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  • View in gallery

    Model results for MJO phase-1 heating for (a) the 0.3σ-level 100-ensemble member day-7–10 mean , (b) the 0.3σ-level top quintile day-7–10 mean , (c) the 0.3σ-level top quintile day-0 mean , and (d) the 0.3σ-level bottom quintile day-0 mean . The box in (b) is the projection region used to calculate quintiles. The contours in (c) and (d) indicate where the top and bottom quintiles have different means at the 0.90, 0.95, and 0.99 confidence levels for a t test. Anomalies in (c) and (d) are divided by 4 for scaling.

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    As in Fig. 1, but for MJO phase-5 heating.

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    Scatterplot of the projection of onto for each set of initial conditions for MJO phase 1 against MJO phase 5. The black line is the best-fit linear curve through the data and the gray dashed line corresponds to the curve .

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    Projection time series over the entire Northern Hemisphere from 20° to 80°N. The black curve corresponds to active MJO analogs for all MJO events. The red curve corresponds to non-MJO analogs for all MJO events. The green curve corresponds to non-MJO analogs for non-MJO days. The blue curve corresponds to somewhat random analogs (see text for details) for all MJO events. (a) The top 5 analogs and (b) the top 30 analogs are used for the forecasts. Dots on the colored curves represent lag days for which the respective curve and the black curve have a statistically different mean according to a two-sample t test.

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    Correlation maps. (from top to bottom) The rows indicate lag-days 0, 2, 4, 6, 8, and 10. (left) Active MJO analogs for MJO events, (middle) non-MJO analogs for MJO events, and (right) non-MJO analogs for non-MJO days. The black contours are DJF climatological 300-hPa height contours every 240 m from 8640 to 9600 m.

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    Correlation maps for day 10. (from top to bottom) The rows correspond to MJO phases 1–8. (left) Active MJO analogs for MJO events and (right) non-MJO analogs for MJO events. The black contours are DJF climatological 300-hPa height contours every 240 m from 8640 to 9600 m.

  • View in gallery

    Lag-day-0 300-hPa geopotential height composites. (from top to bottom) The rows correspond to MJO phases 1–8. (left) Active MJO analogs for MJO events, (middle) non-MJO analogs for MJO events, and (right) the difference between the left and middle .

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    (a) The 300-hPa composite phase-independent geopotential height difference between all MJO analogs () and all non-MJO analogs () for all MJO events. (b) The 300-hPa composite phase-independent geopotential height difference between all active MJO days and all non-MJO days.

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    Area-weighted projection north of 20°N of the composite of for each MJO phase on to the composite of independent of phase, for DJF days when the MJO amplitude is greater than or equal to 1.0.

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    Composite 300-hPa averaged over lag-days 10–20 for MJO phases 1–8.

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    Composite of 300-hPa for (left) MJO phase 1 and (right) MJO phase 5. (from top to bottom) Lag days 0, 3, 6, 9, 12, 15, and 18, respectively.

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    Lag-day-0 300-hPa composites for the (left) top tercile and (right) bottom tercile for (from top to bottom) MJO phase 1–8. Contours indicate where the top and bottom terciles have different means at the 0.90, 0.95, and 0.99 confidence levels according to a two-sample t test.

  • View in gallery

    Lag-day-0 300-hPa composites for the (a) top tercile and (b) bottom tercile averaged over all MJO events and phases. Contours indicate where the top and bottom terciles have different means at the 0.90, 0.95, and 0.99 confidence levels according to a two-sample t test.

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The Impact of the Initial Flow on the Extratropical Response to Madden–Julian Oscillation Convective Heating

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  • 1 Department of Meteorology, The Pennsylvania State University, University Park, Pennsylvania
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Abstract

The response to the Madden–Julian oscillation (MJO) over the Pacific–North American (PNA) region is investigated. In addition, the sensitivity of this response to the interaction between Madden–Julian oscillation forcing and the extratropical initial flow is explored. First, a simple dynamical model is run with an ensemble of 100 randomly selected initial conditions from ERA-Interim data, with no heating, MJO phase-1-like heating, and MJO phase-5-like heating. The 300-hPa geopotential height field is separated into a part that would evolve without an active MJO present, and a part that is a consequence of the MJO heating. A negative 300-hPa geopotential height anomaly centered over northeastern China bounded by positive anomalies on its equatorward and poleward flanks is found to be followed by a large amplitude negative PNA-like response for MJO phase 1 and a positive PNA-like response for phase 5.

A similar study is carried out using observational data. An analog approach—using projections to determine the analogs—is used to approximate the part of the flow that results from the MJO heating. The composite initial flow that corresponds to a large MJO response in observational data somewhat matches that in the model, although there is more variability between phases. Finally, the analog method is used to examine questions related to predictability and the MJO. It is found that predictability is improved by taking into account the presence of the MJO and by choosing analogs with high projections. The presence of an active MJO also increases predictability.

Corresponding author address: Michael Goss, Department of Meteorology, The Pennsylvania State University, 503 Walker Building, University Park, PA 16802. E-mail: mag475@psu.edu

Abstract

The response to the Madden–Julian oscillation (MJO) over the Pacific–North American (PNA) region is investigated. In addition, the sensitivity of this response to the interaction between Madden–Julian oscillation forcing and the extratropical initial flow is explored. First, a simple dynamical model is run with an ensemble of 100 randomly selected initial conditions from ERA-Interim data, with no heating, MJO phase-1-like heating, and MJO phase-5-like heating. The 300-hPa geopotential height field is separated into a part that would evolve without an active MJO present, and a part that is a consequence of the MJO heating. A negative 300-hPa geopotential height anomaly centered over northeastern China bounded by positive anomalies on its equatorward and poleward flanks is found to be followed by a large amplitude negative PNA-like response for MJO phase 1 and a positive PNA-like response for phase 5.

A similar study is carried out using observational data. An analog approach—using projections to determine the analogs—is used to approximate the part of the flow that results from the MJO heating. The composite initial flow that corresponds to a large MJO response in observational data somewhat matches that in the model, although there is more variability between phases. Finally, the analog method is used to examine questions related to predictability and the MJO. It is found that predictability is improved by taking into account the presence of the MJO and by choosing analogs with high projections. The presence of an active MJO also increases predictability.

Corresponding author address: Michael Goss, Department of Meteorology, The Pennsylvania State University, 503 Walker Building, University Park, PA 16802. E-mail: mag475@psu.edu

1. Introduction

The Madden–Julian oscillation (MJO), the primary mode of tropical variability on the intraseasonal time scale, is known to affect the extratropical circulation through the excitation of poleward-propagating Rossby waves. In the context of idealized model calculations, the Pacific–North American (PNA) teleconnection pattern has been shown to arise in response to MJO forcing (e.g., Seo and Son 2012; Yoo et al. 2012a). Support for this driving of the PNA-like anomalies by MJO heating has been found in observational studies such as Mori and Watanabe (2008), Johnson and Feldstein (2010), Moore et al. (2010), Roundy et al. (2010), Franzke et al. (2011), Riddle et al. (2013), and Yoo et al. (2012b). An analogous relationship involving the excitation of the North Atlantic Oscillation (NAO) and the very similar Arctic Oscillation by MJO convection has been found by L’Heureux and Higgins (2008), Cassou (2008), and Lin et al. (2009). These studies find that MJO phases1 1–3 (5–7) (Wheeler and Hendon 2004) are followed 7–10 days later by the negative PNA and positive NAO (positive PNA and negative NAO) phases. Anomalous tropical heating associated with MJO-induced convection results in anomalous divergent wind near the heating source. The advection of the background absolute vorticity by the anomalous divergent wind serves as a Rossby wave source (RWS) (Sardeshmukh and Hoskins 1988; Qin and Robinson 1993), most notably at the northwestern Pacific subtropical jet, which induces Rossby waves to propagate poleward into mid- and high latitudes.

In addition to the MJO heating having a large impact on the flow evolution in midlatitudes, it has been shown with composite analysis by Franzke et al. (2011) that a large amplitude PNA response to tropical convection is preceded several days earlier by the presence of synoptic-scale disturbances over eastern Asia (for the positive PNA) and the northeastern Pacific (for the negative PNA). Upon encountering the MJO-excited wave train, these synoptic-scale disturbances were observed to undergo wave breaking, and their vorticity fluxes were found to amplify the wave train triggered by the tropical convection, with this amplification possibly occurring through a positive feedback between the wave train and the synoptic-scale eddies. These findings suggest that the poleward-propagating wave train excited by the MJO tropical convection is strongly influenced by its encounter with synoptic-scale eddies in the midlatitudes.

Yoo et al. (2012a) ran a model with an ensemble of initial conditions to find the mean midlatitude response in their model to MJO forcing. The question of variability in the MJO response given differing sets of initial conditions, however, was not the focus of Yoo et al. (2012a). In this study, we first address this question with the same model as Yoo et al. (2012a). Specifically, two sets of model runs are performed: one set with the MJO heating absent and the other set with the MJO heating present. For each set, an ensemble of 100 initial perturbations is used. This approach allows us to separate the evolution of the total flow into a part that is due to the initial conditions alone (with the MJO heating turned off), and a part that corresponds to the atmospheric response to the MJO heating (the difference between the model runs with the MJO heating turned on and turned off). With regard to the response to the MJO heating, this includes both the direct wave response to the MJO heating (as in a model run with MJO heating and no initial perturbation) as well as this wave’s interaction with the initial perturbation.

We also address the same question with observational data to investigate the response to MJO driving in the atmosphere. However, because we do not have identical sets of initial conditions for active (analogous to the heating turned on in the model) and nonactive (analogous to the heating turned off in the model) MJO times in the atmosphere, the splitting of the flow into a part that is due to the initial conditions alone and a part that combines the wave response to the MJO heating and its interaction with the initial flow is impossible to achieve precisely. Therefore, we estimate the extratropical flow associated with an active and nonactive MJO with an analog approach. More specifically, we find analogs for a given flow (the flow at the beginning of a specific MJO event) among days in which the MJO is both active and inactive. The analog composites are used to approximate the evolution of the specific initial flow with and without MJO heating. In this manner, the atmospheric response to the MJO heating can be estimated using the same process as that used in the model study.

Following the above approach, with both model and observational data, we will focus on addressing the following two questions: 1) What is the atmospheric response to the MJO? and 2) What particular initial flow configurations lead to the largest, and also smallest, amplitude responses to the MJO? Furthermore, because the analog approach with observational data is a testable forecasting method, by comparing the actual evolution of the flow to various analog forecasts, we will be able to address questions about predictability. More precisely, we will examine the relative importance of different initial flow configurations, as well as whether or not the MJO is active, on the predictability of the flow evolution.

2. Data and methods

a. Model specifications and experiment

This study uses the dynamical core of a National Oceanic and Atmospheric Administration/Geophysical Fluid Dynamics Laboratory (NOAA/GFDL) climate model. The model is run with triangular 42 horizontal resolution and 19 vertical levels in sigma coordinates [see Yoo et al. (2012a) for details]. The model is forced by radiative relaxation. The specific values for the Rayleigh friction, Newtonian cooling, and fourth-order horizontal diffusion coefficients are the same as those in Yoo et al. (2012a). The model climatology is calculated as the mean of the daily fields of the European Centre for Medium-Range Weather Forecasts Interim Re-Analysis (ERA-Interim) dataset (Dee et al. 2011) for December–February (DJF) for the years 1979–2008. Since model drift would be present due to an unbalanced climatological state, the model equations are supplemented with a constant forcing term, which exactly balances the model drift such that the model run with climatological initial conditions does not evolve over time.

The model is also forced with the same MJO-like heating as in Yoo et al. (2012a). The heating field is derived from a composite of the daily, interpolated NOAA/Climate Prediction Center Merged Analysis of Precipitation (Xie and Arkin 1997) based on the amplitude and phase of the Wheeler and Hendon (2004) MJO index. Three sets of model runs are performed—the first with no MJO heating, the second with MJO phase-1 heating, and the third with MJO phase-5 heating. Each set comprises 100 ensemble members with different initial perturbations. The same perturbations are used for each set. The initial perturbations are based on the flow from 100 randomly chosen days in the ERA-Interim dataset (without regard for MJO phase). In the runs with MJO heating, the heating is stationary, and is active from day 0 through day 10. All runs are integrated through day 19.

The temporal evolution of the geopotential in those runs with MJO-like heating is separated into a part that arises from the initial conditions alone—that is, the evolution of the flow without any MJO heating, denoted by —and a part , which can be understood to represent both the direct wave-driven response to the MJO heating and the interaction of the MJO-induced wave response with the initial conditions. The total geopotential can be written as
e1
where is the geopotential in the MJO-forced model runs for a given phase, is the geopotential in the unforced runs, and is determined as a residual. Since and are identical at day 0, must be equal to zero on that day.
For each MJO phase, the mean impact of the MJO is calculated as the average over all 100 ensemble members of the day-7–10 mean of for that phase, denoted by .2 Day 7–10 is chosen because this is the time period for which the PNA response is notably strong in the model (Yoo et al. 2012a). Since each ensemble member is run with a different initial perturbation, the interaction between the MJO and the initial extratropical flow differs among ensemble members. For each ensemble member, its is compared with using a projection approach, that is,
e2
where is the projection value for a particular ensemble member (e) and MJO phase (p), i denotes longitudinal grid points, j denotes latitudinal grid points, and λ is the longitude and θ the latitude at grid point (i, j). The domain over which these projections are performed corresponds to the North Pacific and North America (15°–75°N, 180°–90°W). The term represents the degree to which the MJO-induced portion of the flow for a given ensemble member matches the mean MJO impact for a given MJO phase. Ensemble members are then sorted into five bins based upon the value of . The top (bottom) bin represents those initial conditions that interact with the MJO heating to produce the most amplified (least amplified) impact (measured by their projections) over the part of the PNA region in which the composite anomalies are the strongest.

b. Diagnostic analysis with reanalysis data

For the diagnostic component of this study, ERA-Interim data for 1979–2008 are used. The data are linearly interpolated onto a 2.5° × 2.5° grid. Anomalies are derived by subtracting the DJF mean value for each grid point. The anomalies are then smoothed spatially five times with a 5 × 5 Gaussian filter. The spatial smoothing is done because our focus is on large-scale features. (The MJO phase and amplitude data are made available by Dr. Wheeler at http://cawcr.gov.au/staff/mwheeler/maproom/RMM/.) In this study, the MJO is considered to be “active” when the MJO amplitude is greater than 1.0 (and “non-MJO” otherwise), and an MJO “event” is defined to have taken place when there were at least three consecutive active MJO days of the same phase. The first day of an MJO event is defined to be lag-day 0. Those days that satisfy these criteria for being part of an MJO event are referred to as MJO event days. Table 1 gives the number of MJO events by MJO phase, and Table 2 indicates the number of active MJO and non-MJO days.

Table 1.

Number of MJO events by MJO phase.

Table 1.
Table 2.

Number of active MJO days and non-MJO days.

Table 2.

In contrast to the model data, with reanalysis data, the two terms that contribute to in (1) (i.e., and ) cannot be determined exactly, since for any given day that the MJO is active, it is not possible to find other days with the identical initial flow structure when the MJO is not active. Therefore, for each MJO event, an analog approach is used to approximate , that is,
e3
where is the 250-hPa geopotential determined using active MJO analogs, is the 250-hPa geopotential determined using non-MJO analogs, and and are the corresponding errors that arise from imperfect analogs; the process of choosing analogs is discussed below. Thus, following the notation of (1), and . It is assumed that is small, and that it averages to near zero for a multiple-analog, multiple-MJO-event composite. Therefore, we have
e4
To find analogs with which to determine and , with the exception of those days to be described below, we project the anomaly patterns for all 2708 DJF days within the dataset onto the anomaly patterns for those days that satisfy the criteria for an MJO event day. For these projections, the 2708 days are separated into MJO days and non-MJO days. An area-weighted projection is again used, this time over the entire Northern Hemisphere extratropics from 20° to 80°N. Such a large domain is used for these projections because synoptic-scale disturbances well upstream of the PNA region influence the response to the MJO over this region. Other large, Northern Hemisphere projection regions were tested (not shown), and the results were seen to be relatively independent of the projection region tested. For a given MJO event day, the projections for each active MJO day and non-MJO day, and respectively, are calculated as
e5
where is the anomaly pattern among all active MJO days for which the phase number is within one neighboring phase of the given MJO event’s phase, is the anomaly pattern among all non-MJO days, and is the anomaly pattern for the given MJO event day. A stricter requirement that the days must have a phase exactly matching that of the given event was tested (not shown), and the results were insensitive to this change. Furthermore, those days that are within two days of the MJO event day are excluded from the analogs in order to prevent an event from being considered as its own analog. The days that correspond to the five highest and the five highest for a given MJO event day are considered to be the analogs. The composite of these sets of five analogs are the and , respectively. To test the sensitivity to the number of analogs chosen, the analysis is performed separately for the top 1, 5, 10, 30, and 90 analogs for each MJO event. The sensitivity will be further discussed in section 4.

With and determined, can be approximated using (4). (As we will see in section 4, a modified will need to be used because of a systematic difference between and .) After has been obtained, the process to determine which initial perturbations produce enhanced MJO impacts is the same as with the model data, except for the following two changes. First, for a given MJO phase, each event is projected onto the mean of all the MJO events during the 10–20-day time period, rather than the 7–10-day period used in the model calculations. This period was chosen as it is these days that will be shown to have the largest amplitude response to the MJO over the North Pacific and North America. Second, events are sorted by into three bins, as opposed to five bins in the model study, since there are only about 30 events for each MJO phase. The top bin again represents those initial conditions that interact with the MJO heating to produce the most amplified impact over the part of the PNA region in which the composite anomalies are the strongest.

3. Model experiments

The day-7–10 model response to MJO phase-1 heating is shown in Fig. 1. In the 100-member ensemble day-7–10 composite (Fig. 1a), a negative-PNA-like structure in the 0.3σ-level geopotential height anomaly field can be seen over the North Pacific and North America, with positive anomalies over the midlatitude North Pacific and the southeastern United States, and negative anomalies over the subtropical North Pacific and northwestern North America. [As indicated in the introduction, observational studies typically find a negative (positive) PNA following MJO phase 1 (5).] The top quintile, day-7–10 composite (Fig. 1b) shows the same structure, but with enhanced amplitude over the projection region (outlined in black). The bottom quintile (not shown) has weaker amplitude, and a dissimilar spatial pattern over the projection region, giving a spatial projection onto the 100-ensemble mean that is close to zero. To examine the initial flow that leads to the excitement of the top quintile anomalies, the day-0 (or equivalently , since the day-0 is equal to zero) composite is calculated. As can be seen in Fig. 1c, over eastern Asia, the top quintile, day-0 composite is characterized by a negative geopotential height anomaly centered over northeastern China, with positive geopotential height anomaly centers over the Arctic coast of Siberia and southeastern Asia. Additional anomalies with smaller amplitude and lower levels of statistical significance are present over the North Pacific and North America. The corresponding bottom quintile, day-0 composite (Fig. 1d) shows mostly opposite-signed anomalies over the same locations. A two-sample t test between the top and bottom quintiles was performed at each grid point to test regions where the bins had statistically different means at that grid point, and the contours show those areas at the 0.90, 0.95, and 0.99 confidence levels. The anomalies noted above all show some level of confidence in statistically different bin means.

Fig. 1.
Fig. 1.

Model results for MJO phase-1 heating for (a) the 0.3σ-level 100-ensemble member day-7–10 mean , (b) the 0.3σ-level top quintile day-7–10 mean , (c) the 0.3σ-level top quintile day-0 mean , and (d) the 0.3σ-level bottom quintile day-0 mean . The box in (b) is the projection region used to calculate quintiles. The contours in (c) and (d) indicate where the top and bottom quintiles have different means at the 0.90, 0.95, and 0.99 confidence levels for a t test. Anomalies in (c) and (d) are divided by 4 for scaling.

Citation: Monthly Weather Review 143, 4; 10.1175/MWR-D-14-00141.1

Figure 2 shows the model response to MJO phase-5 heating. The 100-member ensemble day-7–10 composite (Fig. 2a) shows a positive-PNA-like structure in the 0.3σ-level geopotential height anomaly field over the North Pacific and North America, exhibiting anomalies of opposite sign compared to those in Fig. 1a. We note that there are subtle differences in the MJO phase-1 and phase-5 day-7–10 composites. These differences likely arise in large part because the composite-derived heating profile in MJO phase 1 is not the exact opposite of that in MJO phase 5, as can be seen in Fig. 1 of Yoo et al. (2012a). The top quintile, day-7–10 composite (Fig. 2b) again shows the same structure as the 100-ensemble composite, but with enhanced amplitude. As with the MJO phase-1 case, the bottom quintile (not shown) has weaker, spatially dissimilar anomalies over the projection region. However, unlike the day-7–10 composites, which showed an opposite-signed spatial pattern between the cases with MJO phase-1 and phase-5 heating, the day-0 composites for the top and bottom quintiles in the MJO phase-5 runs (Figs. 2c and 2d) show essentially the same spatial patterns as those of the MJO phase-1 heating (Figs. 1c and 1d). This was an unexpected result, and the implications will be discussed further below. Again, the top quintile (Fig. 2c) shows the opposite anomalies over the same locations as compared with the bottom quintile (Fig. 2d). Furthermore, a two-sample t test shows statistically different bin means over many of the same locations.

Fig. 2.
Fig. 2.

As in Fig. 1, but for MJO phase-5 heating.

Citation: Monthly Weather Review 143, 4; 10.1175/MWR-D-14-00141.1

The results from Figs. 1c and 2c indicate that for both phase-1 and phase-5 MJO forcing, a very similar initial flow over eastern Asia is followed by a more amplified MJO response over the PNA region by days 7–10, in spite of the fact that the response over the PNA region is opposite in sign for the two MJO cases. Analogously, Figs. 1d and 2d show that similar initial flows lead to very weak, non-PNA-like responses over the PNA region. This behavior is summarized in Fig. 3. Each point on the scatterplot corresponds to one set of initial conditions. There are 100 points, representing the 100 ensemble members in the MJO phase-1 and phase-5 runs. The position on the abscissa gives the day-7–10 projection over the projection region for MJO phase-1 forcing, where the projection is against the MJO phase-1, 100-ensemble, day-7–10 composite over the same region [see (2)]. Likewise, the position on the ordinate gives the projection over the same region, but for MJO phase-5 forcing. There is a strong positive correlation (r = 0.91) in the plotted data, with the least squares fit curve (solid line) being close to the line (dashed line). This indicates that the same initial conditions are leading to similar day-7–10 projections for both MJO phase-1 and MJO phase-5 forcing in the model.

Fig. 3.
Fig. 3.

Scatterplot of the projection of onto for each set of initial conditions for MJO phase 1 against MJO phase 5. The black line is the best-fit linear curve through the data and the gray dashed line corresponds to the curve .

Citation: Monthly Weather Review 143, 4; 10.1175/MWR-D-14-00141.1

4. Analog approach with reanalysis data

a. Predictability

Predictability can refer to the intrinsic predictability of the atmosphere (i.e., the sensitivity of the evolution of the flow to small perturbations in the initial conditions), or alternatively, to the predictive skill of a model forecast. Often, this latter definition is used in the context of a numerical model. In this study, we treat predictability in the same way, with our “model” being the analog forecast method. This is the sense of predictability used throughout this study.

To address questions of predictability, as discussed in the introduction, projection calculations are performed. Using the ERA-Interim data, the projections are calculated as follows:
e6
Here, where is the lag-day-0 anomaly pattern for each MJO event, and are the corresponding MJO and non-MJO analogs, respectively, as described in section 2, for that day. The lag day is indicated by τ. The region over which these projections are calculated is the same Northern Hemisphere domain from which the analogs are calculated. Projections are first calculated separately for the lag-day 0 and all subsequent lags for each MJO event (see section 2b for the definition of an MJO event) and then averaged over all MJO events. The term [] presents a measure of how well MJO (non-MJO) analogs forecast the response to MJO events. Figure 4a uses the and calculated with the top five analogs. To evaluate the sensitivity to the number of analogs, we illustrate in Fig. 4b the results with 30 analogs. In Fig. 4, the black curve corresponds to the averaged over all MJO events and phases, and the red curve is analogous to the black curve, except that it is calculated for . The blue curve is the same as the black curve, except instead of the top 5 (Fig. 4a) and top 30 (Fig. 4b) values [see (5)], a mean of 5 (Fig. 4a) and 30 (Fig. 4b) randomly chosen values greater than 0.2 is used to calculate . The green curve in Fig. 4 corresponds to the projection of non-MJO analogs onto non-MJO days. For this calculation, projections for 100 non-MJO days are performed, where the analog days chosen are those that have lag-day-0 projections nearest to the mean of the top 5 (Fig. 4a) and top 30 (Fig. 4b) values. This projection, , is calculated as follows:
e7
where is the non-MJO day analog and is the anomaly pattern for a given non-MJO day. The statistical significance of the difference between the MJO analog (black curve) and non-MJO analog (red curve) projections is examined with a two-sample t test. Those days that exhibit statistically significant differences between the two curves are indicated by the large red dots on the red curve. An analogous approach is used to examine the statistical significance of the difference between the black and green and the black and blue curves. As can be seen, all days beyond lag-day 5 (for 5 analogs) and lag-day 8 (for 30 analogs) show projections that are statistically significant at the 95% confidence level for the red curves. The green curve shows statically significant differences in the projections between 3 and 11 days (only for 5 analogs) and the blue curve exhibits statistically significant differences for all days.
Fig. 4.
Fig. 4.

Projection time series over the entire Northern Hemisphere from 20° to 80°N. The black curve corresponds to active MJO analogs for all MJO events. The red curve corresponds to non-MJO analogs for all MJO events. The green curve corresponds to non-MJO analogs for non-MJO days. The blue curve corresponds to somewhat random analogs (see text for details) for all MJO events. (a) The top 5 analogs and (b) the top 30 analogs are used for the forecasts. Dots on the colored curves represent lag days for which the respective curve and the black curve have a statistically different mean according to a two-sample t test.

Citation: Monthly Weather Review 143, 4; 10.1175/MWR-D-14-00141.1

The separation between the black and red curves beyond day 5 (Fig. 4) implies that with similar initial conditions, as indicated by the similarity of their lag-day-0 projections, the presence of the MJO heating during the MJO events has an important impact on predictability, and that the MJO influence takes about 6 days to become apparent, which corresponds well with the above model results and with Yoo et al. (2012a). Comparing the black curve with the blue curve (suboptimal MJO analogs for MJO events) in Fig. 4, it is seen that at all lag days, the optimal analogs give a higher projection than the suboptimal analogs, suggesting that the choice of analogs with the highest projection values coincides with enhanced predictability. This result implies that in the presence of active MJO heating, the particular initial conditions also have a large impact on predictability. Finally, comparing the black curve with the green curve (non-MJO analogs for non-MJO days) in Fig. 4a, beyond day 2, the projection values for the green curves decline to levels below those of the black curve, and remain that way through day 11. This suggests that the presence of an active MJO is associated with greater predictability than when the MJO is not active.

Figure 4b, which illustrates the sensitivity to the choice of the number of analogs, shows most of the same relationships as in Fig. 4a, albeit with much smaller separation between the curves. This smaller separation is intuitive, since including more analogs that are a poorer match for the target pattern would have the effect of worsening the quality of the forecast. The corresponding curves for the other numbers of analogs tested (1, 10, and 90, not shown) follow the patterns seen between the 5- and 30-analog cases, with more analogs leading to smaller projections and less separation between the curves. The one-analog case is similar to the five-analog case, but noisier, with the curves showing more variability with lag. For the purpose of choosing the optimal numbers of analogs, we compared the difference between the black and red curves for all analog cases, searching for the analog case with the greatest separation between the black and red curves, without appearing excessively noisy. It was found that the five-analog case satisfied these criteria. Therefore, for the rest of this study, we will use five analogs in all calculations.

The sensitivity of the results illustrated in Fig. 4 to the phase speed of the MJO and the possible influence of ENSO and other interannual processes is examined as well. For each day in which the MJO amplitude is greater than 1.0, a “phase speed” is calculated. This is done by first calculating the angle θ relative to the Real-time Multivariate MJO index (RMM1) axis for each day using the RMM1 and RMM2 data. (RMM1 and RMM2 are the principal component time series of the two combined EOFs of the Wheeler and Hendon MJO index.) Centered finite differencing is then used to determine the change in that angle with time, /dt. A 5-day running mean of this quantity is used to approximate the average phase speed for a given MJO event. The results in Fig. 4 were reproduced for active MJO analogs and MJO events with a small phase speed (period greater than 90 days). It was found that most of the key findings presented in Fig. 4 were retained (not shown). With regard to ENSO, there is the possibility that the non-MJO analogs could come mostly from active ENSO years and resemble the MJO analogs from all years. For example, the extratropical circulation for non-MJO analogs during La Niña years may be very similar to the extratropical circulation associated with MJO phase-1 analogs. Calculations similar to those presented in Fig. 4 that were limited to ENSO neutral months yielded findings that were qualitatively very similar, providing further support for our analysis.

In Fig. 5, we show correlations that correspond to the curves in Fig. 4a (except for the blue curve) at every grid point for lag-day 0 through lag-day 10. The correlations are calculated as follows. Analogous to the thick black curve, the panels in the left column of Fig. 5 show the correlation at each grid point between and . Similarly, analogous to the thick red curve, the middle column in Fig. 5 illustrates the correlation between and , and analogous to the green curve, the right column in Fig. 5 shows the correlation between and . The black contours are the DJF climatological 300-hPa geopotential height. In general, the region of greatest predictability (for day 6 and onward) using the analog method is near the climatological jet maximum and jet exit region over the Pacific Ocean. The largest correlation values are consistent whether or not the MJO is active (right and left panels in Fig. 5), and also in the case where non-MJO analogs are used to predict MJO events (middle panel in Fig. 5). However, correlation values overall are highest in the left panels, as the projection time series graphs in Fig. 4a would imply.

Fig. 5.
Fig. 5.

Correlation maps. (from top to bottom) The rows indicate lag-days 0, 2, 4, 6, 8, and 10. (left) Active MJO analogs for MJO events, (middle) non-MJO analogs for MJO events, and (right) non-MJO analogs for non-MJO days. The black contours are DJF climatological 300-hPa height contours every 240 m from 8640 to 9600 m.

Citation: Monthly Weather Review 143, 4; 10.1175/MWR-D-14-00141.1

The correlations at every grid point between and and between and at lag-day 10 as a function of MJO phase is shown in Fig. 6. Lag-day 10 was chosen because a reproduction of Fig. 4 for each individual MJO phase (not shown) indicates substantial variability in projections from phase to phase at that lag. Figure 6 shows that, while the high correlation values over the western Pacific are relatively consistent from phase to phase, other areas differ substantially. This suggests that some regions are more or less predictable using the analog approach depending on the MJO phase.

Fig. 6.
Fig. 6.

Correlation maps for day 10. (from top to bottom) The rows correspond to MJO phases 1–8. (left) Active MJO analogs for MJO events and (right) non-MJO analogs for MJO events. The black contours are DJF climatological 300-hPa height contours every 240 m from 8640 to 9600 m.

Citation: Monthly Weather Review 143, 4; 10.1175/MWR-D-14-00141.1

b. Extratropical response to the MJO

The lag-day-0 geopotential height anomaly composite of , , and for each MJO phase as estimated from the analog approach in (4) are shown in Fig. 7. As expected, the MJO analogs and non-MJO analogs yield rather similar spatial structures for each MJO phase. However, most surprisingly, although there is substantial variability in the and composites from phase to phase, the difference between these two quantities, , is remarkably consistent between the eight MJO phases. This implies that there is a systematic difference in the analogs between the set of days when the MJO is inactive, and the set of days when the MJO is active, regardless of MJO phase. Indeed, this is seen in Fig. 8a, which shows that the mean difference between and averaged over all MJO events, regardless of MJO phase, resembles the difference between and for most MJO phases. The difference between the phase-independent composite of all active MJO days and all non-MJO days, weighted by the number of days in each category, is shown for comparison (Fig. 8b), and corresponds well with the systematic difference in Fig. 8a.

Fig. 7.
Fig. 7.

Lag-day-0 300-hPa geopotential height composites. (from top to bottom) The rows correspond to MJO phases 1–8. (left) Active MJO analogs for MJO events, (middle) non-MJO analogs for MJO events, and (right) the difference between the left and middle .

Citation: Monthly Weather Review 143, 4; 10.1175/MWR-D-14-00141.1

Fig. 8.
Fig. 8.

(a) The 300-hPa composite phase-independent geopotential height difference between all MJO analogs () and all non-MJO analogs () for all MJO events. (b) The 300-hPa composite phase-independent geopotential height difference between all active MJO days and all non-MJO days.

Citation: Monthly Weather Review 143, 4; 10.1175/MWR-D-14-00141.1

One potential concern raised by the existence of this systematic difference is that the separation between the black and red curves in Fig. 4, as discussed in section 4a, may in part be a result of this systematic difference, in which a favored spatial pattern exists for active MJO days, with an opposing pattern for non-MJO days. In other words, if the systematic difference is largely responsible for predictability, it is possible that the non-MJO analog forecasts degrade more quickly over time because they do not resemble the systematic difference, whereas the active MJO analogs do. An analysis was performed in which MJO events of each phase were binned into terciles based on how strongly the day-0 field projected onto the systematic difference over the Northern Hemisphere. Figure 4 was then analyzed for each tercile, and it was found that the top and bottom terciles for both the black (active MJO analogs) and red (non-MJO analogs) curves were not statistically distinct from the corresponding curves that include all terciles. It is thus concluded that the systematic difference is not responsible for the predictability differences we see in Fig. 4.

A brief analysis was performed in order to understand this systematic difference. First, the anomalous RWS (Sardeshmukh and Hoskins 1988) was investigated. However, this term varied almost linearly with the MJO phase (not shown), and was, therefore, insufficient as an explanation for the systematic difference, which is nearly independent of phase. Another test was done to examine whether the difference could be associated with a precursor pattern in the midlatitudes that is climatologically followed by an active MJO, but the findings were inconclusive and did not strongly suggest this mechanism. An examination of the sensitivity of the systematic difference to the influence of ENSO was also performed by considering only active MJO analogs, non-MJO analogs, and MJO events during ENSO neutral months. We find that the systematic difference is largely unchanged, suggesting that the systematic difference is unrelated to ENSO.

We interpret the systematic difference to reflect a difference in climatology between times when the MJO is active and times when it is inactive. This interpretation is supported by Fig. 9, which takes the composite of the 300-hPa height anomalies during DJF days when the MJO amplitude is greater than 1.0 for a given MJO phase, and shows an area-weighted projection poleward of 20°N against the composite 300-hPa height anomalies during DJF days when the MJO amplitude is greater than 1.0 regardless of phase. The fact that the composites for seven of the eight phases project positively onto this phase-independent pattern shows that the signal for a different climatology during an active MJO can be discerned in almost every phase, and is not simply explained by the dominance of one or two phases.

Fig. 9.
Fig. 9.

Area-weighted projection north of 20°N of the composite of for each MJO phase on to the composite of independent of phase, for DJF days when the MJO amplitude is greater than or equal to 1.0.

Citation: Monthly Weather Review 143, 4; 10.1175/MWR-D-14-00141.1

This systematic difference in the observational data stands in contrast with the model results, where the initial conditions were identical for the corresponding non-MJO and MJO-forced runs. Therefore, to account for this systematic difference, we subtract the mean of averaged over all events and MJO phases at each lag day from the corresponding mean of . This quantity is defined as the systematic difference for all eight MJO phases. The systematic difference is then subtracted from , which we will denote by . Figure 10 shows the lag-day-10–20 composite of for each MJO phase. The phase-1 and phase-5 patterns somewhat resemble those seen in Figs. 1a and 2a over the North Pacific and North America, although the composites are displaced farther to the east. The lag-day-10–20 period is chosen because that is when the signal appears to have the largest amplitude for most phases. This is in contrast with the model results, which already show a strong signal by lag-days 7–10. We interpret this timing difference as a result of previous MJO phases. Whereas in the model, we only see the effects of a single MJO phase, in reanalysis data, an MJO event is climatologically expected to have been preceded by an active MJO in previous phases. The extratropical response at lag-day 7 could then be a combination of responses to several MJO phases, which might dampen the signal at that time. It is also possible that the eastward displacement of anomalies in the reanalysis data is associated with MJO propagation, in contrast with the stationary MJO used in the model study. The general match we see in phases 1 and 5 between the model and the observations lends support to using rather than for projection calculations using (2).

Fig. 10.
Fig. 10.

Composite 300-hPa averaged over lag-days 10–20 for MJO phases 1–8.

Citation: Monthly Weather Review 143, 4; 10.1175/MWR-D-14-00141.1

Figure 11 shows the lag-day-0–18 composites of for MJO phase 1 and phase 5. With perfect analogs, would be expected to start with zero amplitude, and then over time evolve to have a large impact. Although does not start with zero amplitude, the amplitude of is initially much less than the corresponding , (not shown), and it does increase substantially with lag day as expected. For MJO phase 1, evolves from a spatial pattern with a small amplitude to that resembling the negative PNA. For MJO phase 5, the opposite features are observed over time. These findings suggest that the response to the MJO heating, independent of the initial midlatitude flow, has a large impact in mid- and high latitudes.

Fig. 11.
Fig. 11.

Composite of 300-hPa for (left) MJO phase 1 and (right) MJO phase 5. (from top to bottom) Lag days 0, 3, 6, 9, 12, 15, and 18, respectively.

Citation: Monthly Weather Review 143, 4; 10.1175/MWR-D-14-00141.1

c. Sensitivity to the initial flow

By analogy with Figs. 1 and 2, Fig. 12 shows the lag-day-0 for the top and bottom terciles for all eight MJO phases. The top tercile composite for each phase represents the lag-day-0 pattern that leads to a more amplified response in the lag-day-10–20 period compared with . Likewise, the bottom tercile composite for each phase represents the lag-day-0 pattern that leads to a less amplified response in the lag-day-10–20 period compared with . Figure 13 shows both the top and bottom bin means as well, but for a composite over all MJO events and phases.

Fig. 12.
Fig. 12.

Lag-day-0 300-hPa composites for the (left) top tercile and (right) bottom tercile for (from top to bottom) MJO phase 1–8. Contours indicate where the top and bottom terciles have different means at the 0.90, 0.95, and 0.99 confidence levels according to a two-sample t test.

Citation: Monthly Weather Review 143, 4; 10.1175/MWR-D-14-00141.1

Fig. 13.
Fig. 13.

Lag-day-0 300-hPa composites for the (a) top tercile and (b) bottom tercile averaged over all MJO events and phases. Contours indicate where the top and bottom terciles have different means at the 0.90, 0.95, and 0.99 confidence levels according to a two-sample t test.

Citation: Monthly Weather Review 143, 4; 10.1175/MWR-D-14-00141.1

Although the signal is not as obvious as in the model study, Fig. 12 shows that there is a somewhat consistent anomaly pattern among many MJO phases in a few key regions. First, northeastern Asia shows a positive anomaly in the bottom bin for at least six of the eight MJO phases. The top bin anomalies in the region are less consistent. Second, the Arctic coast of Siberia shows negative anomalies in the bottom bin for six of the eight MJO phases. Again, the top bin anomalies in the region are more variable. Finally, northwestern North America and/or the northeastern Pacific Ocean show a strong negative anomaly in the top bin for four of the eight MJO phases, as well as a strong positive anomaly over northwestern North America in the bottom bin for six of the eight MJO phases. All of these regions also show up well in Fig. 13. There is moderate confidence (exceeding the 0.90 confidence level) that the top and bottom phase-independent bin means differ over northeastern Asia, the Arctic coast of Siberia, and northwestern North America. There is high confidence (greater than the 0.99 confidence level) that the phase-independent bin means differ over northwestern North America. The phase-independent positive anomalies over the Arctic coast of Siberia and negative anomalies over northeastern Asia are consistent with those in the model runs for phases 1 and 5, both for the top and bottom bin means. This lends support to the model result that there is a phase-independent initial flow pattern that interacts with an MJO-induced wave train to amplify the extratropical response over the PNA region.

5. Conclusions

This study used output from an ensemble of numerical model runs (the dynamical core of a NOAA/GFDL climate model) and ERA-Interim data to address the following two questions: 1) What is the response of the atmosphere to the MJO? This includes both the direct Rossby wave response to the MJO and the interaction of this wave with the initial flow. 2) What initial flow configurations are followed by the largest, and smallest, amplitude responses to the MJO? These questions were addressed precisely within the context of the model because identical initial flows can be specified in the model runs both with and without MJO-like heating. Because one can never obtain identical flows with observational data for time periods when the MJO heating is both active and inactive, as was done with the model, we resorted to using an analog approach to address the above question with the observational data. For the analog approach with the reanalysis data, the methodology adopted was analogous to that for the model runs.

The extratropical response to MJO forcing in the model was found to be essentially identical to that in Yoo et al. (2012a). Specifically, a Rossby wave train was excited over the PNA region, with the highest amplitude response occurring about 7–10 days after the MJO heating was turned on. Forcing associated with MJO phase 1 was followed by a negative PNA-like response, while forcing associated with phase 5 was followed by a positive PNA-like response. These PNA-like responses are only apparent after subtracting out the part of the flow evolution associated with just the initial conditions.

From the model calculations, it was found for lag-day 0 that a negative 300-hPa anomaly center over northeastern China and positive anomalies over the Arctic coast of Siberia and southeastern Asia were associated with an amplified MJO response over the PNA region at day 7–10 for both MJO phase 1 and phase 5. These results indicate for the model that the large amplitude response to MJO-like heating over the North Pacific and North America depends upon the presence of large amplitude upstream anomalies over eastern Asia. Furthermore, these findings also indicate that the same midlatitude flow anomalies over eastern Asia at day 0 lead to large amplitude anomalies of opposite sign over the PNA region for the MJO phase-1 and phase-5 heating. Finding same-sign anomalies in the day-0 flow anomalies for both MJO phase-1 and phase-5 heating was rather surprising, since the sign of the anomalous tropical heating and the day-7–10 responses over the North Pacific and North America was reversed for MJO phase 1 versus MJO phase 5. Analogously, when the amplitude of the extratropical response to the MJO heating was very small, the day-0 flows for MJO phases 1 and 5 were also very similar, taking on a spatial structure with opposite sign anomalies compared to those for the large amplitude response. The mechanism by which the day-0 300-hPa geopotential height anomaly pattern over eastern Asia interacts with the MJO-excited wave train to produce a more amplified response over the North Pacific and North America to both MJO phase-1 and -5 heating was not examined. One possibility is that for both MJO phases the same preferred spatial structure for the initial disturbance can amplify the MJO-excited Rossby wave train via a positive transient eddy feedback (Shutts 1983). More research is needed to examine this and other possible mechanisms that cause the model to exhibit such behavior.

To address the same questions with reanalysis data, an analog approach was adopted, for which active (nonactive) MJO days were interpreted as corresponding to model integrations with the heating turned on (off). However, a systematic difference across all eight MJO phases was found between the MJO and non-MJO analogs. The difference arises when analogs are chosen from active versus nonactive MJO periods, which appear to have differing climatological flows. When examining the response to the MJO, this systematic difference is subtracted from the anomalies.

When these factors were taken into account, it was found that the extratropical response to the MJO over the PNA region was roughly similar between model results and the reanalysis data, with a negative PNA-like response for MJO phase-1 heating, and a positive PNA-like response for MJO phase-5 heating. However, in the observational data, the anomalies were shifted somewhat to the east as compared with the model data. Like the model results, these PNA-like responses were only apparent when the analogous flow evolution associated with the initial conditions without MJO-forcing was subtracted.

It is of note that, although the extratropical response to MJO phase 1 (phase 5) is similar over the North Pacific and North America to the extratropical response to La Niña (El Niño), the tropical convection itself has a nearly opposite spatial structure. That is to say, the tropical convection associated with La Niña (El Niño) looks very much like the tropical convection associated with MJO phase 5 (phase 1). This discrepancy could arise because of several factors, including, but not limited, to differences in the response to a stationary versus a moving heating source, or to subtle differences in the spatial structure of the tropical convection between ENSO and the MJO. The latter possibility will be the subject of a future study using the model of Yoo et al. (2012a).

As in the model, there were initial flow anomalies in particular regions that led to either large or small amplitude responses across most MJO phases. These regions were found to be from northeastern Asia, the Arctic coast of Siberia, and northwestern North America. Thus, it appears that if the corresponding anomalies are present in these regions at the beginning of an MJO event, then there is an increased likelihood that the extratropical response will project more strongly onto the composite pattern over the PNA region.

We also tested questions about predictability as it pertains to the analog method, including the importance of the presence of MJO heating, the sensitivity to the initial flow, predictability when the MJO is active versus when it is inactive, and the regional variation of the predictability. Both the MJO heating and the initial flow played important roles in determining predictability. It was found that accounting for the presence of MJO heating during MJO events improved predictability beyond day 7. Furthermore, it was found that the analog forecast is sensitive to the initial flow, in that higher projections at day 0 corresponded with a better pattern match through at least day 20. Predictability was also found to be higher when the MJO was active as compared to those times when it was inactive. Finally, while there were some areas such as the region of diffluent flow east of the climatological Pacific jet where predictability seemed to be high regardless of MJO phase, there are other areas, such as off the coast of California, where there is a strong phase dependence on predictability.

Acknowledgments

The authors offer their gratitude for support through National Science Foundation Grants AGS-1036858 and AGS-1401220, and through National Oceanic and Atmospheric Administration Grant NA14OAR4310190. In addition, we thank Dr. Sukyoung Lee for offering helpful suggestions that improved the quality of this work. We thank two anonymous reviewers whose comments benefited this study. We also thank Dr. Changhyun Yoo for making available the data from his model runs. Finally, we thank the European Centre for Medium-Range Weather Forecasts for providing us with the ERA-40 reanalysis data, and Dr. Matthew Wheeler and the Centre for Australian Weather and Climate Research for providing the MJO index values.

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1

The daily, multivariate Madden–Julian oscillation (MJO) index of Wheeler and Hendon (2004) is defined as the principal component time series of the two leading combined EOFs of the 200- and 850-hPa zonal wind and the OLR, latitudinally averaged from 15°S to 15°N. Eight phases of the MJO are defined by the signs and relative amplitudes of the two principal component time series [see Fig. 8 of Wheeler and Hendon (2004)].

2

The quantity , which contributes to , does not tend toward climatology in the model. Presumably this is because of the crude physics in dynamical core models.

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