Twenty-Four Hour Rainfall Extreme Events

Rainfall does not follow a Gaussian distribution, so you cannot discern its extreme values simply by looking at the ends of a bell curve. Instead, it follows a Gamma distribution, where the waiting times between extreme rainfall events become relevant. By looking at the top 30 twenty-four hour rainfall events for each of 10 stations in Pennsylvania, we can determine the values for an extreme rainfall event for any given period of time at these sites. These calculated extreme values are a good benchmark of how rare a significant rainfall event is.

We determined the extreme rainfall values for a 25, 50, 100, and 200 year period for Allentown, Bradford, Erie, Harrisburg, Johnstown, Lancaster, Philadelphia, Pittsburgh, State College, and Wilkes-Barre. Here are the top 30 rainfall events for these sites:

Allentown		Bradford		Erie		Harrisburg		Johnstown		Lancaster		Philadelphia		Pittsburgh		State College		Wilkes-Barre
date	inches	date	inches	date	inches	date	inches	date	inches	date	inches	date	inches	date	inches	date	inches	date	inches
9/16/1999	6.37	8/14/1994	4.18	6/18/1996	4.61	6/22/1972	9.13	7/20/1977	8.75	9/19/1927	6.6	9/16/1999	6.63	9/17/2004	4.84	6/23/1972	4.71	9/27/1985	5.98
9/27/1985	5.85	9/28/1967	3.95	9/26/1986	3.91	6/21/1972	5.81	7/29/1945	4.27	9/16/1999	6.11	8/27/1971	4.77	10/15/1954	3.56	8/13/1955	3.95	9/16/1999	4.91
9/8/1987	4.86	8/8/1979	3.6	9/17/1996	3.67	8/23/1933	4.66	7/22/1964	4.09	9/8/1987	5.68	9/14/1966	4.69	7/28/1999	3.48	8/18/1994	3.66	10/21/1995	4.01
8/8/1982	4.19	9/12/1975	3.28	8/28/1990	3.29	9/26/1975	4.59	10/16/1954	3.65	7/1/1941	5	6/29/1973	4.62	10/2/1929	3.22	10/21/1995	3.65	11/8/1996	3.37
7/9/1952	4.15	6/16/1984	3.2	8/2/2000	3.14	9/7/1999	4.35	4/9/1942	3.3	9/27/1985	4.96	9/12/1960	4.6	6/24/1996	3.11	10/15/1954	3.42	8/16/1966	3.18
9/1/1952	4.06	8/13/1984	3.2	8/13/1994	3.12	9/14/1973	4.34	8/2/1946	3.23	9/12/1960	4.9	8/8/1981	4.4	8/5/1956	3.06	10/14/1955	3.32	10/19/1996	3.09
10/19/1996	3.67	9/3/1993	3.13	9/29/1999	2.99	9/25/1975	4.28	1/25/1979	3.05	9/25/1940	4.8	7/15/1931	4.38	9/29/1936	3	11/28/1993	3.25	10/9/1976	2.88
8/13/1955	3.63	9/7/1958	3.08	10/18/1988	2.76	9/14/1966	4.07	5/19/1966	3	7/26/1933	4.69	7/5/1989	4.38	7/11/1971	2.96	11/25/1950	3.21	2/11/1981	2.86
6/18/1967	3.5	6/29/1957	2.98	8/2/1987	2.73	7/23/1969	4	10/2/1929	2.9	8/28/1978	4.6	7/23/1927	4.33	6/20/1987	2.96	8/3/1961	3.12	6/1/1982	2.85
6/29/1973	3.42	10/24/1959	2.9	6/13/1994	2.68	10/2/1929	3.95	6/23/1972	2.75	7/7/1984	4.54	8/19/1939	4.25	7/22/1927	2.86	6/19/1996	3.06	4/15/1983	2.83
7/24/1997	3.37	6/26/1997	2.81	11/2/1999	2.47	10/9/1976	3.87	11/22/1952	2.7	7/27/1986	4.44	11/7/1977	3.99	12/30/1990	2.76	6/22/1972	3.02	11/8/1972	2.82
11/8/1972	3.35	8/19/1999	2.74	11/4/1985	2.28	9/10/1968	3.74	7/22/1935	2.57	10/6/1932	4.34	10/25/1980	3.82	7/8/1957	2.71	10/2/1929	2.99	7/30/2000	2.82
8/18/1955	3.34	7/24/1979	2.7	2/15/1990	2.11	9/1/1952	3.6	3/5/1967	2.5	5/22/1942	4.06	7/3/1978	3.66	7/28/2000	2.63	3/3/1994	2.9	6/15/1969	2.76
9/12/1960	3.28	9/2/1980	2.66	6/5/1982	2.04	7/18/1945	3.12	6/21/1929	2.47	8/29/1978	4.06	6/27/1938	3.61	8/9/1953	2.57	9/7/1996	2.7	6/29/1980	2.53
9/14/1973	3.24	9/29/1999	2.58	9/22/1983	2.04	9/16/1934	2.99	9/29/1934	2.46	8/2/1971	3.79	10/19/1966	3.59	7/27/1943	2.53	9/29/1997	2.69	7/12/1990	2.44
5/31/1972	3.23	8/9/1998	2.56	6/17/1984	2	11/8/1943	2.92	7/14/1934	2.45	8/22/1937	3.69	7/29/1980	3.53	3/6/1945	2.52	5/26/1953	2.66	8/15/1969	2.41
6/22/1972	3.23	6/14/1960	2.55	11/5/1985	1.94	9/21/1979	2.8	6/2/1946	2.45	8/13/1955	3.59	11/25/1950	3.46	5/25/1997	2.48	8/29/1988	2.66	7/13/1996	2.4
9/21/1979	3.21	11/25/1950	2.54	7/29/1983	1.86	8/9/1991	2.78	6/17/1978	2.44	8/9/1942	3.57	7/21/1988	3.45	9/8/1940	2.44	10/19/1996	2.63	7/12/1969	2.33
8/27/1971	3.12	9/15/1952	2.52	5/4/1990	1.86	6/2/1959	2.74	8/2/1931	2.4	9/6/1979	3.54	7/18/1994	3.45	8/15/1941	2.4	10/17/1936	2.61	5/31/1972	2.3
9/12/1963	3.06	7/20/1988	2.52	6/5/1986	1.83	7/27/1969	2.74	7/11/1976	2.4	7/6/1937	3.38	7/9/1935	3.41	7/5/1950	2.38	6/18/1984	2.59	6/16/1967	2.29
9/11/1997	3.02	10/26/1980	2.5	6/11/1985	1.81	12/13/1983	2.73	9/18/1927	2.37	8/23/1933	3.35	9/3/1969	3.37	6/27/1998	2.37	9/29/1967	2.51	6/22/1987	2.28
8/9/1987	3.01	6/14/1994	2.49	10/5/1995	1.81	5/2/1929	2.71	5/26/1950	2.37	3/21/2000	3.24	7/30/1971	3.36	6/22/1952	2.34	8/6/1956	2.42	6/5/1986	2.26
7/28/1969	3	12/25/1978	2.47	6/11/1986	1.8	8/19/1989	2.7	10/27/1981	2.34	10/8/1998	3.2	7/23/1938	3.3	5/24/1973	2.31	10/22/1929	2.39	3/14/1986	2.22
3/11/1952	2.99	9/22/1992	2.45	5/19/1986	1.79	12/1/1934	2.69	7/20/1988	2.34	6/12/1968	3.17	8/12/1955	3.29	8/28/1992	2.3	2/15/1984	2.38	11/16/1989	2.22
8/17/1974	2.92	6/22/1972	2.42	7/30/1988	1.74	7/19/1961	2.67	7/19/1988	2.33	9/10/1960	3.16	7/28/1969	3.28	2/23/1975	2.29	11/22/1953	2.36	6/6/2000	2.21
9/5/1949	2.91	6/21/1964	2.37	10/7/1987	1.72	5/8/1960	2.63	8/24/1936	2.3	6/2/1946	3.15	8/23/1933	3.27	7/8/1980	2.27	6/24/1957	2.28	12/13/1983	2.16
5/29/1990	2.9	9/24/1977	2.3	5/18/2000	1.72	5/28/1982	2.58	8/24/1945	2.3	5/30/1948	3.13	9/20/1938	3.18	6/18/1996	2.25	5/6/1944	2.25	6/28/1973	2.12
7/26/1985	2.87	6/21/1972	2.27	6/20/1989	1.71	9/17/1999	2.58	5/31/1953	2.3	7/7/1934	3.1	6/2/1946	3.1	6/24/1950	2.19	8/2/1965	2.23	11/22/1991	2.12
5/29/1984	2.82	7/17/1963	2.26	9/21/1992	1.7	8/5/1986	2.55	7/14/1939	2.24	8/7/1944	2.93	11/8/1972	3.07	6/30/1991	2.18	11/13/1935	2.2	9/6/1968	2.11
8/17/1993	2.79	9/28/1962	2.25	8/4/1994	1.68	10/4/1962	2.54	8/30/1932	2.23	8/19/1939	2.92	6/12/1968	3.05	8/7/1968	2.16	10/12/1927	2.19	4/4/1987	2.07

 

The extreme value x for a period of n years is determined by the following formula:

 

x = y - b ln[-ln(F)]

where y = average - gb (where g is Euler's constant, approximately 0.557)

b = 0.78s (where s is the standard deviation)

F = (n-1)/n

 

Here are the calculated statistical values for each site:

Station	Average	s	b	y	25-year event	50-year event	100-year event	200-year event
Allentown	3.51	0.85	0.66	3.14	5.27	5.73	6.20	6.65
Bradford	2.78	0.49	0.38	2.57	3.79	4.06	4.32	4.59
Erie	2.36	0.77	0.60	2.03	3.95	4.37	4.79	5.20
Harrisburg	3.56	1.35	1.05	2.98	6.35	7.08	7.82	8.55
Johnstown	2.90	1.23	0.96	2.37	5.43	6.10	6.77	7.43
Lancaster	4.06	0.97	0.76	3.63	6.06	6.59	7.13	7.65
Philadelphia	3.84	0.76	0.59	3.51	5.40	5.82	6.23	6.64
Pittsburgh	2.61	0.40	0.31	2.44	3.43	3.65	3.87	4.08
State College	2.87	0.59	0.46	2.61	4.09	4.41	4.73	5.05
Wilkes-Barre	2.76	0.87	0.68	2.38	4.55	5.02	5.49	5.96

Additional Outside Links:

Precipitation Extremes for the NE US
Short-term Precipitation Extremes for the NE US