 (t), m(t), and L(t) are the parameters of the distribution. Equation (16) with the respective parameters N 0 (t), m L(t) was used to reproduce the DSDs corresponding to each 1-min rainfall rate within the 22 July 2006 storm. All the data pertaining to that storm were digitized from Figure 3 of Smith et al. [2009]. [11] Equation (6) was fitted to the data representing the relationship between maximum 1-min rainfall intensity and mean drop diameter for the 25 storms. The DSDs corresponding to the temporal variability of rainfall intensity during the 22 July 2006 event were scaled according to their respective mean drop diameter, and equation (3) was fitted to the scaled DSDs expressed as probability functions. [12] The fitted expressions of equations (3) and (6) were used to compute the different estimates of (t) (equations (10) (12) and (13) (15)) for the 22 July 2006 storm using equation (8), and the storm kinetic energy transferred to the ground surface computed accordingly. 4. Results and Discussion 4.1. Mean Drop Diameter Rainfall Intensity Relationship in Heavy Convective Rains [13] The mean raindrop diameters at the maximum 1-min interval rainfall intensity for the 25 storms, all classified as heavy convective rain events, are plotted versus their corresponding rainfall intensity (Figure 2, black dots). The fitted equation (6) to the 25 points with a = 0.661, b = 0.275, and c = reproduced quite well the d G (I) data (rmsd of 0.039). The mean raindrop diameters corresponding to the 1-min interval rainfall intensities of the 22 July 2006 event are depicted also in Figure 2 (white dots). The fitted d G (I) to the seasonal diameter data seems to correspond quite well also to the intrastorm diameter data (rmsd of 0.025). Consequently, equation (6) with a = 0.661, b = 0.275, and c = represents the relationship between mean raindrop diameter and rainfall intensity for a specific storm as well as 3of7

4 ASSOULINE: KINETIC ENERGY RATES IN VARIABLE INTENSITY RAINFALL Figure 2. The mean raindrop diameters of the 25 storms and their corresponding 1-min interval maximum rainfall intensity (black dots), the fitted equation (6) to the data (solid line), and the mean raindrop diameters corresponding to the 1-min interval rainfall intensities of the 22 July 2006 event (white dots). for a series of storms during the same season and at Princeton, New Jersey. This indicates that the d G (I) relationship could be intrinsic to the raindrop formation processes and to their dependence on intensity, at least in a convectivetype of rainfall at this location. The consequence could then be that the d G (I) expression for a specific site, which is also the scaling factor of the DSD, can be determined from a single storm, or alternatively, from a series of sporadic (d G, I) observations during various rainfall events during the season. Since it is mainly based on heavy convective rainfall data, this result has yet to be validated for other rainfall types Temporal Variability of the DSD in a Single Storm [14] Using d G (I) as a scaling factor removes the effect of rainfall intensity on the shape of the DSD (equation (3)). The result in Figure 2 indicates that the d G (I) relationship is a rainfall characteristic that is valid at both the intrastorm and the seasonal scales at Princeton, New Jersey. This suggests that as a unique scaled DSD, independent of rainfall intensity, was derived from multiyear data collection in a specific geographical region, a unique scaled DSD is expected to characterize the whole family of DSDs induced by the inherent temporal variability in rainfall rates within a single storm as well. The scaled F(d*) for different rainfall intensities within the 22 July 2006 storm, ranging from to 120 mm/h, are depicted in Figure 3. They all collapse into one distribution, indicating that rainfall intensity effect on DSD can be removed also at intrastorm scale, providing a way to deal with the temporal variability of rates inherent to rainfall events. Since the d G (I) relationship used as the scaling factor is similar for the seasonal and the intrastorm scales at a given site, the same scaling law derived from the seasonal level can be applied to the single-storm one. [15] The F(d*) expression in equation (3) was fitted to the data, and represent relatively well the measured trend. The best fit was achieved for n = and g = (rmsd of 0.025). The dashed line in Figure 3 represents the universal/general F(d*) distribution (equation (5)) resulting from the prescribed n = 3 value [Assouline and Mualem, 1989]. Although it overestimates the probability function for small d* values, it apparently still can provide a relatively Figure 3. Scaled F(d*) distributions for different rainfall intensities within the 22 July 2006 storm (symbols) and the fitted equation (3) to the data (solid line). The universal/ general distribution (equation (5)) is represented by the dashed line. good first approximation at the single-storm level when no data are available Temporal Variability of Rainfall Kinetic Energy Rates in Heavy Convective Rains [16] The relationship between the kinetic energy per unit of rainfall mass and the rainfall intensity that characterized the 22 July 2006 storm was computed following the three approaches described in equations (10) (12). The results are depicted in Figure 4. The mean intensity of the storm was I m = 56 mm/h, and the corresponding mean diameter was d m = 1.67 mm, leading to a constant mean = 16.6 (m/s)2. For the range of intensities presented, the h i(i) and (I) estimates depict similar shapes, resembling the usual monotonically increasing (I) function resulting from multiyear data sets analysis [Kinnell, 1981; Park et al., 1983; Mualem and Assouline, 1986]. However, in terms of absolute values, the (I) values are, on average, 20% higher than the h i(i) ones for the rainfall intensity range. The (I) estimates are higher than the ones for I > 25 mm/h, while the h i(i) estimates are higher than the ones for I > 40 mm/h. 4of7 Figure 4. The different estimates of the relationship between the kinetic energy per unit of rainfall mass and the rainfall intensity for the 22 July 2006 storm: (dashed line), h i(i) (solid line), and (I) (bold line).

5 ASSOULINE: KINETIC ENERGY RATES IN VARIABLE INTENSITY RAINFALL Figure 5. Estimates of the kinetic energy rates (top) (t) and (bottom) (t), resulting from the three different methods (equations (10) (12) and (13) (15)) for the 22 July 2006 storm at Princeton, New Jersey. [19] The cumulative kinetic energy for the entire storm can be computed on the basis of the different estimates and rainfall duration, t. The three estimates of kinetic energy, notated as E, hei, and E, to indicate that they result from, i(t), and (t), respectively, are depicted versus rainfall h duration, t, or cumulative rainfall depth, R(t) = R t 0 I(t), in Figure 6. The trends discussed in Figure 5 reflect on the E the E(R) curves. At the end of the storm, it appears that E > hei > E, namely, > > Jm 2. An interesting result is obtained when E(R) is considered (Figure 6, bottom). The constant estimate leads to a nonlinear relationship because of the nonlinear R(t) resulting from to the temporal variability in rainfall rates. However, a much more linear E(R) is depicted when estimates that accounted for temporal variability, h i (t), were used. In numerous models dealing with soil degradation (interill erosion or surface sealing), the cumulative rainfall R(t) is used as a surrogate of E(t), as the independent variable, since it is an easy-to-measure rainfall information, available in most climatic databases [Morin and Benyamini, 1977;Liebenow et al., 1990;Kinnell, 1993; Assouline, 2004]. Assuming that E(t), the physically based variable of the degradation process, can be replaced by R(t), is equivalent to assuming that E(R) is a linear function. From Figure 6, it appears that for the 22 July 2006 storm, this assumption is valid when the temporal variability in rainfall intensity is accounted for. It appears to be less valid when the rainfall is characterized by a mean constant intensity. [17] Data on the temporal variability in DSDs, related to that of the rainfall rates of the 22 July 2006 storm, enable the reproduction of the dynamics of kinetic energy rates, (t), during that single storm. The results from the three different methods to estimate (t) (equations (10) (12) and (13) (15)) are shown in Figure 5. In terms of kinetic energy per unit of mass (Figure 5, top), h i(t) oscillates very close to the level owing to the temporal variability of I, but the average values for the entire storm of both estimates are similar and equal to (m/s) 2. However, when the full DSD at the 1-min level is accounted for, the corresponding rainfall kinetic energy rates (t) are systematically higher than h i(t) and for practically all the rainfall intensity range (the opposite is observed for the very low intensities at the beginning and the end of the storm; Figure 1). The average value for the entire storm is (m/s) 2, approximately 20% higher than the previous estimates. [18] As to kinetic energy per unit time (Figure 5, bottom), three stages are depicted: (1) at the early stage of the storm, when rainfall intensities are relatively low (Figure 1), provides the highest estimates; (2) at the intermediate stage of the storm, for intermediate intensities, all three estimates performs approximately equally; and (3) at the last part of the storm, when rainfall intensities were very high, is the lowest estimate, and h i(t) increase dramatically, (t) being higher than h i(t) by 10% at the peak. For the entire storm, the average values of, h i(t), and (t) are , , and J h 1 m 2, respectively. 5of7 Figure 6. The three estimates of cumulative rainfall kinetic energy E versus (top) rainfall duration t or (bottom) cumulative rainfall depth R(t) for the 22 July 2006 storm at Princeton, New Jersey.

6 ASSOULINE: KINETIC ENERGY RATES IN VARIABLE INTENSITY RAINFALL Figure 7. The error of (t) relative to the mean event estimates and as a function of rainfall intensity during the 22 July 2006 storm at Princeton, New Jersey. [20] The error resulting from the use of information on temporal variability of rainfall intensity and corresponding full DSDs to estimate rainstorm kinetic energy relative to the use of mean storm intensity and drop diameter data is depicted for the 22 July 2006 storm as a function of rainfall intensity (Figure 7). When and (t) are considered, the relative error, defined as {[ (t) ]/ }, increases monotonically from 45% to +45%, being positive for I > 25 mm/h. For and (t), the relative error increases almost linearly from 100% to +210% and is positive for I > 45 mm/h. [21] The relationships between soil degradation processes and factors enhancing or causing them are highly nonlinear and often involve threshold values for degradation initiation [Sharma and Gupta, 1989; Sharma et al., 1991]. Results in Figures 5 7 indicate that some quantitative conclusions from experiments on rainfall-induced soil degradation might be biased when a rainfall event presenting temporal variability is characterized by mean intensity and related mean drop size. It suggests also that calibrated erosion models using experimental data involving rainfall simulators have to be used with caution when applied to natural rainfall events. Furthermore, using more accurate rainfall characteristics achieved by accounting for temporal variability in intensities as input in models calibrated using mean values of rainfall properties might lead to less accurate outputs Sensitivity Analysis of the DSD Representation [22] The data corresponding to the intrastorm DSDs were reproduced using the fitted gamma functions (equation (16)) reported by Smith et al. [2009]. The fitted probability distribution F(d*) (equation (3)) to these data was characterized by n = and g = Possible inaccuracies in DSD representation could have affected the best fit n and g values, and consequently, the presented results. The sensitivity of the results to F(d*) were estimated by considering the distributions generated by ±15% variation in n and g. The F S (d*) distribution, resulting from n = 4.0 and g = 0.6, increased the weight of small drops, while the F L (d*) distribution, resulting from n = 3.0 and g = 0.4 increased the weight of the large ones. The different distributions, expressed as probability density distributions, f(d*), are depicted in Figure 8a. The corresponding results in terms of (I) are shown in Figure 8b. The F S(d*) distribution generated a lower (I) relationship and the F L(d*) distribution, a higher one, compared to F(d*). However, the effect is relatively small. Therefore, the effect of inaccuracies in DSD representation on the trends presented in Figure 4 in terms of would have been minor. However, as the weight of small drops is increased, the difference between (I) and h i(i) decreases. 5. Summary and Conclusion [23] Temporal variability in rainfall intensities is inherent to the rainfall formation process. Since intensity influences the shape of the DSD, accounting for temporal variability in rainfall intensity during a storm has a significant impact on its erosive power. Analysis of data on 1-min rainfall intensity and corresponding DSD at both the seasonal and the intrastorm scales for convective rainfall events, reported by Smith et al. [2009], leads to the following conclusions. [24] 1. The relationship between the mean drop size and the rainfall intensity seems to be valid at both the seasonal and the intrastorm scales, indicating that, for convective rainfall at the Princeton, New Jersey site, it can be determined from a single storm, or alternatively, by a series of sporadic measurements during various rainfall events along the season. [25] 2. The rainfall intensity effect on the DSD could be removed also at the single-storm level, similarly to the way it is removed at the seasonal level, using the same scaling law. [26] 3. Storm rainfall kinetic energy estimates accounting for temporal variability in rainfall intensity while assigning Figure 8. (a) The DSDs used for the sensitivity analysis. (b) The corresponding impact of the different DSDs on (I) compared to (short-dashed line). 6of7

7 ASSOULINE: KINETIC ENERGY RATES IN VARIABLE INTENSITY RAINFALL to each rate its corresponding mean drop size are lower (20% on average) than estimates accounting for the full DSD corresponding to the variable rainfall intensity within the storm. [27] 4. Compared to estimates based on mean intensity and corresponding mean drop size, accounting for temporal variability and related full DSDs may induce a relative error between 45% and +45% for kinetic energy per unit of mass, and between 100% to +210% for kinetic energy per unit of time, depending on rainfall intensity. [28] Notwithstanding the relatively limited data for the convective rainfall events from one location during one season, the high erosive potential of such intense rainfall events make the results of practical importance for erosion and sediment transport modelers even at this preliminary stage. Moreover, the similarity between the trends of the scaled DSD(I) relationship at the single-storm level and those derived from multiyear data sets, is consistent with studies in other geographical regions, and suggests that this rainfall characteristic might be preserved and scalable from seasonal to intrastorm for other rainfall types and locations. This could provide a way to deal with the temporal variability of intensities inherent to rainfall events. [29] Acknowledgments. The author is thankful to three anonymous reviewers, Matthias Steiner, the Assistant Editor, Paolo D Odorico, and the Editor, Scott Tyler, for their insightful comments. Contribution 602/09 of the Agricultural Research Organization, Institute of Soil, Water, and Environmental Sciences, Bet Dagan, Israel. References Agnese, C., and V. Bagarello (1997), Describing rate variability of storm events for infiltration prediction, Trans. ASAE, 40, Assouline, S. 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