a search for short range climate predictability
TRANSCRIPT
Dynamics of Atmospheres and Oceans, 3 (1979) 485--497 485 © Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands
A SEARCH FOR SHORT RANGE CLIMATE PREDICTABILITY
RUSS E. DAVIS
Scripps Institution of Oceanography, La Jolla, California 92093 (U.S.A.)
(Received 13 July 1978; accepted 16 August 1978)
Davis, R.E., 1979. A search for short range climate predictability. Dyn. Atmos. Oceans, 3: 485--497.
1. INTRODUCTION
Observations of apparent co-occurrences of anomalous sea-surface tempera- ture (SST) and sea-level pressure (SLP) patterns over the North Pacific Ocean have led many to speculate that the ocean may be a cause of atmospheric anomalies and, because the ocean develops slowly due to its thermal inertia, this might provide a limited ability to predict short-term (months to seasons) climatic variability in the atmosphere. The collected works of Namias (1975) presents numerous examples of co-occurrences of SST and SLP anomalies and dynamical arguments to explain how these co-occurrences may come about. To grossly oversimplify, it is suggested that an SST anomaly is gener- ated, most probably by atmospheric forcing and that the ocean's thermal inertia causes this anomaly to persist while being modified by advection and subsequent forcing by the atmosphere. As it persists, the SST anomaly influ- ences atmospheric development, primarily through the influence of horizontal temperature gradients acting on baroclinic processes in the lower atmosphere.
For the last two years I have been attempting to translate Namias' picture of ocean--atmosphere interaction into a quantitative model of predictability. From such a model it should be possible to determine: if there is any predict- ability associated with the North Pacific SST/SLP system; which factors signal the recurrent developments; and if practical forecasts can be made.
The procedure employed involves: an a priori (not associated with predic- tion skill) selection of possible factors contributing to predictability; deriva- tion of data parameters anticipated to be linearly related to the estimands of interest (usually SLP anomaly); determination of the artificial prediction skill anticipated if there is no true predictability (the result of sampling errors in statistics); determination of the hindcast skill of the data parameters (i.e. the ability to predict the realizations from which the prediction model is derived); estimation of the true predictability implied; and display of the pat- terns of data and estimands involved in the presumably predictable develop- ments.
486
To date, data parameters have been selected from the fields of one- or three-month anomalies of SST and SLP. The number of such parameters is limited by employing the a priori criterion that the importance of a datum is approximately proportional to the amount of variance of the parent field it explains. Hence the data parameters are the amplitudes of Empirical Ortho- gonal Functions (EOFs) of the data field. Examples of these patterns, de- scribing the year-round anomaly variance, are shown in Figs. 1 and 2. An important feature disclosed is that SLP is a spatially simple field with approxi-
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400 .. ~ "
200
I t l I 1 I I I l L 1 1 l 120°E 140 ° 160 ° I I!0 ° 160 ° 1400 120 ° IO0°W
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, ::. ~ ::::::::::::::::::::::::::::::::
200 I 4 " ~
I I I I I I 1 I i I 1 1 120OE 140 ° 160 ° 180 ° 160 ° 140 ° 120 ° IO0°W
Fig. 1. The three principal empirical orthogonal functions describing SLP anomalies.
60 °
2 0 •
120°E 140 ° 160 ° 180 ° 160 ° 140 ° 120 ° IO0°W
40 ° "'"::i" ~ ~' '::::i:::::?~:i:i:i:i:i. ~ ~ - ~ , - - - - ' - - ~ " " ~ _ ". ============================== ":!i:::iiii'!!i!i!i!iiii
. - - ::::::::::::::::::::.:.
~) 0 0 ~ ~ ~ . , , , ' . . *::::::
120°1[ 140 ° 160 ° 180 ° 160 ° 140 ° 120 ° 100OW
L .... 2 0 o
t 2 0 ° [ 140 ° 1t~0O 180 ° I&O ° 1400 120 ° IO0°W ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: ~ii~i~i~i~i~i~i~i~i~i~i~i~i~i~!~i~i~i~i~i~i~i~i~i~i~i~i~i~i:i~i.~.~ .... ":i:~:~:~:~:i:~:~:~:~:!:i:i:i:~:i:~:~:~:!:i:!:i:!:i:i~i?i:i:~:!:!:i:i:i:! !:!::i:i:i:ii:i: :::::::::::::::::::::::::::::::::: ================================================== ~i'ii~iii!iii! 7 " . :!ii:" - , 2 ""::~i~i~i~i~i!!i!iii!i!i!ii~ili~i!i~i!i!!!!!!i!i! • i~::i!i!i~::~::~::~::~::~::~!::::. : 0 . =============================================================
i i I I I I I I I I I I I I 120°E 140 ° 160 ° 180 ° 160 ° 140 ° 120 ° IO0°W
Fig. 2. The fou r pr inc ipa l empi r ica l o r t h o g o n a l f u n c t i o n s descr ib ing SST anomal ies .
487
488
mately 80% of the variance described by four EOFs while SST is spatially complex requiring ten EOFs to describe 75% of the variance. EOFs selected to describe variability in selected seasons produce qualitatively similar results but the details are seasonally dependent. The time scales of SST and SLP dif- fer markedly, SLP being associated with an essentially white frequency spec- trum below 1 cycle mon -1 while large-scale SST patterns have red spectra decaying faster than f-1.
Namias' physical models do not involve intrinsically nonlinear mechanisms connecting anomalies. On general grounds, even though the detailed physics is nonlinear, the relation between anomalies is anticipated to be quasi-linear since these anomalies represent small perturbations of fields dominated by the mean state and the synoptic scale variability. Hence only linear relations between SST- and SLP-anomalies have been explored.
Artificial estimation skill results from errors in the calculation of data estimand covariances. This was first clearly enunciated by Lorenz (1956) who showed that artificial skill depends essentially only on the number of data variables used in estimation and the length of the record from which the sample covariances are computed. From the available record, sample co- variances are computed as
N
{xy} = ( l /N) ~ x ( i ) y ( i ) i = l
and differ from the true covariance (xy} by the sampling error. If the skill of hindcasting an estimand y using an estimate :9 is defined as
Sn = ( ( S ¢ - - Y ) 2 } / { Y 2 }
and the estimate is a linear one
iq
where the x n are rotatect to be sample uncorrelated so (X ,Xn} = 5,m(Xn2}, then the greatest hindcast skill is
SH : ~ ( Y X . } 2 / ( ( Y 2} (X2}) tl
Lorenz's work, extended by Davis (1977a) shows that an average SH will exceed the true estimation skill for the ideal linear estimate :~,
S = ((y -- y)2}/(y2) ~ ~ (yx . }2 / (y2)(x2} , rt
because the expected square sample correlation is, on average, greater than
489
the true correlation squared. In fact
(SH) ~ S + M/N* ,
where N* is the effective number of realizations in the sample record. N* is equal to N if the samples are serially uncorrelated and less than N if not. Davis (1977a) gives several ways of estimating the expected artificial hindcast skill, (S A) = (SH) - -S .
It is the dependence of (SA) on M which requires that for meaningful results the data variables must be limited in number on the basis of a priori criteria. For the thirty-year North Pacific SST/SLP records, if the number of data variables exceeds five or ten the hindcast skill becomes heavily depen- dent on SA.
The true estimation skill of a system can be estimated as ~ = SH -- (SA), but this estimate itself becomes quite uncertain as the ratio S h/(SH) becomes as large as 0.5.
Once having found the hindcast skill and an estimate of the true estimation skill, it is desirable to portray the data/estimand patterns in a succinct way. As shown by Davis (1977a) this can be accomplished using Principal Estimator Patterns (PEPs). These involve rotating the data variables to find new (uncorre- lated) data parameters:
which describe estimation skill most efficiently, in a manner analogous to the way in which EOFs efficiently describe the variance of the field from which they are derived. With each PEP datum there is the component of the esti- mand field associated with it through the linear estimator. My experience with North Pacific SST/SLP suggests that one PEP datum/est imand pair usu- ally describes all the prediction skill found.
2. YEAR-ROUND MODEL
The first search for SST/SLP anomaly predictability involved seeking a statistical prediction model which was, itself, not a function of time. Such a model might be expected to provide a picture of the results of mechanisms which function similarly in all seasons. Two hindcast models were constructed, one linking SST data with SST anomalies at another time and the second link- ing SST data with SLP anomalies. Details are given in Davis (1976). The results were straightforward and are summarized in Fig. 3 which shows the hindcast skill for estimating SST or SLP one month anomalies in month t + r using as data SST observations in month t. The skill refers to the average over a region from approximately 20 to 55°N in the Pacific and over all months of the year.
It is clear that SST can be specified over ranges --3 < T < 3 months with significant skill. This results primarily from persistence of SST anomalies but the estimators clearly show anomaly movement which is consistent with
490
,o / \
oo / \\,,, /.
/ 0 • % . . "
S H / . ~ 0 / . /~
0.I I $LP/ o
I I I I I °°2-',2 -6 I I I I I 0 6 12
LAG (months) Fig. 3. Skill of e s t imat ing SST and SLP in m o n t h T + lag using as da ta ten SST modes f rom m o n t h ~'. The skill SI-I, descr ibed in the t ex t , measures the f r ac t ion of the en t i re spat ial field cor rec t ly es t imated . The t op curve refers to es t imat ing one m o n t h averages of SST; the lower curve is SLP e s t ima t ion skill. The ho r i zon ta l l ines at the r ight are the art if icial skill expec t ed when the re is no t rue skill.
advection, primarily in the West Wind Drift. Specification of SLP from SST clearly shows that SST is related to SLP
anomalies, that a small fraction of SLP anomaly in month t can be specified from SST observations in that month, that specification of SLP anomalies in
60" ~ 60 °
40 °
1 - o~ ~----=~--X~//[///// "4,\ -~
20 o _ O ° c ~ ~ ~ 2 ° °
I I I I I I I I 180 ° 160" 140 ° 120" I O 0 ° W
Fig. 4. Principal pa t t e rns for seasonal ( 3 - m o n t h average) SLP anomal ies p red ic t ing m o n t h l y SST a n o m a l y one m o n t h af te r cen te r m o n t h of SLP season. Pr incipal pa t t e rn s are based on yea r - round stat ist ics. The SLP data pa t t e rn is respons ib le for 56% of the h indcas t skill achievable f rom 5 SLP EOFs, which is SH = 0.27.
491
the previous two months is equally skillful, but that SLP cannot be predicted (using this model) from SST. No significant ability to specify SLP in one month from SLP observations in another month was found.
These results are consistent with the following model. The atmosphere, as indicated by SLP, rapidly affects SST and SST anomalies persist much longer than do SLP anomalies. Unfortunately, the ability to predict future SST and to specify SLP from knowledge of simultaneous SST does not imply an ability to predict SLP.
To depict the spatial relation between SLP anomalies in month t and the predicted SST anomaly in month t + 1 the PEPs for the eastern North Pacific were computed; one is shown in Fig. 4. This pattern explains only 60% of the associated hindcast skill, SH = 0.27. The structure could be explained either as Ekman transport inducing anomalies in a mean SST gradient or in terms of the cooling effect: of winds from the north and vice versa. Neither provides an unambiguous explanation but the advection model seems most promising if modified for upwelling effects along the coast.
3. SEASONALLY DEPENDENT MODELS
The model of section 2, and consequently the inferences drawn from it, were subject to various criticisms such as: (1) SLP is not an appropriate atmo- spheric variable; (2) EOFs lose the important features of SST data; (3) use of both eastern and western North Pacific data loses the ocean to atmosphere connection and (4) seeking a model which does not depend on the season hides or masks seasonally dependent processes. Subsequent investigation has yet to show any validity to the first three objections but the latter is both obviously true and of significance in assessing the results of the year-round model.
An example of this is provided by the reconciliation of the year-round model of section 2 with the results of Namias (1976) in which a highly signifi- cant correlation o f - -0 .76 between summer SST and autumn SLP anomalies averaged over three months and a 2000 km X 1500 km region just south of the Aleutians was found. This correlation contrasts with the conclusion of the year-round model in section 2, and was interpreted by Namias as an example of demonstrated ocean--atmosphere feedback. Exploring this apparent para- dox led to the conclusion (Davis, 1977b) that the connection found by Namias was not found by the year-round model because it exists only in the summer--fall transition and does not result from a mechanism which is operable throughout the year.
This conclusion was arrived at by an exhaustive search of possible season- ally dependent models allowing predictability of three month SLP anomalies from either one month SST anomalies or three month SLP anomalies. Using as data four SLP EOFs or five SST EOFs the hindcast skill for predicting SLP anomalies over the eastern North Pacific (120 to 180°W, 20 to 60 ° N) was found for prediction ranges from two to twelve months. The results are sum-
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2 3
4 5
6 7
8 9
10
11
12
12
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0
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0
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0
.09
0
.09
0
.14
0
.18
0
.17
0
.18
0
.12
0
.11
0
.09
0
.12
1--
3
0.11
0
.14
0
.18
0
.20
0
.16
0
.17
0
.17
0
.13
0
.08
0
.07
0
.10
0
.13
2--
4
0.1
1
0.1
4
0.2
0
0.1
9
0.2
1
0.1
8
0.1
3
0.0
9
0.0
9
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0
0.1
0
0.1
1
0.1
0
1.9
3--
5
0.1
1
0.1
5
0.1
7
0.2
1
0.2
1
0.1
5
0.1
1
0.1
2
0.1
1
0.1
0
0.0
9
0.1
3
0.1
0
0.1
0
1.9
1.
9
4--
6
0.1
0
0.1
3
0.1
7
0.1
7
0.1
4
0.1
2
0.1
1
0.1
1
0.0
9
0.0
7
0.0
8
0.0
8
5--
7
0.1
0
0.1
2
0.1
8
0.1
6
0.1
1
0.0
8
0.0
8
0.0
9
0.0
7
0.1
1
0.1
1
0.0
7
6--
8
0.1
0
0.2
0
0.2
4
0.2
1
0.1
0
0.0
8
0.0
8
0.0
7
0.0
8
0.1
4
0.1
5
0.1
1
0.1
0
0.1
5
0.1
1
2.0
2.4
2.1
7--
9
0.1
0
0.2
2
0.2
6
0.1
8
0.1
2
0.1
5
2.2
2
.6
8--
10
0
.10
0
.25
0
.22
0
.16
0
.12
2
.6
2.2
9--
11
0
.09
0
.32
0
.29
0
.23
0
.20
3.
5 3
.2
10
--1
2
0.1
0
0.2
3
0.1
3
0.1
3
2.3
11
--1
0
.10
0
.09
0
.05
0.0
9
0.0
6
0.0
9
0.1
0
0.1
2
0.1
4
0.1
5
0.1
5
0.1
8
0.0
9
0.0
9
0.1
4
0.1
4
0.1
4
0.1
8
0.1
9
0.1
7
0.1
4
0.1
2
0.1
5
0.1
4
0.1
3
0.1
5
0.1
8
0.1
7
0.1
3
0.0
7
0.1
0
0.1
2
0.1
3
0.1
3
0.1
1
0.1
3
0.1
2
0.1
0
0.0
7
0.1
1
0.1
3
0.1
2
0.1
3
0.1
5
0.1
4
0.1
2
0.0
9
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Tab
le I
ex
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t th
at "
Dat
a m
on
th"
refe
rs t
o t
he
cen
ter
mo
nth
of
the
thre
e-m
on
th S
LP
an
om
aly
use
d a
s d
ata
Data months
SA
Range months
2
3
4
5
6
7
8
9
I0
11
12
12
--2
0
.08
0
.15
0
.07
0.
11
0.11
0.
11
1--
3
0.07
0
.16
0
.08
0.
11
0.0
9
0.0
8
2--
4
0.0
8
0.21
0
.09
0
.06
0
.08
0
.11
3--
5
0.0
8
0.2
3
0.0
7
0.0
8
0.1
2
0.1
2
4--
6
0.07
0
.15
0
.10
0
.13
0
.14
0.
17
0.07
0
.10
1.
9 2.
3
5--7
0.
07
0.1
5
0.1
3
0.1
9
0.1
5
0.1
6
0.1
2
0.0
7
0.0
9
2.6
2.0
2.4
6--
8
0.0
6
0.2
2
0.2
2
0.2
3
0.1
7
0.17
0
.16
0
.17
0
.11
0
.10
3.
4 3.
6 2.
6 2.
6
7--
9
0.07
0
.19
0
.14
0
.18
0.
17
0.1
5
0.0
8
0.1
1
0.1
0
0.0
8
2.2
2.7
2.5
2.2
8--
10
0.
07
0.1
9
0.1
2
0.1
3
0.1
0
0.0
6
9--
11
0
.08
0
.25
0
.14
0
.10
0
.06
0
.06
10
--1
2
0.1
8
0.2
9
0.1
0
0.0
8
0.0
6
0.0
6
11--
1 0
.08
0
.22
0
.06
0
.08
0
.09
0
.07
0.1
2
0.1
3
0.1
0
0.0
6
0.0
5
0.0
7
0.0
8
0.0
8
0.0
7
0.0
8
0.07
0
.07
0.0
9
0.0
9
0.1
0
0.0
9
0.0
6
0.0
6
0.1
5
0.1
6
0.1
2
0.0
7
0.0
4
0.0
6
0.0
7
0.0
9
1.9
2.1
0.2
0
0.1
8
0.11
0
.06
0
.05
0
.06
0
.12
0
.11
2.
7 2.
4
0.1
9
0.1
6
0.11
0
.09
0.
11
0.0
9
0.1
2
0.0
9
2.6
2.3
0.1
6
0.1
2
0.1
4
0.1
5
0.17
0
.16
0
.10
2.
5
0.0
9
0.0
9
0.1
6
0.1
7
0.1
4
0.0
3
0.0
5
0.1
0
0.1
1
0.0
9
0.1
0
0.0
5
0.0
9
0.1
5
0.1
2
0.0
8
0.0
9
0.0
6
0.1
2
0.1
5
0.0
9
0.0
5
0.0
4
0.1
0
0.1
2
0.1
2
0.0
7
0.0
3
0.0
4
494
marized in Tables I and II where the hindcast skill, SH, and estimated artificial skill, SA, for each type of data are depicted according to the prediction range and the season from which the data is selected. When the hindcast skill is apparently significant the estimated true skill, :~, and the ratio SH/SA are also shown. It is claimed that the likelihood of a chance occurrence of one value of SH/(SA) > 2.5 is less than 10%. There are at least three distinct examples exceeding this 90% significance occurrence; the chance of exceeding this criterion on any particular data/prediction range pair is less than 1/200.
The interesting patterns which emerge are: (1) A significant skill in predicting autumn and winter SLP from SST three
months prior is found. (2) Significant skill in predicting the autumn and winter SLP from summer
SLP is found. (3) The utility of SST to SLP predictions decreases rapidly with prediction
range while SLP to SLP prediction skill decreases less rapidly, sometimes increasing with range.
The fact that SLP is predictable from itself causes reservations about Namias' interpretation that the correlation of summer SST and autumn SLP is evidence of ocean--atmosphere feedback. It could be that summer SST is a passive response to the summer SLP anomalies which "cause" the autumn SLP development.
60 o ~ i 60 o
2o° - "~ ] rnb J 20°
1 I ~ I I [ I I S O ° 1 6 0 ° 1 4 0 ° t 2 0 ° 1 0 0 ° W
Fig. 5. The principal data and estimand patterns for predicting autumn SLP from July SST. The SST data pattern is a col(] pool along 37°N and a warm pool in the northern Gulf of Alaska (contour interval 0.25°C, negative anomaly shade(]). The estimand SLP pattern is one of westerly flow over the cold anomaly and a low pressure over the Aleutians (isobars, shown as heavy lines with arrows indicating geostrophic flow direc- tion) are separated by 1 mb.
1 8 0 ° 1 6 0 ° 1 4 0 ° 1 2 0 ° I O 0 ° W
495
60 = 60 °
40" 4 0 °
2 0 = 2 0 =
1 8 0 ° 1 6 0 ° 1 4 0 ° 1 2 0 ° I O 0 ° W
Fig. 6. The principal patterns for predicting autumn SLP from summer SLP. The summer data pattern (light lines indicating isobars separated by 1 rob) is a high over the Bering Sea and flow offshore from Alaska. The pattern predicted is similar to that predicted by SST (Fig. 1) being westerly flow along 40°N and a low pressure over the Aleutians.
The Principal Estimation Patterns for the four interesting cases of SLP predictabili ty are shown in Figs. 5--8. The SST to SLP patterns are similar for both summer and autumn data, the patterns of summer SLP to autumn or winter SLP differ markedly.
6 0 °
4 0 °
60 =
40 =
2 0 ° 2 0 =
1 8 0 = 1 6 0 = 1 4 0 = 1 2 0 = 1 0 0 = w
Fig. 7. As Fig. 5 fo r October SST predict ing w in te r SLP. The SST pat tern very much resembles the SST da tum for Ju ly SST predict ing au tumn SLP and the SLP est imand is similar, w i th somewhat stronger wester ly f l ow along 40 'N.
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60 °
-Imb 40 ° 40 ° _Omb~~ 2 0 ° - 20 °
I I I I I 1 I 180 ° 1 6 0 ° 1 4 0 ° 1 2 0 ° I O 0 ° W
Fig. 8. As Fig. 6 for May- - Ju ly average SLP pred ic t ing winter SLP. The SLP p a t t e r n (l ight isobars s~para ted by 0.5 m b ) is a low a r o u n d 40°N, 140°W. The pred ic ted win te r SLP anomaly , s imilar to t h a t of Figs. 5--7, is d o m i n a t e d by a low over the Aleut ians .
Attempts were made to explain these examples of predictability in terms of models in which the present state of SLP and SST as the sum of a predict- able part determined by prior SST and SLP anomalies plus an unpredictable part. The results are not conclusive but it appears that any such model must include active transfer in both directions between SLP and SST. It is, how- ever, entirely possible that neither SST nor SLP plays a dynamically signifi- cant role in determining subsequent SLP. Thus, both the SST and SLP pat- terns allowing predictability and the subsequent SLP anomalies they predict may be passive responses to some external effect.
4. CONCLUSIONS
The search for statistical models which allow predictability of North Pa- cific SLP leads to results interesting both in the context of methodology and with regard to short term climate variability.
Of fundamental importance is the fact that any body of data can be used to test only a limited number of hypotheses. Testing many hypotheses is equivalent to building prediction models with large numbers of candidate- data parameters. The unavoidable sampling errors in testing such models will inevitably lead to inconclusive results, strongly dependent on the sampling errors themselves. Thus hypotheses should be formulated on firm dynamical grounds, tested in comprehensive dynamical models and finally compared with statistically derived pictures of recurrent development. Various tech- niques for deriving such pictures of recurrent development are available but they can rarely determine the underlying mechanisms. Rather they result
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only in descriptions of those developments which are recurrent more than is expected by chance.
Of physical interest are the following conclusions which pertain to SST! SLP anomalies in the mid-latitude North Pacific:
(1) The only detectable pattern of SST/SLP connection which occurs throughout the year is one of the atmosphere leading the ocean.
(2) Significant predictability of SLP anomalies in autumn and winter is obtained using as data either SST anomalies three months prior or SLP anomalies in the summer.
(3) If the recurrent patterns of SLP development result from dynamical influences of the prior SST or SLP then the observations are consistent only with connections from both fields; neither can be the sole influence.
It is unfortunate, but the statistical models which show fairly conclusively that there is true predictability intrinsic to the SST/SLP system can probably not produce very useful forecasts. This is so because achievable forecast skill is expected to be less than the intrinsic true skill by the artificial hindcast skill. With the available 30-year records this reduction means that achievable forecasts can probably predict less than 10% of the anomalous SLP variance. It is hoped that efforts underway to extend the historical record backward in time can provide the additional realizations required to allow achievable forecast skill to approach the estimated intrinsic true skill, which for predic- tion of winter SLP anomalies from both SST and SLP is greater than 25%. A skill of 25% corresponds to a prediction--observation correlation of 0.5.
REFERENCES
Davis, R.E., 1976. Predictability of sea surface temperature and sea level pressure anom- alies over the North Pacific, J. Phys. Oceanogr., 6: 249--266.
Davis, R.E., 1977a. Techniques for statistical analysis and prediction of geophysical fluid systems. J. Geophys. Astrophys. Fluid Dyn., 8(4): 245--277.
Davis, R.E., 1977b. Predictability of sea level pressure anomalies over the North Pacific Ocean. J. Phys. Oceanogr., 8(2): 233--246.
Lorenz, E.N., 1956. Empirical orthogonal functions and statistical weather prediction. Report 1, Statistical Forecasting Project, MIT Dept. of Meteorology.
Namias, J., 1975. The collected works of J. Namias. University of California, San Diego, 1975.
Namias, J., 1976. Negative ocean--air feedback over the North Pacific in the transition from warm to cold seasons. Mon. Weather Rev., 104: 1107--1121.