Definitions and characteristics of extreme precipitation
(Ben Burford, February 14, 2006)
1. Definitions
1.1 Intergovernmental Panel on Climate Change (IPCC) Definition.
“An extreme weather event is an event that is rare within its statistical reference distribution at a particular place.
Definitions of “rare” vary, but an extreme weather event would normally be as rare as or rarer than the 10th or 90th
percentile. By definition, the characteristics of what is called extreme weather may vary from place to place.”
1.2 Basic statistical definition - sort into ascending order, take the top 10%.
All wet day totals (mm/day) over the data period are sorted into ascending order. They are then grouped into 10 classes,
each with 10% of rainfall events in them (so, class 1 is the 10% of lowest daily precipitation totals, the next 10% become
class 2, etc., until the heaviest 10% of events make up class 10).
Class 10 is then the group of extreme precipitation
events.
1.3 A variation on the basic statistical definition - group by classes of 10% of precipitation amount.
All wet day totals over the data period are sorted into ascending order. They are then grouped into 10 classes, but instead
of taking the 10% of lightest events as the lowest class, as many of the lightest events as is necessary to provide 10% of
the total precipitation for the period are taken (an approximate average figure is that the lightest 50% of events contributes
10% of the total rainfall). These events are then designated as class 1. The next class consists of as many of the next
lightest events as are required to also contribute 10% of the total precipitation, and so on. In most cases, 0.5–1.5% of the
heaviest events are sufficient to contribute the final 10% of the total, and these are designated as class 10.
Note: both satisfy IPCC definition
The classes from the second definition can be thought of as 10 equal amount quantiles, whereas the first definition used
equal frequency quantiles. The disadvantage of using frequency quantiles is that the lightest 5 or 10% of events
contribute such a small amount of the total precipitation that trends in this contribution can never be very large, thus
predisposing the largest changes in the contributions to be found in the heavy event quantiles. “Amount quantiles”, on
the other hand, give each group an equal opportunity to exhibit large contribution trends.
However, the very small
number of events in the heavy class of the amount quantiles could make the results of this approach rather noisy.
1.4 Same as 1 or 2 above, but with a different percentage:
95th, 97.5th, 99th, etc. percentile.
1.5 Return period
Extreme precipitation event – exceedence of a threshold that corresponds to the daily precipitation amount exceeded in
the time series on average once per XX (e.g 100) days.
One study on trend analysis studied several groups (moderate, strong, extreme and intense) – daily rainfall events with an
average return period of 10, 30, 100 and 365 days.
Results suggested that long-term changes in the frequency
distribution of precipitation might more readily be resolved by considering more moderate rather than the most extreme
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events.
1.6 Tail of the Gamma distribution
The gamma distribution fits the distribution of precipitation data well, and is often used in studies of precipitation.
Extreme precipitation – those events observed at the tails of frequency distribution functions (pdf).
Gamma frequency distributions can be fitted to each time series of precipitation (e.g. following the maximum likelihood
approach). Extreme values are the data points above the XX (e.g. 75th) percentile.
1.7 Multiple day window (e.g. 5 day window)
Add up the daily precipitation values over a series (window) of days (e.g. over 5 days). The window of days is an
extreme precipitation event if the total precipitation is greater than XX% of the yearly average. For example, a 5 day
window is an extreme precipitation event if the 5 day total has more precipitation than 10% of the yearly average.
After checking the first window of XX (e.g. 5) days, shift one day and check again. Thus in a 100 day period there
would be, for example, a check of 96 different 5 day windows.
Further, a single XX (e.g. 5) day window can be extended if successive XX day periods also qualify as extreme
precipitation events (e.g. a 5 day window can grow to 6 days, 7 days, etc. if every successive 5 day window qualifies as
an extreme precipitation event).
Additional factors in the definition of extreme precipitation events? (Quote from CEOP IP):
“Extremes to be studied . . . are those with a ‘climatologically significant duration and/or spatial extent’ as opposed to
individual, short-term events such as thunderstorms, hurricanes or flash floods. This perspective then includes an
extended wet period (producing a substantial period of precipitation for one to several days that affects areas on scales of
at least 105 km2)”
9 grid cells of 1 x 1 degree at the equator equal 111,000 km2
Questions regarding the configuration and timing of the grid cells:
Temporal overlap? (1 day common to adjacent grid cells?)
Spatial overlap? (consider various patterns)
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2. Characteristics
2.1 Strength of Extreme Precipitation – the “Threshold Surplus” (TS)
The severity (strength) of extreme precipitation events can be obtained by calculating the “Threshold Surplus” (TS).
Threshold Surplus - the difference between the extreme precipitation event total (e.g. 5 day precipitation amount) and the
amount of XX% (e.g. 10%) of the yearly average.
For example, if the 5 day precipitation amount is 197 mm, and 10%
of the yearly average is 116 mm, then the “Threshold Surplus” (TS) is 81 mm.
2.2 Concentration Index
Put the data in increasing order (lowest to highest precipitation per day). Plot the percent of total of precipitation days,
vs. percent of total of precipitation.
Then, the “Concentration Index” (CI) = area between curve and diagonal.
Example – for Valencia in the plot below, 90% of precipitation days provides 45% of the annual precipitation. This
means that 10% of the precipitation days provides 55% of the annual precipitation.
This characteristic the
“Concentration Index”, is quantified as the area between the curve and the diagonal.
Figure: Martin-Vide, J., 2004. Spatial distribution of a daily precipitation concentration index in peninsular Spain.
International Journal of Climatology, 24: 959-971.
2.3 Gamma distribution – alpha and beta value
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“The gamma distribution fits the distribution of precipitation data well.”
Figure: Jones, C., D.E. Waliser, K.M. Lau, and W. Stern, 2004. Global occurrences of extreme precipitation and the
Madden-Julian oscillation: observations and predictability. Journal of Climate, 17, 4575-4589.
Figure depicts 4 combinations of alpha and beta values: small values of alpha and beta (India), large alpha and small beta
(storm track in the north Atlantic), small alpha and large beta (western Pacific), and large alpha and large beta (Amazon).
Small values of the shape parameter alpha indicate that the distribution is very strongly skewed to the right as is the case
in India (note that only the nonzero values of precipitation were used). In contrast, large values of alpha indicate that the
distribution tends to approximate the form of Gaussian distributions such as in the north Atlantic. Note, however, that
the asymmetry in the tails is still quite evident. The scale parameter beta represents the ‘‘stretch’’ or ‘‘squeeze’’ in the
gamma density function to the right or left.
In summary:
Alpha - Small: skewed to the right; Large: more Gaussian
Beta - Small: “stretched”; Large: “squeezed”
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Figure: Jones, C., D.E. Waliser, K.M. Lau, and W. Stern, 2004. Global occurrences of extreme precipitation and the
Madden-Julian oscillation: observations and predictability. Journal of Climate, 17, 4575-4589.
2.4 Classified according to origin - tropical cyclone, monsoon, other.
2.4.1 Tropical Cyclone – e.g. classified according to the Global Tropical Cyclone Climatic Atlas.
The Global Tropical Cyclone Climatic Atlas (maintained by Fleet Numerical Meteorology & Oceanography Detachment
(U.S. Navy)) has global information on tracks of tropical cyclones. If an extreme precipitation event occurs within a given
area surrounding the time and location of a tropical cyclone track, the event can be classified into the group of tropical
cyclone-caused extreme precipitation.
2.4.2 Monsoon – CEOP defined?
Define times and areas (bounding box/polygon) of the various monsoon systems/seasons. Extreme precipitation events
which fall into the time/space bounds can be attributed to monsoon systems.
Can CEOP project provide the time/location definitions?
2.4.3 Other databases, such as databases of storm events?
CEOP members can search for databases of weather and climate events that can be used to characterize extreme
precipitation events.
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