Statistics and Probabilities

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Statistics and Probabilities Averages and
means Percentiles and deciles Terciles
Seasonal predictions as probabilities
Distribution curves and chocolate wheels
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Commonly used climate statistics
Mean or arithmetic average Adding up all values
and dividing by the number of values Eg, the
average monthly rainfall (MM) recorded on an
island from 1960 to 1990 was 121, 165, 98, 65,
32, 31, 34, 68, 95, 108, 132, 135 Average annual
rainfall between 1960 and 1990 was 1084 mm The
average monthly rainfall during this period was
1084/12 90.3 mm
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The Median Here, we rank the rainfall amounts
from smallest to greatest 31, 32, 34, 65, 68,
95, 98, 108, 121, 132, 135, 165 The median
monthly rainfall is about 96.5 mm (a little
higher than the arithmetic mean) One half of the
months recorded rain above 96.5 mm and the other
half below 96.5 mm. This is also known as the
50th percentile.
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Percentiles The 80th percentile, for example, is
that figure below which rainfall in 80 of the
months will lie. 31, 32, 34, 65, 68, 95, 98,
108, 121, 132, 135, 165 80 of 12 is 9.6 So
our 80th percentile is about 126 mm
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Deciles The rainfall is said to be in decile 1
if it less than or equal to the 10th
percentile In decile 2 if less than or equal to
the 20th percentile but above the 10th
percentile In decile 3 if less than or equal to
the 30th percentile but above the 20th
percentile
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Rainfall amount 1 June 2003 to 31 May 2004
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Rainfall deciles 1 June 2003 to 31 May 2004
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Rainfall percentages 1 June 2003 to 31 May 2004
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Rainfall anomalies 1 June 2003 to 31 May 2004
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Terciles Three possible outcomes for a
particular series of events For example, with
rainfall, it could be (a) Wetter than normal
range (7th to 9th decile) (b) Normal range (4th
to 7th decile) (c) Drier than normal range (1st
to 4th decile)
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If there is no bias in our predictions, the
probability of each of these will be
33.33 However if we have an El Nino or a La
Nina situation the probabilities will be skewed
in some way.
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For a particular location the rainfall
distribution curves may look like
El Nino
Normal
La Nina
For example During an El Nino event, this
location receives lower rainfall more often than
normal or higher rainfall
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The Rainfall Chocolate Wheel
La Nina
El Nino
Normal
For this particular location, during an El Nino
situation, there is a 50 chance of receiving
below average (or median) rainfall, a 25 chance
of average rainfall, and a 25 chance of
higher than average rainfall But the wheel
must still be spun!
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For a small number of spins, the results might
almost be random but over a large number those
odds will emerge. Climate forecasting through
probabilities is the same - long term use of the
odds will inevitably produce a long term skill,
but in the short term errors will be
perceived. Careful communication of the
seasonal climate outlooks is therefore
essential.
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For the September to November period, the chances
of above median rainfall are between 60 and 70
in the SW corner of WA. So with climate patterns
like the current, about 6 or 7 seasons out of 10
are expected to be wetter than average in SW WA,
with about 3 or 4 out of 10 being drier.
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• Communication to specialist users
• and the general public
• Through mass media (newspapers, radio, TV)
• Through specialist media (Internet, Weather
• channels)
• Through direct communication ( e-mail to
• clients, special bulletins prepared by the
  NWS)

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Important to develop all three where possible
Mass media have a good coverage. Need to develop
a good relationship with the editors responsible
for weather/ climate coverage to ensure the
message gets through. Particular caution needed
with headline summaries that can be
misleading. Frequent (say once per month)
meeting with the media representatives a good
idea.
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National Weather Service Seasonal Climate
Outlook Over SE Australia, there is a 60 to
70 chance that rainfall will be less than the
median over the next 3 month period. So with
climate patterns like the current, about 6 or 7
seasons out of 10 are expected to be drier than
average in this area, with about 3 or 4 out of
10 being wetter. Media headline EXPERTS TIP
RETURN OF THE DROUGHT Careful phraseology and
caveats of the NWS stripped away to produce a
(probably highly misleading) headline
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Advantage of Internet and personal
communication is that your words are the ones
that are issued. Develop a phraseology and
method of communicating that are readily
understood. Communicating probabilities is
difficult - people want YES/NO answers which we
cant provide because of the complexity of
weather and climate. But we can the most likely
outcome, and if used routinely a skilled SCO
service will inevitable produce benefits - that
is a mathematical certainty.