The Meteorological Magazine 1991-01: Vol 120 Iss 1422

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The
Vieteorological
January 1991
Vol. 120 No. 1422
Magazine
551.509.331:551.524.36(410)
Temperature predictions for the UK winter 17
can
T.D. Hewson FEp
Joint Centre for Mesoscale Meteorology, University of Reading 04 199)
Le NEE
Summary LiisaN G
The suggestion that the shape of the late autumn circumpolar vortex can be used to forecast UK winter
temperatures is discussed and a simple mathematical predictor proposed. This predictor is assessed using
correlation tests on a 44-year data set; investigating also the predictability of individual months and the value of
different predictor periods. A simulation of real-time forecasts suggests that useful skill could have been achieved.
1. Introduction
Several articles appearing in Weather over the last Excluding the aforementioned leaves those of Murray
10 years have dealt specifically with long-range temper- (1972 and 1977) as perhaps the best. In a five-category
ature predictions for the winter period in the United system he achieved about 7 correct forecasts out of 24.
Kingdom. The prediction method used was essentially A major incentive for this work was that the financial
statistical and was based on upper-air patterns occurring worth of accurate long-range forecasts would be very
across the higher latitudes of the northern hemisphere great indeed.
during October and November. It was first described by
Davies and Reeve (1980). In Davies et al. (1986) a simple 2. Physical background
verification of the technique against 17 winters,
although not conclusive, did give reason to believe that 2.1 Link between autumn upper-air
useful skill could be achieved. A similar but more patterns and winter temperatures
quantitative approach used in Davies (1989) and Hughes (1981) investigated ‘Central England’ temper-
Ratcliffe (1990) produced equally encouraging results. atures in 357 winter months. Of the 52 he classified as
Again, though, the databases analysed were rather ‘very cold’, 48 were of a north-easterly, easterly or south-
small, being 10 and 12 winters respectively. easterly type. This is clear evidence that winter temper-
In this investigation a quantitative adaptation of the atures in the United Kingdom are very closely related to
prediction method described in Davies et al. (1986) is wind direction. It is of course the atmospheric flow
tested out on a 44-year data set. This begins in section 3, patterns which dictate the wind direction; these can be
and included is an attempt to identify the best ‘predictor’ divided into two simple categories:
periods and also the ‘most predictable’ parts of the (a) a mobile westerly type giving above average
winter. In section 6, real-time predictions are simulated temperatures, due to anticyclones to the south of the
for the last 19 winters, by creating for each winter new British Isles, and
regression equations based only on previous years. (b) a blocked easterly type giving below average
Section 2 gives a comprehensive description of the temperatures, due to anticyclones to the north of the
physical mechanisms underlying the statistics. British Isles.
To put this study into some sort of context it is As far as the predictive method is concerned the main
worthwhile considering which, to date, have been the factor affecting the probability of either (a) or (b)
most accurate long-range UK temperature predictions. occurring is considered to be the forcing effect of
Meteorological Magazine, 120, 1991
‘boundary conditions’ occurring at the earth’s surface was constructed to represent the frequency of each
during the winter. Boundary conditions likely to be direction of orientation. This diagram was the basis for
important are sea surface temperatures, snow cover and the winter prediction, whereby a large east-west
sea-ice cover; it is principally the forcing effect of sea ice component on it pointed to a high probability of the
which is being considered here. This is the same cold flow pattern (b) occurring, whilst if other
mechanism alluded to in Davies et al. (1986), and in orientations were dominant the chances of getting mild
earlier work. (Davies (1989) proposes a different type (a) conditions were increased.
mechanism, in which the high pressure present at high
latitudes in cold winters is explained by net poleward
mass transport 1-3 months earlier.) 2.2 The importance of the east-west
Observational studies indicate that the sea-ice pattern component
sets itself for the winter late in the autumn (Davies et al. To understand the significance of the ‘east-west
1986). The shape of this pattern should depend largely component’ the following ‘thought experiment’ should
on the distribution of cold air around the North Pole in prove helpful.
October and November; a distribution which will be During winter the higher latitudes of the northern
evident from upper-air patterns. Thus there should be a hemisphere have to accommodate a certain amount
connection between. upper-air patterns around the of deep, cold, tropospheric air. For convenience
North Pole late in the autumn, and winter temperatures consider ‘higher latitudes’ to be north of 50°N. The
across the United Kingdom. ‘certain amount’ can be represented by a domain of
A good guide to the distribution of cold air around any shape whose area is equal to that bounded by a
the North Pole on a given date can be gained from latitude circle at 65°N. What then will dictate the
circumpolar 1000-500 mb thickness charts. Contour possible configurations of this domain? In other
height charts for the lower stratosphere (e.g. 100, words how easily can different locations support the
200 mb) also provide a good guide, as low contour presence of very cold air above (see Fig. 1)?
heights at such levels usually reflect the presence of deep,
cold tropospheric air below. Most patterns on these Sea water rapidly modifies very cold air, warming it
charts can be approximated by an ellipse, such that the up through vigorous convection. Sea ice, snow and land
lowest thickness values or lowest contour heights (and have a much smaller modifying effect; mainly because
hence coldest air) are in alignment with its major axis. It their heat capacities are lower, but also because only in
then seems reasonable to expect the most pronounced sea water is it possible to redistribute heat rapidly by
sea-ice development to be in that direction too. advection and mixing. So the main restriction on the
The original prediction method entailed analysing configuration of the cold air domain is that it cannot be
one chart per day for (say) a 30-day period and allowed to encroach very far into sea areas (‘seas open all
identifying the direction of orientation of the major axis year’ in Fig. 1). Given a homogeneous planet the most
on each. Then from these 30 directions a polar diagram likely configuration would be a circular one centred on
Above 2000 m
Land or permanent pack ice
Below 2000 m - ~ [=== Seas open all year F=4 Sea areas covered by pack ice in spring
ea: Boundary of coldest tropospheric air => Main depression tracks aaa Airflow affecting the United Kingdom
Figure 1. Circumpolar maps illustrating how the distribution of cold tropospheric air around the North Pole in winter can dictate which
airstreams affect Britain: (a) mobile westerly, (b) blocked easterly. The block alongside represents *1.6 X 10° km’, a measure of the extreme
interannual variability of winter sea-ice cover (see text).
Meteorological Magazine, 120, 1991
the North Pole, but clearly this is disallowed here
because of the presence of seas north-west of Norway.
Fig. l(a) shows a configuration which is about as
close to the circular type as it is possible to get. This type
of pattern is quite common. It is best thought of as
representing an average over several days (in reality
short-wave troughs would be observed to run east
around the vortex, at least across the Atlantic). Such a
pattern would be accompanied by a strong baroclinic
zone extending east or north-east across the Atlantic,
with deepening depressions tracking between Iceland
and Scotland. This results in mild south-west or westerly
winds prevailing over the United Kingdom, but with
some colder outbreaks of north or north-westerlies.
Fig. 1(b) illustrates another configuration in which
the cold air has almost split up into two centres. The
land-sea distribution dictates that if there are going to
be two major centres then these must be located over the
Soviet Union and North America. This type of pattern is
also fairly common, though not nearly as common as
(a). The southward displacement of cold polar air over
Canada results in a backing of the jet stream south of
Greenland and in turn this can often steer depressions
up the Davis Strait west of Greenland. The resulting Figure 2. Polar diagram representing winter blocking frequency
warm advection between Greenland and Iceland helps (solid line) and ‘sea water extent’ north of 50°N (dashed line) as a
function of longitude. ‘Sea water extent’ was calculated from Fig. | to
build high pressure to the east of Iceland, or perhaps be the sum, along a longitude line, of the total distance occupied by
reinforce a Scandinavian anticyclone. In this way the ‘seas open all year’ and half the distance occupied by ‘sea areas covered
United Kingdom comes under the influence of east or by pack ice in spring’. Scales are linear, the central circle being zero.
north-easterly winds. If these are fuelled by the cold-air
centre over the Soviet Union it can become very cold distribution does take place then it is probably
indeed (as happened for example in February 1956, worthwhile looking at the areas in which sea ice forms
January 1972 and January 1987). and melts each year. These correspond roughly with the
Synoptic charts indicate that there are many possible sea areas ‘covered by pack ice in spring’ on Fig. 1 —
configurations of the very cold air, but it is felt that most subsequently referred to as ‘key areas’.
winter patterns can be roughly approximated by one of To increase the chances of (b) occurring, and
the above. persisting for some time, it seems important that the key
Fig. 2 gives some observational evidence for these areas which fall within the domain have as great a cover
ideas. It shows a frequency distribution, as a function of of sea ice as possible during the winter because this
longitude, of atmospheric blocks occurring north of would reduce the chances of the cold air being warmed
about 50°N during the seven northern hemisphere out from below. Equally important, perhaps, is that the
winters from 1980/81 to 1986/87 (taken from Fig. 1 in key areas which fall outside the domain in (b) have as
Tibaldi and Molteni(1990)). It is immediately clear that little sea-ice cover as possible. Reducing the amount of
there is a strong link between block frequency at a given sea ice in these areas which fall outside the domain in (b)
longitude and the extent of ‘sea water’ along that would also seem to make (a) less likely.
longitude, albeit with a small phase shift in the Such an explanation would only be plausible if the
Atlantic/ European sector. The two maxima — over the interannual variability of winter sea-ice cover were
Pacific and the Atlantic — fit in well with the reasonably large. The box drawn alongside Fig. 1(b)
atmospheric pattern in Fig. 1(b). Whilst Fig. 2 partly represents* the difference between the greatest and least
represents a ‘chicken and egg’ scenario, it also seems to ‘mid-winter’ areal extents of sea-ice (defined as where
show that boundary conditions at the earth’s surface do cover is greater than 10%) observed between 1973 and
have a forcing effect on the atmospheric circulation, in 1989 (data from NOAA, USA). Here the term ‘mid-
which the main physical mechanisms are those outlined winter’ means averaged over a 2-month period beginning
above.
To tackle the forecasting problem one must now * The maps in Fig. | are ona zenithal equidistant projection, implying
consider how the chances of (b) occurring in winter that the ratio between area on the page and area on the earth’s
might be influenced by atmospheric patterns occuring in surface is not quite fixed, but a slowly varying function of latitude.
The area of the block alongside is normalized to 65°N . If normalized
autumn. to 90°N, the area would be 3% smaller than shown, or to 50°N then
If a feedback mechanism which involves sea-ice 5% larger.
Meteorological Magazine, 120, 1991
1 January. This area is considered large enough to rarely have much amplitude by the time they reach this
support the above arguments (especially as energy height in the atmosphere. The 200 mb level was next
considerations suggest the attendant anomalies in sea best, followed by the thickness patterns. Consideration
surface temperatures might be even more marked — the was given to using 50 mb charts, but at this level the
latent heat of fusion of ice is about 80 times greater than patterns were too close to circles to be of any use. So
the specific heat capacity of water). 100 mb charts were used wherever possible (1960
How then can sea-ice patterns which favour pattern onwards), thickness patterns for years when only they
(b) come about? The formation of sea ice must to some were available (1946-57), and 200 mb charts for 1958
extent depend on the distribution of cold air around and 1959. It was felt that the disadvantages of using
the North Pole during October and November, and different chart types were far outweighed by the
naturally a distribution similar to that indicated by the advantages of having a long data set.
domain in (b) is going to favour sea-ice development in All charts were necessarily of the northern hemisphere
the right areas. If this domain were approximated by an circumpolar type, and there was one for each day, the
ellipse the orientation of the major axis would probably analysis time usually being midnight. They came from
be 90°W — hence the importance of the ‘east-west three sources — the European Meteorological Bulletin
component’. The longer such a pattern persists during for 1976 onwards, the Soviet SINOP bulletin for 1958-
the autumn the greater will be the chances that the 75, and the Meteorological Office (hand plotted) for
desired sea-ice patterns have developed. 1946-57.
It is also worthwhile outlining two of the limitations Scarcity of observations made it quite difficult using
of these ideas. Where sea ice develops will partly be some of the 1946 and 1947 charts. There is, however, a
determined by the early autumn sea surface temperatures; fair degree of confidence in the orientations found for
no real account of this is taken here. Also an over- these years, particularly 1946.
simplified view of sea ice has been taken. Rarely if ever
does it have a well-defined edge — the distance in which 3.1.2. Temperatures
the fractional cover of sea ice ranges from 10/10 (pack The UK Monthly Weather Review provided the
ice) to 1/10 can easily be over a hundred miles. winter temperature data to verify against; as anomalies
from 30-year climatological means for the Engiand and
3. Method Wales region. Scotland and Northern Ireland were
In Davies et al. (1986) the retrospective temperature excluded on the grounds that, with a relatively wide
predictions were based on subjective analysis of the expanse of sea to the east, temperatures there would be
shapes of polar diagrams, whilst for the verification all less sensitive to a change in wind direction from west to
winters were classified into just two categories, cold or east.
mild. Here the intention was to improve upon this by Anomalies were extracted for both the individual
adopting a quantitative approach. The polar diagram’s winter months and the winter as a whole; assuming for
shape would be represented by a single number, or convenience that ‘winter’ is comprised of December,
‘winter index’; and actual temperature levels would be January and February.
used in preference to categorized ones.
3.1 Data sources 3.2 Derivation of the winter index
Clearly two basic types of data were required: autumn In order to create a winter index, a simple weighting
upper-air charts to base the ‘predictions’ on, and winter system was devised whereby each occurrence of a
temperature levels to verify against. The number of particular orientation of the circumpolar vortex on the
years it was possible to investigate was limited to 44 upper-air charts scored a set number of points. The final
because of a lack of appropriate upper-air charts before winter index was then calculated by summing the points
1946. scored in a given period, such as I-15 November; the
idea being that the magnitude of this score was
3.1.1. Upper-air charts indicative of the likely severity of the forthcoming
Davies concluded that November’s charts would winter. Table I shows the weighting system used — the
probably be a more useful guide to winter temperatures choice of ‘scores’ is explained below.
than those of October, perhaps because more sea ice
forms in November than October. Thus this study
concentrates on late in the autumn, using a 45-day Table I. Weighting system for calculating winter indices
period from 17 October to 30 November in every year.
The choice of which types of chart to use was Point score Orientation
60°W 70°W 80°W 90°W 80°E Others
determined by two factors, availability and suitability.
The 100 mb level proved most suitable, indeed frequently
Axis ratio > 2: z 4 4 4 2 0
the contours at this level are roughly elliptical (wave Axis ratio < 2: 1 2 2 2 | 0
number 2), as the smaller more transient wavelengths
Meteorological Magazine, 120, 1991
From past studies it is apparent that the important used. Here, for example, it was not always possible to
‘east-west component’ is made up principally of approximate the atmospheric pattern with an elliptical
orientations 70°W, 80°W and 90°W; hence these shape. Sometimes the patterns were almost circular
directions are afforded the highest weights of all making a direction of orientation much harder to
(subsequently referred to as ‘COs’, meaning ‘cold identify precisely. To reduce the impact of this problem
orientations’). Physically there is only a small difference two sets of scores were incorporated into the weighting
between two adjacent orientations, such as 60°W and system (one being simply a factor of two greater than the
70° W, or 90° W and 80°E. So for consistency it was felt other). For the atmospheric pattern on a particular
that some weight had also to be given to 60° W and 80° E; chart to realize the higher of the two scores the necessary
half the score allocated to the COs was chosen. This also condition was that the ‘axis ratio’ (meaning the ratio of
meant that the relationship betweeen ‘orientation’ and the length of the major axis to the length of the minor
‘score’ was free from large discontinuities. axis of the ellipse judged to best fit the atmospheric
Davies et al. (1986) also defined ‘mild orientations’ as pattern) was greater than or equal to two. This approach
being those between 0° W and 50° W; saying that out of is also physically consistent with the ideas presented
all possible orientations these were the ones most likely earlier, because the greater the axis ratio the more
to precede mild winter weather. To take account oft his, elongated will the cold polar air have become, and thus
negative scores could have been added to Table I for all the greater will be the forcing of sea-ice development
orientations between 0°W and 50° W. The reasons for along that direction of elongation (i.e. the orientation).
leaving them scoring zero were twofold: Davis had Fig. 3 shows one of the 100 mb charts used. To
generally put much more emphasis on the COs, and the approximate the contour pattern with an ellipse the
COs were far more common — occurring more than analyst must concentrate on the area north of 50°N, as
twice as often as the mild orientations. this is where most of the sea ice will be forming. With
Within any subjective analysis of archived data, this guideline in mind it should be fairly easy to see why
unfortunately there is always scope for the analyst to the orientation came out as 90°W and the axis ratio
interpret the data in a way which will lead to results about 3; giving a score of 4. Most patterns were easier to
which are more interesting or more significant than approximate with an ellipse than this one.
would have been the case had an objective analysis been
Figure 3. 100 mb analysis for 0000 UTC on 24 November 1985, with ellipse superimposed. Tickmarks are at 10° intervals.
Meteorological Magazine, 120, 1991
So to calculate the winter indices the following Initially four indices were calculated for each year;
procedure was adopted: one for the 45-day period, and also one for each of
(a) On each chart the direction of orientation of the the 15-day periods 17-31 October, 1-15 November and
circumpolar vortex was identified (45 charts for each 16-30 November (see Table II). By dividing up in this
of the 44 years). way it would be seen whether or not the predictive value
(b) On those charts where the orientation was 60° W, of an index depended on the part of the autumn on
70° W, 80° W, 90°W or 80°E the axis ratio was also which it was based.
calculated.
(c) According to the results of (a) and (b) a points
score (0, 1, 2, 4) was assigned to each date. 4. Results
(d) The points scored in a given period were As the winter index increases so should the temper-
summed. This sum was the winter index. ature of the winter months, on average, decrease.
Table ll. Winter indices and temperature anomalies for England and Wales, 1946-89
Year* Winter index (WI) Temperature anomalies (TA) Wi TA
England and Wales (°C)
17-31 1-15 16-30 17 Oct.- Dec. Jan. Feb. Winter 1-30 Jan. and Feb.
Oct. Nov. Nov. 30 Nov. mean** Nov. mean***
1946 18 20 50 88 — {4 2.1 —$.7 —34 70 —3.8
1947 0 9 17 26 0.7 ‘A 0.4 0.7 26 0.8
1948 4 l 5 10 1.1 1.2 1.4 1.2 6 1.3
1949 4 10 5 19 1.2 0.2 1.3 0.9 15 0.7
1950 12 10 42 64 ae —§.3 —0.5 a 52 —0.4
1951 7 29 20 56 1.0 2.3 —0.8 —0.4 49 — 3
1952 36 33 12 81 —1.4 —0.6 0.1 [email protected] 45 —0.3
1953 8 11 ] 28 2.6 a =—iF —0.0 20 —i§2
1954 15 4l 17 73 2.1 ~i3 2.9 —0.6 58 —29
1955 4 15 23 42 1.3 —0.3 —4.4 1s 38 “23
1956 12 19 11 42 1.3 1.4 1.1 1.3 30 1.3
1957 16 38 30 84 0.0 =§5 0.7 0.0 68 0.1
1958 4 19 34 57 0.2 =—30 0.2 —0.6 53 —=0
1959 16 30 10 56 1.4 0.1 —0.2 0.5 40 0.0
1960 12 25 7 44 ~@5 6.3 a7 0.6 32 1.1
1961 17 8 7 32 ——5 0.4 0.3 —0.4 15 0.4
1962 9 46 38 93 — —§3 ES —4.0 84 —4.9
1963 4 0 5 9 —295 =03 0.5 —0.6 5 0.1
1964 22 3 39 64 —}.2 0:1 —i7 0.7 42 —0.4
1965 17 56 8 81 <2 —§.7 ‘7 0.2 64 0.4
1966 2 47 28 77 0.5 0.7 1.6 0.9 75 1.1
1967 0 28 5 33 —0.5 0.7 =o —@.5 33 —0.4
1968 0 21 32 53 —45 1.9 ~25 —@.7 53 —0.3
1969 50 5 14 69 aa 0.1 —0.7 —0.7 19 —0.3
1970 5 5 49 59 =—0.5 0.9 0.9 0.4 54 0.9
1971 10 14 I 25 1.7 0.2 0.5 0.8 15 0.3
1972 41 12 3 56 1.0 0.9 0.5 0.8 15 0.7
1973 3 13 0 16 0.1 2.5 1.9 1.5 13 2.2
1974 34 8 4 51 pe 3.2 1.0 25 17 2.1
1975 5 3 35 43 0.5 az 0.8 1.2 38 1.5
1976 25 12 11 48 —23 0:5 1.5 ~0.5 23 0.5
1977 3 0 26 29 3 —0.1 <=.) 0.1 26 —0.6
1978 10 23 44 77 —s -s9 “3 i 67 aT
1979 16 15 4 35 1.2 —0.9 2.1 0.8 19 0.5
1980 3 12 3 18 0.9 1.2 —§.5 0.6 15 0.4
1981 42 12 2 56 a —0.4 1.3 =—10 14 0.4
1982 16 10 19 45 <2 3.0 —-14 0.5 29 0.8
1983 0 5 0 5 1.2 0.2 0.0 0.5 5 0.1
1984 22 43 9 74 06 27 —i3 =—_ 3 52 —2.0
1985 6 Il 41 58 1.6 0.1 —4.5 —0.8 52 2s
1986 20 50 19 89 1.2 —2.6 0 —@.S 69 —{4
1987 Il 10 23 44 1.0 1.8 1.1 1.3 33 1.5
1988 22 26 8 56 2.6 2.7 2.3 25 34 23
1989 11 41 9 61 0.3 3.1 a7 23 50 3.4
* Year is the year containing October, November and December.
** Winter mean = (Dec. X 31 + Jan. X 31 + Feb. X 28.25)/90.25
*** Jan. and Feb. mean = (Jan. X 31 + Feb. X 28.25)/59.25
Meteorological Magazine, 120, 1991
However there is nothing to suggest that any relation- relating temperature to winter index will be required.
ship between the two variables would necessarily be Least squares regression techniques were employed to
linear. Perhaps then the best statistical test to apply to achieve this; putting ‘best-fit’ polynomial curves through
the data sets in the first instance is one based purely on the data points. Brooks and Carruthers (1953) suggest
rank. using this approach when there is no theoretical
guidance as to the nature of the correlation. They also
4.1 Rank correlations state that rarely in meteorology would there be
Kendall’s coefficient of rank correlation (described in justification in using anything more complex than a
Williams 1986) was calculated for all possible pairings of second-order curve (i.e. quadratic). Hence that was
‘temperature anomaly’ against ‘winter index’, yielding what was used. The usual assumptions about data distribution
the results shown in Table III. applied.
Three cases were considered:
Table lll. Kendall coefficients of rank correlation, calculated (a) January temperature compared with a 45-day
for winter indices against winter temperature anomalies; 44 index (17 Oct.—30 Nov.)
ranks in each case (b) February temperature compared with 15-day
index (16-30 Nov.)
Winter index England and Wales temperature anomaly (c) January-February temperature compared with
Dec. Jan. Feb. Winter 30-day index (1-30 Nov.)
17-31 Oct. —0.093 —0.159 +0.081 —0.111 These pairings were chosen after careful examination
1-15 Nov. —0.011 —0.273* +0.007 —0.099
of the coefficients in Table III; the intention being to
16-30 Nov. —0.145 —0.172 —0.329** —0.329**
match up a given predictand with it’s most accurate
17 Oct.-30 Nov. —0.197 —0.327** —0.158 —0.332**
predictor. Table II shows all data points used, Fig. 4 the
* and ** indicate significance levels of 95% and 99.5% fitted curves, and Table IV useful statistics derived from
respectively. No coefficient was significant at the 99.95% level.
The following conclusions can be drawn from the
coefficients:
(a) All but two of the coefficients are negative,
strongly supporting the idea that higher winter
indices point to lower winter temperatures.
& represents more than one occurrence
(b) Considering December alone, no coefficient (aO°nbCso)em 6ra vleyd rn n L 1 1 L 1 n 1
quite reaches the 95% level, suggesting little if any 0 10 20 30 40 50 60 70 80 90 100
45-day winter index (17 October-30 November)
predictability. In turn this suggests that the correct
prediction of the very cold December in 1981 (Reeve
1982) may have been fortuitous. 3)
(c) Of the three winter months the results for S 4
=
January are perhaps most encouraging, suggesting o3O 4
re]
that some accuracy in long-range forecasts could be c
bed 4
achieved here. 3
(d) For February there are surprisingly large differ- 5 J
8 — e ee
ences between the four coefficients; but there would
e) —6 1 wih, 1 i 1 2
seem to be some predictability if the late November 0 10 20 30 40 50 60
index were used alone. 15-day winter index (16-30 November)
(e) November has more predictive value for the
forthcoming winter than does late October.
oO
— 4
=
In view of( b), (c) and (d) it would seem sensible not to oO
3 4
try to use the winter index to forecast the temperature 3
Cc
for the whole winter, but rather to concentrate on -oO 4
®
forecasting for just January and February.
@® 4
ao
2
ie) —6 1 i 1 rn An rn i 1
4.2 A way of preparing future forecasts
0 10 20 30 «640 50 60 70 80 90
Rank correlations help illustrate whether relationships
30-day winter index (1-30 November)
between two sets of variables exist, but they don’t really
allow a forecast of one to be made knowing the other.
Figure 4. Plots of temperature anomaly against winter index, with
Clearly if proper predictions for January and February best-fit quadratic curves added for (a) January, (b) February and (c)
are to be made then either a graph or an equation January and February combined.
Meteorological Magazine, 120, 1991
Table lV. Statistics relating to the graphs in Fig. 4
(a) (b) (c)
Equation (y=) — 0.00125x* + 0.088x — 0.5 — 0.00015x? — 0.066x + 1.1 —0.00090x* + 0.034x + 0.3
Variance 36 24 28
explained (%)
Significance 99.995 99.5 99.95
level (%)
Standard error 1.4 1.8 1.4
of estimate (°C)
Prediction accuracy 1.8 z2 1.8
for 75% confidence (°C)
the regressions. Use of both linear and quadratic could be a long-range predictability ‘peak’ in the latter
coefficients was justified at the 95% level only in case (a), part of the winter across much of the northern
but to maintain consistency and facilitate inter- hemisphere.
comparison all coefficients were retained in all three Namias (personal communication from Davis) has
cases. found that November is a better predictor of conditions
The reader may decide whether there is sufficient in January and February in the USA than is October.
justification for making two separate forecasts (using This is in agreement with conclusion (e) in section 4.1,
(a) and (b)) rather than just a single forecast (using (c)). and so must lend further weight to the results of this
The author’s view is that two separate forecasts could be investigation.
made, because the differences between the coefficients It is important to consider what level of significance
for January and February in Table III are so large. needs to be achieved to justify there being a physical
However it is acknowledged that no physical explanation relationship between winter index and winter temper-
has been offered for these large differences. atures. It is common for the 95% level to be used in ‘a
priori’ type regressions — where there is a sound
5. Discussion physical reason for expecting a relationship to exist
Perhaps the most illuminating of the figures in Table between two variables. Nicholls (1980) states that a
IV are those showing ‘variance explained’. It would be higher confidence level is appropriate when the
interesting to see how these figures compared with those relationship is ‘a posteriori’ — i.e. with no physical
produced by other long-range forecasting techniques. reasoning behind it. This investigation perhaps falls
Barnston and Livezey (1989) infer that the operational between these two extremes — a physical reason has
seasonal weather forecasts issued by the Climate been given but it is perhaps open to question. Either way
Analysis Center in the USA achieve a skill level around the levels indicated in Table IV are too high to be
15%. Unfortunately these are categorical forecasts dismissed lightly, even though there was an element of
where the skill has been calculated in such a way that ‘selectivity’ involved in choosing the predictors. It is
comparison with ‘variance explained’ is not valid. To worth noting here that in some past papers in this field
overcome this problem the points on Fig.4 were all sorts of predictors have been investigated, only to
reanalysed as if forecasts in three equi-probable find that not much more than 5% of them reach a
categories had been made. For the three cases (a), (b) significance level of 95% (see for example Bergen and
and (c) this yielded respective skill levels of 14, 16 and Harnack, 1982).
16% — clearly on a par with the above. This result is How ‘useful’ then might a prediction made using the
particularly encouraging in view of the long lead-time above graphs be? This can be directly answered by
(1-3 months) between prediction and event. quoting the values for ‘variance explained’. Alternatively
Barnston and Livezey investigated complex analogue- the ‘75% confidence limits’ might be useful — an
based prediction methods for all four seasons for the example will serve to illustrate their worth.
USA using a 35-year database. The best skill level they Assuming that having analysed the October and
could achieve was 16% for the winter season. There was November charts, and calculated a 45-day index, a
also an indication that the latter months of the winter prediction for January was required. Say the index was
(i.e. January, and more especially February) were more 80. This reads off at about —1.5°C, the most likely
predictable than December. This ties in well with temperature anomaly. Then it could also be said that
conclusion (b) in section 4.1, and suggests that there there was about a 75% chance that the temperature
Meteorological Magazine, 120, 1991