Implications of 30–70-Day Boundary Effe

1338
JOURNAL OF CLIMATE
VOLUME 17
MM5 Modeling of the Madden–Julian Oscillation in the Indian and West Pacific
Oceans: Implications of 30–70-Day Boundary Effects on MJO Development
WILLIAM I. GUSTAFSON JR.*
AND
BRYAN C. WEARE
Atmospheric Science Program, Department of Land, Air, and Water Resources, University of California, Davis, Davis, California
(Manuscript received 25 March 2003, in final form 7 October 2003)
ABSTRACT
The results of an experiment designed to isolate the initiation phase of the Madden–Julian oscillation (MJO)
from 30–70-day boundary effects is presented. The technique used to accomplish this involves employing the
fifth-generation Pennsylvania State University–National Center for Atmospheric Research (PSU–NCAR) Mesoscale Model (MM5), as first presented in the companion paper to this paper. Two runs, each 2 yr long, are
integrated forward from 1 June 1990. The first run, called the control, uses the unmodified National Centers for
Environmental Prediction (NCEP)–NCAR reanalysis (NRA) dataset for boundary conditions. The second run,
called the notched, uses the same NRA dataset for the boundary conditions, with the exception that all signals
with periodicities in the 30–70-day range have been removed. Any signals in the 30–70-day range subsequently
generated by the notched run are then solely due to signals generated from within the model domain or from
signals entering through the domain boundaries with frequencies outside of the MJO band. Comparisons between
2-yr means from each run indicate that filtering the boundaries does not significantly modify the model climatology. The mean wind structure, thermodynamic state, and outgoing longwave radiation (OLR) are almost
identical in the control and notched runs. A 30–70-day bandpass filter is used to isolate MJO-like signals in
the runs. Comparisons of 30–70-day bandpassed zonal wind, moist static energy (MSE), and OLR reveal that
the notched run develops many of the expected characteristics of MJO episodes, but with a weaker signal. Largescale, organized structures develop that possess seasonal shifts in amplitude, mirroring observed MJO activity,
have opposite wind directions in the upper and lower troposphere, and propagate eastward during most strong
episodes. The results suggest that neither remnants from previous MJO episodes nor extratropical feedbacks
within the MJO time band are necessary for MJO initiation. However, the control run is more organized than
the notched run, implying that 30–70 signals outside the model domain influence the MJO signal. There is also
some evidence that the recharge–discharge mechanism plays a role in MJO formation.
1. Introduction
The Madden–Julian oscillation (MJO) encompasses
variations of many atmospheric parameters that propagate eastward along the equator and have periodicities
around 30–60 days. The MJO has long been described
in terms of convection and equatorial wave dynamics
(Madden and Julian 1994). Hendon and Salby (1994)
connect the Kelvin–Rossby coupled wave system of Gill
(1980) with observations through analysis of satellite
outgoing longwave radiation (OLR) and temperature
measurements. However, there are multiple hypotheses
regarding initial MJO organization, including local instability processes (Fasullo and Webster 2000; Hu and
Randall 1994, 1995; Kemball-Cook and Weare 2001),
* Current affiliation: Pacific Northwest National Laboratory, Richland, Washington.
Corresponding author address: Dr. William I. Gustafson Jr., Pacific
Northwest National Laboratory, 3200 Q Ave., MSIN K9-30, Richland, WA 99352.
E-mail: william.gustafson@pnl.gov
q 2004 American Meteorological Society
extratropical waves (Matthews and Kiladis 1999), and
circumnavigating equatorial waves (Lau and Peng
1987). This paper is a companion to Gustafson and
Weare (2004) and presents preliminary results from a
new approach to investigating the MJO initiation process. As opposed to past modeling studies of the MJO,
this approach uses a regional model where signals entering and leaving the domain can be controlled. This
is done by filtering the lateral and surface boundary
conditions to remove waves of certain types. In this
paper, influences within MJO time scales are removed
to determine how feedbacks and wave structures in the
MJO time band from outside the MJO initiation region
alter MJO development. These filtered influences include both feedbacks between the tropical and extratropical regions on MJO time scales, remnants of previous MJO events that have circumnavigated the equator, and feedbacks from far-field wave structures that
would otherwise develop outside of the model domain
and alter the MJO structure. In this paper these filtered
influences will cumulatively be referred to as ‘‘boundary
effects’’ and specifically refer to these influences for
signals in the 30–70-day time band.
15 MARCH 2004
GUSTAFSON AND WEARE
Studies to date are not convincing regarding the role
of previous MJO episodes. One proposed theory for
what determines the periodicity of the MJO is the influence of MJO waves that circumnavigate the equator
and organize the next MJO convective episode as the
waves pass through the Indian Ocean. There is at least
some evidence that this may occur for stronger MJO
episodes (Knutson and Weickmann 1987; Matthews
2000; Rui and Wang 1990). Modeling studies also tend
to show this type of behavior (e.g., Bladé and Hartmann
1993). However, Hendon and Salby (1994) showed that
the autocorrelation time between successive MJO episodes is only one period for the convection, which they
interpret as evidence that circumnavigating waves are
not the physical mechanism determining the MJO period. Furthermore, Bladé and Hartmann’s (1993) model
experiments suggest that circumnavigating waves are
not a prerequisite for periodic MJO-like signals to develop. However, these results are not conclusive because
their model does not completely prevent previous waves
from circumnavigating the globe, allowing for very
small remnants to travel around the globe and possibly
phase lock with the next episode.
Questions as to the importance of circumnavigating
waves is one area in which the new regional modeling
technique excels. By using a regional model, one can
filter the boundary conditions to remove nearly the entire influence of 30–70-day boundary effects. This provides a truer test than was possible in Bladé and Hartmann’s model of what determines the periodicity of the
MJO. In the case presented in this paper, seasonality is
also maintained in the boundary conditions so that the
seasonal fluctuations of the MJO can be observed. Because the MJO signals are filtered from the boundary
forcings, this also means that intraseasonal oscillations
that develop within the model will be forced to have a
scale on the order of the model domain size or smaller.
Thus, a possible disadvantage of this approach, as presented here, is that the oscillations will not resemble the
MJO exactly, but they do maintain many of the important characteristics.
2. Data and methodology
a. Model description
The model used for this study is the fifth-generation
Pennsylvania State University–National Center for Atmospheric Research (PSU–NCAR) Mesoscale Model
(MM5) version 3.4 (Grell et al. 1995). The specific details of the model configuration can be found in the
companion paper of this issue by Gustafson and Weare
(2004). The model domain extends across the tropical
Indian and west Pacific Oceans, approximately from
248S to 248N and from 448 to 1818E. This allows for
waves to develop within the model that have sizes equivalent to what would be wavenumber 3 for a global model. The specific region has been chosen based upon the
1339
life span of the MJO with the convective activity developing in the western Indian Ocean, propagating east,
and decaying near the date line. The time period for the
runs presented in this paper covers a 24-month period
beginning 1 June 1990. The model lateral and sea surface temperature (SST) boundaries are forced using variations of the National Centers for Environmental Prediction (NCEP)–NCAR reanalysis (NRA) dataset,
which uses a copy of the Reynolds SST reanalysis (Kalnay et al. 1996).
As shown in Gustafson and Weare (2004), the model
is able to reasonably reproduce the mean equatorial climate as well as intraseasonal oscillations that resemble
the MJO, based on comparison to the NRA and satellite
OLR observations. The primary differences between the
model and NRA means are that at 850 hPa the zonal
wind has an overall easterly bias in the model as well
as difficulty reproducing the wind patterns in the Indian
monsoon region. Also, as compared to satellite OLR,
the mean OLR peaks along the equator are shifted toward the edges of the domain leading to a reversal in
the equatorial OLR gradient. The model-generated 30–
70-day intraseasonal oscillations reproduce many of the
observed characteristics, with the noted exception of
weaker and less organized OLR anomalies than in observations.
b. Experimental procedure
The goal of this experiment is to determine the role
of 30–70-day boundary effects on successive MJO formation. To do this, two runs were made with MM5. The
first, called the control, is a standard model run designed
to determine the model climatology and the structure of
MJOs within the model domain. The second, called the
notched, differs from the control in that the lateral and
SST boundary forcings are filtered to remove MJO signals. This filtering is done using an inverted 1201-point
(equivalent to 301 day) Lanczos bandpass filter (Duchon
1979) to remove signals in the 30–70-day time band
from the 6-hourly NRA data. The response function for
this ‘‘notch’’ filter is shown in Fig. 1. By removing the
30–70-day signals, the MJO is effectively removed from
the forcing data, allowing, as will be seen, the notched
run to develop intraseasonal signals independently of
any MJO signals on the boundaries while still experiencing the same seasonal shifts and higher-frequency
forcings that may influence MJO formation. The portion
of the signal removed with the notched filter has zero
mean and does not change the overall signal outside of
the filtered band. However, removing the 30–70-day
signals reduces the average variance of the 200-hPa
wind speed along the model boundaries by a factor of
0.89. With this filtering, the notched and control runs
are compared in a manner similar to what is done in
general circulation model perturbation/control experiments (Roeckner et al. 1999).
1340
JOURNAL OF CLIMATE
FIG. 1. Response functions for the Lanczos digital filters used in
this paper. The solid line is the 30–70-day notch filter constructed
with weights over 301 days used to filter the model boundary conditions. The short dashed line is the 30–70-day bandpass filter constructed with 201 days of weights used to isolate the MJO in the
model output. The long dashed line represents a perfect 30–70-day
bandpass filter for comparison.
c. Data postprocessing
To identify MJO-like signals in the model runs, a
series of diagnostic and statistical analyses are performed. Unlike most MJO investigations, the model
runs in this experiment only cover a 2-yr time period
and only one-third of the longitudinal extent of the
globe. This poses strong limitations on the type of analyses performed, as well as on the establishment of significance for the statistical tests. For example, spatial
filtering to isolate wavelengths close to wavenumber 1
or 2 is not possible. Also, over the 2-yr period, only
sixteen 45-day periods can occur, limiting the number
of degrees of freedom. Because of these and other limitations, the presented analyses have been chosen to
provide a range of approaches, focusing on several wellobserved features of the MJO: eastward propagation,
periodicity, organized vertical and horizontal wind
structure, and organized convection.
In order to simplify interpretation, data from the completed model runs are interpolated horizontally and temporally to a daily 2.58 grid using area-weighted averages
of the corresponding grid cells. The original data, which
is on sigma levels, is interpolated vertically to pressure
levels. The resulting dataset is used when doing the
bandpass and other calculations.
To isolate the MJO signal a 201-point (equivalent to
201 days) 30–70-day Lanczos bandpass filter (Duchon
1979) is applied to the regridded, daily model output.
The response function for this filter is shown in Fig. 1.
The choice of 201 points is a compromise between
maintaining enough data for analysis and the effectiveness of the filter.
VOLUME 17
As discussed above, a suite of diagnostic and statistical techniques are used in this study to analyze the
30–70-day signals in the model output with each technique being chosen to identify one or more salient features of the MJO with some overlap between techniques.
Using multiple techniques helps to identify the features
based upon different basic assumptions and, therefore,
gives more confidence in the results even though the
time series are short. Brief descriptions of each technique follow with more detailed descriptions available
in the accompanying paper by Gustafson and Weare
(2004).
Spectral analysis is used to identify the presence of
activity in the 30–70-day time band for a series of eight
points along the equator. These points (see Fig. 3a) are
the same points used in Gustafson and Weare (2004),
and the bandwidth is twice the Rayleigh frequency f R
where f R 5 1/731 day 21 . The range within which the
two spectra would be considered the same is determined
based upon the 95% significance level, compared to a
background red-noise spectrum, leading to a 5% indication that the two spectras would be different. Crossspectral analysis is also performed to identify how the
activity in the 30–70-day band is related between these
eight equatorial points. The resulting squared coherence
between the points identifies the tendency for anomalies
to fluctuate concurrently at each point and the phase
difference between the points helps to identify the
anomalous wave structure moving between the points.
Propagation and, to an extent, spatial scale are seen
using Hovmöller diagrams, although their interpretation
tends to be quite dependent on the chosen contour levels.
The structure of the anomalies is further elucidated
through empirical orthogonal function (EOF) analyses
of time series composed of vertical profiles and time
series of variables on pressure levels. The EOFs reveal
patterns of variance within the series, and the associated
principal component (PC) time series identify the
strength of the revealed pattern at any given time. The
PCs are further evaluated using the Matthews EOF technique (Matthews 2000) where the PCs are used to generate amplitude and phase indices. The amplitude index
serves to identify active MJO periods during the model
runs, and the phase index identifies the approximate
periodicity and propagation characteristics of the anomalies.
In addition to the analysis techniques used in Gustafson and Weare (2004), singular value decomposition
(SVD) analysis is used in this paper (Bretherton et al.
1992; Wallace et al. 1992). While similar to EOFs, in
that SVDs isolate coherent patterns of variance in time
series, the SVDs specifically isolate patterns of strong
covariance between two different variables as opposed
to patterns of variance for a single variable. This gives
the advantage of being able to determine if strongly
coherent covariance patterns develop between variables,
such as OLR and 200-hPa zonal wind, and to see how
this coupling changes over time. The spatial domain
15 MARCH 2004
GUSTAFSON AND WEARE
1341
FIG. 2. Two-year mean wind vectors and magnitudes for the notched run at (a) 200 and (c) 850 hPa. Increased shading indicates higher
wind speeds, and the vectors are scaled based upon the 10 m s 21 reference vector. Also shown are the differences between the notched and
control run wind vectors and magnitudes for (b) 200 and (d) 850 hPa. The reference vector for these plots is 1 m s 21 and the shading
represents the difference in magnitude between the two runs. Vectors are plotted every 2.58 in latitude and every 58 in longitude.
used for the SVD analysis extends across the full width
of the domain but is limited to latitudes between 12.58S
and 12.58N. Tests using the full latitudinal extent of the
domain revealed that excess noise was introduced into
the SVD results, particularly for the notched run along
the north and south boundaries. Therefore, the region
of transition between the model interior and the north
and south lateral boundaries was excluded. Shading on
the heterogeneous correlation plot is shown for correlations exceeding 0.5, which roughly corresponds to significant correlations at the 95% confidence level.
3. Model results and comparisons
a. Reproduction of climatology
To determine if filtering the boundaries has greatly
modified the mean state of the model climatology a
comparison is done for 2-yr means of the control and
notched runs. By establishing that the mean state is
similar between the two runs, it follows that the conditions under which the MJO forms are also similar.
The first comparison is between the winds at 200 and
850 hPa. Figure 2 shows the 2-yr mean winds for the
notched run and the difference between the two model
runs. Overall, the two runs have very similar mean wind
patterns. At 200 hPa the flow is characterized by easterly
winds along the equator and westerly winds poleward
of 158. Differences between the control and notched runs
show little organized, large-scale patterns. The wind
magnitudes at 200 and 850 hPa are not statistically different at the 95% level for more than 98% of the points
based on Student’s t test and the magnitudes of the differences are almost entirely less than 1 m s 21 . At 850
hPa the flow is characterized by easterly winds south
of the equator and for the entire eastern half of the
domain. The differences at 850 hPa are almost all smaller than 0.5 m s 21 , and the direction of the differences
is much more zonal than at 200 hPa, but again highly
unorganized. It should be noted that the equatorial flow
in the west Pacific differs from the equivalent region in
the NRA. Along the equator in the west Pacific the
model 850-hPa zonal wind is more easterly than in the
NRA (Gustafson and Weare 2004). This could alter the
feedback mechanisms associated with MJO propagation
and development by providing an environment more
susceptible to wind-induced sensible heat exchange
feedbacks (Emanuel 1987).
Figure 3 shows the mean OLR for the notched run
and the difference between the notched and control runs.
The convection, as represented by the OLR, occurs primarily along the equator and is strongest east of Papua,
New Guinea. The control and notched OLR patterns are
very similar with the differences smaller than 10 W m 22 .
The differences show no large-scale organization and
appear to be randomly distributed throughout the domain. Similar to the winds, the OLR means are not
statistically different at the 95% level for more than 98%
of the points, based on Student’s t test. However, Gustafson and Weare (2004) have noted that the peak model
OLR in the Indian Ocean is west of the observed location leading to a reversal of the longitudinal OLR
gradient in this region. The model also has a strong
negative zonal gradient in the eastern West Pacific where
the observations have a near-zero gradient.
Comparisons between maps of mean temperature,
mixing ratio, precipitable water, and moist static energy
(MSE) (not shown) also reveal that the control and
notched runs have very similar thermodynamic mean
1342
JOURNAL OF CLIMATE
VOLUME 17
structures, the vertical wind structure, the eastward
propagation, and the periodicity of the intraseasonal signals.
1) 30–70-DAY
FIG. 3. Two-year mean of (a) notched run OLR and (b) the difference between the mean notched and control run OLR. The contour
interval is (a) 15 and (b) 3 W m 22 . Letters along the equator indicate
longitudes used for spectral and other analyses, as discussed in the
text. The lettered longitude locations are as follows: A, 458E; B, 608E;
C, 82.58E; D, 102.58E; E, 1258E; F, 1458E; G, 167.58E; H, 182.58E.
states. At 850 hPa the temperatures agree almost entirely
within 0.25 K, the mixing ratio difference is almost
entirely below 0.5 g kg 21 , and the MSE difference is
mostly smaller than 0.6 3 10 3 J kg 21 , or about 0.2%
of the mean value. The mean 1000–700-hPa precipitable
water values differ by only 1.1 kg m 22 . In the upper
troposphere the differences are again small with the temperature at 200 hPa generally within 0.2 K and the mixing ratio at 300 hPa within 0.03 g kg 21 for the two runs.
Vertical profiles of mean MSE (not shown), similar to
Fig. 5 in Gustafson and Weare (2004), also show very
small differences. These differences are two to three
orders of magnitude less than the mean values.
b. MJO comparisons
Even though 30–70-day intraseasonal time signals
have been removed from the model boundary forcings,
30–70-day signals still develop within the model domain. This is shown clearly through spectral analysis
of the 200-hPa zonal winds for eight points along the
equator (Fig. 4). On the western and eastern domain
edges, points A and H, the spectral power for the
notched run shows gaps in the 30–70-day range due to
the boundary filtering. For the interior points, B through
G, the model develops clear signals in the 30–70-day
time band for both the control and notched runs. Although the MJO signal is generally weaker in the
notched run, the notched run spectral power is within
a magnitude of the control run power. Given that intraseasonal time signals develop in the model independently of the boundaries, the next step is to determine
what form these signals take and whether or not they
are similar to the control run MJO. The specific MJO
aspects to be identified are the large-scale, organized
ZONAL WIND
Hovmöller diagrams of 30–70-day 200-hPa zonal
wind (Fig. 5) give a qualitative idea of the intraseasonal
signals in the two runs, specifically identifying eastward
propagation and relative oscillation strength. Periods of
propagating westerly winds exist during boreal fall
1990, summer 1991, and to a lesser extent for the
notched run, during fall/winter 1991. Anomalies propagate to the east during many of these periods with the
exception of some weaker anomalies. Comparing the
notched run 30–70-day zonal winds with the control run
winds reveals several differences. First, the notched oscillations often develop farther east than in the control,
roughly around 708–808E, whereas oscillations in the
control run typically enter from the western domain
boundary. Second, the notched oscillations are strongest
in the western half of the domain and are less likely to
propagate as far across the domain as in the control run.
In particular the summer oscillations seem to weaken
over the Maritime Continent in the notched run. Third,
the 30–70-day 200-hPa zonal wind anomalies are weaker in the notched run, with a maximum value of 5.3 m
s 21 , as opposed to 9.4 m s 21 in the control run. At 850
hPa (not shown), the difference between maximum values is less; the maximum values are 4.4 and 6.9 m s 21
for the notched and control run, respectively.
The Matthews EOF technique is used to quantitatively identify active 30–70-day wind oscillations and
the corresponding periodicity and propagation. This
technique is more quantitative and less subjective than
the Hovmöller plots. Figure 6 shows the two EOF maps
used to construct the 30–70-day 200-hPa zonal wind
Matthews indices. These maps have complimentary patterns with one map having mostly the same sign (EOF1
for the control, and EOF2 for the notched), and the other
map having a dipolelike pattern (EOF2 for the control,
and EOF1 for the notched). When the two EOF maps,
along with the corresponding PCs, are used to reconstruct the zonal wind time series, one can see the eastward propagation of 30–70-day anomalies moving
across the domain. In the notched run the first two EOFs
are much noisier due, in part, to the smaller region over
which propagation occurs. Animations of the reconstructed notched run time series shows most of the dominant, spatially organized patterns forming in the middle
of the Indian Ocean and then propagating both west and
east, but generally not farther east than the Maritime
Continent. At 850 hPa the reconstructed notched run
zonal wind time series also has coherent patterns that
form in the mid-Indian Ocean, as well as occasional
signals that propagate eastward from near the western
boundary.
Figure 7 presents the Matthews amplitude indices for
15 MARCH 2004
GUSTAFSON AND WEARE
1343
FIG. 4. Spectral power of 200-hPa zonal wind averaged from 58S to 58N for points A through H as indicated in Fig. 3a. Solid lines
represent the notched run and dashed lines the control run. The shaded region represents periodicities between 30 and 70 days. The cross
in the legend indicates the bandwidth (-) and the range ( | ) beyond which the two spectra are considered not to be the same at the 5% level.
the 200- and 850-hPa zonal wind. The most notable
feature of the notched run amplitude indices is the strong
seasonality of the MJO signal, particularly at 200 hPa.
During the two boreal winters and intervening summer
the amplitude is much stronger than during the other
portions of the year. At 850 hPa the winter periods have
somewhat increased amplitude, but the summer peak is
almost twice as big as the winter peaks. The 850-hPa
summer peak occurs about 2 months prior to the corresponding 200-hPa peak, indicating some degree of
separation between the activity at each level. This does
not happen in the control run where the upper and lower
peaks occur simultaneously. Another difference is that
the notched run amplitude index magnitude ranges between about 20% and 60% of the control run magnitude
during the peak times.
Figure 7 also presents the phase indices for the 200and 850-hPa zonal winds. In the control run the phase
advances smoothly from 08 through 1808 and from
21808 back to 08 during strong amplitude index peaks.
This is indicative of the eastward propagation seen in
the Hovmöller diagrams (Fig. 5). In the notched run the
phase also advances during the summer peaks and for
the 200-hPa winter 1990 peak. However, the phase decreases with time during winter 1992 and at 850 hPa
during winter 1990. This decreasing phase is due to the
strongest signal in the EOF maps being on the western
half of the domain. During this first winter the strong
MJO signal develops in the Indian Ocean and then propagates both east and west. Because the 850-hPa phase
index identifies the strongest motion as in the western
portion of the domain, the index identifies the westward
propagation. The eastward propagating westerly wind
signal seen in the corresponding Hovmöller is missed.
During the second winter, Hovmöller diagrams of the
notched zonal wind indicate that the strongest, organized activity is east of 1108E so the phase index again
misses the eastward propagation.
Further evidence of notched run propagation can be
seen using cross-spectral analysis. Table 1 lists the phase
1344
JOURNAL OF CLIMATE
VOLUME 17
FIG. 5. Normalized Hovmöller plots of 30–70-day bandpassed 200-hPa zonal wind averaged from 88S
to 88N for the (a) notched and (b) control runs. Increased shading density reflects greater magnitudes and
positive values are also contoured. Each plot is scaled by the maximum value in the series: 5.3 m s 21 for
the notched run and 9.4 m s 21 for the control run.
FIG. 6. First two EOF maps of 30–70-day bandpassed 200-hPa zonal wind for the (a), (b) control and (c), (d) notched runs. Positive values
are shaded with solid contours, negative values are white with dashed contours, and the contour interval is 0.03 (units are incorporated into
the PCs).
15 MARCH 2004
1345
GUSTAFSON AND WEARE
FIG. 7. (a), (b) Matthews amplitude indices for the 30–70-day bandpassed zonal wind at 200 and 850 hPa, respectively. The amplitude
index includes a 45-day running mean for smoothing. (c), (d) Matthews phase indices for the 30–70-day bandpassed zonal wind at 200 and
850 hPa, respectively. The phase index is only plotted for times when the smoothed amplitude index exceeds 35% of its maximum value.
Black lines are for the notched run and gray lines are for the control run.
angle and squared coherencies for base points C and E
compared to the remaining points A through H. Overall,
the two model runs have very similar phase angles for
the 32 possible combinations of points; twenty-four
points match within the 95% confidence intervals. Base
point C shows the best propagating characteristics with
the phase angles advancing from point A through G in
the control run, and for the 58.2-day periodicity in the
notched run. The 38.8-day periodicity has advancing
phase angles up to point F. At base point E, both runs
have more localized propagation with the phase angles
advancing from point D through G for both periodicities.
The number of points having a significant squared coherency at the 95% level is similar between the two
runs.
In addition to propagation, the Matthews phase indices can be used to roughly determine the periodicity
of the intraseasonal signal in the models. This is done
by measuring the time between successive zero crossings of the phase index. At 850 hPa the resulting periodicities for times with advancing phase angles range
from 36 to 44 days in the control run and from 41 to
TABLE 1. Squared coherency (Coh. 2 ) and phase from cross-spectral analysis of 30–70-day bandpassed 200-hPa zonal wind (U200bp)
averaged from 58S to 58N for the two base points C and E and the two periodicities 38.8 and 58.2 days. Regions A through H are as indicated
in Fig. 3a. Bold values indicate that the squared coherency differs from zero at 95% confidence. Ninety-five-percent confidence intervals
for the phase are shown when they can be calculated.
Base point 5 C
Notched
U200-bp
Region
A
B
C
D
E
F
G
H
38.8 days
Phase
255
17
0
28
50
6 52
6 43
60
65
6 16
51
2169
61 6 35
Base point 5 E
58.2 days
Coh.
2
Phase
0.44
0.47
1.00
0.88
0.69
0.34
0.10
0.52
265
26
0
26
51
6
6
6
6
6
59
176 6
72 6
0.44
0.78
1.00
0.97
0.96
0.68
0.04
0.81
258
3
0
10
38
38.8 days
Coh.
7
37
0
5
11
73
20
58.2 days
Phase
Coh.
0.84
0.50
1.00
0.87
0.75
0.30
0.39
0.65
2120
28 6 29
250 6 16
222 6 2
060
9 6 13
111
7.5 6 44
0.16
0.56
0.69
0.94
1.00
0.74
0.17
0.47
2123
212
251
223
0
7
69
6 15
6 11
62
60
6 10
114
4 6 13
0.79
0.70
0.75
0.96
1.00
0.78
0.25
0.72
0.85
0.89
1.00
0.82
0.47
0.38
0.21
0.63
276
222
239 6 2
226 6 1
060
19 6 11
87
25 6 10
0.26
0.76
0.96
0.98
1.00
0.76
0.13
0.79
2111 6 15
215
238 6 44
223 6 6
060
21 6 9
134 6 47
23 6 8
0.70
0.32
0.47
0.85
1.00
0.79
0.46
0.81
2
2
Phase
Coh. 2
Control
U200-bp
A
B
C
D
E
F
G
H
243
11
0
14
39
55
6 51
6 10
60
61
62
6 17
130
60 6 8
6
6
6
6
6
56
118
63 6
6
4
0
8
44
21
1346
JOURNAL OF CLIMATE
FIG. 8. First EOF of vertical profiles of 30–70-day bandpassed
zonal wind for the (a) notched and (b) control runs averaged from
58S to 58N for points B through G as indicated in Fig. 3a.
45 days in the notched run. At 200 hPa, the control run
periodicity is 44 days, but the notched run is harder to
calculate due to increased fluctuations of the phase index. Here, the periodicity ranges from 30 days for the
one time when the phase index advances consistently
to around 42 days when the phase index is decreasing
in time.
VOLUME 17
The vertical zonal wind structure of the model MJO
is isolated by taking EOFs of vertical profiles of 30–
70-day zonal wind at points B through G (Fig. 8). The
resulting profiles reveal the strong first baroclinic nature
of the MJO signal with the wind direction changing once
within the troposphere. The average percent of variance
explained by these profiles is 50% and 67% for the
notched and control runs, respectively. Overall, comparison of the sample profiles reveals that the notched
profiles are similar to those in the control run. Some of
the profiles, for example, point C, match almost exactly
whereas points E and F near the Maritime Continent
have larger differences. For these latter two points the
level of wind directional change is much lower in the
notched run. Also, the notched run profiles have smaller
magnitudes above the tropopause.
To concurrently identify the large-scale, organized
wind patterns that form in the upper and lower troposphere, an SVD analysis is performed (Bretherton et al.
1992; Wallace et al. 1992). Figure 9 presents the two
most important left and right heterogeneous correlation
maps, which represent the 200- and 850-hPa zonal
winds, respectively. A similar analysis for the NRA (not
shown) reveals patterns akin to the control run. Parallel
to the results of the EOF analysis, the first two SVD
maps for each level in the control run form a coupled
pair where the first SVD has uniform sign and the second
has a dipolelike pattern with the zero crossing between
FIG. 9. SVD heterogeneous correlation maps for 30–70-day bandpassed zonal wind at 200 and 850 hPa. For the control run: (a), (b) SVDs
1 and 2 at 200 hPa, and (c), (d) SVDs 1 and 2 at u850. For the notched run: (e), (f ) are SVDs 1 and 2 at 200 hPa, and (g), (h) SVDs 1
and 2 at u850. The contour interval is 0.25 and regions significant at the 95% level are shaded.
15 MARCH 2004
FIG. 10. First EOF of vertical profiles of 30–70-day bandpassed
MSE for the (a) notched and (b) control runs averaged from 58S to
58N for points B through G as indicated in Fig. 3a.
the positive and negative regions roughly splitting the
domain in half. In the notched run, the sign reversal is
also apparent between the left- and right-heterogeneous
correlation maps for both SVDs 1 and 2. However, the
single-sign/dipolelike appearance between the two SVD
maps is more difficult to interpret due to smaller regions
with significant values. The fact that organized regions
result from this analysis indicate that the notched run
is indeed developing organized systems within the domain that exhibit the required sign reversal observed
for the MJO.
2) MOIST
1347
GUSTAFSON AND WEARE
STATIC ENERGY
Changes to the thermodynamic structure of the atmosphere during MJO episodes are examined using
EOFs of 30–70-day MSE profiles for points B through
G. The overall shape of the profiles is similar for the
notched and control runs, as seen in Fig. 10. The value
of the profiles is completely of one sign with the largest
anomalies just above the top of the boundary layer,
around 850 hPa. This leads to increased low-level gradients, and, thus, shifts in the low-level stability as the
MJO develops. The main difference between the
notched and control runs is that the increased low-level
gradients seen in points D and G of the control run do
not exist in the notched run. Instead, these profiles have
shapes similar to the remaining profiles.
The timing of these stability changes is not consistent
enough in the notched run to statistically determine a
relationship between the 30–70-day zonal wind and the
MSE profiles. In the control run significant negative
correlations exist between these profiles at the 95% level
for the MSE, leading the zonal wind by about 10 days.
However, in the notched run the only significant correlations occur for point F and then for the MSE lagging
FIG. 11. (a) Matthews amplitude indices for the 30–70-day bandpassed OLR. The amplitude index includes a 45-day running mean
for smoothing. (b) Matthews phase indices for the 30–70-day bandpassed OLR. The phase index is only plotted for times when the
smoothed amplitude index exceeds 35% of its maximum value. Black
lines are for the notched run and gray lines are for the control run.
the zonal wind by about 2 days. For comparison, this
relationship is also seen in the control run at point F.
3) OUTGOING
LONGWAVE RADIATION
Examining OLR provides a more stringent test of how
the dynamic and thermodynamic variables in the model
interact because the cloud field is very dependant upon
the feedbacks between them. Also, OLR is not directly
forced by the boundary conditions and, therefore, is
entirely model dependant. Parallel to the analyses performed on the zonal wind, similar techniques are used
on the OLR to identify the following: active MJO times;
large, organized patterns in the time series; propagation;
and periodicities.
Consistent, organized structures identified by the
Matthews EOF technique clearly show the seasonality
of the MJO. Figure 11 presents the Matthews EOF amplitude and phase indices for the notched and control
run 30–70-day OLR. The seasonality of the OLR amplitude indices is even clearer than seen in the zonal
wind. The timing of the amplitude peaks matches well
between the two runs. The largest difference occurs during the second winter where the notched run peaks about
40 days before the control run. The notched run summer
peak coincides with the summer peak in the 850-hPa
zonal wind. The summer peak for the notched run 200hPa zonal wind corresponds to a local minimum in the
OLR. This may be due to the 850-hPa-level winds having a greater influence on convective development.
Propagation of the 30–70-day OLR can be identified
through multiple techniques, including the Matthews
phase index, cross-spectral analysis, and, subjectively,
with Hovmöller diagrams. Because of the noisiness of
1348
JOURNAL OF CLIMATE
VOLUME 17
FIG. 12. First two EOF maps of 30–70-day bandpassed OLR for the (a), (b) control and (c), (d) notched runs. Positive values are shaded
with solid contours, negative values are unshaded with dashed contours, and the contour interval is 0.03 (units are incorporated into the
PCs).
the OLR time series, the results differ between the techniques. First, the results from the Matthews phase indices will be examined. The 30–70-day OLR phase indices consistently advance during times of strong amplitudes for both runs, indicating consistent changes in
the OLR patterns during strong intraseasonal oscillations. While advancing phase angles have indicated
propagation for the zonal wind, this is not as clear for
the OLR. Figure 12 presents the two EOF maps corresponding to the phase index. Because the OLR field
is so noisy, these maps are not the expected ideal single
valued and dipole patterns indicative of the eastward
propagation typically associated with the MJO. Animations constructed from these OLR maps and the corresponding PCs identify more locally propagating patterns, particularly in the equatorial Indian Ocean, and
also smaller north–south propagating patterns. In the
control run, propagation in the west Pacific favors turning toward the South Pacific convergence zone, but in
the notched run the signals maintain a more constant
latitude.
Figure 13 presents the 30–70-day OLR Hovmöller
diagrams for both runs. Even though the Matthews EOF
technique was able to identify coherent fluctuating patterns in the full OLR fields, identifying these patterns
in the 88S–88N region averaged for the Hovmöller diagrams is difficult. During the winter periods rough,
eastward propagation across the domain can be seen in
the control run. Unfortunately, in the notched run convection appears to occur in ‘‘bursts’’ with little activity
in between each burst. During the first winter, these
bursts can be connected to approximate eastward propagation, but during the second winter no argument can
be made for propagation. One feature that the Hovmöller
diagrams identify is the tendency for what appears to
be a stationary oscillation in the OLR near 708 and
1108E. Both runs have this pattern during the first winter
and spring, but to a lesser extent later in the runs. This
feature is corroborated by the animations made from the
first two OLR EOF maps.
In another attempt to quantify the propagation of the
model OLR, cross-spectral analysis for base points C
and E has been done and is shown in Table 2. Overall,
few points have significant squared correlations at the
95% level. However, for 58.2-day periodicities both runs
show propagation, albeit with large uncertainties: the
notched run has advancing phase values from points C
through G and the control run has advancing phase values from points B through E. The notched run reveals
no noticeable propagation at the 38.8-day periodicity in
comparison to the control, which shows no pattern for
this periodicity at base point C.
Even with the weakly propagating characteristics of
the notched run 30–70-day OLR, the coherent OLR
patterns still fluctuate on a relatively consistent time
scale. Using the phase indices in Fig. 11 to gauge the
periodicity of the notched run intraseasonal oscillations,
the periodicity ranges from 41 to 47 days, depending
on the episode. This compares to 40–44 days in the
control run.
In an attempt to identify the relationship between the
zonal wind and OLR, SVD analyses were performed
between OLR and 200-hPa zonal wind and also for OLR
and 850-hPa zonal wind. Due in part to the short, 2-yr
time series, as well as the noisiness of the OLR, significant spatial patterns were not identified by these
analyses.
4. Discussion and conclusions
Based on the experiment presented in this paper external forcing in the form of incipient MJO episodes
from outside the Indian Ocean is unnecessary for the
formation of 30–70-day intraseasonal oscillations.
However, with the current model setup, once initially
developed, the intraseasonal oscillations do not fully
conform to observed MJO characteristics. Two model
runs have been made using MM5 with a domain extending from eastern Africa to the date line. The first
run functions as the control and is forced by the NRA.
15 MARCH 2004
1349
GUSTAFSON AND WEARE
FIG. 13. Hovmöller plots of 30–70-day bandpassed OLR averaged from 88S to 88N for the (a) notched
and (b) control runs. Increased shading density reflects greater magnitudes, and positive values are also
contoured.
TABLE 2. Squared coherency (Coh. 2 ) and phase from cross-spectral analysis of 30–70-day bandpassed OLR (OLR-bp) averaged from 58S
to 58N for the two base points C and E and the two periodicities 38.8 and 58.2 days. Regions B through G are as indicated in Fig. 3a. Bold
values indicate the squared coherency differs from zero at 95% confidence. Ninety-five-percent confidence intervals for the phase are shown
when they can be calculated.
Notched
OLR-bp
Base point 5 C
38.8 days
Base point 5 E
58.2 days
Region
Phase
Coh.
B
C
D
E
F
G
175
060
168 6 36
162
153
56
0.02
1.00
0.51
0.13
0.28
0.25
267
060
2129
169
2161
88
0.11
1.00
0.04
0.11
0.22
0.06
2
Phase
38.8 days
Coh.
2
58.2 days
Phase
Coh.
2
Phase
Coh. 2
0
17
30
37
10
0.21
1.00
0.67
0.55
0.50
0.78
153 6 26
2162
92
060
78 6 42
2176
0.58
0.13
0.24
1.00
0.48
0.13
130
244 6 30
4
060
25 6 37
234 6 77
0.01
0.55
0.35
1.00
0.50
0.39
211 6 34
060
12 6 7
67 6 29
35
1 6 17
0.52
1.00
0.84
0.55
0.25
0.67
2169
2169
226
060
45
64
0.22
0.11
0.03
1.00
0.36
0.11
2131
267
234
060
14
230
0.15
0.55
0.32
1.00
0.52
0.32
0
19
44
36
6
5
6
6
6
6
6
Control
OLR-bp
B
C
D
E
F
G
1350
JOURNAL OF CLIMATE
The second run is forced by a filtered version of the
NRA in which all signals with periodicities in the range
of 30–70 days are removed. This effectively removes
the MJO signal from the boundaries of the notched run
without altering the overall flow outside these periodicities. Comparing the control and notched runs confirms that removal of the 30–70-day band has not altered
the climate in the notched run. Only small differences
have been found between the two runs when comparing
2-yr means. Even more importantly, with the 30–70day periodicities removed, the notched run still develops
large-scale, propagating oscillations in the 30–70-day
band. Based upon the spectral power of 200-hPa zonal
wind, these periodicities develop across the entire domain, including close to the western boundary where
30–70-day boundary effects would have the most influence.
The strength of the 30–70-day intraseasonal signals
is less in the notched run, compared to the control. Even
though the exact difference in strength varies between
the particular event and the method used to define the
amplitude, the general consensus among the techniques
used in this paper is that the notched oscillations are
roughly 50%–75% as strong as in the control run, with
direct spectral measurements giving a larger difference.
Depending on whether one compares the Matthews amplitude indices or the Hovmöller diagrams, and then
depending on the variable, the first winter produces the
strongest notched oscillations with the strength diminished during the second winter. The reason for the differences between winters is currently not understood.
Many of the defining characteristics of the MJO are
generated. However, due to the lack of a consistent relationship between the relatively noisy OLR and wind,
it is not possible to demonstrate a coherent relationship
between these variables, as seen in observations. Examination of notched run zonal wind, MSE, and OLR
reveals systematic, coherent anomalies that develop
within the 30–70-day band. The notched run develops
anomalous patterns with periodicities near 40 days, with
peak amplitudes during boreal winter and late summer.
Propagation is also seen, most clearly in the zonal wind,
originating in the Indian Ocean and moving away from
this region. Propagation of the OLR anomalies occurs
over smaller distances and is less evident due to the
noisiness of the OLR signal. The vertical structure of
the 30–70-day anomalies matches well with what would
be expected for MJO-type signals in the model. Comparing the 30–70-day vertical zonal wind profiles of the
notched and control runs reveals very similar patterns
with one sign reversal within the troposphere and peak
wind speeds near the tropopause. SVD analysis of the
850- and 200-hPa zonal wind reveals that the sign reversals form over large coherent regions of the model
domain. Finally, vertical profiles of 30–70-day MSE are
also very similar between the two runs, having uniform
sign and the largest anomalies just above the top of the
boundary layer. This variation near the boundary layer
VOLUME 17
top gives credence to the buildup of energy prior to
MJO passage, as identified by Kemball-Cook and Weare
(2001), and further implies that the boundary layer recharge mechanism is important for MJO formation. The
MJO event is associated with MSE building up in the
lower troposphere and then being released during peak
MJO convection.
With the formation of 30–70-day intraseasonal oscillations in the notched run, some arguments can be
made regarding the role of 30–70-day boundary effects
on MJO development. The notched run was able to develop the intraseasonal oscillations without any influence from remnants of previous MJO episodes or extratropical influences in the 30–70-day time band. This
leaves at least two other possibilities for triggering the
episodes. The first is higher-frequency waves propagating into the Indian Ocean region. This possibility has
been suggested in studies by Matthews and Kiladis
(1999) who noted a greater incidence of higher-frequency waves entering the Indian Ocean during the MJO
formation phase. The second possibility is that the formation and periodicity is determined by local feedback
mechanisms. Studies of radiosonde soundings by Kemball-Cook and Weare (2001) suggest a regional building
up of instabilities that are then released as MJO convection develops. Future experiments using the method
presented in this paper will be aimed at determining the
role of frequencies less than 30 days on MJO formation.
The difference between the control and notched runs,
particularly the weaker MJO signals and propagation in
both the west and east directions, suggests that the
boundary filtering has altered important physics related
to the MJO. The simplest explanation for the differences
would be the limited domain size in which the notched
run MJO must form. Without 30–70-day signals in the
boundaries, the notched run MJOs are completely confined within the model domain. This is a severe constraint, given the global influence of the MJO. A second
explanation is that direct feedbacks are required that are
not contained in the model domain. For example, even
though circumnavigating MJO signals do not appear to
be necessary for MJO formation, they could be important for organizing nascent MJOs developing in the Indian Ocean.
To improve the model MJO structure, work is being
done to determine why the current runs do not form as
well organized mesoscale convective complexes, as seen
in satellite observations of OLR. The noisiness of the
MM5 OLR field has proven disappointing in this analysis. This is most likely due to inadequacies in the Betts–
Miller convective scheme used for the runs, or at least
in the tuning of this scheme within MM5. A second
strong contender is the boundary layer scheme and how
it handles fluxes to and from the ocean. Because most
MJO theories rely on feedbacks between convection and
dynamics, the lack of large, organized convective regions proves to be a substantial shortcoming of the current model configuration. It is believed that if the model
15 MARCH 2004
GUSTAFSON AND WEARE
can be improved to better capture this phenomenon, a
truer MJO signal will be produced.
A more robust analysis could also be done by extending the current methodology to include an ensemble
of model integrations. With only one control and one
notched run, the cause of the differences between the
runs cannot be uniquely identified. While a portion of
the differences is most likely due to the filtered boundary conditions, the exact percentage cannot be stated
because some of the differences are also due to natural
variability. Multiple model integrations could be used
to quantify the natural variability of MJO activity with
the current model configuration and then to determine
more exactly the significance of the boundary forcing.
Acknowledgments. We would like to thank Daniel
Hodyss for his helpful discussions. NCEP–NCAR reanalysis data were obtained from the NCAR mass storage system through NCAR University Projects
36131021 and 36131022. This work was partially supported by NSF Grant ATM-9613779 and by the University of California Office of the President through the
Campus Laboratory Collaboration Program. Further
support was received from the Department of Energy
(DOE), under the auspices of the Atmospheric Sciences
Program of the Environmental Sciences Division of the
Office of Biological and Environmental Research, under
Contract DE-AC06-76RLO 1830 at the Pacific Northwest National Laboratory. Pacific Northwest National
Laboratory is operated for the U.S. DOE by Battelle
Memorial Institute.
REFERENCES
Bladé, I., and D. L. Hartmann, 1993: Tropical intraseasonal oscillations in a simple nonlinear model. J. Atmos. Sci., 50, 2922–
2939.
Bretherton, C. S., C. Smith, and J. M. Wallace, 1992: An intercomparison of methods for finding coupled patterns in climate data.
J. Climate, 5, 541–560.
Duchon, C. E., 1979: Lanczos filtering in one and two dimensions.
J. Appl. Meteor., 18, 1016–1022.
1351
Emanuel, K. A., 1987: An air–sea interaction model of intraseasonal
oscillations in the tropics. J. Atmos. Sci., 44, 2324–2340.
Fasullo, J., and P. J. Webster, 2000: Atmospheric and surface variations during westerly wind bursts in the tropical western Pacific.
Quart. J. Roy. Meteor. Soc., 126, 899–924.
Gill, A. E., 1980: Some simple solutions for heat-induced tropical
circulation. Quart. J. Roy. Meteor. Soc., 106, 447–462.
Grell, G. A., J. Dudhia, and D. R. Stauffer, 1995: A description of
the fifth-generation Penn State/NCAR mesoscale model (MM5).
NCAR Tech. Note NCAR/TN-3981STR, 122 pp.
Gustafson, W. I., and B. C. Weare, 2004: MM5 modeling of the
Madden–Julian oscillation in the Indian and west Pacific Oceans:
Model description and control run results. J. Climate, 17, 1320–
1337.
Hendon, H. H., and M. L. Salby, 1994: The life cycle of the Madden–
Julian oscillation. J. Atmos. Sci., 51, 2225–2237.
Hu, Q., and D. A. Randall, 1994: Low-frequency oscillations in radiative–convective systems. J. Atmos. Sci., 51, 1089–1099.
——, and ——, 1995: Low-frequency oscillations in radiative–convective systems. Part II: An idealized model. J. Atmos. Sci., 52,
478–490.
Kalnay, E., and Coauthors, 1996: The NCEP/NCAR 40-Year Reanalysis Project. Bull. Amer. Meteor. Soc., 77, 437–471.
Kemball-Cook, S. R., and B. C. Weare, 2001: The onset of convection
in the Madden–Julian oscillation. J. Climate, 14, 780–793.
Knutson, T. R., and K. M. Weickmann, 1987: 30–60 day atmospheric
oscillations: Composite life cycles of convection and circulation
anomalies. Mon. Wea. Rev., 115, 1407–1436.
Lau, K. M., and L. Peng, 1987: Origin of low-frequency (intraseasonal) oscillations in the tropical atmosphere. Part I: Basic theory. J. Atmos. Sci., 44, 950–972.
Madden, R. A., and P. R. Julian, 1994: Observations of the 40–50day tropical oscillation—A review. Mon. Wea. Rev., 122, 814–
837.
Matthews, A. J., 2000: Propagation mechanisms for the Madden–
Julian oscillation. Quart. J. Roy. Meteor. Soc., 126, 2637–2651.
——, and G. N. Kiladis, 1999: The tropical–extratropical interaction
between high-frequency transients and the Madden–Julian oscillation. Mon. Wea. Rev., 127, 661–677.
Roeckner, E., L. Benotsson, J. Feichter, J. Lelieveld, and H. Rodhe,
1999: Transient climate change simulations with a coupled atmosphere–ocean GCM including the tropospheric sulfur cycle.
J. Climate, 12, 3004–3032.
Rui, H., and B. Wang, 1990: Development characteristics and dynamic structure of tropical intraseasonal convection anomalies.
J. Atmos. Sci., 47, 357–379.
Wallace, J. M., C. Smith, and C. S. Bretherton, 1992: Singular value
decomposition of wintertime sea surface temperature and 500mb height anomalies. J. Climate, 5, 561–576.