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Probability of Exceedance Forecast >
Degree Day Introduction
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This experimental outlook product gives the probability that a
temperature or precipitation quantity will be exceeded at the location in question, for the given season at the given lead time. The locations
are one of 102 forecast divisions in the mainland U.S., or an individual station in other regions.
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Understanding the Degree Day "Probability of Exceedance" Forecast Graphs
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Definitions, Data Source, Method, and Seasonal Format of the Forecasts
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The degree day totals used here refer to the accumulated departures of the daily
mean temperature from
65°F
, on one side of 65°F (i.e., only below 65°F or only above 65°F), over a given
calendar period. For heating degree days, only departures of daily mean temperatures below
65°F are accumulated, while for cooling degree days only departures above
65°F are accumulated. The daily mean temperature is the average of the
daily minimum and the daily maximum temperature, and is not an integrated or time-weighted
temperature average. Degree day forecasts are presented only for the core heating and cooling
times of the year. Included in these are, for heating: The 5-month period
Nov-Dec-Jan-Feb-Mar
, and the three embedded 3-month periods of Nov-Dec-Jan, Dec-Jan-Feb and Jan-Feb-Mar; and
for cooling: the 5-month period
May-Jun-Jul-Aug-Sep
, and the three embedded 3-month periods of May-Jun-Jul, Jun-Jul-Aug and Jul-Aug-Sep.
The raw degree day and mean temperature data consist of 1-month means, obtained several months
after the month's completion from the
National Climatic Data Center (NCDC)
in Asheville, North Carolina. (NCDC's home page is http://www.ncdc.noaa.gov/.)
During the delay period before those "final"
data become available, a preliminary version of the most recent data is used. This
version, while usually differing slightly from what will become the final
data, is often a very close approximation, differing at most by a few
tenths of a degree for a given month. These same facts apply also to the degree day totals.
Here at the Climate Prediction Center, multi-month degree day
totals and mean temperatures are computed from the 1-month NCDC data. In
computing the mean temperatures, monthly means are weighted by their
respective numbers of days, with leap year Februarys counted as
having 29 days. The NCDC data are given for 344 climate divisions. At CPC
these data are used to compute the data at the 102 larger climate
divisions used here at CPC, and shown on the maps in this web site.
Each of the 102 divisions is an integral combination of 1 or more of
the 344 divisions used at NCDC. In the West, some of the 102 climate
divisions correspond exactly to one NCDC climate division, while in
other parts of the U.S. several NCDC divisions are combined to form a
single one of our 102 divisions. This creates an approximately equal-area
representation across the 102 divisions, in contrast to the original 344
divisions which tend to be smaller in the eastern U.S. than in the
western U.S. due to the more densely spaced constituent stations in
the east. (Each of the 344 divisions normally includes observations
from 3 or more cooperative stations, and often considerably more. When
one or more is missing, NCDC adjusts the mean as a function of the
normally differing histories of each station.) The heating season degree day
forecasts are posted beginning the prior summer, and the
cooling season degree day forecasts are posted beginning the prior winter. In the labeling
of the year for the winter heating degree day outlooks, the year of the last month
of the period is given (e.g. the year of the Nov-Dec-Jan-Feb-Mar 1999-2000 period is called "2000"; the same holds for Nov-Dec-Jan 1999-2000).
All degree day forecasts are based on the temperature
forecasts for the same target period, with the added factor of the
correspondence between temperature and degree day totals
. That correspondence
is determined using 67 years of data, covering the 1931-1997 period.
during times of
the year when the mean temperature is far from 65°F (e.g. in much of
the northern part of the U.S. in winter, and near the Gulf of Mexico and
southeastern states in summer), there is a one-to-one correspondence between
the degree day forecasts and the temperature forecasts. In locations and
times of the year when daily mean temperature may be on either side
of 65°F, the correspondence between the
temperature forecasts and degree day forecasts is nonlinear, and this
correspondence is accounted for in the degree day forecasts presented here.
The correspondence between seasonal mean temperature and degree days is
derived empirically. A set of 6 to 9 of points of correspondence is developed from
the means of groups of approximately 10 of the 67 cases apiece, where each group represents
overlapping portions of the temperature distribution (e.g. the top 15%, the 70 to
90 percentile group, etc.) spanning from one tail of the distribution through the middle
to the other tail. The poorly sampled end points of the distribution are approximated
as a linear extrapolation of the results of nearby but less extreme cases. After establishing
the 6 to 9 base points of mean correspondence, these are connected by straight lines
and then the discontinuities are smoothed with several sweeps of running mean filters.
Visual inspection of the results indicates that the resulting fit is good, and,
in most cases, has little or no error with respect to the raw data.
When the seasonal mean temperature is so far from 65°F that the daily mean temperature
rarely or never crosses 65°F, the fit is a straight line. The cases having the largest
residual error are those whose mean temperatures are closest to, or even on the opposite
side of, the 65°F threshold. The residuals are virtually completely in the form of
scatter, as opposed to the broader nonlinear shape of the curve. The latter feature
is handled very well by the fitted correspondence curve. The use of quadratic and cubic
fits to the raw data was also tried, and while results were good the method was found to
be too sensitive to outliers when they are positioned on or near the ends of the curve.
In the degree day forecast graphs, the linearity of the relationship between seasonal mean
temperture and degree day total is indicated by two correlation measurements, to be described
below.
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The effects of the elongated Februarys during
leap years
are not included in these developmental analyses, nor are they included in the forecasts.
That is to say, the observed data for leap years have been reduced to what they would be
with a 28-day February (February 29 data are included, but the outcome for, say, February
is multiplied by [28/29]). Correspondingly, the degree day forecasts given
for leap year winters do not account for the extra day. Therefore, it is the
users' responsibility to make their own adjustment by increasing the number of forecasted
degree days for the longer season in their own way.
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This text description for the degree day graphs is similar to that given for
the temperature and precipitation probability of exceedance graphs, but is
somewhat more abbreviated. The reader is encouraged to consult the
temperature and precipitation description if further explanation is desired.
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Purpose of the Graphs
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The "probability of exceedance" curves give the forecast probability that a degree day
total, shown on the horizontal axis, will be exceeded at the location in question,
for the given season at the given lead time. The information on these graphs is
consistent with the information given in the maps of temperature probability anomaly--a
part of the multi-season climate outlook that has been issued since 1995.
Those forecast maps show the probability anomaly of the most favored tercile of
the climatological temperature distribution: below normal, near normal, or above normal.
The graphs shown here provide additional detail about the degree day forecast probability
distribution at an individual location i.e., any one of 102 climate regions in the mainland
U.S. The additional information comes about through the display of the entire probability
distribution, as opposed to just the probability anomaly of the most favored tercile.
The probability of exceedance of the temperature itself is available on another branch of
this CPC web site, http://www.cpc.ncep.noaa.gov/pacdir/NFORdir/jo1.html.
Although skill in temperature and degree day forecasting is in most cases modest in absolute
terms, there is nonetheless justification to issue a complete forecast
probability distribution. Showing the distribution is our attempt to accurately
convey the sense of the forecast while also showing the degree of uncertainty (which is
often high) contained in that forecast.
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What the Curves Mean
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Each graph contains four curves. One of the four is actually a set of two curves.
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The first curve
, shown in black, shows the
"normal"
, or climatological probability distribution.
Sometimes no black line appears in the graph. When that is the case, the black line is hidden
underneath the thick red line, which shows the forecast distribution (to be explained below).
The climatological distribution is derived by computing the average, and also computing a
measure of the amount of year-to-year variation around that average. The curve is therefore
called a "fitted" curve, because it is defined using a formula that
makes it possible to construct
a smooth curve to the data. The data may not be so smooth and regular, but the formula
only uses the average and the typical deviations from that average to define the curve.
The center (such as the average [mean] or the median) of this distribution is based on the
historical record of observations at the given location and season during the period used as
the normal base period. For example, in 1999 the normal base period is 1961-90. After reaching
the year 2001 or 2002, the base period will be updated to 1971-2000. The value of the center
of the distribution, or normal, is printed numerically near the top of the graph. The
variability, or range, of the climatological distribution is based on a period longer than
the normal base period. This is done in order to obtain a more accurate estimate of the
variability. Getting an acceptably accurate estimate of the variability requires more cases
than getting an acceptably accurate estimate of the center of the distribution. The
additional years used in getting the variability estimate occur immediately prior to the base
period. For temperature and degree days, 10 extra years are used.
Gradual trends within the 40 years are not allowed to contribute to the variability, however;
this is accomplished by using a sliding 30-year period, within the
40-year period, for the means about which the variations are defined.
For temperature, the value of the center of the distribution represents the mean, or
average, and is the temperature at which the curve crosses
the 50% line from the vertical axis. For degree days this is the case also,
but only when excursions of the daily mean on the "wrong" side of the 65°F
F threshold are rare or nonexistent. The "wrong" side implies above 65 during
the heating season, and below 65°F during the cooling season.
This occurs in locations that are warm in the winter, such as southern Florida,
or that are not hot in the summer, such as the high country of Nevada, Montana or Idaho.
When such excursions occur,
the degree day distribution is no longer a linear, or symmetric, function of the temperature,
but rather becomes a skewed function of the temperature. In that case,
the value at which the curve crosses the 50% line (the median) is considered the
normal. That is, the average is not used to represent the normal for degree days,
because more cases tend to be on one side of the average than on the other--a feature of a
skewed, or asymmetric, distribution.
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The second curve
, shown in yellow, labeled
"observed data"
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is a probability of exceedance curve derived from the observed data without any
model fitting. It steps down by 3.33% every time one of the 30 observations in the
normal base period no longer exceeds the value shown on the x-axis.
This curve is displayed so that the user may observe how good a fit the smoothed
climatological curve is to the actual degree day data. The fitted curves are based on a
Gaussian distribution for temperature, and on an empirical temperature-versus-degree day
correspondence for degree day data, using data from the 1931-97 period of record.
The curve based directly on the data is expected to be somewhat rough and irregular,
with gaps in some places and clustering in others. This irregularity is caused by the
lack of a very long sampling period--i.e., 30 years rather than several hundred years of
observations. If the same number of observations were sampled from an earlier period and
the underlying climate were identical, the places having gaps and clusters would be
expected to change. When the irregularities are changeable from one sample to another
and have equal chances of appearing in various places in the distribution, the smooth
fitted climatological curve is thought to estimate the true
population distribution better than the curve formed from any single sampling of
the data. However, in some cases there may be a physical reason for deviations
from a smooth distribution. In that case, sampling 500 years of data would not eliminate
these features of the curve. However, these features would be expected to appear somewhat
more smoothly (less "noisy" or jumpy) than features caused purely by sampling variations.
For example, a tendency for a plateau of shallow slope might appear near the middle of the
"probability of exceedance" distribution, where the steepest slope is usually found, or
a steep slope might be found off the center of the distribution. At CPC we believe that
in most cases the fitted curve is a better representation of nature than the raw data
curve. That is, most of the irregularities in the raw data curve occur by chance alone,
and would not appear if it were possible to sample a much larger set of cases.
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The third curve
, shown in red, labeled
"final forecast"
, represents the probability distribution of the final official CPC forecast. The
downward slope of the final forecast curve may
be slightly steeper than the slope of the climatological curve, in proportion to
the confidence associated with the final forecast. (Several aspects of the confidence are
indicated in each graph; these are described below.) This is because when a forecast is
thought to be relatively skillful (as, for example, when there is a strong ENSO event in
progress and the location is one in which an ENSO impact is anticipated), the range of
possibilities is smaller than if no useful forecast knowledge were in hand. This represents
a decrease in the uncertainty, which shows up as a narrower range of degree day values
within which the probability of exceedance changes by a given amount. In some cases there
is a shift of the forecast curve relative to the normal curve, but without a steeper slope
in the forecast curve. This would indicate some confidence in the shift away from the normal,
but without a decrease in the range of possibilities in the shifted climate. This might occur
when a trend, or climate change relevant to the present decade as a whole, is believed to
be occurring. A fourth pair of curves, shown by thin red lines, represents an
"error envelope"
. It is drawn on either side of the main final forecast curve, paralleling that
curve. These lines illustrate our estimate of the amount of possible error associated with
the forecast curve. The forecast curve itself already conveys uncertainty about the forecast;
this is why it is shown in a probabilistic framework and usually has a downward slope that
is not much steeper than the slope of the fitted climatological curve. In addition to this
inherent uncertainty, there is also some uncertainty related to other aspects of the forecast.
Examples of these additional error sources are (1) errors in the most recent observed data
used to determine the forecasts, (2) errors in the forecasters' perception, judgement and
understanding of the current climate state, and (3) imperfections in the fit of the
climatological and forecast distributions to the actual data (as
revealed by the differences between the yellow curve and the black curve).
All of these factors could result in some error in the positioning of the forecast curve
as a whole. While an accurate evaluation
of the size of this error is not possible, an approximation is provided by the error
envelope. The approximation is based on the expected sampling variability of the
climatological probability of exceedance using 45 years of data.
The resulting envelope is thought to be nonconservative--i.e. the size of the
error in the position of the forecast curve is more likely to be over-represented than
under-represented.
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How to Read a "Probability of Exceedance" Curve
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As an example, suppose we first examine the "normal" curve in any one of the graphs.
Like the other two curves, the normal curve begins near the 100% level in the upper left
portion of the graph. This indicates that the probability that the degree day total will
exceed the amount shown by the number given at the extreme left of the horizontal axis
(near the lower left corner of the graph) is close to 100%. This makes sense, because the
amount has been chosen to be far below the expected normal at the given station
and season--an amount that may never have been observed during the normal base period. This low
value is chosen because it is unlikely, but possible. As the value is increased
from the left toward the right side of the graph, the probability of it being exceeded begins
to decrease, decreasing most rapidly near the middle of the climatological distribution,
shown near the middle portion of the graph. The boundaries between the climatologically
lowest and middle tercile, and between the middle and highest tercile, are indicated by
vertical lines that intersect the normal curve where the probability of exceedance is 66.7%
and 33.3%, respectively. Vertical lines indicating the median, or 50% probability of
exceedance, and the 10% and 90% probabilities of exeedance, are also shown. In the right
portion of the graph, the "probability of exceedance" line continues to decline and
approaches 0% as the horizontal axis values become so large as to be very unlikely to
be exceeded. Because the curve continues to decrease from near 100% to near 0% as the
degree day total on the horizontal axis increases, the probability that the degree day
total will be between any two values on the graph can be determined by subtracting the
lower probability of exceedance value from the higher probability of exceedance value.
In the case of the "normal" curve, this probability is with respect to the normally
expected climatology for the station and season. When the probability is determined with
respect to the "final forecast" curve, it is a statement of CPC's forecast probability.
It is useful to compare this probability with that for the normal climatology to appreciate
the difference attributable to the current climate state and climate outlook. Because of
the modest level of skill in many cases, this difference may often be minor, and,
in the case of the "CL" (climatological probability) temperature forecast, there is no
difference for degree days at all.
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Automatic Probability Evaluation
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In subtracting two "probability of exceedance" values in order to evaluate the
probability of occurrence between a lower and upper limit, it is often difficult
to obtain an accurate visual estimate of the probability of exceedance from the graph.
For this purpose, the process will be automated for users' convenience in the future.
The option to use this utility will be provided on each graph. The user will only need to
select a region, a lead time, and the lower and upper limits of degree days within which a
probability is to be evaluated. The answer will be computed with respect to both the
climatological (normal) and the "final forecast" probability of exceedance curves.
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Caution Required for the Tails of the Curves
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Each of the curves is constructed on the basis of historical observations, and/or the
nature and strength of the impacts of the estimated current and future climate state.
Near the middle of the distribution there has been plentiful data sampled, because the
middle of the distribution is most likely and most frequently observed. On the other hand,
in the tails, or extremes, of the distribution, there have only been a few cases. Sometimes
there may have been no cases in a large portion of a tail, and then just a single observation
far out on the extreme part of that tail.
Whatever the exact configuration of the observations, the tails are less certain
than the middle and the shoulders of the distribution. Therefore, conclusions based on the
extreme tails of the distribution are particularly dangerous, and should be made with caution.
A warning about the upper and lower 7% tails of the curves is posted on each graph. The
middle 86% of the probability distribution, ranging from the 93% to the 7% probability of
exceedance values, is considered to be reasonably well sampled, in contrast with the outer
7% tails. [Technical note: These cutoffs span the ±1.5 standard deviation interval with
respect to the mean for a Gaussian distribution, within which usable numbers of observations
are thought to have been sampled.]
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Numerical information printed on the graphs
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Above and to the right of the probability of exceedance curves, selected summary
information is printed. The block of text at the upper left shows the
point forecast,
or best guess of the numerical degree day forecast. While the point forecast is
expressed as an exact number, the certainty that the result
will turn out to be this number is extremely low.
The point forecast is only given to represent the middle, or center, of the forecast
distribution, and does not imply that we can make an accurate numerical forecast.
Underneath the point forecast, the
anomaly forecast
, or the departure of the point forecast from the normal, is shown. Beneath the anomaly
forecast is the
normal (or center)
, based on the observations during the normal base period as discussed above. The normal
is represented by the degree day total that corresponds to the mean temperature.
To the right of the above set of numbers, the
percentile (%ile)
shows the percentage of cases in the fitted
climatological distribution that would be expected to be lower than or equal to
the point forecast. For example, if the %ile is 60.0, the point forecast ranks at or
above 60.0 percent of the climatological distribution, and less than 40.0 percent of it.
It is a forecast for a somewhat, but not highly, above normal degree day total. Because of
the fairly large degree of uncertainty in the outcome of our forecasts, it is not common
for our point forecasts to rank in the top or bottom 20 percent of the climatological
distribution. Beneath the %ile of the forecast, the forecast percentage of the normal
degree day total is shown. Next is given the
linear correlation between the mean temperature and the degree day total
for this location and season. When the mean temperature is
far enough away from 65°F (e.g. Minneapolis in winter, or Miami
in summer), there is a -1.00 correlation between temperature and heating
degree days and a +1.00 correlation between temperature and cooling degree
days. This implies that the degree day forecast is completely determined
by the temperature forecast. When daily temperatures within the season
may be on the opposite side of 65°F than it normally is, the linear
correlation with temperature is degraded and degree day totals vary more
slowly and less predictably as a function of seasonal mean temperature than would
otherwise be the case. The degree to which the degree day versus temperature
relationship departs from linearity is shown by the "
Cor with T
" statistics. The first correlation is that of all 67 years in the 1931-97 period. The
second correlation ("mid20%") is the correlation using only the years whose
temperature was in the middle quintile of the distribution (the
40 to 60 percentile range). In restricting the
range of the temperature in this way, deviations of the correlation from
plus or minus 1.00 show up more easily (although the end of the distribution
whose temperature is closest to, or crosses, 65°F
generally has lower correlation than the other end), giving the user a more
sensitive indicator of lack of linearity in the heart of the distribution.
In addition to the standard versions of the point forecast, the anomaly,
and the percentage of normal, a
weighted version
of each of these is also given, shown in parentheses and indicated with "
w:
". While the standard version is based solely on the point forecast, the weighted version
takes the entire degree day distribution into account, incorporating the
possible nonlinear portion of the correspondence with temperature. It
integrates the degree day forecast across the its range of associated
temperatures, weighting by the probability. When the degree day versus
temperature relationship is completely linear (i.e. when daily temperatures
never cross 65°F), the standard and weighted degree day forecasts
should be identical. When there is some nonlinearity (e.g. southern Florida
heating degree days in Nov-Dec-Jan), then the weighted results come out
more conservative (less anomalous) than the standard results. When the two
versions differ, the version of choice depends upon the users' preference
and philosophy. On the upper right side of the graph,
50% and 90% confidence intervals
are given for the forecast. The 50% confidence interval gives lower and upper degree day
totals. The lower amount corresponds to the 25%ile (75% probability of exceedance) of the
forecast distribution, and the upper amount is the amount that corresponds to the 75%ile
(25% probability of exceedance) of the forecast distribution. The values falling between
these two limits form an interval that CPC believes has a 50 percent chance of occurring.
The 90% confidence interval covers a wider range of values, ranging from the 5%ile
(95% probability of exceedance) to the 95%ile (5% probability of exceedance) of the
forecast. The ranges of amounts covered by the 50% and 90% confidence intervals give an
idea of the expected error associated with the point forecast. When the degree day versus
temperature correspondence is nonlinear (skewed), the distance upward to the top of the
confidence interval is not equal to the distance downward to the lower boundary of the
confidence interval. The ranges covered by the 50% and 90% confidence intervals are usually
fairly wide, in keeping with the uncertainty associated with the point forecast.
Note that there is some uncertainty for the confidence intervals themselves, just as
there is uncertainty for the probability of exceedance curves themselves (as indicated by
the "error envelope").
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Directly below the forecast confidence intervals, three types of measures of
confidence in the forecast
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are posted, both numerically and verbally. These are estimates of three aspects of
the skill expected in the case of the particular forecast. The first, the confidence in
shift direction, is a confidence that the degree day total will deviate
from the normal in the direction indicated, without regard to the size of the deviation.
The second, the confidence in the point forecast (contraction of the forecast distribution),
is confidence that the degree day total will be close to the
point forecast. The third, the integrated confidence, is confidence that the probability
distribution as a whole will be different from the climatological probability distribution.
The verbal descriptions that accompany these confidence levels are, in ascending order:
none, low, fair, moderate and high. Plus and minus signs appear for cases close to the
categorical boundaries. Each of the three aspects of confidence is further described next,
enabling the user to decide which confidence (or confidences) is most applicable to their
needs.
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Confidence in shift direction:
This is a measure of how confident we are that the degree day total will deviate
from the normal in the direction specified, whether below or above the normal.
The measure, more specifically, is the ratio of the estimated probability that the climate
will deviate in the forecast direction to the estimated probability that it will deviate in
the opposite direction. For example, if the confidence in the shift direction is 2.00, it
indicates that we believe there is twice the probability of a deviation in that direction
than in the opposite direction. If the forecast direction is below the normal, a 2.00
confidence would mean that the probability of below normal
conditions is 66.7% and the probability of above normal conditions is 33.3%. If
there is no confidence whatsoever regarding which side of the normal will occur,
the ratio is exactly 1. Note that the ratio is not that of the probability of the
more favored outer tercile to the other, but rather a ratio of the forecast probabilities
of occurrence of one half of the climatological distribution to the other half. The dividing
line between the two halves is the numerical value of the normal (or center of the distribution) that is posted in
the upper left corner of the graph.
When the "climatological probabilities" (CL) forecast is issued, the shift direction confidence
is at its minimum of 1. It may also be 1, however, for a non-"climatological probabilities"
forecast--when there is confidence in other aspects of the forecast. One example
would be when the likelihood of the near normal category is higher than would be expected
climatologically--and the chance of above normal and below normal are both reduced from the
climatological chance. This could occur, for example, in a season and at a location having
fairly high sensitivity to the state of the ENSO, in a case when the ENSO condition is
expected to be very close to normal (i.e. neither an El Niño nor a La Niña
tendency is expected). In such a case, although the chances of large deviations from normal
are reduced, the direction of the shift from normal is just as uncertain as it would be
without any knowledge of the ENSO condition. Forecasts for directional shifts may be
considered somewhat useful when this confidence measure exceeds 1.5, and more clearly useful
when it exceeds 1.8 or even 2 (which is uncommon). It should also be noted that a high
confidence in the shift direction usually, but not always, means that the size of the shift
is expected to be large. The amount of the expected
shift can be seen in the anomaly of the point forecast. In cases with high confidence in
the point forecast (another type of confidence, described below), the confidence in the
shift direction may be high even though the predicted size of the shift is only moderate.
This is possible because the shift direction refers to any amount of shift in the indicated
direction, regardless of size.
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Confidence in the point forecast (contraction of forecast distribution):
This is a measure of how narrow, or limited, the distribution of possibilities about the point
forecast value is believed to be, compared with the distribution of the historical observations
about the normal value. Given our current state-of-the-art in climate prediction, confidence
in the point forecast is often small. When the forecast distribution has the same, or nearly
the same, width as the climatological distribution, this indicates a relative absence of
forecast knowledge that would limit the range of possibilities. The measure, more specifically,
is the fraction of the width [standard deviation] of the forecast distribution to the width of
the climatological distribution. When the forecast distribution is no narrower than the
observed climatological distribution, the confidence is 1. Confidence values of less than
0.9 are considered somewhat helpful, and below 0.8, while rare, are still more helpful.
This confidence measure is increased in locations and seasons when climate conditions are
known to be related to governing forces (such as ENSO), and the status
of these forces is able to be somewhat correctly anticipated for the period being
forecast. An example of this would be the degree day total during the winter in Minnesota
and other regions in the northern Plains of the U.S., which is partly determined by the
ENSO state, given that the ENSO state itself is somewhat predictable for forecasts made
after the preceding summer. In such a forecast,
the possibilities for Minnesota degree days are somewhat more limited than they
would be with no knowledge of the influence of ENSO or no knowledge of what the
ENSO state would likely be during the future period being forecast. This particular
confidence measure is not related to the amount of shift of the point forecast from the
normal; rather, only the width of the probability distribution about its own central
value (the point forecast) is relevant here. Therefore, forecasts that are close to the
normal still may rate relatively high on this confidence measure.
Likewise, in some cases there may be a noticeable shift of the point forecast from the
normal, but little or no narrowing of the distribution. This could occur, for example, when
there is a gradual, long-term trend that is used in determining the forecast, but when there
is little or no information about differences between the climate this year and the last
few years of the same season. In that case, all recent years would be affected by the general
trend approximately equally, but their large differences from one another related to factors
besides the trend are poorly forecast.
[Technical note: This confidence measure is the standard error of estimate in a linear
regression model. For example, when it is 0.866, the expected skill of the
forecast is describable with a linear correlation coefficient of 0.5.]
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Integrated confidence: an integrated distributional difference from climatology
. This is a measure of the estimated totality of all differences between the forecast
distribution and the climatological distribution. It includes both distributional shifts
and narrowing (i.e. confidence in the point forecast over and above the confidence that
would be associated with a climatological forecast), as in the context of the two confidence
parameters described above. It would also include distributional deviations of other
types that may prove to be possible to predict in the future, such as a widening of the
distribution (e.g., as related to an expectation of greater than normal intraseasonal
variation), or asymmetric or irregular features of the distribution as may be related to
specific climate conditions in certain geographical locations (e.g. involving terrain, or
land vs. water). This measure, specifically, is estimated as the
total of the differences in probabilities of exceedance between the climatological
distribution and the forecast distribution over the 9 points on the climatological
distribution corresponding to its 0.90, 0.80, 0.70, ....., 0.20, and 0.10 probability of
exceedance values. This sum of the differences is then scaled with respect to the result
which would be attained when the forecast distribution is completely separated from the
climatological distribution. In the case of complete separation, the climatological
probability of exceedance remains at 1 (or 100%), or at 0 (or 0%), while the forecast
distribution moves through all of its intermediate values. Complete separation, which is
currently unattainable given today's state-of-the-art in climate prediction, would produce
a integrated confidence score of 1, while a total absence of separation (as in the case of
the "climatological forecast") would produce a score of 0. Integrated confidence values of
0.2 are considered moderately useful by today's standards, and values of 0.3 are clearly
useful. In examining the integrated confidence values that accompany the graphs, it becomes
clear that distributional shifts tend to account for the majority of the integrated confidence
value, while distribution narrowing contributes to a lesser degree. This characteristic
implies that occurrences of strong climate forcing conditions, whether related to ENSO,
strong decadal trends in progress, or other factors, represent "forecasts of opportunity",
and that forecast skill (and utility) are not constant from year to year for a given location,
season and lead time. Of the three confidence measures discussed here, the only one that
remains nearly constant from year to year is the confidence in the point forecast,
showing the narrowness of the forecast distribution relative to the climatological
distribution. Fortunately, our current lack of strong point forecast confidence does not
prevent us from having fairly high shift direction confidence under certain
circumstances.
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The middle block of text
on the right side of the graph provides estimated
probabilities, for the final forecast, of selected categorical outcomes
with respect to the climatological degree day distribution.
Included are the probability of the highest 10% of the climatological distribution,
the highest third (called "above normal" in the traditional maps of temperature
forecast probability anomaly), the middle third ("near normal"), the lowest
third ("below normal") and the lowest 10% of the climatological distribution.
The probabilities are indicated on the right side of each line of text, and are given
to the nearest tenth of one percent. The boundaries of the degree day totals that define
these categories, are shown in parentheses in each text line.
When the "CL" (climatological probability) is given on the map of temperature forecast
probability anomaly, the probabilities shown in this block of
text will show just that: 10.0%, 33.3%, 33.3%, 33.3%, and 10.0%.
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www.nws.noaa.gov 
