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Forecasts of Surface Temperature and Precipitation Anomalies over
the U.S.
contributed by D. Unger
Screening multiple linear regression (SMLR) is used to predict seasonal temperature and precipitation amounts for
locations over the mainland United States. Predictor data consist of northern hemisphere 700-mb heights, near global
SSTs and station values of mean temperature and total precipitation amount from the 3-mo period prior to the forecast
initial time of December 1, 1996. Forecasts for the mean temperature and total precipitation are made for a series of
13 overlapping 3-mo periods, at one month intervals, beginning with Jan-Feb-Mar 1997 and extending through Jan-Feb-Mar 1998. Regression relationships were derived from data for the 1955-95 period. Forecasts were produced from
single station equations for 59 stations approximately evenly distributed throughout the U.S.
All predictors and predictands were expressed as standardized anomalies relative to the developmental data.
Precipitation amounts were transformed by taking their square roots prior to standardization in order to help normalize
their distribution. Twenty-five candidate predictors, selected from gridpoint values in regions of known importance for
climate prediction, were offered for screening in the regression development. A few predictor locations were chosen
on the basis of data examination of the first 20 years of the sample, referred to here as the base period. Information
from the most recent 20 years was never used for selection of candidate predictors (Unger, 1996a). One additional
predictor, carbon-dioxide concentration from Mauna Loa Observatory, was offered in order to capture long-term trends
in the data. This crude trend variable provides the screening procedure with a convenient predictor with which to
identify stations that have simple trends in their predictand values.
Initial testing indicated that cross-validation cannot be used for SMLR (Unger 1996b) so a variation of a retroactive
real time (RRT) validation technique was used. To estimate skill by RRT, a forecast equation was derived from the base
period and applied to the next year's data to obtain independent data results. The case was then added to the
developmental sample, a new relationship was derived and applied to the following year's data. Independent data
statistics accumulate on a year by year basis in exactly the same way as an operational forecast procedure, except
retroactively. Forecasts were obtained for the base period years by application of RRT in reverse: deriving from the
future years and applying to the most recent year in the withheld period (now the first half of the sample). Each earlier
case was then included in the development sample, the relationships re-derived and applied to the next earlier case. This
bi-directional RRT (BRRT) validation technique provides that each available case contribute to a skill estimate as
independent data in a way similar to cross-validation except with a great reduction in the distortion of results, due to
redundant sampling in cross-validation (Unger, 1996b).
A forward selection screening procedure was used for equation development. The top 5 terms were selected for
each equation. Separate statistics were accumulated for each equation length, so that results for all the one, two, three,
four and five term equations were calculated. The optimum equation length was then estimated by an objective learning
procedure that used the past performance at each RRT trial to "predict" which equation would perform the best on the
next. Verification statistics from this "best guess" forecast were also kept separately and were used to obtain the final
skill estimate of the forecasts.
The verification used was the temporal correlation coefficient between forecast and observation on the 40
independent cases at each of the 59 stations. An average correlation coefficient was computed from the root mean
squared correlation coefficient with the signs retained both in the squaring process and the final square root. Field
significance was measured by comparison of scores from actual target years against scores determined from 500
randomly shuffled target periods. Field significance expresses the percentage of cases in which the random forecast
series outperformed the actual forecasts.
The final forecasts are post-processed to obtain an estimate of the likelihood of the above, normal, or below class
being observed, as defined by the terciles of the distribution for each forecast element and location. A forecast is
assigned a class on the basis of the forecast distribution and skill. An estimate of the increased likelihood of a given
class is made to place the forecast in a format similar to the operational long lead forecasts issued by the CPC (O'Lenic,
1994). Currently, these probability assignments are obtained from the relationship between probability of a given class
being observed, the inflated SMLR forecast and the predictive skill (inflation sets the forecasts variance equal to
observed variance at each station). This relationship is based on forecast performance on independent data. If the
correlation skill of the forecast is under approximately .3, the forecast is not assigned to a class and is regarded as a
climatological forecast.
The forecasts for JFM 1997 are shown in Figs. 1 and 3 with the corresponding skill estimates for each station
shown in Figs. 2 and 4. Shading indicates areas of sufficient skill to assign a tercile category to the forecast. Contours
within the shaded areas on the forecast maps indicate an estimate of a 5 and 10 percent probability anomaly for the
category. Note that the skill estimates are based on the actual forecasts, and not the post processed category
assignments, which are presented only for clarity of presentation.
The numbers plotted in Figs. 1 and 3 indicate station values of the regression forecast for the standardized anomaly
of temperature or the square root of precipitation amount. Forecasts are damped according to the forecast-observation
correlation on independent data so that the squared error between forecast and observation will be minimized. Non-zero
numbers plotted outside of shaded regions generally indicate forecast anomalies of substantial magnitude at stations
with some skill, but lower than the skill threshold to choose a forecast category with confidence.
Regression forecasts (Fig. 1) show above normal temperatures this JFM over much of the southern U.S. The
primary predictor for stations to the west of New Mexico is the CO2 trend variable, while the warmth in the east is
associated more with 700-mb heights and SST's in the North Pacific. The average correlation for this forecast is .24
with a field significance of .000.
Precipitation forecasts for JFM 1997 (Fig. 3) are only slightly less skillful than for temperature forecasts, with an
average correlation of .20 and a field significance of .002. Cool SSTs in the equatorial Pacific near South America are
associated with dry forecast conditions in Florida, Kansas, and southern Texas, and also with the wet conditions to the
south of the Great Lakes. There is only a slight suggestion of dry in the central Pacific Coast.
Figure 5 shows the temperature forecast for summer (JJA) 1997. Warmth along the East Coast and in the West are
mostly due to long term trends. The below normal temperatures forecast in the north-central US are due to associations
with SST anomalies off the East Coast and temperatures in the region. The skill estimates for this forecast are shown
in Figure 6. The average correlation for this forecast is .22 with a field significance of .000.
O'Lenic, E., 1994: A new paradigm for production and dissemination of the NWS's long lead-time seasonal climate
outlooks. Proceedings of the Nineteenth Annual Climate Diagnostics Workshop. College Park, Maryland,
November 14-18, 1994, 408-411.
Unger, D. A., 1996a: Long lead climate prediction using screening multiple linear regression. Proceedings of the
Twentieth Annual Climate Diagnostics Workshop. Seattle, Washington, October 23-27, 1995, 425-428.
Unger, D. A., 1996b: Skill assessment strategies for screening regression predictions based on a small sample size.
Preprints, Thirteenth Conference on Probability and Statistics in the Atmospheric Sciences. San Francisco, CA.,
February 21-23, 1996, 260-267.