AGU Meeting 2011 : NG51 E-1 679
Stochastic and deterministic aspects of observed seasonal-mean precipitation
variations and extreme event occurrences over the United States
Dan G i an otti , Bru ce T. An d erson , an d G u i d o D. Sal vu cci
G eog raph y an d E n vi ron m en t, Boston U n i versi ty
Research questions
Where and when can we predict changes in climate better?
Where and when is it fundamentally stochastic?
Unexplained variance in annual precipitation occurrence counts
By using the AIC to select model
chain orders and pooling, model
complexity can be determined
without introducing artificial
variance due to overfitting. For
each day, models are created
with 6 chain orders and 60
pooling sizes, fit to the historical
occurrence patterns, and the best
model is selected using AIC. For
each station, 1000 simulated time
series are then created using the
appropriate (variable) memory
selection using AIC and
and transition probabilities, both Pooling
the selected chain orders for that
of which are functions of the day pooling in Tuscon, AZ
of the year. Average daily
occurrence frequencies are identical between the observed and
simulated datasets, but variance is smaller for the stationary
stochastic model than the observed data which reflects the
impacts of climatic forcings and long­term trends upon
precipitation statistics.
Premise
The observed interannual variance in monthly, seasonal, and
annual precipitation occurrence is much higher than can be
explained by purely stochastic, stationary processes [1]. This
unexplained variance suggests processes and drivers that have
the potential to be separated from the stochastic part of
precipitation: potential predictability [2,3]
Our approach is to separate and model the stationary stochastic
components and then determine how much variance remains
unexplained. By modeling each day of the year individually
using weather station data, we can assess spatial and seasonal
patterns in interanual variability.
Methods
Our historical record
data is drawn from
774 weather stations
of the USHCN data
set [4]: only stations
that are more than
95% complete over
at least 80 years are
analyzed.
AIC and Models
Results
Less unexplained variance
Ex: Tuscon, AZ
Unexplained variance in 89-day
precipitation occurrence counts
More unexplained variance
Unexplained variance in 89-day
precipitation occurrence counts
We use variable­order Markov
chains to recreate the patterns of
stochastic behavior in the observed
data.
Ex: If it doesn't rain Dec 7­8 in Tuscon, how likely is it to rain
on the 9th?
Ans: About 9%. If it does rain on the 8th, the likelihood increases
to about 40%.
It is important to decide how many days of memory should be
used. Additionally, to better determine transition probabilities
between precipitation patterns and to better capture the
likelihoods of rare events, it might be benificial to pool the
patterns from neighboring days. To determine the appropriate
chain order (memory) and pooling we use the Akaike
Information Criterion (AIC) [5].
Potential predictability as defined by unexplained variance can
be expressed in many ways. Here we present the unexplained
variance in the number of wet days in a year, as well as the
unexplained variances in the number of wet days for
December–February and June–August.
Observed variance
Stochastic variance
Observed variance and stochastic
variance for Tuscon, AZ.
January 1 5th
July 1 5th
Unexplained precipitation variance for 774 weather stations defined as a fraction of observed variance
for annual number of
th
precipitation days (top), number of precipitation days in an 89-day
window centered on January 1 5 (bottom left), and number
th
of precipiataion days in an 89-day window centered on July 1 5 (bottom right). All values except those in contours are at the
90% confidence level.
References
[1] Shea, D.J. and R.A. Madden, 1990: Potential for long­range prediction of monthly mean surface temperatures over North America, J. Climate, 3, 1444­1451.
[2] Katz, R.W., and M.B. Parlange, 1998: Overdispersion phenomenon in stochastic modeling of precipitation, J. Climate, 11, 591­601.
[3] Wilks, D.S., 1999: Interannual variability and extreme­value characteristics of several stochastic daily precipitation models, Agric. Forest Meteo., 93, 153­169.
[4] Karl, T.R., C.N. Williams, Jr., F.T. Quinlan, and T.A. Boden, 1990: United States Historical Climatology Network (HCN) serial temperature and precipitation data, Environmental Science Division,
Publication No. 3404, Carbon Dioxide Information and Analysis Center, Oak Ridge National Laboratory.
[5] Akaike, H., 1974: A new look at the statistical model identification, IEEE Trans. Auto. Cont., 19, 716–723.
Additional information
Support for this research was provided
by the National Science Foundation.
Those areas with a high percentage of unexplained varaiance are
poorly explained by a stationary model and thus are good
candidates for improved predictability arising from to long­term
trends, periodic climate forcings, or internal feedbacks. The most
notable areas of high potential predictability are those along the
Great Lakes, Appalachian Mountains, and Four Corners regions.
Also notable are the highly stochastic regions shown in the
maps, particularly along the West Coast. In these areas, there
may be little room for interannual prediction, although seasonal
trends are clearly evident on shorter time­scales.
Questions related to the research are
encouraged and can be directed to Dan
Gianotti:
gianotti@bu.edu
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