1. Introduction
There has been a growing interest of scientific, operational, and application communities in providing forecasts in the subseasonal time range, a range that lies between the conventional medium-range weather (lead times up to 2 weeks) and seasonal (3–12 months) forecasts. The subseasonal forecast is particularly important since many management decisions, such as in agriculture and food security, fall into this band. Skillful predictions of anomalous weather events, such as extreme precipitation events, in the subseasonal time scale could provide policy makers, emergency management, and stakeholders advanced warnings to prepare for mitigation measures.
Realizing the crucial role of subseasonal prediction on bridging the gap between weather forecasting and climate prediction, there is a current international effort focused on the subseasonal prediction problem. The World Climate Research Programme (WCRP) and World Weather Research Programme (WWRP) Subseasonal to Seasonal (S2S) Prediction Project has recently been launched with the goal of advancing predictive capability at this time scale (Vitart et al. 2012). Accordingly, much attention has been paid by NOAA/NWS and the White House to produce operational multimodel ensemble forecasts at weeks 3 and 4.1 The North American Multimodel Ensemble (NMME; Kirtman et al. 2014) project is launching subseasonal intercomparison assessment of contributing climate model forecasts (Robertson et al. 2015). Additionally, the newly formed National Research Council (NRC) committee is charged with the goal of developing a 10-yr U.S. research agenda to advance subseasonal prediction.2 Such efforts provide unprecedented scientific opportunity to make significant strides in process-level understanding for subseasonal phenomena.
The Madden–Julian oscillation (MJO; Madden and Julian 1971, 1972) is the dominant mode of subseasonal variability in the tropical atmosphere and ocean. The MJO is a special type of organized tropical convection that is distinct from other forms of tropical phenomena by its vast horizontal scale (wavenumbers 1–5), subseasonal time scale (30–60 days), and eastward propagation over the Indo-Pacific warm pool. Enhanced or suppressed convection associated with the MJO affects the global weather and climate system (e.g., Zhang et al. 2013), thereby providing a source of potential predictability in subseasonal time scale. It is hoped that realizing uncapped predictability of the MJO is a key toward improving the subseasonal forecast.
The last two decades have witnessed substantial changes in the mode of MJO prediction. Until the early 2000s, dynamical models were inferior to statistical models in terms of MJO prediction, mainly due to their lack of MJO simulation capability. In most centers, MJO prediction was not a part of operational forecast suite of products until about 2010. Furthermore, the number of ensemble members was limited and forecasts, when they were made, were not issued frequently enough because of the expense of computing resources. In the most recent decade, MJO prediction has benefitted from the significant strides in the ability of models to represent the MJO (e.g., Zhang et al. 2013). Various operational forecast centers are now releasing MJO forecasts and are continuously upgrading their systems by improving model configurations (e.g., improved physics), new ensemble generation methods, better initialization schemes, and increased resolution. Current operational forecasting systems now show useful MJO prediction skill up to 3–4 weeks (Vitart and Molteni 2010; Vitart et al. 2010; Rashid et al. 2011; Vitart et al. 2012; Zhang and van den Dool 2012; Zhang et al. 2013; H. Kim et al. 2014; Neena et al. 2014; Vitart 2014; Wang et al. 2014; Xiang et al. 2015). However, this achievement is still below the theoretical estimate of predictability, which may be 6–7 weeks (e.g., Waliser et al. 2003). Thus, there would seem to be room for further enhancing MJO prediction by improving various aspects of the prediction system based on a better understanding the MJO phenomena. Understanding strengths and weaknesses of the current prediction systems would be the first step toward enhancing the MJO prediction skill.
There is consensus emerging from recent studies regarding the factors affecting the MJO predictability and prediction skill. The main factors, besides the ability of the model, are the geographic location of the MJO convection center (i.e., MJO phase) and the magnitude of the MJO signal (i.e., MJO amplitude) in the initial conditions. Earlier, ECMWF and NCEP forecast systems showed a high sensitivity of their MJO prediction skill to the initial MJO phase. They showed relatively low skill when the MJO convection is initially located over the Indian Ocean and propagates over the Maritime Continent, a problem known as the Maritime Continent MJO prediction barrier (Vitart et al. 2007; Seo et al. 2009; Vitart and Molteni 2010; Wang et al. 2014). However, recent studies showed that the predictability of the MJO is not sensitive to MJO phases, suggesting that the Maritime Continent prediction barrier is a modeling problem, rather than a predictability issue (H. Kim et al. 2014; Neena et al. 2014).
Another crucial factor that affects the MJO prediction is its initial amplitude. It has been documented that the MJO prediction skill is higher when the MJO amplitude is initially relatively large (Rashid et al. 2011; Zhang and van den Dool 2012; H. Kim et al. 2014; Neena et al. 2014; Vitart 2014; Wang et al. 2014; Xiang et al. 2015). In previous studies, initial amplitudes are classified into two or three different categories (e.g., weak, moderate, and strong) and the averaged MJO prediction skill of each category are compared. In all models, prediction skill shows a monotonic increase with the initial MJO amplitude, meaning that initially stronger MJOs possess higher prediction skill. However, the linearity of the relationship between initial MJO amplitude and MJO prediction skill has not yet been fully explored.
Although it has been shown that MJO prediction strongly depends on initial MJO phase and amplitude, the physical mechanisms behind these constraints are not well understood. Based on previous studies, there is one simple question that can be asked: Do MJO forecasts with similar initial amplitude and phase always result in similar skill? For example, if two forecasts are initialized with similar amplitude of MJO convective anomaly in the Indian Ocean, do they always result in comparable skill? If not, what ocean–atmosphere conditions and physical processes drive some MJO events to be more predictable than others? If a prediction system systematically fails or succeeds in forecasting an MJO that meets a certain set of conditions, understanding the processes behind those relationships may provide a key for improving the prediction system. In particular, realizing a growing interest in the processes involved in the MJO propagation over the Maritime Continent,3 this study aims to advance our understanding of the Maritime Continent prediction barrier issue. In addition, we investigate the possible influence of the mean biases on MJO propagation and prediction.
Section 2 introduces details of the data and methodology. In section 3, we examine the relationship between the initial MJO amplitude and the prediction skill and identify the high- and low-skill MJO events. The characteristics of high-skill versus low-skill events, in terms of initial condition and propagation, will be compared in section 4. In section 5, the relationship between the mean biases and MJO prediction is investigated. A summary and discussion follow in section 6.
2. Data and methodology
a. Data
We will use the reforecast data from the ECMWF monthly forecasting system (e.g., Vitart 2014) that has been used for real-time forecasts in the current operations. In many studies, the ECMWF system has been shown as superior compared to other systems, particularly for MJO prediction (e.g., H. Kim et al. 2014; Neena et al. 2014; Vitart 2014). MJO prediction skill in ECMWF system has gradually improved since 2002, benefited by the substantial improvement of physical parameterization, ocean–atmosphere coupling strategy, ensemble generation methods, data assimilation, etc. (Vitart 2014). The ECMWF Variable Resolution Ensemble Prediction System (VAREPS; hereafter EC) is a fully coupled model system with a large set of reforecasts generated with the purpose of evaluating and calibrating the model forecast. In the WCRP/WWRP S2S Prediction Project, two publicly available reforecasts of the ECMWF system are versions cy40r1 and cy41r1. Version cy40r1 has been used for operation before 14 May 2015 and version cy41r1 is the current operational version with the reforecasts being produced in real time. Therefore, the reforecast covering all seasons for cy41r1 will not be available until May 2016. In this study, we analyze the reforecast output of version cy40r1. Details of this version can be found at the ECMWF website.4
The reforecast of cy40r1 consists of a five-member ensemble generated at the same date as the real-time forecasts for the past 20 years starting from January 1994. The reforecast used in this study is projected to 32-day horizons every Thursday with the first 10 days at about a 32-km horizontal resolution (spectral truncation T639 or 0.28125° latitude/longitude) and changes to about a 64-km resolution (spectral truncation T319 or 0.5625° latitude/longitude) from day 11. Orography fields (represented by surface geopotential) prescribed in the EC reforecasts for the T639 and T319 reforecasts are obtained from the ECMWF website.5 There are 91 vertical levels extending to 0.01 hPa. Reforecasts have been initialized from ERA-Interim (Dee et al. 2011) and Ocean Renalysis System 4 (ORAS4; Balmaseda et al. 2013). The atmospheric model is coupled to the ocean from day 0. The reforecast data cover 20 years from 1994 to 2013, resulting in total 5200 sets of 32-day integrations (52 sets per year × 20 yr × 5 ensembles). Daily mean fields of outgoing longwave radiation (OLR), zonal wind at 200 hPa (U200) and 850 hPa (U850), sea surface temperature (SST), and precipitation (Precip) are extracted from the reforecast. We use the zonal wind field from ERA-Interim products, OLR from the Advanced Very High Resolution Radiometer (Liebmann and Smith 1996), NOAA Optimum Interpolation Sea Surface Temperature (Reynolds et al. 2007), and precipitation from the Global Precipitation Climatology Project version 2.2 (Adler et al. 2003). These datasets will be referred to as “observation” for convenience. The observational period extends from 1981 to 2013. A daily climatology is calculated over the period from 1981 to 2013 for observations, and from 1994 to 2013 for the EC reforecast.
b. MJO index
The Wheeler and Hendon (2004) Real-Time Multivariate MJO (RMM) index is calculated following Gottschalck et al. (2010). RMM indices, RMM1 and RMM2, are the time series of the principal component of the first and second empirical orthogonal functions (EOFs) of the OLR, U200, and U850 averaged between 15°N and 15°S. RMM1 represents the anticorrelation in convection between the Indian Ocean and western Pacific Ocean, and RMM2 represents convective activity over the Maritime Continent. The circulation patterns (U200 and U850) represent a dynamically coherent baroclinic structure associated with the convective anomaly. These two modes explain about 27% of the total observed variance. Predicted RMMs are obtained by projecting the reforecast anomalies of zonal winds and OLR onto the observed eigenvectors. More details of the methodology can be found in H. Kim et al. (2014). Figure 1 represents the observed MJO life cycle in eight different phases by compositing the OLR and U850 anomalies without discrimination for amplitude or season.
MJO life cycle composite maps for OLR (W m−2, shading) and 850-hPa zonal wind (contour interval is 0.5 m s−1, and zero contours are omitted) anomalies calculated for each of the eight MJO phases (P1–P8) for all season from 1981 to 2013.
Citation: Journal of Climate 29, 11; 10.1175/JCLI-D-15-0862.1
MJO life cycle composite maps for OLR (W m−2, shading) and 850-hPa zonal wind (contour interval is 0.5 m s−1, and zero contours are omitted) anomalies calculated for each of the eight MJO phases (P1–P8) for all season from 1981 to 2013.
Citation: Journal of Climate 29, 11; 10.1175/JCLI-D-15-0862.1
MJO life cycle composite maps for OLR (W m−2, shading) and 850-hPa zonal wind (contour interval is 0.5 m s−1, and zero contours are omitted) anomalies calculated for each of the eight MJO phases (P1–P8) for all season from 1981 to 2013.
Citation: Journal of Climate 29, 11; 10.1175/JCLI-D-15-0862.1
c. Measures of MJO prediction skill: Collective and segment prediction skill
The conventional measures of MJO prediction skill use a collection of MJO forecasts and calculate scalar metrics [e.g., bivariate anomaly correlation coefficient (ACC)] as a function of forecast lead time (e.g., Lin et al. 2008). For example, when the RMM is employed, for each lead time, the RMM1 and RMM2 for all cases considered are used to calculate the scalar metrics that represent a general prediction skill of a forecast system. The same method can be applied to subsets of forecasts (e.g., those starting from different MJO phases or amplitude). By comparing the prediction skill of each subset, one could examine the sensitivity of prediction skill to various factors (e.g., RMM prediction skill in various phase or amplitude as a function of lead time). However, this conventional method, which is a collective skill measure, cannot be applied to an individual forecast set that has only one predicted value at different lead times. Hence, using a collective skill measure, one cannot group individual forecasts by their prediction skill.
3. Identification of the high-skill and low-skill MJO events
In this section, we will identify the high- and low-skill MJO events in order to compare their characteristics. Before separating the MJO events, we will briefly review the overall MJO prediction skill in the current EC forecast system. The general RMM prediction skill of the current EC forecast is measured by the collective prediction skill first. The prediction skill of ensemble mean for all season is about 30–32 days as measured by the bivariate anomaly correlation coefficient exceeding 0.5. This is about 3–5 days improvement compared to its previous operational version (H. Kim et al. 2014; Vitart 2014). Particularly, skill increases significantly when the predictions start at phase 2 (Fig. 1), with approximately 0.2 improvement of ACC for the mean from days 25 to 30 compared to the previous version used in H. Kim et al. (2014). Experiments with the coupling from day 0 [rather than from day 10 as in the previous version in H. Kim et al. (2014)] produced a slight improvement in MJO skill scores [a gain of about 1 day of predictive skill; see Fig. 13 in Janssen et al. (2013)]. While there is still a gap between the predictability and prediction skill, the gap is getting narrower by continuously improving the system.
We classify individual reforecasts into a few groups depending on the initial MJO amplitude and the segment prediction skill of them. We focus on a specific initial MJO phase: phase 2, in which the convection center is located over the Indian Ocean (Fig. 1) and where the MJO is expected to propagate across the Maritime Continent during the forecast period. The selection of a particular initial MJO phase is motivated by the fact that there has been a growing interest of understanding the critical processes involved in the MJO propagation, particularly from the Indian Ocean to the western Pacific, and that the Maritime Continent prediction barrier still exists in many operational forecasting systems.
a. MJO initial amplitude and prediction skill relationship
As a first step toward identifying the high- and low-skill events, the relationship between initial MJO amplitude and the segment prediction skill is examined. A total of 670 reforecasts (134 events × 5 ensembles) with initial phase 2 are selected. To categorize the skill by its initial amplitude, we define the amplitude as the square root of RMM12 plus RMM22 based on the observation. The events of the initial amplitude greater than 1.5 are selected as strong MJO events (total 42 cases out of 134 cases), events with initial amplitude between 0.7 and 1.5 as moderate MJO events, and the rest as weak or non-MJO events. Two amplitude thresholds, 0.7 and 1.5, are chosen arbitrarily to categorize about 50% of reforecasts as moderate MJO events (total 68 events). It needs to be emphasized that events are selected based on the observed initial amplitude and phase. Figure 2 shows the segment prediction skill as a function of initial amplitude. It is clear that the segment prediction skills for initially strong MJO events are skewed to relatively high values with having only one case lower than 0.5, while the skills in the moderate and weak or non-MJO groups are widely distributed. If we take the average of skill for each amplitude category, skill increases monotonically with amplitude from 0.62 in the weak or non-MJO group, to 0.70 in the moderate group, and to 0.82 in the strong group, consistent with previous studies. However, when the skills of reforecasts are considered individually, the initial amplitude–prediction skill relationship is not linear. Particularly, the skills of the moderate category are broadly scattered and not clearly skewed in any direction. Identifying factors in oceanic and atmospheric conditions that lead a reforecast to having a relatively high skill or low skill would help in improving the prediction system. For further analysis, reforecasts in the moderate category (a total of 68 events) are grouped into high- and low-skill cases, and the difference in their oceanic and atmospheric conditions as well as the physical processes during forecast period will be examined in the subsequent sections. To clarify that high- and low-skill events do not depend strongly on season, we further distinguish these phase-2 MJO events by season (not shown). Most of the strong MJO events occurred in boreal winter (November–April) and weak or non-MJO events in summer (May–October). However, the frequency of moderate MJO events is less sensitive to seasons. Because the seasonality of MJO prediction is an important topic, this will be investigated in future work.
Relationship between the initial MJO amplitude (x axis) and ensemble mean segment prediction skill (y axis) for the forecasts starting at phase 2. Two gray vertical lines indicate initial amplitudes of 0.7 and 1.5.
Citation: Journal of Climate 29, 11; 10.1175/JCLI-D-15-0862.1
Relationship between the initial MJO amplitude (x axis) and ensemble mean segment prediction skill (y axis) for the forecasts starting at phase 2. Two gray vertical lines indicate initial amplitudes of 0.7 and 1.5.
Citation: Journal of Climate 29, 11; 10.1175/JCLI-D-15-0862.1
Relationship between the initial MJO amplitude (x axis) and ensemble mean segment prediction skill (y axis) for the forecasts starting at phase 2. Two gray vertical lines indicate initial amplitudes of 0.7 and 1.5.
Citation: Journal of Climate 29, 11; 10.1175/JCLI-D-15-0862.1
b. High-skill versus low-skill events
To examine the characteristics of high-skill versus low-skill events starting at phase 2 with moderate amplitude (hereafter, simply high-skill and low-skill events), we classify reforecasts into high- and low-skill events based on their segment prediction skill. If the segment skill is equal to or above 0.74, the event is considered a high-skill event; the rest are low-skill events. The threshold value 0.74 is determined arbitrarily to split the high- and low-skill events equally (each has 34 events). Using each of 34 (170) events of the 32-day ensemble-mean (individual ensemble members) forecast sets, the collective prediction skill is calculated as a function of lead days (Fig. 3). The skill of ensemble mean is clearly higher than that of the individual ensembles in the high-skill MJO, and there is a large interensemble spread. In low-skill events, although the prediction skill stays much the same as high-skill events up to day 5, the skill drops rapidly as lead time increases. The skill in the ensemble mean reaches correlation of 0.5 at day 16 in low-skill events, whereas for high-skill events the correlation stays above 0.7 during the entire period. This suggests that, even starting at similar amplitude and phase, some events are better predicted with an additional two weeks of skill.
Collective prediction skill (bivariate ACC) as a function of forecast lead days for high-skill (red) and low-skill (blue) events initialized at phase 2 in ensemble mean (thick lines) and individual ensembles (thin lines).
Citation: Journal of Climate 29, 11; 10.1175/JCLI-D-15-0862.1
Collective prediction skill (bivariate ACC) as a function of forecast lead days for high-skill (red) and low-skill (blue) events initialized at phase 2 in ensemble mean (thick lines) and individual ensembles (thin lines).
Citation: Journal of Climate 29, 11; 10.1175/JCLI-D-15-0862.1
Collective prediction skill (bivariate ACC) as a function of forecast lead days for high-skill (red) and low-skill (blue) events initialized at phase 2 in ensemble mean (thick lines) and individual ensembles (thin lines).
Citation: Journal of Climate 29, 11; 10.1175/JCLI-D-15-0862.1
To condense the characteristics of the amplitude and propagation change by forecast lead days, we compare RMMs composites in a phase-space diagram (Fig. 4). Since the initial phases and amplitudes are computed based on the observation and not prediction, slight differences exist between observed and predicted RMMs even on day 1 due to the model error. Predicted RMMs of individual ensembles on day 1 are plotted together with the ensemble mean. While all observed MJO events start on phase 2 (not shown), some predicted MJOs start in slightly different phases. Because of the limited number of samples, we do not investigate the details of each case but focus on the mean statistics of high- and low-skill events. In the composite of high-skill events (Fig. 4), while the predicted amplitude of the ensemble mean is weaker than the observed during the entire forecast period, the predicted events propagate over the Indian Ocean to western Pacific with comparable phase speed to observation, leading to a relatively high prediction skill. In the low-skill events, both observed and predicted RMMs propagate faster than the high-skill events and lose their amplitude rapidly.
RMM composite phase-space diagram for high-skill (red) and low-skill (blue) events starting at phase 2 in observation (solid lines with open circle) and prediction (dotted lines with closed circle). Circles represent every 5 days from day 1 (square). Red and blue (orange and light blue) dots represent the ensemble mean (individual ensembles).
Citation: Journal of Climate 29, 11; 10.1175/JCLI-D-15-0862.1
RMM composite phase-space diagram for high-skill (red) and low-skill (blue) events starting at phase 2 in observation (solid lines with open circle) and prediction (dotted lines with closed circle). Circles represent every 5 days from day 1 (square). Red and blue (orange and light blue) dots represent the ensemble mean (individual ensembles).
Citation: Journal of Climate 29, 11; 10.1175/JCLI-D-15-0862.1
RMM composite phase-space diagram for high-skill (red) and low-skill (blue) events starting at phase 2 in observation (solid lines with open circle) and prediction (dotted lines with closed circle). Circles represent every 5 days from day 1 (square). Red and blue (orange and light blue) dots represent the ensemble mean (individual ensembles).
Citation: Journal of Climate 29, 11; 10.1175/JCLI-D-15-0862.1
4. Favorable initial conditions and key physical processes for MJO propagation across the Maritime Continent
a. Initial condition and propagation characteristics
We have shown that the initially moderate MJO events can result in either high or low skill forecasts. Are there clear differences in initial conditions that translate into changes in prediction skill? To answer this question, we examine the initial oceanic and atmospheric conditions and propagation characteristics. Figure 5 compares the composite maps of the predicted OLR and SST anomalies at day 1 for both high- and low-skill events. The predictions shown in Fig. 5 are similar to the observations (not shown). The initial distribution of OLR anomalies in high-skill events (Fig. 5a) show a clear dipole pattern of convection with enhanced convective anomalies over the Indian Ocean and strongly suppressed convective anomalies in the western Pacific. The convective anomalies over the western Pacific are associated with positive SST anomalies (maximum > 0.3 K). In contrast, for the low-skill events (Fig. 5b), even though the convective anomalies have similar amplitude and phase in the Indian Ocean, the signal over the western Pacific is almost absent, resulting in a monopole convective anomaly structure. Given that the initial amplitude and phase of the RMM-defined MJOs are similar in the two categories (high and low skill), the drastic contrast in the convective pattern is surprising. This issue will be addressed later.
The composite maps of predicted SST (K, shading) and OLR anomalies (W m−2, contour) at day 1 for (a) high-skill and (b) low-skill MJO events. The SST anomalies are multiplied by 100. Negative OLR anomalies are dashed contours with 4 W m−2 intervals and omitting the values from −5 to 5 W m−2.
Citation: Journal of Climate 29, 11; 10.1175/JCLI-D-15-0862.1
The composite maps of predicted SST (K, shading) and OLR anomalies (W m−2, contour) at day 1 for (a) high-skill and (b) low-skill MJO events. The SST anomalies are multiplied by 100. Negative OLR anomalies are dashed contours with 4 W m−2 intervals and omitting the values from −5 to 5 W m−2.
Citation: Journal of Climate 29, 11; 10.1175/JCLI-D-15-0862.1
The composite maps of predicted SST (K, shading) and OLR anomalies (W m−2, contour) at day 1 for (a) high-skill and (b) low-skill MJO events. The SST anomalies are multiplied by 100. Negative OLR anomalies are dashed contours with 4 W m−2 intervals and omitting the values from −5 to 5 W m−2.
Citation: Journal of Climate 29, 11; 10.1175/JCLI-D-15-0862.1
To examine the propagation characteristics, the longitude–time composites of OLR and U850 are employed (Fig. 6). The observed counterparts for the high-skill events have relatively well-organized eastward propagation with anomalous low-level easterly wind preceding the convection anomaly (Fig. 6a). An opposite phase of MJO convection anomaly develops over the western Indian Ocean at around day 15 associated with the westerly wind anomaly to the east of the suppressed convection. These characteristics are captured to some extent in the prediction but with weaker amplitude than observed (Fig. 6b). The predicted low-level wind anomaly shows eastward propagation to the eastern Pacific until day 32. For the low-skill events (Figs. 6c,d), both the observations and forecasts exhibit a propagation of convective anomaly that is much faster than that in the high-skill events, with a phase speed resembling that of the convectively coupled equatorial Kelvin wave (e.g., Wheeler and Kiladis 1999). In short, the high- and low-skill events show clear differences in their initial conditions, especially the distribution of convective anomaly, and in their representation of eastward propagation. In the high-skill (low skill) events, the initial condition of convection is characterized by a dipole (monopole) structure, and the phase speed of the eastward propagation is about 5.0 m s−1 (9.0 m s−1), calculated by predicted U850 change from day 1 to day 10. Interestingly, in both high- and low-skill events, predicted OLR signal becomes weak after around day 15.
Longitude–time composites of the OLR (W m−2, shading) and U850 (m s−1, contour) anomalies averaged over 10°S–10°N for (a),(b) high-skill and (c),(d) low-skill MJO events in (left) observation and (right) prediction. Contour interval is 0.4 m s−1 and zero contours are omitted.
Citation: Journal of Climate 29, 11; 10.1175/JCLI-D-15-0862.1
Longitude–time composites of the OLR (W m−2, shading) and U850 (m s−1, contour) anomalies averaged over 10°S–10°N for (a),(b) high-skill and (c),(d) low-skill MJO events in (left) observation and (right) prediction. Contour interval is 0.4 m s−1 and zero contours are omitted.
Citation: Journal of Climate 29, 11; 10.1175/JCLI-D-15-0862.1
Longitude–time composites of the OLR (W m−2, shading) and U850 (m s−1, contour) anomalies averaged over 10°S–10°N for (a),(b) high-skill and (c),(d) low-skill MJO events in (left) observation and (right) prediction. Contour interval is 0.4 m s−1 and zero contours are omitted.
Citation: Journal of Climate 29, 11; 10.1175/JCLI-D-15-0862.1
Recent studies have emphasized the importance of the dipole structure in the convective anomaly for the propagation of the MJO (D. Kim et al. 2014; Adames and Wallace 2015). D. Kim et al. (2014) showed that a suppressed convective anomaly over the western Pacific is a necessary condition for an enhance convection over the Indian Ocean to propagate across the Maritime Continent. By analyzing the moist static energy of the MJO, D. Kim et al. (2014) suggested that the suppressed anomaly over the western Pacific plays a critical role in inducing a Rossby wave response to its west. The circulation anomalies and resulting anomalous meridional moisture advection associated with the Rossby wave response provide favorable conditions for the propagation of the MJO across the Maritime Continent. The moisture budget analysis of Adames and Wallace (2015) showed similar results. That is, an initial state with a dipole convective anomaly pattern favors the MJO propagation across the Maritime Continent.
Collectively, these results suggest that the horizontal pattern of convective anomaly in the initial conditions could be a useful indicator of how skillful a prediction will be for the cases in which there is initial intermediate MJO amplitude. To test this argument, the relationship between the observed western Pacific (15°S–15°N, 120°E–180°) OLR anomaly (OLRwp) at day 1 and the segment prediction skills for all initially strong and moderate events starting at phase 2 are sought (Fig. 7). Although the prediction skills are not clearly separated as a function of the OLRwp, most of the relatively high skill events have initially drier western Pacific to the east of the Maritime Continent. The frequency of a dry western Pacific occurring is higher in high-skill than in low-skill events. It seems that the drier western Pacific is a necessary but not sufficient condition for high-skill MJO prediction events.
Segment prediction skill (y axis) and observed OLR anomaly over the western Pacific (WP) (x axis; 15°S–15°N, 120°E–180°) at day 1 for all initially strong and moderate events.
Citation: Journal of Climate 29, 11; 10.1175/JCLI-D-15-0862.1
Segment prediction skill (y axis) and observed OLR anomaly over the western Pacific (WP) (x axis; 15°S–15°N, 120°E–180°) at day 1 for all initially strong and moderate events.
Citation: Journal of Climate 29, 11; 10.1175/JCLI-D-15-0862.1
Segment prediction skill (y axis) and observed OLR anomaly over the western Pacific (WP) (x axis; 15°S–15°N, 120°E–180°) at day 1 for all initially strong and moderate events.
Citation: Journal of Climate 29, 11; 10.1175/JCLI-D-15-0862.1
b. Ocean–atmosphere interaction
Previous studies revealed the importance of the ocean feedback to the MJO propagation (e.g., review in DeMott et al. 2015). The warm SST east of the MJO convection in the Pacific Ocean supports the MJO propagation by affecting SST-modulated heat fluxes, thus enhancing the boundary layer moisture convergence that maintains the convective anomalies and fuels the eastward propagation (e.g., Lindzen and Nigam 1987; Maloney and Sobel 2004; Back and Bretherton 2009; Hsu and Li 2012; Hirata et al. 2013). Figure 5a suggests that the ocean feedback process is associated with the high-skill events. The positive western Pacific SST anomaly at day 1 indicates that the suppressed convection allows a steady warming of the SST due to the weak surface wind and enhanced downward solar radiation. To examine the temporal changes of the convection and underlying SST, the area-averaged OLR and SST anomalies over the western Pacific (15°S–15°N, 110°–160°E) are compared as a function of lead days (Fig. 8). Since the SST does not change significantly during the short forecast period, we have removed the 32-day SST average of each 32-day segment in both observation and prediction, respectively. During observed high-skill MJO (Fig. 8a), positive SST and positive OLR anomalies (suppressed convection) over the western Pacific are present at day 1. During the initial suppressed phase in the western Pacific, and prior to maximum convection, low-level easterly wind anomalies become significant over the warm western Pacific (Fig. 6a) where the climatological westerly wind dominates. Decreased evaporative cooling and enhanced downward solar radiation raise SST anomalies to the east of the convection (e.g., Hirata et al. 2013). After about day 5, the suppressed convective anomaly decreases its amplitude and changes to a convectively active phase (Fig. 8a). During the convection phase, reduced solar heating and evaporative surface cooling and mixing via strong low-level westerly induce SST change to negative anomalies. For both observation and predictions, this convection–SST phase relationship is well captured during the eastward propagation for high-skill MJO events. However, in low-skill events, no significant SST–convection phase relationship can be found in the western Pacific in both observation and prediction (Fig. 8b).
Area-averaged (15°S–15°N, 110°–160°E) values for SST (K, red) and OLR (W m−2, black) anomalies as a function of forecast lead days for (a) high-skill and (b) low-skill MJO. Observed values are denoted by the solid lines and predicted values are marked with open circles.
Citation: Journal of Climate 29, 11; 10.1175/JCLI-D-15-0862.1
Area-averaged (15°S–15°N, 110°–160°E) values for SST (K, red) and OLR (W m−2, black) anomalies as a function of forecast lead days for (a) high-skill and (b) low-skill MJO. Observed values are denoted by the solid lines and predicted values are marked with open circles.
Citation: Journal of Climate 29, 11; 10.1175/JCLI-D-15-0862.1
Area-averaged (15°S–15°N, 110°–160°E) values for SST (K, red) and OLR (W m−2, black) anomalies as a function of forecast lead days for (a) high-skill and (b) low-skill MJO. Observed values are denoted by the solid lines and predicted values are marked with open circles.
Citation: Journal of Climate 29, 11; 10.1175/JCLI-D-15-0862.1
c. Drawbacks of using the RMM index
Before we move on the investigation of the mean bias and prediction skill relationship, we will discuss some drawbacks in using the RMM index as a measure of the MJO. In the RMM phase-space diagram (Fig. 4), we showed that in the high-skill events, the RMM-defined MJO signal shows propagation even after day 15 (Fig. 4) and prediction maintains high skill throughout (Fig. 3). However, even in high-skill events, the convective signal becomes almost absent after lead day 15 (Fig. 6). If the forecast convective signal is marginal after day 15, then what causes such a high prediction skill until day 32? It has become apparent that the fractional contribution of winds to the variance of RMMs is relatively larger than the contribution of the convective fields. This is a major weakness of the RMM index (Straub 2013; Ventrice et al. 2013; Liu et al. 2016; Wolding and Maloney 2015). To address this issue in our results, Fig. 9 shows the observed and predicted anomalies (averaged over 10°S–10°N) of three variables used in defining the RMM index. On day 1, while overall predicted amplitude is slightly weaker than the observed, the convection and wind anomalies are well captured in the predictions (Figs. 9a,b), resulting in high skill at the beginning of the forecast (Fig. 3) in both high- and low-skill events. However, for the day 20–25 average in high-skill events (Fig. 9c), although the predicted convective anomaly shows negligible strength over the Indo-Pacific region compared to the observation, the wind anomalies still have comparable magnitudes (Fig. 9c). Therefore, although the reforecasts do not predict the convective anomaly correctly, the prediction skill could result in high skill after day 15 since the fractional contribution of winds to the RMM is larger than the convection signal (Straub 2013).
Latitudinal average (10°S–10°N) of OLR (W m−2, gray and black), U850 (m s−1, blue), and U200 (m s−1, red) anomalies for observation (solid lines and gray shading) and prediction (dashed lines) at day 1 for (a) high-skill and (b) low-skill events and for (c) days 20–25 average for high-skill events.
Citation: Journal of Climate 29, 11; 10.1175/JCLI-D-15-0862.1
Latitudinal average (10°S–10°N) of OLR (W m−2, gray and black), U850 (m s−1, blue), and U200 (m s−1, red) anomalies for observation (solid lines and gray shading) and prediction (dashed lines) at day 1 for (a) high-skill and (b) low-skill events and for (c) days 20–25 average for high-skill events.
Citation: Journal of Climate 29, 11; 10.1175/JCLI-D-15-0862.1
Latitudinal average (10°S–10°N) of OLR (W m−2, gray and black), U850 (m s−1, blue), and U200 (m s−1, red) anomalies for observation (solid lines and gray shading) and prediction (dashed lines) at day 1 for (a) high-skill and (b) low-skill events and for (c) days 20–25 average for high-skill events.
Citation: Journal of Climate 29, 11; 10.1175/JCLI-D-15-0862.1
Another issue is that both high- and low-skill events are selected as the initially moderate category for phase 2, although the initial convective anomalies in the western Pacific have different structure (dipole versus monopole mode; Fig. 4). In both observation and prediction, the western Pacific dry anomaly is apparent in the high-skill events (Fig. 9a) but not in the low-skill events (Fig. 9b). However, the anomalous low- and upper-level wind patterns at day 1 are similar between high- and low-skill events. These similar wind patterns and amplitude at day 1 force these events to be categorized as moderate phase-2 events. Therefore, when the RMM index is used for the prediction of MJO convective signal, it may potentially misinform the skill of the MJO. To compensate for the weakness of RMM index in representing the convection, several alternative methods have been introduced (e.g., Kiladis et al. 2014; Liu et al. 2016). However, the use of proper MJO index depends on how one defines the MJO phenomena. In this study, we will continue to use RMM as an index for MJO events, bearing in mind the drawbacks, since most of MJO prediction studies and operational predictions still rely heavily on the RMM index.
5. Systematic mean biases and the possible influence on MJO prediction
To explain the possible barrier for MJO prediction, we examine the relationship between the MJO prediction skill and the systematic mean bias in the EC reforecasts. Figure 6 showed that the convective signal in the reforecasts almost disappears after about day 15 when the MJO convection center reaches the western Pacific. We assumed that the mean bias could be an important factor that deteriorates the MJO propagation farther east. Figure 10 shows the climatological annual mean bias of precipitation, SST, and zonal winds (U850 and U200) averaged over the entire lead days (days 1–32) for the entire reforecast period (20 yr) for all events starting at phase 2, regardless of the initial amplitude. Excessive precipitation bias is found in the vicinity of the Maritime Continent, in agreement with other studies of various state-of-the-art coupled climate models (e.g., DeMott et al. 2014). A warm SST bias is found in the equatorial Indian Ocean extending to the western Pacific with a maximum over the Maritime Continent oceans (Fig. 10b). The warm SST biases could increase low-level moist static energy, thus inducing favorable conditions for convection and the related excessive precipitation. Over the equatorial central to eastern Pacific, cold SST biases are dominant with a significantly large maximum value of about −1.0 K. The strong SST gradient between the western and eastern Pacific induces a strong pressure gradient and associated low-level easterly (Fig. 10a) and upper-level westerly bias (Fig. 10b), similar to those found in climate models (e.g., Lin 2007).
Climatological annual mean bias for phase-2 events in (a) precipitation (mm day−1, shading) and U850 (contour interval is 1 m s−1, and zero contours are omitted) and (b) SST (K, shading, multiplied by 10) and U200 (contour interval is 2 m s−1). (c),(d) As in (a),(b), but for initial bias. Dashed lines indicate negative values.
Citation: Journal of Climate 29, 11; 10.1175/JCLI-D-15-0862.1
Climatological annual mean bias for phase-2 events in (a) precipitation (mm day−1, shading) and U850 (contour interval is 1 m s−1, and zero contours are omitted) and (b) SST (K, shading, multiplied by 10) and U200 (contour interval is 2 m s−1). (c),(d) As in (a),(b), but for initial bias. Dashed lines indicate negative values.
Citation: Journal of Climate 29, 11; 10.1175/JCLI-D-15-0862.1
Climatological annual mean bias for phase-2 events in (a) precipitation (mm day−1, shading) and U850 (contour interval is 1 m s−1, and zero contours are omitted) and (b) SST (K, shading, multiplied by 10) and U200 (contour interval is 2 m s−1). (c),(d) As in (a),(b), but for initial bias. Dashed lines indicate negative values.
Citation: Journal of Climate 29, 11; 10.1175/JCLI-D-15-0862.1
To examine the temporal change of these biases, the initial bias (day 1) is compared (Figs. 10c,d). Wet biases in the vicinity of the Maritime Continent and the associated low-level easterly wind in the western Pacific appear at day 1 (Fig. 10c). At day 1, strong cold SST bias, which is likely an ocean initialization error, and associated upper-level wind bias are already occurring in the equatorial eastern Pacific (Fig. 10d). The excessive precipitation bias over the Maritime Continent regions and the east–west SST gradient bias may induce a pressure gradient bias that, in turn, could enhance the wind biases after day 1. Such an enhanced easterly wind bias over the tropical Pacific can induce steep eastward shoaling of the thermocline and thus exaggerate positive oceanic–atmospheric Bjerknes feedback (Bjerknes 1966). The enhanced Walker circulation is likely to enhance the ocean upwelling, thus contributing to the cold SST bias in the regions of easterly biases. Moreover, the strong wind bias may cause an excessive latent heat flux and contribute to the cold SST bias as well. While the cold SST bias is confined to the eastern Pacific at the beginning of the forecast, it continuously shifts to the west as lead time increases (not shown). In addition to this basinwide feedback, the interaction between local SST and shortwave solar flux could also play a role on enhancing the mean bias. Over the cold tongue region, cold SST bias could increase the static stability of the boundary layer, thus increasing the low cloud amount that, in turn, decreases the surface downward shortwave flux, thus cooling the SST (Klein and Hartmann 1993; Peters and Bretherton 2005). This local positive feedback in the cold tongue region and the basinwide Bjerknes feedback could jointly enhance the Walker circulation until the bias fields reach their equilibrium state.
In short, the initial wet precipitation bias in the Maritime Continent and the cold SST bias in equatorial Pacific lead to an enhanced Walker circulation and amplify the positive ocean–atmosphere feedback to some extent. However, it is unclear where the biases originate and what causes their development. Since the atmospheric and oceanic fields are closely coupled, bias in one field could impact other fields. More work is needed to understand the origin of the biases in the reforecasts.
Another factor that amplifies the bias could be the model resolution. A wet bias is found over the Maritime Continent vicinity at day 1 (Fig. 10c). Figure 11 compares the change of precipitation and U850 biases. Values are averaged over 5°S and 5°N as a function of forecast lead days. The easterly wind bias increases as forecast lead day increases, but the wet bias maintains a comparable magnitude until day 10 (Fig. 11). At day 11, the time when the model changes its horizontal resolution from about 32 to 64 km, the wet bias almost doubles in magnitude in the center of the Maritime Continent (Fig. 11). The low- and upper-level wind biases rapidly amplify, consistent with the growing wet bias.
Mean bias for precipitation (shading) and U850 (contour interval 1 m s−1, and zero contours are omitted) averaged over 5°S–5°N as a function of forecast lead days.
Citation: Journal of Climate 29, 11; 10.1175/JCLI-D-15-0862.1
Mean bias for precipitation (shading) and U850 (contour interval 1 m s−1, and zero contours are omitted) averaged over 5°S–5°N as a function of forecast lead days.
Citation: Journal of Climate 29, 11; 10.1175/JCLI-D-15-0862.1
Mean bias for precipitation (shading) and U850 (contour interval 1 m s−1, and zero contours are omitted) averaged over 5°S–5°N as a function of forecast lead days.
Citation: Journal of Climate 29, 11; 10.1175/JCLI-D-15-0862.1
Schiemann et al. (2014) showed that increasing horizontal resolution improves the precipitation simulation particularly in Maritime Continent region due to better representation of complex orography. Figure 12 compares the subgrid orography (represented in surface geopotential) used as boundary conditions up to day 10 (Fig. 12a) and after day 11 (Fig. 12b). It represents the height of the terrain with respect to the model-defined Earth. Up to day 10, the orography is at finer resolution (32 km) and represents complex and heterogeneous regions. After day 11, since the resolution decreases (64 km), there are relatively fewer grid points that resolve the complexity of land regions. The wet bias and low-level convergence east of the convective Maritime Continent region could be enhanced immediately when the resolution changes.
Orography represented by surface geopotential (m2 s−2, divided by 1000) in the land surface boundary condition prescribed (a) before day 10 and (b) after day 11.
Citation: Journal of Climate 29, 11; 10.1175/JCLI-D-15-0862.1
Orography represented by surface geopotential (m2 s−2, divided by 1000) in the land surface boundary condition prescribed (a) before day 10 and (b) after day 11.
Citation: Journal of Climate 29, 11; 10.1175/JCLI-D-15-0862.1
Orography represented by surface geopotential (m2 s−2, divided by 1000) in the land surface boundary condition prescribed (a) before day 10 and (b) after day 11.
Citation: Journal of Climate 29, 11; 10.1175/JCLI-D-15-0862.1
How do those biases hinder the MJO eastward propagation and thus prediction? The wet bias over the Maritime Continent could induce a local Walker circulation that, in turn, would promote a descending motion over the western Pacific. Also, the easterly anomaly over the western Pacific would advect a drier air into the western Pacific where the mean moisture gradient is negative. Both horizontal and vertical circulation biases would make the west Pacific area unfavorable for the development of anomalous convection, thereby weakening MJO propagation to the western Pacific. Moreover, the strong wind biases over the equatorial Pacific may inhibit the MJO propagation after day 15 when the MJO enters the western Pacific and the MJO associated wind has the opposite sign to the wind bias. The relationship between the mean bias and MJO prediction deserves further investigation.
6. Summary and discussion
We examined the characteristics of MJO propagation across the Maritime Continent in the ECMWF ensemble prediction system using a 20-yr reforecast dataset produced by the recent operational version (cy40r1). We focused on MJO events initialized over the Indian Ocean (phase 2) and investigated the key dynamical factors attributed to the MJO propagation and prediction. Analysis of the initial MJO amplitude and prediction skill relationship shows that the initial amplitude–prediction skill relationship is not linear. Particularly, when the prediction starts with moderate amplitude, predictions can have either high or low skill depending on the initial ocean-atmospheric condition. In the high-skill events, the initial condition is characterized by a clear dipole pattern of convection with an enhanced convective anomaly over the Indian Ocean and strongly suppressed convective anomalies in the western Pacific. This suppressed convective anomaly is a necessary condition for enhanced convection over the Indian Ocean to propagate across the Maritime Continent. Therefore, high-skill events result in a relatively well-organized eastward propagation with anomalous low-level easterly wind preceding the convection anomaly. According to the results found in this study, the horizontal pattern of convective anomaly in the initial conditions could be a useful indicator of predicting how skillful the prediction will be for the cases in which the initial MJO amplitude is intermediate. During the propagation, the convection–SST phase relationship is well captured in the high-skill events. In low-skill events, the western Pacific suppressed convection is almost absent, the propagation is poorly organized, and a convection–SST relationship is not obvious.
However, even in high-skill events, the amplitude of the predicted convection anomaly decreases significantly after about day 15. We found that the systematic mean biases partially influence extended MJO prediction. The initial wet bias in the Maritime Continent region, the cold bias in the Pacific SST, and the associated wind biases grow as lead day increases. These strong biases over the Maritime Continent to Pacific Ocean make the west Pacific area unfavorable for the MJO propagation, thus limiting the prediction. In spite of continuous improvement, the biases over the Maritime Continent and the neighboring oceans are known as a challenge for state-of-the-art coupled GCMs (e.g., DeMott et al. 2014).
The Maritime Continent is the region of the largest precipitation and tropical heating, and it modulates the global weather and climate through teleconnection. To improve the MJO prediction, in addition to model development for better MJO simulation, the correct representation of the mean climate particularly over the Maritime Continent is crucial. It has to be accompanied by solving the MJO mean state tradeoff issue, which is the fact that improving the MJO simulation tends to degrade other aspects such as the mean state (Kim et al. 2011; Boyle et al. 2015). The need for such model improvements is also necessary to improve predictions for both the tropics and extratropics and for subseasonal to longer time scales. An ongoing international effort6 will be of great significance to foster our understanding of the Maritime Continent prediction barrier.
While our current study provides some new findings in the area of MJO prediction, there are nonnegligible weaknesses, which are mainly due to the lack of sufficient reforecast sample size and variables. First, the proposed mechanism of the suppressed convection anomaly in the western Pacific playing a role on the eastward propagation is based on existing studies (Hirata et al. 2013; D. Kim et al. 2014) but the limitations in reforecast data availability presented a challenge in exploring detailed mechanisms. Second, we analyzed the MJO prediction irrespective of the season. Generally, the MJO is expected to be better predicted during the boreal winter compared to the summer because of the more pronounced MJO signal (e.g., Wang et al. 2014). The boreal summer intraseasonal oscillation (BSISO) has distinct characteristics that distinguish it from the MJO (e.g., Lawrence and Webster 2002; Kikuchi et al. 2012). Therefore, to accurately evaluate the current state of the MJO (or BSISO) prediction, an appropriate method should be applied to specific season. Third, we used mixed cases of primary and secondary MJO in our analysis, although primary and secondary MJOs have distinct characteristics as well as different predictability (e.g., Matthews 2008). Neena et al. (2014) showed that the predictability of the secondary MJO is about 5 days greater than that of the primary MJO in the ECMWF system. Fourth, we have shown (Fig. 2) that initially strong MJOs generally have high skill, and weak or no MJOs have lower skill, so we focused on the moderate category. However, looking closely at Fig. 2, one can find that some ensemble members have extremely high skill (about 0.98) even in the weak MJO category and extremely low skill even in the strong MJO category. Besides the initially moderate MJO category, investigating the characteristics of high- and low-skill MJOs in each strong and weak category will be of great significance to foster better MJO prediction. Fifth, we only focused on the MJO events that are initialized at phase 2. This was done intentionally as our aim is to understand the characteristics of MJOs propagating over the Maritime Continent. We plan to extend our study to MJOs starting at various phases in further study. Last, MJO activity exhibits a significant interannual change through the modulation of the tropical mean state, such as El Niño–Southern Oscillation (ENSO) or the Indian Ocean dipole (IOD) mode [see review in DeMott et al. (2015)], but we have not distinguished MJO events by these climate modes in this paper. The limitations listed above cannot be overcome without having sufficient number of variables, frequently initialized reforecasts, and large ensembles. Moreover, the results of the present study may depend on the forecast system. Whether the conclusion of this study is hold for other forecasting systems is questionable. Subsequent studies may be necessary with multimodel ensembles that have large sets of ensemble members to help identify common weakness and strengths in the current MJO forecasts. For future work, we plan to examine our hypothesis in multimodel ensembles from the WCRP/WWRP S2S Prediction Project (Vitart et al. 2012) and the NMME reforecasts (Kirtman et al. 2014).
Acknowledgments
The constructive and valuable comments from anonymous reviewers are greatly appreciated. We thank ECMWF for providing the data and Dr. Hai-Ru Chang for helping with data downloading. The National Science Foundation under Grant NSF-AGS 0965610 and the KMA R&D Program under Grant KMIPA 2016-6010 provided funding support. D. Kim was supported by the National Aeronautics and Space Administration Grant NNX13AM18G.
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