THE RESPONSE OF A SIMPLE MODEL ATMOSPHERE TO SEA SURFACE

TEMPERATURE ANOMALIES IN THE NORTH PACIFIC

BY

Zeda Xing

A thesis submitted to the Faculty of Graduate Studies and Research in partial fulfillment of the requirements for the degree of

Master of Science

Department of Atmospheric and Oceanic Sciences McGill University, Montreal, Canada

June, 1997

Copyright @by Zeda Xing, June 1997

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Abstract

The responses to positive and negative sea surface temperature (SST) anomaiies

in the North Pacific are computed with a time-dependent, quasi-geostrophic, global

spectral mode1 with a T21 horizontal resolution and three Ievels in the vertical. The

sirnplicity of the model allows a large number of cases starting from different initial

conditions to be run. The model produces on average a ridge (low) downstream

of the warm (cold) SST anomdy, but the average response to the warm anomaly

is much weaker and statistically less significast than that to the cold anomaly. In

the case of the warm SST anomaiy, the s t o m track is displaced northward into the

high-pressure atmospheric anomaly, whereas in the case of the cold SST anomaly, the

storm track is moved southward, away from the atmospheric low-pressure anomdy.

The higher level of atmospheric nonlineazity in the wann cases leads to more case-

tecase variability in the model response to the SST anomaly than for the cold SST

anomaly. The resdts are compared with those of previous work in the literature

where the response of a GCM to a w m SST anomdy was found to be weaker and

st at ist icdy less significant t han that to a cold anomaly.

Résumé

Les réponses à des anomalies positives et négatives de la température à la sur-

face de la mer (TSM) du Pacifique Nord sont cdculées à l'aide d'un modèle quasi

géost rophique, global, spectral de résolut ion horizontale T2 1 à trois niveaux. La

simplicité du modèle permet la simulation d'un grand nombre de cas partant de

conditions initiales différentes. Le modèle produit une crête (dépression) en aval

d'une anomalie positive (négative) de TSM, mais la réponse à l'anomalie positive

est en moyenne beaucoup plus faible et statistiquement moins significative que celle

à l'anomalie aégative. Pour l'anomalie positive de TSM, la trajectoire des tempêtes

se trouve plus au nord dans l'anomalie de haute pression, tandis que pour l'anomalie

négative de TSM, la trajectoire des tempêtes est déplacée vers le sud, plus loin de

l'anomalie de basse pression. La nonlinéarité de l'atmosphère est plus importante

pour le cas chaud, ce qui produit plus de variabilité dans les réponses que pour le

cas froid. Les résultats sont comparés avec ceux d'autres études où la réponse d'un

modèle de circulation générale (MCG) à l'anomalie positive de TSM était plus faible

et statistiquement moins significative que celle à l'anomalie négative.

Acknowledgment s

I would like to thank my supervisors, Professors Jacques Derome and Charles Lin,

and post-doctoral fellow, Dr. Hai Lin, for their

researdi. Their supervision, encouragement and

appreciated.

1 am grateful to Dr. Ruping Mo, who gave

wi t h the word processor.

constant guidance t hroughout this

invaluable assistance are genuinely

me valuable advice and helped me

1 am indebted to Dr. Franco Molteni for making his three-level quasi-geostrophic

mode1 available.

Special thanks go to my family, my friends, and other students for their encour-

agement and moral support.

This research was funded by the Natural Sciences and Engineering Research

Council and the Atmospheric Environment Service of Canada.

Contents

Abstract

Résumé

Acknowledgments iii

List of Figures

1 Introduction

1.1 Mechanisms responsible for interannual seasonal variability in the

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . atmosphere 1

. . . . . . . . . . . . . . . . . . . . . . . . 1.2 Hypothesis and motivation 4

. . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Previous related studies 6

2 Model description and experimental design

. . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Mode1 description 11

. . . . . . . . . . . . . . . . . . . . 2.2 Sea surface temperature anomdy 15

. . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Experimentd setup 17

3 Results 24

. . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Themodelclimatology 24

. . . . . . . . . . . . . . . 3.2 500 hPa height response to SST anornaly 25

. . . . . . . . . . . . . . . . . . . . . . . 3.3 Significance of the response 35

. . . . . . . . . . . . . . . . . . . . 3.4 The heat flw at air-sea interface 45

. . . . . . . . . . . . . . . . . . . . . . . 3.5 Transient activity difference 50

4 Conclusion

Reference

List of Figures

a)Anomalous 700 hPa height in the cold minus control case. The

contour interval is 10 m. b)The t-statistics corresponding to Fig.

l . la [Ekom Pitcher et al. (1988)l. . . . . . . . . . . . . . . . . . . . . .

a)Anomalous 700 hPa height in the w m minus control case. The

contour interval is 10 m. b)The t-statistics corresponding to Fig. 1.2a

[from Pitcher et al. (1988)l. . . . . . . . . . . . . . . . . . . . . . . .

Schematic representation of the SST anomaly. ( T ) as a function of

latitude (9). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

a) Cold SST anomaly in the North Pacific ; b) Total SST distribution

. . . . . . . in the negative anomaly case. The contour interval is 2K.

a) Warm SST anornaly in the North PaQfic ; b) Total SST distribution

. . . . . . . in the positive anomaly case. The contour intenml is 2K.

Schematic representation of the experiments. A single overbar de-

. . notes tirne averaging and a double overbax is an ensemble average.

2.5 An example of 500 hPa height at day 31. The contour interval is 50

m. The height shown is the deviation from the area-averaged 500 hPa

height. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.1 500 hPa streamfunction from observations averaged for nine winters

from ECMWF data. The contour interval is 5 x 106m2s-'. [From Lin

(1995)l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.2 Stremfimction at 500 hPa averaged for the 200-winter integrations

. . . of the mode1 control m. The contour interval is 5 x I06m2s". 27

3.3 Observed 500 hPa zona1 wind averaged for nine winters from ECMWF

data. The contour interval is 5 m/s. . . . . . . . . . . . . . . . . . . . 28

3.4 Zona1 wind at 500 hPa averaged for the 200-winter integrations of the

mode1 control run. The contour interval is 5 mis. . . . . . . . . . . . 29

3.5 Anomalous 500 hPa height in the cold SST minus control case. The

contour i n t e d is 5 m. . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.6 Anomalous 500 hPa height in the warm SST minus control case. The

contour interval is 5 m. . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.7 Ensemble average 500 hPa height differences between two control

mns. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.8 The statistical significance of the change in the 500 hPa height field

in thecold case. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.9 The statistical significance of the change in the 500 hPa height field

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . in the wasm case. 40

3.10 The averaged statistical significance of the change in the 500 hPa

. . . . . . . . . . . . . height field for 50 integrations in the cold case. 41

3.11 The averaged statistical significance of the change in the 500 hPa

. . . . . . . . . . . . height field for 50 integrations in the warm caae. 42

3.12 The averaged statistical significknce of the change in the 500 hPa

. . . . . . . . . . . . . height field for 20 integrations in the cold case. 43

3.13 The averaged statistical significance of the change in the 500 hPa

. . . . . . . . . . . . height field for 20 integrations in the wasm case. 44

3.14 Heat Aux at the seasurface averaged for 200 integrations in the control

. . . . . . . . . . . . . . . . . . run. The contour interval is 50W/m2. 46

3.15 Climatological heat flux (sensible plus latent heat) nt the sea surface.

The contour interval is 50W/m2. [from Esbensen and Kushnir (1981)] 47

3.16 a)The averaged sir-sea heat flux in the cold case. b) The heat fiw

difference between the cold and control nuis. The contour interval is

. . . . . . . . . . . . . . . . . . 50W/m2 for a) and 10W/m2 for b). 48

3.1 7 a)The averaged air-sea heat flux in the warm case. b) The heat flux

difference between the warm and control rus. The contour intervals

. . . . . . . . . . . . . . . . are 50W/m2 for a) and 10W/m2 for b). 49

3.18 Simulated air temperature anomaly (solid) and climatological mode1

streamfunction (dashed) at 650 hPa in the wasm case. The contour

interval is 5 x 10~rn~s" for the streamfunction and 0.2K for the tem-

perature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

3.19 Simulated air temperature anomaly (solid) and climatological mode1

stredunction (dashed) at 650 hPa in the cold case. The contour

interval is 5 x 106m2s-' for the strearnfunction and 0.2K for the tem-

perature. . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 52

3.20 Transient activity difference between wann and cold runs. The con-

tour interval is 2.5 m. . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

Chapter 1

Introduction

1.1 Mechanisms responsible for interannual sea-

sonal variability in the at mosphere

An improvement in our understanding of the processes responsible for interannual

fluctuations in the mean seasonal atmospheric states will be necessary if more use-

lu1 mem-seasonal predictions are to be achieved. Two mechonisrns accounting for

the int erannud variation of the ext rat ro pical mean-seasonal at mosp henc circulation

have been discussed recently. The first involves some extemal forcing such as anorna-

lies in the sea-surface temperature (SST) or in the land or ice conditions. Anomdous

ocean forcing can generate significant va.riability in the atmosphere on a seasonal

time scde. In particular, the Pacific/North ~ r n e r i c & ( ~ ~ ~ ) teleconnection pattern

has often been found to chaxacterize the midlatitude response to a warm equatorial

Pacific ocean in model studies (Shukla and Wallace 1983; Cubasch 1985; Lau 1985).

A theoretical explanation for the linkage between tropical SST anomalies and the

PN A pattern was provided by atmospheric Rossby wave energy dispersion ( Hoskins

and Karoly 1981; Branstator 1985). There has been much interest in recent years in

understanding the air-sea interaction in midlatitudes. By removing the component

of the observed extratropical variability that is dependent on ENS0 (El Niiio South-

ern Oscillation), Zhang et al. (1996) demonstrated the remarkable resilience of the

linear relationship between the North Pacific SST anomalies and the PNA pattern

in the hernispheric 500 mb height field. Similarly, recent observational studies by

Wallace and Jiang (1987), Iwasaka et al. (1987), and Wallace et al (1990, 1992)

have shoivn that the atmospheric circulation anomalies in the P X 4 sector exhibit

a high correlation with SST anomalies in the North Pacific, exceeding that with in

the tropical Pacific anomalies.

Teleconnection patterns with a monthly or seasonal time scde can also be

in part a consequence of dynamical processes operating within the atmosphere it-

self, i.e., due to interna1 dynamicd processes. This is supported by the results of

Lau (l98l), who obt ained realistic teleconnection patterns with a general circula-

tion model with no time-dependent external forcing other than the annual cycle.

Significant low-fiequency (periods longer than about 10 days) vaziations can aiso be

produced in atmospheric models with no variations in the externd forcings (e.g.,

Robinson 1991; Hendon and Hartmann 1985). Since the midlatitude atmospheric

flow is nonlinear, the internal dynamics due to instabili ty and non-linear interactions

arnong different scales of motion c m produce low-fiequency atmospheric variabil-

ity. For example, the interaction between low-and high-frequency transients was

found to be an important mechanism for the maintenance of local maxima in the

low-frequency vanability (Sheng and Derome 1993). A number of studies have con-

cluded that the mean-seasonal PNA anomaly pattern can be induced and maintained

by transient eddy forcing in linear models (Kok and Opsteegh 1985; Held et al. 1989;

Hoerling and Ting 1994; and Ting and Hoerling 1993). The observational study by

Klasa et al (1 992) clearly shows that the synoptic-scale eddies play a crucial role in

the maintenance of the mean-rnonthly PNA pattern.

The relative importance of the internal dpamics and exterrial forcing in

governing the low-frequency variability in the atmosphere is of crucial importance

in the predicability of the extratropical atmospheric variabilit-y. The potentidy

predictable part of the low-fkequency variability (and in particular the interannual

vaziability) is more likely controlled by the extemal forcing, while the "natural"

variability caused by internal processes is probably unpredictable. It would thus be

of considerable interest to detennine the conditions under w hich internal processes

are relatively unimportant, in which case the flow is more dependent on the exterrial

forcing and thus potentially more predictable.

1.2 Hypothesis and motivation

Lin and Derorne (1997) used observational data to study the difference in the at-

mospheric interna1 dynarnic processes between winters wit h a positive time-meas

PNA index and those with a negative time-mean index. The PNA index is defined

following Wallace and Gutzler (1981) as

1 PNA Index = -[z'(20° N, 160° W ) - z*(45*N, l6S0W)

4

+rœ(55" N, 115' W ) - z*(30° N , 85" W ) ] ,

where z' representa normalized height anomalies. The positive (negative) PNA index

is associated with negative (positive) height anomalies over the North Pacific and

Florida and positive (negative) height anomalies over Hawaii and Alberta. Their

results motivated the hypothesis underlying this thesis. During winters with an

enhanced time-mean positive PNA pattern, the transient eddy activity was found to

be reduced over the North Pacific, especidy for the transients with periods from 10

to 90 days. Two expianations were provided for this reduced low-frequency activity.

Firstly, there is a weaker kinetic energy transfer from the lazge-scale seasonal mean

flow to the low fiequency eddies. Secondly, there is reduced synoptic-scale eddy

forcing of the low-frequency flow due to a strong seasonal-mean Aleutian low which

is a stnking feature in the geopential height dunng positive P N A winters. The

latter tends to keep baroclinic synop tic-scale eddies moving dong its sout hem Bank,

and this sout hward deflection of the baroclinic eddies results in a weak interaction

with the low-frequency eddies over the North Pacific. Recall that part of the low-

frequency activity due to the intemal dynarnics has been identified earlier as being

an unlikely predictable part of interannual variability. Lin and Derome's results

thus suggest that the atmospheric response to an external SST forcing would be less

influenced by low-frequency eddies over the North Pacific during a season with a

positive PNA pattern. In this case, the low-frequency activity is reduced and there

might thus be more predictability of the time-mem forced anomaly. Chen and Van

Den Do01 (1995) had formulated the same hypothesis based on their analysis of

North Pacific pressure anomalies. They had also Found that winter months with a

low-pressure anornaly in the North Pacific exhi bi ted a lower level of t ransient eddy

activity in that region than winter months with a high pressure anomaly.

The above suggests the following hypothesis: An external forcing that pro-

duces a low-pressure anomaly over the North Pacific (as during the positive PNA

phase) should lead to a iower-than-normal level of transient eddy activity over the

North Pacific, and hence to a higher-amplitude, more predictable atmospheric re-

sponse than an externd forcing which produces a high-pressure anomaly with a

higher level of transient eddy activity in the North Pacific. We do not restnct our

attention to positive ând negative PNA conditions, as in Lin and Derome (1997).

We consider instead a broader class of flows, namely, those which due to some forc-

ing have a low or high pressure anomaly over the North Pacific. The goal of this

thesis is to test the above hypothesis.

1.3 Previous related studies

There are two related previous studies which are particularly relevant. Cubasch

(1985) investigated the European Centre for Medium-Range Forecasts (ECMWF)

GCM response to tropical El NifiofLa Niiia SST anomalies. To estimate the degree

of linearity of the response to an SST anomaly, half of the experiments were carried

out with positive equatorial SST anomalies in the eastem Pacific, and the other half

wit h the corresponding negative anomalies. A significant P N A-like response was

found in the extratropical Northern Bemisphere when positive SST anomalies were

imposed. On the other hand, experiments with SST anomalies of equal amplitude

but of opposite sign did not yield a statisticdy significant response over the North

Pacific. Lin (1995) gave a possible explanation of Cubasch's findings. With a pos-

itive PNA response, or negative geopotential anomaly over the North Pacific, the

atmosphere is forced to a state with less transient activity. On the other hand, with

a positive geopotential anomdy over the North Pacific, the generd circulation may

be forced towards a state where more kinetic energy is converted from the mean flow

to the Iow-frequency t ransients, wit h more interaction between t h e high-and low-

fiequency eddies. In the latter case the atmospheric internai nonlinear processes

may be too strong to yield a significant time-mean forced response.

Unli ke Cu basch who st udied the at mospheric response to tropical SST anoma-

lies, Pitcher et al. (1988) investigated the sensitivity of the NCAR GCM to SST

anomalies in the North Pacific. They chose observed SST anomalies, with negative

anomalies near the dateline and positive anomalies off t h e North American west

coast. A series of 1200-day integrations were carried out in which this basic anomaly

was multiplied by Il and f 2. The model response to the basic anomaly and to

twice its value was a PNA pattern. However, the response to the basic anomaly

multiplied by -1 and -2, Le., with a positive anomdy near the dateline and a nega-

tive one of the North Arnerican west coast, was not statisticaily significant over the

North Pacific. Fig. 1.1 shows the model response to the basic cold SST anomdy

and its t-statistic. In their study, the response is significant at the 95% significance

when the t-statistic exceeds 2.15. The corresponding results for the warm anomaly

are shown in Fig. 1.2. Palmer (1988) commented on Pitcher et al.'s results, arguing

that with positive SST anomalies in the North PacXc, the general circulation wodd

be forced towards a less barotropically stable state where the intemal variability

ternal variability may be too large to give a significant response to the extemal SST

forcing. This is similar to Lin's explmation of Cubasch's results described earlier.

In this thesis, we present resuits which confirm the previous tentative suggestions.

This thesis is orgonized as follows. The model description and experimental

design are described in Chapter 2. The results are presented in Chapter 3 including

the model climatology, the 500 hPa height response to cold and warm SST onornalies,

t heir significance and the difference in the level of transient activity between the cold

and warm SST cases. The conclusions are given in Chapter 4.

Fig l.la

Fig 1.lb

Figure 1.1: a)Anomalous 700 hPa height in the cold minus control case. The contour

intetval is 10 m. b)The t-statistics correspondhg to Fig. 1. la [from Pitcher et al.

(isss)].

Fig 1.2a

Fig t .2b

Figure 1.2: a)Anomalous 700 hPa height in the warm minus control case. The

contour interval is 10 m. b)The t-statistics correspondhg to Fig. 1.2a [Eiom Pitcher

et al. (1988)l.

Chapter 2

Model description and

experimental design

2.1 Model description

The model used in this study is Marshall and Molteni's (1993) spectral, three-level

quasi-geostrophic model rnodified with the addition of a heat flux at the sea-air

interface. This model has a global domain and pressure as the vertical coordinate.

The series of spherical harmonies used in the representation of the streamfunction

has a tnmgular tmcation at total wavenumber 21 (T21). The prognostic equations

for the quasi-geostrophic potential vorticity at 200, 500 and 800 hPa have the foxm

&i - = -J(+i,qi) -Di + F i +Q, dt (2.1)

where q is the potential vorticity, + the strearnfunction, D o linear operator thôt

represents dissipative terms, J the Jacobian, F the forcing term and Q is propor-

tional to the sensible and latent heat flux at the ocean-atmosphere interface. The

index i=l, 2 or 3 refers to the 200, 500 and 800 hPa pressure level. The diabatic

heating resulting from the heat flux at the air-sea interface is applied to the 500-800

hPa layer only, the lowest layer where the t hennodynamic equation applies.

The potential vorticity is defined as:

where f = tasin4 , Ri (=700km) and R2 (=450km) are the Rossby radii of defor-

mation for the 200-500 hPa layer and the 500-800 hPa layer, respectively. h is the

orographic height and Ho a scde height (set to 9 km).

The dissipative terms Di, 4 and 4 represent the effects of Newtonion relax-

ation of temperature, a linear drag on the 800-hPa wind and a horizontal diffusion of

vorticity and temperature. The temperature relaxation has an e-foldlng time scale

of 25 days. The linear drag damps the low-level wind on a spindown time scde

of 3 days over the oceans, about 2 days over low-latitude land and 1.5 days over

mountains above 2 km. A strongly scale-selective horizontal diffusion in the form of

cd v8 qi damps total wavenumber 21 on a 2-day timescale.

The potentid vorticity forcing terms Fi, Fa and F3 are computed from ob-

servations, as follows. Averaging equation (2.1) over time, we get

where i=l, 2, 3, ond the overbar represents the time average. One would expect the

average potential vorticity tendencies to be negligibly small over a significantly long

period of observations. Therefore, the extemal forcing can be obtained through:

The Fi fields were computed h m the daily (12 GMT) analyses of the ECMWF

at the three pressure levels for a period of 9 winter seasons from 1980/81 to 1988/89,

where winter is defined as December, January and February. The time average of

- the Fi fields was then computed and & = Fi was assumed in (2.1), that is, a time-

independent forcing was used.

The ocean-to-atmosphere sensible and latent heat flux term takes the form

where vaoo is the horizontal wind speed at 800 hPa, T8 the sea-surface temperature

and TeEO the air temperature at 650 hPa. A value of 20°C is added to to yield

an approximation to the air temperature near the sea surface; this is needed as the

mode1 has only three vertical levels. The exchange coefficient a is determined from

the climatological sensible and latent heat flux Q, as shown below.

The air-sea heat flux Q is taken from Esbensen and Kushnir (1981). and

are obtained from the daily ECMWF horizontal wind (u, v ) data over a period

of 9 winter seasons as follows. The strearnfunction is obtained from the vorticity

through the equatioo: v2z,b = - - s, and then converted to geopotential

height when the latter is needed to compute Tao using the hydrostatic equation.

The wind speed Vm is obt ained directly from the streamfunction. and TeS0 are

calculated doily fiom the observational data for 9 winter seasons and then averaged

in (2.8). The climatological distribution of the SST (T,) is taken from Esbensen and

Kushnir (1981).

2.2 Sea surface temperature anomaly

The SST anomaly used in this study has the following functiond form:

Here A is longitude and q5 latitude; A is the amplitude of the SST anomaly and

Ao, are the central longitude and latitude of the anomaly respectively. L, is the

longitudinal scale and L, the meridional scde. Wit h this Gaussian distribution, the

anornaly pattern is a reasonable representation which decreases exponentially in two

dimensions.

The two parameters in (2.9) L, and L,, provide the longitudinal and merid-

ional scales. As shown in Fig. 2.1, the anornalous SST is reduced to e-' of its

amplitude at a distance L, = dd - applying the same idea to the longitude

dimension, L, = Ad - JO. A meridional scale L, = 15' and a longitudinal scale

L, = 20' are used for the anomdy.

The central position of the SST anornaly, A. and $0, is set to 170°W,45*N.

As the mode1 is quasi-geostrophic and is not meant to simulate tropical dynarnics,

we restrict our attention to a mid-latitude anornaly. The amplitude of the anomdy

is set to a large value of f lOK. It is much larger than observed anomalies associated

with interannual Mnability which is of order 1 - 2K. A strong forcing is imposed so

Figure 2.1: Schematic representation of the SST anomaly. ( T ) as a function of

latitude (O).

that the forced response can be unambiguously identified from weather noise.

The SST anomdy imposed over the climatological distribution takes the form:

In the mode1 calculation, the anomaly field is mapped to a Gaussian grid before

conversion to spectral coefficients.

The total SST field (Ts) is thus

where Tc is the ciimatological SST.

The cold and warm anomalies are shown in Fig. 2.2a and Fig. 2.3a respec-

tively. The corresponding total SST distribution in the cold and waxm cases c m be

seen in Fig. 2.2b and Fig. 2.3b.

2.3 Experimentalsetup

To demonstrate clearly the effect of the SST anomalies on the meon seasonal flow,

the following approach is used. Three series of uperpetual winter " integrations axe

performed with the external forcing Fi obtained fiom winter observations: without

Fig 2.2a

Fig 2%

Figure 2.2: a) Cold SST anomaly in the North Pacific ; b) Total SST distribution

in the negative anomaly case. The contour interval is 2K.

Fig 2.3a

Fig 2.3b

Figure 2.3: a) W m SST anomaly in the North Pacific ; b) Total SST distribution

in the positive anomaly case. The contour interval is 2K.

an SST anomaly, with a positive and with a negative SST anomaly. For output

and display purposes the model streamfunction output is converted to geopotential

height using the linear balance equation with latitude dependent Coriolis parameter:

4 = f d

Fig. 2.4 shows a summary of the experiments. Model integrations are labeled

as "control mn" and "perturbed mnn. The control run is integated using the

climatological SST and the perturbed run using the anomalous SST, which is the

climatological plus or minus the anomaious SST. In each case, a 120-day integration

is performed with the fint 30 days as the spin-up. After the initial spin-up period,

model output data are saved once per day for 90 days. To evaluate the robustness of

the results, itatisticdy independent integrations in each run are created by adding

smd-amplitude random numbers to the initial conditions. These runs axe denoted

as 1 + ci in Fig. 2.4. The JO-day spin-up is long enough to allow the initial noise to

grow so that the subsequent model states are independent of each other. In the nuis

with an SST aomaly the 30-day spin-up period also d o w s the model to adjust to

the perturbed SST forcing.

As the mode1 is computationdy efficient, a large number of experiments c a n

be performed to ensure the significance of the response. In fact, 200 integrations

were done for each of the control and perturbed nuis. In other words, 200 slightly

different initial conditions were used to simulate the response.

Control Run Perturbed Run

(with climatological SST) 1 (with anomdous SST)

Figure 2.4: Schematic representation of the experiments. A single overbar denotes

time ilveraging and a double overbax is an ensemble average.

Fig. 2.5 provides an example of the 500 hPa height a t day 31 for a typicd

control run experirnent. A realistic winter atmospheric state is obtained, with pre-

vailing westerlies in the middle and high latitudes, a planetary scale trough over the

east coast of Asia and North America and synoptic scale wave perturbations.

Ensemble averages of the control and perturbed run experiments and their

difference were calculated to obtain the response to the anornalous SST on the

mean-seasonal atmospheric circdation. The statistical significance of the difFerence

between theensemble averages was dso computed using the Student's t-test. Finally,

the level of transient activity was calculated to explain the mechanisms accounting

for the stability or predictability of the mode1 response to the SST anomaly.

Figure 2.5: An example of 500 hPa height at day 31. The contour interval is 50 m.

The height shown is the deviation from the area-averaged 500 hPa height.

Chapter 3

Results

3.1 The model climatology

As our mode1 is based on the quasi-geostrophic equations, we focus our attention

on the results north of 20°N. The set of 200 control run experiments shown in Fig.

2.4 serves as a reference state. It is important to veri& the model climatology. The

latter is obtained by averaging the model output over days 31-120 of each experi-

ment to obtain winter averages, and then ensemble averaging over the 200 control - -

integrations to get Z2ao. Figs. 3.1 and 3.2 compare the observed and simulated

mean 500 hPa streamfunction fields for the Northern Hemisphere. The model cli-

matology generdy agrees with that observed, although the amplitude of the model

East Asian trough is weaker and the North European trough is stronger than their

O bserved counterparts.

Not only are the large-scale troughs in the midtroposphere simulated by the

model, but also the low-frequency eddies and t h e synoptic-scale transients were sim-

ilarly well reproduced (Lin 1995). Lin's version of the model did not have an air-sea

heat flux at the lower boundary, and he found that the distribution of the simulated

low-and high-frequency height variance is in general agreement with observations.

In our case, Figs. 3.3 and 3.4 show the observed and sirnulated seasonal average

zond wind pattern at 500 hPa. Even though there are differences between the model

results and the observations, the overall agreement is qui te good.

3.2 500 hPa height response to SST anomaly

The ensemble mean 500 hPa height Merences between the perturbed and control

- - - nuis, - Zm, are given in Figs. 3.5 and 3.6. The former is for the cold SST

anomdy case, and the latter for the warm SST case.

For the cold SST case, Fig. 3.5 shows that the height anornaly mainly appears

over the North Pacific and the east coast of North America. There is a negative

anomaly over the North Pa&c at about 20' longitude downstream of the SST

anomdy, a weaker positive anomaly over the Beaufort Sea and another negative one

just east of Newfoundland. The two negative anomalies are linked to each other

Figure 3.1: 500 hPa streamfunction fiom observations averaged for nine winters

fiom ECMWF data. The contour interval is 5 x 106m2s-'. [From Lin (1995)]

Figure 3.2: Streamfunction at 500 hPa averaged for the 200-winter integrations of

the mode1 control m. The contour interval is 5 x 106m2s'1.

Figure 3.3: Observed 500 hPa zonal wind averaged for nine winters from ECMR'F

data. The contour interval is 5 mis.

Figure 3.4: Zona1 wind at 500 hPa averaged for the 200-winter integrations of the

mode1 control run. The contour interval is 5 m/s.

Figure 3.5: Anomalous 500 hPa height in the cold SST minus control case. The

contour interval is 5 m.

Figure 3.6: Anomalous 500 hPa height in the warm SST minus control case. The

contour in te rd is 5 m.

aad do not separate as clearly as found in other studies (Cubasch, 1985; Pitcher et

al., 1988). This zona1 comection is due to a more northerly displacement of the

positive anomaly to the Beaufort Sea in our study; Pitcher et al. (1988) obtained a

strong positive anornaiy over western Canada instead. The response is strongest in

the North Pacific. The anomaly pattern does not closely resernble that of Pitcher

et al. who obtained a PNA teleconnection pattern. We note that not only are the

models used in the two studies different, but the location and shapes of the SST

anomalies are also different, thus a close match between the two responses should

not be expected.

As in several previous studies, we use two SST anomalies of different signs to

increase the understanding of the model response. An immediate question raised is

the lineaxity of the model response to forcing of opposite signs. The 500 hPa height

anomaly for the warm SST anomaly is shown in Fig. 3.6. Hoskins and Koroly (1981)

assumed in their experiments that the effect of the anomaly in the rnidlatitudes is

linear to a first approximation. This implies that a positive anomdy produces a

wave train with a reversed phase compared to a negative anomaly. This is to some

extent consistent with Figs. 3.5 and 3.6. The height anomalies in the warm and cold

cases are reversed with respect to each other with some displacement in location, and

some difference in the amplitude. The wamn (cold) SST anomaly produces a high

(low) pressure onomdy downstrearn. The amplitude of the warm anomaly is only

half of that of the cold anomdy. We wiIl return to this manifestation of nonlinearity

in the model response in the following section. In Pitcher et al. (1988), the cold

SST anomaly led to a significant low pressure anomaly in the response, whereas the

warm anornaly did not produce a significant response. This trend is also found in

our study, in that the waxm aaorndy produced a weaker response. The latter is

also more difFused than the former. For example, Fig. 3.6 shows the positive height

anomaly not only appears in the North Pacific and North America, but a broad

positive anomaly is also Eound over Russia. These anomalies form a planetary scale

belt at midlatitude, md the low anomaly centre is displaced northward to the pole.

In order to show that the height anomalies are generated by anomalous SSTs

and not by chance, mother experirnent was done. The mode1 was rerun with cli-

matological SSTs, but this time another set of randorn numbers was imposed at

the beginning of the integrations. The ensemble average 500 hPa height differencm

between this second control ensemble and the first control ensemble provides a mea-

sure of the uncertainty in the model climatology. This ciifference is shown in Fig.

3.7; we see a s m d and nondescript anomdy pattern. This result demonstrates the

significance of the model response to the anomalous SST forcings. The forced re-

sponses do stand out from noise and the model climatology is sufficiently stable to

be a reference atmospheric state.

Figure 3.7: Ensemble average 500 hPa height differences between two control nuis.

3.3 Significance of the response

In each of the 200 runs that we have performed with an SST anomaly of a given

sign, transient disturbances interact with the forced anomaly. Because of the chaotic

nature of the flow, these transient disturbances are not predictable for more than

approximately two weeks. This means that in each run the transient disturbances

evolve differently and influence in a different way the response to the SST anomaly.

Consequently different runs produce somewhat different forced anomalies. Similarly,

in the unforced (control) runs, the differences in the initial conditions lead to different

flow evolutions. The question then &ses: " What are the chances that a given control

run could differ from the control climatology by as much as a forced run does?" In

other words, is it not possible that the differences we observe between the forced

and control nuis is just happening by chance, that it could be observed also with

unforced runs alone? If instead of comparing an individual run with the control

climatology, we compare the average of an ensemble of n runs with the control

climatology, we will find that, as n increases, the ensemble average of the n control

runs will converge to the control climatology. This was seen in the previous section.

However, the ensemble average of the n forced runs may be significantly different

from the control climatology; the difference is precisely the forced signal. In that

case we can be confident that the clifFerence between the ensemble mean of the forced

nuis and the climatology represents the forced response and is not the result of a

With a h i t e number of ensemble members n which is srnalier than 200 (say

10, 20 or 30), it is not clear what the chances are of finding an unforced ensemble

average that differs from clirnatology by as much as the forced ensemble average.

To examine this question we use the Student's t test, which provides a measure of

confidence that the forced response could not have &sen by chance, i.e., it could

not have been observed using the unforced nuis alone as a result of the natural

variability of the model.

Figs. 3.8 and 3.9 give the statistical significance of the change in the 500 hPa

height field for the cold and warm cases, respectively. They show the responses are

significant for both cases since the high significance regions correspond well with

the height anomalies shown in Figs. 3.5 and 3.6, except for the anomalies in the

polar region. Thus a significant response to the altered SST is obtained, whether

the latter is positive or negative, at least when a very large number of cases (n=200)

are m. We note that in practice GCMs cannot in general be nui for as many cases

as for our simple QG model. We thus examine t h e significance levels for s m d e r

ensembles. With the assumption that in a GCM simulation experiment, 50, instead

of 200, integrations are feasibh, we divided our 200 integrations into four sets of

50 integrations. The significance t-value in each set was calculated and the four t-

values were averaged. Figs. 3.10 and 3.11 show this averaged statistical significance

of the height anomalies for the set of 50 integrations. Corresponding to a strong

low height anomaly during the cold case, a broad high significance region covers the

North Pacific, while a much smdler significant response is found for the warm case.

If the sample number of integrations is further reduced to 20, the difference

between warm and cold mns can be more clearly seen. Figs. 3.12 and 3.13 provide

the averaged statistical significance of the height anomalies for the set of 20 inte-

gations. As expected, the significance levels generally decrease and the significant

areas shrink in both cases. Nevertheless, the negative SST anomaly produces a sig-

nificant response in the North Pacific, where a strong low height anomaly is found.

In cornparison, Fig. 3.13 hardly shows any significant response area for the warm

case, particularly in the North Pacific where the high pressure anomaly produced

by warm SST anomaly is only about half as strong as that of the cold anomaly

(Fig 3.6). There is thus a difference in the significance levels between the mode1

responses to the opposite forcings.

Our results are consistent with those of Cubasch (1985) and Pitcher et al.

(1988). It would appear that the wave train in t h e case of the positive SST anornaly

is more influenced by the internai variability than that of the cold SST anomaly,

which leads a less significant mode1 response. This conclusion could not have been

drawn from Figs. 3.8 and 3.9. The inconclusive feature shown in Figs. 3.8 and 3.9

stems fiom the large number of samples involved. We can see this by inspection of

the definition of Student's t test:

Here xi, Yi are 500 hPa height of the perturbed and control run, respectively, at

a given grid point. s, y are the perturbed and control climatology. Ni, Nz are

the sample numbers (200 for the case of Fig 3.8 and 3.9) and es is a measure of

the combined standard deviation. The statistical significance value plotted in the

following pages is (1 - t)100%. For Ni = N2 = N >> 2, the fraction in the left part

of the formula (3.2) is half the sum of the variances of x and y and that sum can

be assumed not to change much as N increases. The factor (l/Nt + l/Nz) however

goes to zero and so does es. If 3 and remain nearly constant as N inneases, we

see that t gets large as N gets large.

Therefore, a sample of 200 is so large that highly significant results were ob-

tained for both the cold and warm cases. In fact, the huge sample number concealed

the essential difference of the response to the two opposite forcings which, however,

was detected by an approach with smaller sample numbers. In conclusion, the dif-

ference in statistical significance between the cold and warm experiments is more

easily detectable with a sample of moderate size.

Figure 3.8: The statisticd significance of the change in the 500 hPa height field in

the cold case.

Figure 3.9: The statistical significance of the change in the 500 hPa height field in

the warm case.

Figure 3.10: The averaged statisticd significance of the change in the 500 hPa height

field for 50 integrations in the cold case.

Figure 3.11: The averaged statistical aignificance of the change in the 500 hPa height

field for 50 integrations in the wôrm case.

Figure 3.12: The averaged statistical significance of the change in the 500 hPa height

field for 20 integrations in the cold case.

Figure 3.13: The averaged statistical significance of the change in the 500 hPa height

field for 20 integrations in the warm case.

3.4 The heat flux at air-sea interface

As the present study is concerned with the mode1 response to an anornalous SST, it

is relevant to examine the air-sea heat flux Q (see equation (2.7)). Fig 3.14 shows the

heat flux at the sea surface averaged over 200 winter integrations in the control run.

This heat flux distribution is reasonable, but the maximum heating over the Pacific

is displaced too far toward the equator compared to observed climatological heat

flux (sensible plus latent heat) as seen in Fig. 3.15 (Esbensen and Kushnir, 1981).

The averaged heat flux in the cold case and the heat flux difference between the cold

and control runs are shown in Figs 3.16 a and 3.16 b, respectively. Corresponding

to the cold SST anomaly, a reduced heat flux is found right over the anomalously

cold water. It is noteworthy that the heat flux difference between the warm and

control cases (Fig 3.17 b) is alrnost identical to the cold case except for a reversal

of sign. Given the results of the 500 hPa height response and its significmce, the

model seems to respond differently to the opposite SST anomalies even if the heat

source/sink have the same amplitude.

For a 10K SST anomaly, the oceanic heating rate to the whole atmospheric

column is calculated to be about 0.66K/day. This persistent heating throughout

the mode1 int egration should be bdanced by horizont ai cold advect ion or vertical

motion, otherwise the model would not be stable. Fig 3.18 shows the model air

d 60E 120E 180 120W BOW

Figure 3.14: Heat flux at the sea surface averaged for 200 integrations in the control

nui. The contour interval is 50W/m2.

Figure 3.15: Climatological heat flux (sensible plus latent heat) at the sea surface.

The contour interval is 50W/m2. [from Esbensen and Kushnir (1981)]

Figure 3.16: a)The averaged air-sea heat flux in the cold case. b) The heat flux

ciifference between the cold and control nuis. The contour intervd is 50W/m2 for

a) and 10W/rn2 for b).

Figure 3.17: a)The averaged air-sea heat flw in the warm case. b) The heat flux

difference between the warm and control runs. The contour intenmls are 50W/m2

for a) and 10W/m2 for b).

temperature anomaly (ensemble mean) and climatological strearnfunction at 650

hPa in the warm case. Cold advection prevails over the North Pacific where the

diabatic heating takes place. Likewise, for the cold case, Fig 3.19 shows that warm

advection tends to cornpensate the diabatic cooling over the North Pacific. The

vertical motion field was not saved dunng the integrations, so it is not possible

to comment on the role of the adiabatic cooling or wamning due to the vertical

advect ion.

Transient act ivity difference

In order to shed some light on why the mode1 responds differently to cold and warm

SST anomalies, we now examine the transient activity difference between the two

series of forced runs. Our measure of "transient activity" wili be

1 - - T.A. = [- C ( z i - ~ ) ~ ] ' f ~ ,

90 ,, where Z- is the t h e average (over 90 days) of 2, the 500 hPa height, and i is the day

index. In other word, T.A. is the temporal standard deviation of z at a fixed point

in space. We can then produce a map of T.A. for each r u and then compute an

average T.A. over the 200 control (or perturbed) runs. We are interested in seeing

whether the transient activity T.A. is affected by the presence of SST anomalies.

More precisely, we look at the difference in the transient activity (T.A.) between the

Figure 3.18: Simulat ed air temperat ure anomaly (solid) and climatological mode1

streamfunction (dashed) at 650 hPa in the warm case. The contour interval is

5 x 10~rn~s- ' for the streamfunction and 0.2K for the temperature.

Figure 3.19: Simulated air temperature anomaly (solid) and climatological mode1

streamfunction (dashed) at 650 hPa in the cold case. The contour intervol is

5 x 106m2s-' for the streamfunction and 0.2K for the temperature.

warm and cold ensembles. Fig. 3.20 shows this difference, that is, T.A. (ensemble

of cold runs) - T.A. (ensemble of wami runs). The magnitude of the difference in

the transients is about 1 / lOof that of the simulated transients themaelves.

Fig. 3.20 supports the hypothesis proposed in the Introduction. There is

a lower level of transient eddy activity over the North Pacific when a strong low-

pressure anomaly is generated by a cold SST anomaly, than when a weaker high-

pressure momdy is created by a warm SST anomaly of the same amplitude. The

lower transient activity in the cold case also suggests an expianation for the differ-

ence in the height anomaly amplitudes in the North Pacific and in the predictability

between these two cases. For the cold SST case, the weaker interna1 dynkmical

processes in the North Pacific, such as high and low frequency transients and the in-

teraction with the forced disturbônce, lead to a more stable, predictable atmospheric

response. In other words, when a low-pressure anomaly over the North Pacific oc-

curs, internd processes become relatively less important than in the case of a high

pressure anomaly corresponding to a w m SST anomaiy, and consequently the sea-

sonal mean flow is relatively more dependent on the external forcing and thus more

predictable.

Figure 3.20: Transient activity difference between warm and cold runs. The contour

interval is 2.5 m.

Chapter 4

Conclusion

In the present study, the response of a simple nonlinear model atmosphere to pre-

scr-ibed SST anomalies in the North Pacific was examined in an attempt to improve

our understanding of the air-sea interaction on seasonal time scales. The feedback

fiom the atmosphere to the ocean, while important for a complete understanding of

t h e ocean-atmosphere interaction, was ignored. The model response was also limited

by the simplicity of the model, e.g., it is a dry model which does not include the

release of latent heat. However, our intention was to sMpiiS the problern in order

t o better understand the clifference in the response of the model to cold and warm

SST anomalies in mid-latitudes. The model produces a w m high ( cold low) down-

stream of the wamn (cold) SST anornaly, but the response to the wamn anornaly is

much weaker and statisticdy lesa significant than that to the cold anomaly.

The present experiments offer an explanation of the results obtained in the

earlier studies of Cubasch (1985) and Pitcher, et al. (1 988). They found an asymme-

try in their GCM response with respect to the polazity of the SST anomaly pattern.

The asyrnmetry of the response was also found in our model. Our results show that

a cold SST anomaly in the North Pacific produces a low-pressure anomdy there as

in previous studies. This leads to less transient eddy activity over the North Pa-

cific cornpared to the case of a w m SST anomaly which produces a high pressure

atmospheric anomaly. The consequence is that the cold SST anomaly produces a

statistically more significant atmospheric response t han the warm anomaly.

There is a growing interest in the meteorologicd community in the possibility

of produchg useful seasonal forecasts. The present study should contribute to a

better understanding of the predictability of the extratropical atmosphere on the

seasonal t ime scale.

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