Universal Power Law for Relationship between Rainfall Kinetic Energy and Rainfall Intensity

Table 1

Empirical relationships between time-specific rainfall kinetic energy (, J/m²/h) and rainfall intensities (, mm/h).

Equation forms	References				(mm/h)	Number observation	Location/altitude
Exponential function	Blanchard, 1953 [30]	23.7	0.710	0.031	0–127	29	Honolulu, Hawaii, USA/670–2250 m
	Kinnell, 1981 [3]	29.3	0.281	0.018	2–309	200	Miami, Florida, USA/3 m
		29.2	0.894	0.048	19–229	50	Rhodesia from Hudson [11]/1230 m
	Rosewell, 1986 [24]	29.0	0.596	0.040	1–146	13,438	Gunnedah, Australia/305 m
		26.4	0.669	0.349	1–161	6,360	Brisbane, Australia/25 m
	Brown and Foster, 1987 [17]	29.0	0.720	0.050	0–250	315	MS, USA/180 m
	McIsaac, 1990 [4]	29.2	0.510	0.011	2–170	19,000	Majuro, Marshall Islands/3 m
		28.8	0.450	0.033	1–194	18,021	Pina Range/Fort Sherman, Panama/50 m
	Azevedo Coutinho and Pereira Tomás, 1995 [31]	35.9	0.559	0.034	0–120	8190	Mértola, Algarve, Portugal/21 m
	Jayawardena and Rezaur, 2000 [32]	36.8	0.691	0.038	0–150	18	Hong Kong/50 m
	Fornis et al., 2005 [28]	30.8	0.550	0.031	0–142	5822	Cetral, Cebu, Philippine/44 m
	Lim et al., 2012 [33]	24.3	0.730	0.130	0–142	1,841	Chungcheong, South Korea/58 m
	Lee and Won, 2013 [34]	30.0	0.740	0.068	1–108	25,017	Gangwon, South Korea/842 m
Logarithmic function	Wischmeier and Smith, 1958 [13]	11.9	8.73		n.a	n.a	Washington, USA; from Laws and Parsons [2]
	Onaga et al., 1988 [35]	9.81	10.6		n.a	n.a	Okinawa, Japan
	Zanchi and Torri, 1980 [36]	9.81	11.25		1–140	n.a	Firenze, Central Italy/90 m
	Kinnell, 1981 [3]	17.1	5.23		2–309	315	Miami, Florida/3 m
		9.71	9.26		19–227	200	Rhodesia from Hudson [11]/1230 m
	Brandt, 1990 [37]	8.95	8.44		0–105	92	USA, DSD from Marshall and Palmer [18]/35 m
	Fornis et al., 2005 [28]	11.93	7.82		0–142	5822	Cetral, Cebu, Philippine/44 m
	Lee and Won, 2013 [34]	6.04	12.37		1–108	25,017	Gangwon, South Korea/842 m
Linear function	Hudson, 1965 [38]	29.9	4.29		n.a	n.a	Zimbabwe
	Kinnell, 1981 [3]	30.1	5.48		2–309	315	Miami, Florida, USA/3 m
		29.9	4.29		19–227	200	Rhodesia from Hudson [11]/1230 m
	Rosewell, 1986 [24]	24.5	1.25		1–146	13,438	Gunnedah, Australia/305 m
		24.8	1.29		1–161	6,360	Brisbane, Australia/25 m
	Sempere-Torres et al., 1992 [39]	34.0	5.59		20–100	n.a	Cevennes, France
	Usón and Ramos, 2001 [40]	23.4	0.77		0–20	n.a	North-East, Spain
	Fornis et al., 2005 [28]	29.0	2.47		0–142	5822	Cetral, Cebu, Philippine/44 m
Power Law function	Smith and de Veaux, 1992 [26]	13.0	1.21		n.a	n.a	Oregon, USA
		11.0	1.23		n.a	n.a	Alaska, USA
		18.0	1.24		n.a	n.a	Arizona, USA
		11.0	1.17		n.a	n.a	New Jersey, USA
		10.0	1.18		0–240	n.a	North Carolina, USA
		11.0	1.14		n.a	n.a	Florida, USA
	Uijlenhoet and Stricker, 1999 [29]	7.20	1.32		0–105	92	Based on Marshall and Palmer [18] parameterization/35 m
		8.53	1.29
		8.46	1.17
		8.89	1.28
		10.8	1.06
		7.74	1.35
	Steiner and Smith, 2000 [41]	11.0	1.25		n.a	n.a	Northern Mississippi, USA
	Fornis et al., 2005 [28]	12.1	1.19		0–142	5822	Cetral, Cebu, Philippine/44 m
	Kim et al., 2010 [42]	9.6	1.19		0–38	423	Gyeoggi, South Korea/115 m
	Lim et al., 2012 [33]	15.1	1.13		0–142	1,841	Chungcheong, South Korea/58 m