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(which is a blend of Middletown and Capital City), Johnstown, Lancaster, Philadelphia, Pittsburgh, State College, and Wilkes-Barre.

Notes: Lancaster records are taken from a co-op site (ID: LRCP1) for years earlier than 2000. After 2000, these records are taken from the airport (ID: KLNS). Johnstown records are taken from the co-op site (ID: JTWP1) for years prior to 1993, the co-op site (ID: DUNP1) for years between 1993-2000, and from the airport (ID: KJST) for years after 2000.

Here are the top 30 rainfall events for these sites(through 2011):

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
10/8/2005 8.71 9/28/1967 4.91 7/22/1947 10.37 6/22/1972 9.13 7/20/1977 8.75 9/16/1999 6.11 9/16/1999 6.63 9/17/2004 4.84 9/18/2004 5.05 9/27/1985 5.98
9/16/1999 6.37 6/17/1984 3.55 9/14/1979 4.66 9/7/2011 7.71 6/16/1912 4.46 9/8/1987 5.68 10/8/2005 5.53 10/15/1954 3.56 6/23/1972 4.71 9/16/1999 4.91
9/27/1985 5.85 7/29/1980 3.17 6/18/1996 4.61 6/21/1972 5.81 9/7/1996 4.44 10/8/2005 5.6 8/14/2011 4.84 7/28/1999 3.48 6/26/1895 4.01 8/18/1955 4.40
9/30/10 5.73 8/7/2007 3.11 10/15/1954 4.35 9/26/1975 4.59 7/29/1945 4.27 9/27/1985 4.96 8/27/1971 4.77 10/2/1929 3.22 8/13/1955 3.95 11/25/1950 4.29
7/10/2010 5.67 6/21/1972 3.02 9/30/1959 3.99 9/14/1973 4.34 7/22/1964 4.09 8/28/1978 4.6 9/14/1966 4.69 6/24/1996 3.11 8/18/1994 3.66 10/21/1995 4.01
9/8/1987 4.86 3/11/1992 3.02 9/26/1986 3.91 9/25/1975 4.28 10/16/1954 3.65 7/7/1984 4.54 7/12/2004 4.68 8/5/1956 3.06 10/21/1955 3.65 7/13/1948 3.91
9/18/2004 4.59 6/22/1972 2.86 9/15/2002 3.84 9/14/1966 4.07 4/9/1942 3.3 7/27/1986 4.44 6/29/1973 4.62 9/29/1936 3 10/15/1954 3.42 8/11/2003 3.69
8/8/1982 4.19 6/16/1982 2.71 9/17/1996 3.67 7/23/1969 4.00 8/2/1946 3.23 8/29/1978 4.06 9/12/1960 4.6 7/11/1971 2.96 10/14/1955 3.32 9/30/2010 3.69
7/9/1952 4.15 7/21/1988 2.61 8/28/1990 3.29 10/7/2005 3.97 7/20/1996 3.23 9/6/1979 3.54 8/27/2011 4.55 11/30/2010 2.95 11/28/1993 3.25 12/4/1950 3.60
9/1/1952 4.06 9/21/1992 2.52 6/17/1937 3.28 6/25/2006 3.95 11/8/1997 3.15 9/27/2008 3.35 8/8/1981 4.40 6/17/2009 2.92 11/25/1950 3.21 9/18/2004 3.49
9/28/2008 3.83 7/28/1981 2.5 7/24/1935 3.26 10/9/1976 3.87 1/25/1979 3.05 11/25/1950 3.3 7/5/1989 4.38 12/30/1990 2.76 10/1/2010 3.21 11/8/1996 3.37
10/19/1996 3.67 8/14/1994 2.49 8/2/2000 3.14 7/21/1994 3.84 5/19/1966 3.00 3/21/2000 3.24 4/15/2007 4.19 7/8/1957 2.71 8/18/1901 3.19 8/28/2011 3.23
8/13/1955 3.63 1/21/1959 2.45 8/13/1994 3.12 9/10/1968 3.74 9/12/2008 2.94 10/8/1998 3.20 11/7/1977 3.99 7/28/2000 2.63 8/28/1903 3.12 8/16/1966 3.18
8/13/2011 3.57 6/20/1989 2.44 9/29/1999 2.99 8/12/2010 3.65 10/2/1929 2.90 9/23/2003 3.18 10/25/1980 3.82 8/9/1953 2.57 8/3/1961 3.12 10/19/1996 3.09
6/18/1967 3.5 6/11/1986 2.41 4/5/1947 2.95 9/28/2004 3.51 9/29/1997 2.87 9/6/2008 3.00 7/3/1978 3.66 5/25/1997 2.48 6/19/1996 3.06 11/16/2006 3.00
4/2/2005 3.46 6/19/1983 2.40 7/11/1967 2.79 7/23/1997 3.48 5/29/1911 2.85 7/19/1988 2.90 10/19/1966 3.59 6/24/1950 2.38 6/22/1972 3.02 7/9/1952 2.97
6/29/1973 3.42 7/12/1990 2.40 10/18/1988 2.76 10/14/1955 3.47 3/21/1912 2.83 7/15/1994 2.83 7/29/1980 3.53 6/27/1998 2.37 10/2/1929 2.99 5/31/1950 2.90
7/24/1997 3.37 10/25/1980 2.38 8/2/1987 2.73 4/16/2011 3.46 6/19/1996 2.80 9/22/1979 2.81 11/25/1950 3.46 6/24/1951 2.32 9/9/2004 2.97 10/9/1976 2.88
8/28/2011 3.37 8/7/1979 2.36 6/28/1957 2.72 9/18/2004 3.38 6/23/1972 2.75 5/5/1989 2.80 7/21/1988 3.45 6/12/1948 2.31 3/3/1994 2.90 8/13/1955 2.86
7/12/2004 3.36 9/17/2004 2.35 9/4/1944 2.69 9/30/2010 3.22 9/30/2010 2.73 10/21/1995 2.80 7/18/1994 3.45 5/24/1973 2.31 10/8/2005 2.83 2/11/1981 2.86
11/8/1972 3.35 9/13/1977 2.34 6/13/1994 2.68 9/19/2000 3.18 9/11/1905 2.72 9/11/2009 2.79 9/3/1969 3.37 8/28/1992 2.30 5/20/1894 2.79 6/1/1982 2.85
8/18/1955 3.34 8/16/1969 2.32 8/3/1964 2.66 9/16/1999 3.15 11/22/1952 2.70 5/29/1948 2.76 7/30/1971 3.36 2/23/1975 2.29 10/1/1911 2.78 4/15/1983 2.83
8/9/1942 3.30 6/5/1986 2.32 11/22/1956 2.62 11/8/1943 3.07 3/18/1908 2.70 11/17/2006 2.75 4/30/1947 3.29 7/8/1980 2.27 9/7/1996 2.7 8/6/2011 2.83
9/12/1960 3.28 6/28/1980 2.31 6/10/1962 2.48 9/1/1952 2.88 8/19/1906 2.64 6/26/1995 2.74 8/12/1955 3.29 8/16/1952 2.25 9/29/1997 2.69 11/8/1972 2.82
9/14/1973 3.24 5/28/1984 2.31 8/3/1980 2.47 6/2/1946 2.86 9/15/1911 2.62 9/29/2006 2.73 7/28/1969 3.28 6/18/1996 2.25 5/26/1953 2.66 7/30/2000 2.82
5/31/1972 3.23 9/17/1987 2.27 11/2/1999 2.47 7/8/1988 2.84 7/22/1935 2.57 7/3/1978 2.67 9/28/2004 3.22 6/26/2008 2.23 8/29/1988 2.66 9/6/2011 2.81
6/22/1972 3.23 11/30/2010 2.27 8/20/2007 2.46 9/27/2007 2.81 3/5/1967 2.50 7/13/1996 2.62 4/16/2011 3.11 6/30/1991 2.18 6/5/1909 2.64 6/15/1969 2.76
9/15/2003 3.23 9/22/1992 2.24 9/8/1942 2.33 9/21/1979 2.80 9/24/1897 2.47 12/12/1983 2.60 11/8/1972 3.07 7/26/2004 2.17 10/19/1996 2.63 9/1/2003 2.59
9/21/1979 3.21 6/28/1973 2.21 7/23/2010 2.33 5/21/1947 2.78 6/21/1929 2.47 9/14/1951 2.5 6/12/1968 3.05 6/2/2010 2.17 8/17/1909 2.61 9/12/1960 2.54
8/27/1971 3.12 8/27/1987 2.21 10/12/1946 2.31 8/9/1991 2.78 9/29/1934 2.46 11/10/1990 2.45 10/1/2010 3.00 8/7/1968 2.16 10/17/1936 2.61 9/17/2004 2.54


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