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  • View in gallery

    The first two combined EOFs of OLR (dashed line), 200-hPa velocity potential (solid line), and 850-hPa zonal wind (dotted line) from 3 yr of ECMWF operational analyses.

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    Equatorial Hovmoeller diagrams of the anomalies from the 1991–2003 climatology from ERA-40 of 200-hPa velocity potential (contour interval 3 × 106 m2 s−1), 850-hPa zonal wind (contour interval 2 m s−1), and OLR (contour interval 15 W m−2) for the forecast period from 15 Dec 1992 to 4 Mar 1993. In each panel the zero contour is suppressed. Negative values are contoured and shaded; positive values are shaded but not contoured.

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    Correlation of the observed RMM1 and RMM2 time series with the ensemble mean forecast (solid black line), each individual ensemble member (dotted gray lines), and the persistence of the atmospheric initial conditions (solid gray line) time series, based on 48 start dates.

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    Time series of the best (dotted line) and worst (solid line) anomaly correlation between the predicted 200-hPa velocity potential and observations for the period of days 10–15 for each forecast from 15 Dec 1992 to 31 Jan 1993.

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    Evolution of the variance of RMM1 and RMM2 as a function of the time lag. The dotted gray line represents the analysis. The solid black, dotted black, and solid gray lines correspond to the 5 ensemble members of CONTROL, PHYS1, and PHYS2, respectively.

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    Equatorial Hovmoeller diagrams of the anomalies from the 1991–2003 climatology of (left) VP200 (contour interval 3 × 106 m2 s−1), (middle) zonal wind at 850 hPa (contour interval 2 m s−1), and (right) OLR (contour interval 15 W m−2) from 24 Dec 1992 to 10 Feb 1993 of all the 48 forecasts (48 starting dates) at day 10 concatenated to produce a single time series. The forecasts at a time lag of day 10 from (top) CONTROL and (bottom) PHYS2. Negative values are contoured and shaded; positive values are shaded but not contoured.

  • View in gallery

    Correlation of the observed RMM1 and RMM2 time series with the ensemble mean forecast time series, based on 48 start dates, for the CONTROL (solid black line), PHYS1 (dotted black line), and PHYS2 (solid gray line). The results obtained when the atmospheric model is coupled to an ocean (a) GCM and (b) mixed layer model.

  • View in gallery

    (Left) Equatorial Hovmoeller diagrams of the anomalies from the 1991–2003 climatology from ERA-40 and analysis of VP200 (contour interval 3 × 106 m2 s−1) from 31 Dec 1992 to 1 Feb 1993. Hovmoeller diagrams of the ensemble mean of (middle left) CONTROL, (middle right) PHYS1, and (right) PHYS2 starting on 31 Dec 1992. Negative values are contoured and shaded; positive values are shaded but not contoured.

  • View in gallery

    Correlation of the observed RMM1 and RMM2 time series with the ensemble mean forecast time series, based on 48 start dates, for different resolutions of the atmospheric model: TL63 (solid black line), TL95 (dotted black line), TL159 (solid gray line), and TL255 (dotted gray line).

  • View in gallery

    Correlation of the observed RMM1 and RMM2 time series with the ensemble mean forecast time series, based on 48 start dates. The score of PHYS1 with mixed layer model (solid black line), the score of PHYS1 with mixed layer model starting from climatological ocean initial conditions (dotted black line), and the score of PHYS1 with mixed layer model with ERA-15 as the atmospheric initial conditions instead of ERA-40 (solid gray line) are shown.

  • View in gallery

    Equatorial Hovmoeller diagrams of the anomalies from the 1991–2003 climatology of VP200 (contour interval 3 × 106 m2 s−1) from 15 Dec 1992 to 31 Jan 1993 for (left) ERA-15 and (right) ERA-40. Negative values are contoured and shaded; positive values are shaded but not contoured.

  • View in gallery

    Impact of initial perturbations on the 10–15-day anomaly correlation of (a) VP200 and (b) OLR forecasts. We first identify the initial perturbation, which produces the best and worst CONTROL forecasts. The impacts of exactly the same perturbations are tested in the three model configurations: (left) CONTROL, (middle) CONTROL + ML, and (right) PHYS1 + ML. Shown are the scatter diagrams of best CONTROL (x axis) vs worst CONTROL (y axis). The differences between best CONTROL and worst CONTROL are maintained in the three different configurations. Each circle represents 1 forecast (there is 1 forecast per day from 15 Dec 1992 to 31 Jan 1993) and the black square represents the mean over the 48 cases.

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Monthly Forecast of the Madden–Julian Oscillation Using a Coupled GCM

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  • 1 European Centre for Medium-Range Weather Forecasts, Reading, United Kingdom
  • | 2 NCAS Centre for Global Atmospheric Modelling, University of Reading, Reading, United Kingdom
  • | 3 European Centre for Medium-Range Weather Forecasts, Reading, United Kingdom
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Abstract

A set of five-member ensemble forecasts initialized daily for 48 days during the Tropical Ocean Global Atmosphere Coupled Ocean–Atmosphere Response Experiment period are performed with the ECMWF monthly forecasting system in order to assess its skill in predicting a Madden–Julian oscillation (MJO) event. Results show that the model is skillful in predicting the evolution of the MJO up to about 14 days, but the amplitude of the MJO is damped after a few days of integration. In addition, the model has some deficiencies in propagating the MJO through the Maritime Continent. The same experiment framework is used to quantify the impacts of changing the model physics, the ocean model, the atmospheric horizontal resolution, and the initial conditions on the skill of the monthly forecasting system. Results show that there is a scope for extending the skillful range of the operational monthly forecasting system to predict the evolution of the MJO by at least a week. This is achieved by using an improved cloud parameterization together with a better representation of the mixing of the upper ocean. An additional set of experiments suggests that degrading the quality of the initial conditions (by using the 15-yr ECMWF Re-Analysis instead of the 40-yr ECMWF Re-Analysis) significantly degrades the skill of the model to predict an MJO event and that increasing the horizontal resolution of the atmospheric mode had only a minor impact on the MJO forecasts. In addition, results show that there is a significant sensitivity to the initial perturbations of the ensemble members, and therefore, targeting perturbations on the MJO could improve the skill of the monthly forecasting system. While the propagation of the MJO was sensitive to most of the changes described in this paper, only the change in cloud parameterization improved the strength of the MJO. The propagation of the MJO over the Maritime Continent remains an issue.

Corresponding author address: Frédéric Vitart, European Centre for Medium-Range Weather Forecasts, Shinfield Park, Reading RG2 9AX, United Kingdom. Email: nec@ecmwf.int

Abstract

A set of five-member ensemble forecasts initialized daily for 48 days during the Tropical Ocean Global Atmosphere Coupled Ocean–Atmosphere Response Experiment period are performed with the ECMWF monthly forecasting system in order to assess its skill in predicting a Madden–Julian oscillation (MJO) event. Results show that the model is skillful in predicting the evolution of the MJO up to about 14 days, but the amplitude of the MJO is damped after a few days of integration. In addition, the model has some deficiencies in propagating the MJO through the Maritime Continent. The same experiment framework is used to quantify the impacts of changing the model physics, the ocean model, the atmospheric horizontal resolution, and the initial conditions on the skill of the monthly forecasting system. Results show that there is a scope for extending the skillful range of the operational monthly forecasting system to predict the evolution of the MJO by at least a week. This is achieved by using an improved cloud parameterization together with a better representation of the mixing of the upper ocean. An additional set of experiments suggests that degrading the quality of the initial conditions (by using the 15-yr ECMWF Re-Analysis instead of the 40-yr ECMWF Re-Analysis) significantly degrades the skill of the model to predict an MJO event and that increasing the horizontal resolution of the atmospheric mode had only a minor impact on the MJO forecasts. In addition, results show that there is a significant sensitivity to the initial perturbations of the ensemble members, and therefore, targeting perturbations on the MJO could improve the skill of the monthly forecasting system. While the propagation of the MJO was sensitive to most of the changes described in this paper, only the change in cloud parameterization improved the strength of the MJO. The propagation of the MJO over the Maritime Continent remains an issue.

Corresponding author address: Frédéric Vitart, European Centre for Medium-Range Weather Forecasts, Shinfield Park, Reading RG2 9AX, United Kingdom. Email: nec@ecmwf.int

1. Introduction

The Madden–Julian oscillation (MJO) is the dominant mode of variability in the Tropics on time scales exceeding one week but less than a season (Madden and Julian 1971). The MJO has a significant impact on the Indian (Murakami 1976; Yasunari 1979) and Australian monsoon (Hendon and Liebmann 1990). It plays an active role in the onset and development of an El Niño event (e.g., Kessler and McPhaden 1995) and has an impact on tropical cyclogenesis over the eastern North Pacific (Maloney and Hartmann 2000) and over the Atlantic (Mo 2000; Maloney and Hartmann 2002). Ferranti et al. (1990) provided evidence that an improved representation of the MJO in the European Centre for Medium-Range Weather Forecasts (ECMWF) forecast model (achieved in that case by relaxing the tropical circulation toward analysis) could lead to a considerable increase of skill for the extratropics after 10 days of forecast. These results indicate that the MJO is an important source of predictability for the intraseasonal time range (more than 10 days and less than a season), and therefore, it is important for a monthly and seasonal forecasting system to have skill in predicting the evolution of the MJO.

It is not clear what the theoretical limit of predictability of the Madden–Julian oscillation is, but statistical predictive models of the MJO display useful predictive skill out to at least 15–20-day lead times (e.g., Waliser et al. 1999b; Lo and Hendon 2000; Wheeler and Weickmann 2001; Mo 2001). The skill of NWP models is often less than that of statistical prediction techniques (e.g., Waliser et al. 1999a; Vitart 2003). Climate models also generally have a poor representation of the Madden–Julian oscillation. Slingo et al. (1996) found that none of the atmospheric GCMs that took part in the Atmospheric Model Intercomparison Project were able to capture the spectral peak associated with the MJO, and a recent assessment of Intergovernmental Panel on Climate Change Fourth Assessment Report coupled models by Lin et al. (2006) showed only a slight improvement.

Waliser et al. (2003) found that the National Aeronautics and Space Administration general circulation model (chosen because of its relatively realistic MJO representation) displayed potential predictability out to about 25–30 days for velocity potential at 200 hPa (VP200) and to about 10–15 days for rainfall in the Eastern Hemisphere during periods of strong MJO activity, which suggests that there is scope for improving the prediction of the MJO in NWP models beyond what current statistical methods can achieve.

The goal of the present paper is to evaluate the relative sensitivity of the MJO forecast skill to changes in different components of the forecasting system. Some of those sensitivities are already well known, like the sensitivity of the MJO to the physics parameterization (e.g., Wang and Schlessinger 1999; Maloney and Hartmann 2001) in the context of climate models. However, the main goal of the present paper is rather to “quantify” the impact of different factors (ocean–atmosphere coupling, atmospheric resolution, physic parameterization) in the context of operational monthly forecasting. The present paper is a companion paper to Woolnough et al. (2007), hereafter WVB), which focused on the impact of atmosphere–ocean interaction on the MJO and showed that a better representation of the mixing processes in the ocean model improves the MJO forecasts. It will discuss the sensitivity of the results presented in WVB to the atmospheric model.

The experiment setting is described in section 2. The MJO diagnostics are described in section 3. The skill of the ECMWF monthly forecasting system in predicting an MJO event is evaluated in section 4, followed by an evaluation of its sensitivity to changes in the physics parameterization (section 5), in horizontal resolution of the atmospheric model (section 6), and in the initial conditions (section 7). Finally, section 8 discusses the main results of this paper.

2. The experiment setting

The experiment setting is identical to the one described in WVB and follows an approach suggested by P. Webster (2005, personal communication). Each experiment consists of a series of 32-day forecasts using a five-member ensemble initialized at 0000 UTC each day from 15 December 1992 to 31 January 1993 inclusive, during the Intensive Observing Period of the Tropical Ocean Global Atmosphere Coupled Ocean–Atmosphere Response Experiment (TOGA COARE). The timing of the events is such that the initial conditions for the 48 forecasts include all the phases of the MJO as identified by the combined EOF analysis technique and each forecast lead time captures each phase of the MJO at least once.

The control integration (CONTROL) uses the operational ECMWF monthly forecasting model (Vitart 2004). The atmospheric component is the Integrated Forecast System (IFS) cycle 28R3, with a TL159 horizontal resolution (1.125° × 1.125°) and 40 vertical levels. The oceanic component is the same as used for the ECMWF seasonal forecasting system 2 (Anderson et al. 2003). It is based on the Hamburg Ocean Primitive Equation from the Max Plank Institute (Wolff et al. 1997), with a resolution in the extratropics of about 1° and a higher meridional resolution in the equatorial region (about 0.3°), but with modified physics and an explicit barotropic solver (Balmaseda 2004; Anderson and Balmaseda 2004).

Atmospheric initial conditions are obtained from the 40-yr ECMWF Re-Analysis (ERA-40; Uppala et al. 2005). Oceanic initial conditions originate from the real-time ECMWF operational ocean analysis system (Balmaseda 2005). The model is integrated for 32 days with 5 slightly different initial conditions. One forecast, called the control forecast, is run from the operational oceanic analysis and ERA-40 without perturbations. The four other integrations, the perturbed members, start from slightly different atmospheric and oceanic initial conditions. The atmospheric component is perturbed using the singular vector method (Buizza and Palmer 1995), in the extratropics and in some tropical areas to target tropical cyclones (Puri et al. 2001). In addition, in order to take account of the effect of uncertainties in the model subgrid-scale parameterizations, the tendencies in the atmospheric physics are randomly perturbed during the model integrations (Palmer 2001). Oceanic initial conditions are perturbed in the same way as in the operational ECMWF seasonal forecasting system (Vialard et al. 2005).

After a few days of coupled integrations, the model mean climate begins to be different from the analysis. Therefore, the forecast anomalies need to be derived from the model climate, which is dependent on the starting calendar date and the lead time. In this study, the model climate is provided by a five-member ensemble of 32-day coupled integrations starting 1 week apart from 15 December until 31 January of the following year for the years 1991 to 2003 (1992 excluded). The ensemble members used to generate the model climate are perturbed in the same way as above. The forecast anomalies from 15 December 1992 to 31 January 1993 are then calculated by subtracting the ensemble mean of the model climate with the same starting date (calculated by daily interpolation of the integrations 1 week apart). Separate model climates are calculated for all the experiments using the appropriate model setup.

3. MJO diagnostics

To evaluate the skill of the monthly forecasting system in predicting the MJO, a combined EOF analysis of velocity potential at 200 hPa, outgoing longwave radiation (OLR), and zonal wind at 850-hPa anomalies (relative to the 1991–2003 climate) averaged between 10°S and 10°N has been performed on the ECMWF operational analysis from 1 January 2002 to 31 December 2004. This period is long enough to have a good representation of the intraseasonal variability. In addition, the period 2002–04 was chosen because of the lack of a strong ENSO event, which avoids the need to filter the interannual variability. The same EOF analysis applied to ERA-40 and a different set of years without strong ENSO activity (1989–91) gave similar results, suggesting that the results in this paper are not that dependent on the choice of the period where the EOF analysis has been applied. The MJO diagnostic is similar to the method used in Wheeler and Hendon (2004), although Wheeler and Hendon used 200-hPa zonal wind rather than 200-hPa velocity potential. Figure 1 shows the first two EOFs of this analysis, which clearly describe variations associated with the MJO. The positive (negative) phase of EOF2 describes convection active (suppressed) over the Indian Ocean region and suppressed (active) over the west Pacific. The positive (negative) phase of EOF1 describes active (suppressed) convection over the Maritime Continent region. Analysis and forecasts can be projected onto these two EOFs to describe the phase of the MJO in terms of two time series, Realtime Multivariate MJO series 1 (RMM1) and 2 (RMM2). These two time series can be plotted as a succession of points in RMM1–RMM2 phase space such that the MJO is described by a clockwise propagation in this phase space.

Figure 2 shows the Hovmoeller diagrams of the anomalies (relative to the 1991–2003 climate) of 200-hPa velocity potential, 850-hPa zonal wind, and OLR from the ERA-40 for the forecast period (15 December 1992–4 March 1993). Two MJO events can be seen during this period. Negative velocity potential and OLR anomalies correspond to the active phase of the MJO.

4. Skill of the coupled model

To evaluate the skill of the monthly forecasting system in predicting the MJO, a linear correlation is performed between the observed time series of RMM1 and RMM2 with the forecast time series at different lead times (Fig. 3). In the present paper, we consider that the forecasts are skillful when the anomaly correlation is higher than 0.6. This definition is traditionally used by operational centers like ECMWF to define the limit of useful skill of operational forecasts, and is slightly stronger than in Murphy and Epstein (1989), who claim that forecasts with an anomaly correlation larger than 0.5 are more skillful than climatology. The main conclusions of the paper are insensitive to this threshold.

The correlation of the observed time series with persistence of the atmospheric initial conditions (Fig. 3) falls away to 0.6 after only 6 days. With the individual ensemble members, the linear correlation falls away to 0.6 between day 12 and 13 for RMM1 and between day 11 and day 14 for RMM2, which is considerably better than persistence. The scores are slightly higher when scoring the ensemble mean. The linear correlation between analysis and the ensemble mean forecast decreases to 0.6 by about day 13 for RMM1 and day 14 for RMM2 and to 0.4 by day 14 for RMM1 and day 17 for RMM2. Therefore the ECMWF monthly forecasting system seems to have some useful skill in predicting the propagation of MJO up to about 14 days in advance. This result is consistent with the skill obtained with 30 real-time cases (51 ensemble members) of the operational monthly forecasting system taken every 2 weeks from 27 March 2002 (Vitart 2003). However, the skill of the coupled model seems to be lower than the skill of statistical models that can display useful predictive skill out to at least 15–20-day lead times (e.g., Waliser et al. 1999b; Lo and Hendon 2000; Wheeler and Weickmann 2001; Mo 2001), although a direct comparison is difficult, because the skill is not always measured the same way.

However, the scores displayed above do not indicate which phase of the MJO is well predicted. Figure 4 displays the time evolution of the best and the worst anomaly correlation of velocity potential at 200 hPa, averaged between 10°N and 10°S and with the forecast lead time of 10–15 days, obtained in each five-member ensemble forecast as a function of the starting date from 15 December 1992 to 31 January 1993. The best scores (dotted line in Fig. 4) are always above 0.5, except for a short period between 6 and 11 January 1993. This period corresponds to the forecasts starting with an MJO event in the Indian Ocean, and the period of days 10–15 of those forecasts corresponds to the MJO over the Maritime Continent. When the convection is over the Maritime Continent in the initial conditions (forecasts starting from 13 to 19 January), the performance of the model remains lower than in the other periods. This confirms the work of Vitart (2003), who showed that the ECMWF operational monthly forecast has some difficulties in propagating the MJO across the Maritime Continent. According to Fig. 4, there are periods of high predictability with the worst score generally above 0.7 (e.g., from 25 December to 30 December, which corresponds to the starting dates when the convection is over the date line).

Although the monthly forecasting system displays some skill in predicting the evolution of the MJO up to 15 days, it does not maintain the intensity of the MJO for more than a few days (solid black lines in Fig. 5). The variance of the principal components (PCs) PC1 and PC2 is significantly lower than in the analysis by more than 30% after only 10 days in the forecast. After about 14 days, the amplitude of PC1 and PC2 remains constant as the model has reached its radiative–convective equilibrium. This result is consistent with Vitart (2003) using real-time forecasts sampled over more than a year. As a consequence, the impact of the MJO on the extratropics after 10 days is likely to be underestimated by the model, despite the fact that the model has some skill in predicting the MJO propagation (Fig. 3).

5. Sensitivity to the physics parameterization

a. Description of the experiments

The simulation of the MJO in GCMs is notoriously sensitive to aspects of the physical parameterizations (e.g., Wang and Wang 1999; Maloney and Hartmann 2001). However, those studies investigated the impact of changing the physical parameterizations on the general statistics of the MJO. Instead, in the present study, we investigate the impact of changing some aspects of the physical parameterization on the predictive skill of the monthly forecasting system. In this paper, two changes in the physical parameterization were considered.

The deep convective scheme used in the present model is a mass-flux scheme described in Tiedtke (1989). The scheme is designed to minimize the convective available potential energy (CAPE), the closure being the condition that CAPE should be zero. There is no observational evidence that such a condition should apply in the real world. Increasing the threshold of CAPE is known to significantly impact the transients in the model (Tokioka et al. 1998; Vitart et al. 2001). Tompkins and Jung (2003) have shown that often experiments that alter the convective scheme (such as increase its sensitivity to midtropospheric humidity) influence the tropical climate primarily by altering the balance between grid-scale and parameterized convective motions, and that increasing the proportion of grid-scale convection increases the tropical wind variance and strengthens Kelvin wave activity.

By increasing the CAPE threshold, the convective parameterization scheme is partially suppressed, and a greater proportion of deep convective heating is represented by grid-scale motions, leading to the increased variance in the tropical winds. Vitart et al. (2003) have shown that this increased wind variability produces better seasonal forecasts of the 1997 El Niño event due to the stronger westerly wind events over the western Pacific, which had an important role in the intensification of this El Niño event. In the present paper, the first change in the physics parameterization (hereafter PHYS1) consists of increasing the CAPE threshold to 100 from 0 J kg−1.

While this threshold may appear small relative to the values typically quoted for the tropical atmosphere, it is worth recalling that this CAPE quantity is not the simple pseusoadiabatic ascent used to measure conditional instability from tropical thermodynamic soundings. Rather, it is the CAPE calculated by the parcel ascent as modeled by the convection scheme. This calculation includes the effect of water loading on updraft buoyancy, and equally significant, the effect of entrainment of ambient air. The result is that CAPE values are much smaller, typically less than 500 J Kg−1, and thus the 100 J Kg−1 threshold represents a significant perturbation to the scheme. Tests using much higher threshold values produce a severe suppression of the convection scheme, detrimentally impacting the authenticity of the modeled tropical climate.

The second change in the physical parameterization will be referred to as PHYS2. This model introduces a simple parameterization that allows ice supersaturation, compatible with the cloud scheme that allows partial cloud coverage (Tompkins et al. 2007). The package also includes an implicit formulation for handling the ice sedimentation process, with the ice sedimentation velocity set to a fixed value of 15 cm s−1 for numerical stability. In addition, a process is implemented to convert cloud ice into snow according to the autoconversion formulation of Sundqvist et al. (1989), but using the rate coefficient from Lin et al. (1983) and with a critical ice mixing ratio threshold set to 10−4 kg kg−1.

The net effect of the PHYS2 package is to increase the upper-tropospheric humidity significantly, and also to increase upper-tropospheric cloud ice amounts. Implementing PHYS2 leads to an improved model tropical climate, most notably with increased precipitation over equatorial South America and the Maritime Continent, where underestimation in both regions has been a longstanding climate bias. These improvements appear to arise from feedbacks with radiation and dynamics, whereby the increased radiative forcing of the clouds leads to increased low-level convergence into the convective regions, thereby increasing deep convective self organization. In support of this, separate sensitivity tests with radiative scheme-tuning parameters that increase the radiative impact of clouds also lead to similar changes in the simulated climate. Moreover, this mechanism has also been documented on smaller scales in cloud-resolving model simulations of deep convection (Tompkins and Craig 1998). Here it will be seen whether these changes that increase convective organization in the mean climate also affect the transient behavior of deep convection in connection with the MJO.

PHYS1 and PHYS2 have been run in the same framework as the monthly forecasting system (CONTROL; five-member ensembles of 32-day integrations from 15 December 1992 to 31 January 1993). Because the model bias can be affected by changes in the physics parameterization, a model climate has been created for each change in the model physics in the same way as for the control forecast. Therefore, each model integration is corrected by removing the bias computed using the corresponding model physics.

b. Results

1) Intensity of the MJO

A major shortcoming of the current monthly forecasting system is that the intensity of the MJO in the model decreases dramatically after only a few days. PHYS1 does not seem to improve the intensity of the MJO in the monthly forecasting system (dotted black lines in Fig. 5), except after day 15 for PC1. It is quite surprising that the intensity of the MJO with PHYS1 slightly increases after 15 days of forecast, when it decreases or stabilizes with the other parameterizations of atmospheric physics. PHYS2 on the other hand improves the intensity of the MJO up to day 15 (solid gray lines in Fig. 5) for PC1 and during the 32-day integrations with PC2. For instance, PHYS2 displays a loss of the PC1 (PC2) variance of only about 5% (25%) by day 10 instead of 30% (50%) with CONTROL. Throughout the 32 days of the forecasts, the variance of PC2 remains statistically significantly higher with PHYS2 than with CONTROL and PHYS1 at the 90% level of confidence according to the Wilcoxson–Mann–Whitney (WMW) test (e.g., Wonnacott and Wonnacott 1997). Therefore PHYS2 is likely to generate a stronger impact of the MJO on the midlatitudes through stronger teleconnections and could improve the extratropical skill because of the MJO.

Figure 6 displays a Hovmoeller diagram of the ensemble of mean velocity potential at 200 hPa, zonal wind at 850 hPa, and OLR for CONTROL and PHYS2 for a forecast lead time of 10 days, concatenated to produce a single time series. After 10 days of forecast, the MJO propagation is much stronger in PHYS2 than in CONTROL for the velocity potential at 200 hPa and OLR. The 10-day forecast of the MJO in PHYS2 is indeed close to analysis for those two variables. CONTROL displays very little skill to predict the OLR anomalies 10 days in advance (Fig. 6, right panel) as is often the case with GCMs. PHYS2 displays a remarkable improvement in the forecast of OLR anomalies, with a forecast at day 10 consistent with analysis (Fig. 2, right panel). On the other hand, PHYS2 seems to have a much weaker impact on the zonal wind at 850 hPa (Fig. 6, middle panel). PHYS2 improves the intensity of the easterly anomalies associated with the suppressed phase of the MJO, but it improves just marginally the intensity of the westerly anomalies associated with the active phase of the MJO after 1 January 1993, which remain much weaker than in the analysis. This is surprising, since the 10-day forecast of OLR and velocity potential at 200 hPa during the active phase of the MJO is significantly improved by PHYS2.

2) MJO propagation

Figure 7a displays the linear correlation between the observed time series of RMM1 and RMM2 with forecast ensemble mean time series obtained with CONTROL, PHYS1, and PHYS2. PHYS1 seems to improve the forecast of PC1 after day 13. The forecast correlations with PHYS1 fall away to 0.6 one day after CONTROL. Between day 13 and day 24, PHYS1 produces forecasts that are statistically significantly better at the 90% level of confidence, according to the WMW test, than those obtained with CONTROL, although the correlations are quite low. PHYS2 seems also to slightly improve the forecasts of PC1, in particular in the medium range, with a small but statistically significant improvement. After day 15 the scores of PHYS2 are closer to CONTROL than to PHYS1. Both PHYS1 and PHYS2 improve the forecast of RMM2 quite substantially. The scores of PHYS1 and PHYS2 for PC2 are indeed very close. With PHYS1 and PHYS2, the correlations are higher than 0.6 until day 17 and 16, respectively, instead of day 14 for Control, which means a gain of 2–3 days of predictability during this phase of the MJO.

In summary, both PHYS1 and PHYS2 seem to improve the prediction of the propagation of the MJO. PHYS1 has a more beneficial impact on the prediction of PC1 than PHYS2 after 15 days. This can be illustrated by the example of the forecast starting on 31 December 1992 (Fig. 8). With CONTROL, the convection in the ensemble forecast mean does not cross the Maritime Continent as in the analysis (Fig. 8, left). Instead the convection stays in the Indian Ocean. This is also the case with PHYS2 (Fig. 8, right panel). Although PHYS2 produces a more intense MJO (this will be discussed in the next subsection), the convection is still in the Indian Ocean after 30 days. With PHYS1, the MJO crosses the Maritime Continent as in the analysis.

3) Sensitivity to the ocean–atmosphere coupling

The role of coupled processes in the MJO was investigated in WVB. They found that an improved representation of the mixing in the upper ocean, by using a high vertical resolution mixed layer model, produced an improvement in the MJO forecast, particularly for the phases of the MJO where the convection is active over the Indian Ocean or west Pacific (PC2). They attributed this improvement to an enhanced sensitivity of the SST to the surface fluxes, and in particular to the ability of the mixed layer model to simulate the diurnal cycle of mixing in the upper ocean and SST during the suppressed phase of the MJO.

The experiments in WVB were performed using the same atmospheric model as CONTROL. In the present paper the same experiments as in WVB were repeated with PHYS1 and PHYS2 in order to evaluate the sensitivity of their results to the atmospheric model; it is likely that the impact of the mixed layer model on the MJO is dependent on the skill of the atmospheric model in producing an MJO. Therefore PHYS1 (better MJO propagation than in CONTROL) and PHYS2 (better propagation and stronger MJO than in CONTROL) can be used to investigate the sensitivity of the atmosphere–ocean coupling on the MJO. In other words, in this section we try to answer the following question: are the improvements obtained in WVB independent of the improvements due to PHYS1 or PHYS2 and vice versa?

The ocean mixed layer model used in the present study is the same as in WVB. It is based on a K-profile parameterization (KPP) vertical mixing scheme of Large et al. (1994). It has a vertical domain of 200 m with 29 vertical levels. The vertical grid is stretched such that the top model level is 1.4 m thick with 16 levels in the top 30 m. In the horizontal direction the mixed layer model uses only half of the grid of the full dynamical model, as it does not resolve the dynamical processes. The atmospheric initial conditions contain the same perturbations as the control ensemble and stochastic physics is included as well. However, the ocean initial conditions are not perturbed in the mixed layer (ML) experiment.

The experiments CONTROL, PHYS1, and PHYS2 have been repeated but with the atmospheric component coupled to the mixed layer model rather than to the ocean GCM. Figure 7b displays the linear correlations of PC1 and PC2 obtained in those experiments along with the linear correlations obtained in the control experiment, for comparison. The comparison between the scores displayed in Figs. 7a,b shows the impact of the oceanic mixed layer model with the three different model parameterizations.

The impact of the mixed layer model on PC1 (Fig. 7b, left) is modest, as already mentioned in WVB. For PC1, the difference in the physics parameterization between the different models seems to have a much stronger impact than the coupling to the oceanic mixed layer model. For instance, PHYS1 displays significantly better scores after day 14 than all the other models, although the difference is not as large as when the models are coupled to an ocean GCM (Fig. 7a).

The mixed layer model has a larger impact on PC2 (Fig. 7b, right). It has a positive impact for all the models. For example, with PHYS2 the anomaly correlation falls away to 0.6 at day 21 instead of day 16. This represents a gain of 5 days of predictability for PC2. For the period of days 10–18, PHYS1 and PHYS2 improve equally the scores of PC2, and the impact of the high vertical resolution mixed layer model seems to be additive to the impact of PHYS1 or PHYS2. After day 18, the mixed layer model seems to be the major source of improvement in the skill of the models and PHYS1 displays the same score as the control forecast, whereas PHYS2 produces still better forecasts than the control. This suggests that the impact of the mixed layer model is not the same with PHYS1 and PHYS2. The fact that PHYS2 generates a stronger MJO (see previous section) than PHYS1 may explain why the mixed layer model has a stronger impact with PHYS2 than with PHYS1.

6. Sensitivity to the horizontal resolution of the atmospheric model

Section 5 has shown that the skill of the monthly forecasting system at predicting the MJO is very sensitive to the choice of the physical parameterization. In this section, the sensitivity to changes in the horizontal resolution of the atmospheric model will be evaluated. CONTROL has a horizontal atmospheric resolution of TL159. TL159 indicates a spectral triangular truncation at 159 with linear grid and represents a grid resolution of approximately 120 km. The same experiment as CONTROL has been repeated but with three different horizontal resolutions of IFS: TL63 (about 300 km), TL95 (about 200 km), and TL255 (about 80 km). The vertical resolution is the same (40 vertical levels) in all the experiments.

Results suggest that the atmospheric horizontal resolution has little impact on the scores of PC1 (Fig. 9, left). The anomaly correlation is higher than 0.6 until about day 13 in the 4 experiments. On the other hand, PC2 seems to display some sensitivity to the horizontal resolution of the atmospheric model after about 6 days of forecast. The experiments with TL63 and TL95 display the same level of skill. This is also the case for TL159 and TL255. However, the model with a TL159 or a TL255 resolution displays anomaly correlations higher than 0.6 three days longer than the model with a TL63 or TL95 resolution. This difference is statistically significant. Therefore the prediction of the MJO with CONTROL seems to improve between 200- and 120-km horizontal resolution. The results also suggest that for the ECMWF monthly forecasting system (TL159 resolution), increasing the resolution to TL255 and therefore quadrupling the cost of the model would lead to little improvement in the prediction of the MJO.

In their study, Tompkins and Jung (2003) also compared integrations using TL95 and TL159 and documented a sensitivity of the simulated MJO. Part of the sensitivity could be attributed to the altered balance between grid-scale and parameterized convection, with the TL159 model having a higher level of grid-scale activity. Grid-scale convection is related directly to midtropospheric vertical velocity and is thus constrained to provide latent heating in phase with large-scale waves in the Tropics. In contrast, the triggering and location of parameterized deep convection relies much more heavily on the boundary layer moist static energy and the distribution and strength of the convective inhibition. In the ECMWF model, the CAPE closure time scale is tuned for each horizontal resolution in an attempt to keep the grid-scale/parameterized convective balance invariant, but this study shows that even minor changes in this balance can impact the statistics of the MJO significantly.

Changing the model resolution has no significant impact on the amplitude of the MJO (not shown). All the experiments display the same loss as CONTROL of between 30% and 50% by day 10 in the variance of PC1 and PC2.

7. Sensitivity to the initial conditions

This section investigates the sensitivity of the MJO monthly forecasts to the quality of the atmospheric and oceanic initial conditions and to the atmospheric initial perturbations.

a. Sensitivity to the quality of the initial conditions

To test the impact of the ocean initial conditions on the skill of the monthly forecasting system in predicting SSTs, the same experiment as PHYS1 with a mixed layer model has been repeated but with the ocean mixed layer model initialized from the SST climatology from 1991 to 2003 instead of from the ECMWF ocean analysis. In both experiments, the ocean component of the coupled system is active and the SSTs evolve during the forecast.

For PC1, the model integrations with climatological SSTs in the initial conditions display slightly lower scores (Fig. 10), but the difference is not statistically significant, as with the other sensitivity experiments. If the impact of the oceanic initial conditions is local, this would not be surprising because PC1 represents the convection either over the Maritime Continent or over Africa, and therefore is less impacted by oceanic initial conditions. With PC2, the difference is once again much larger than with PC1. Using climatological SSTs instead of the initial conditions from the ocean data assimilation system degrades the prediction of PC2 between day 8 and day 20. After day 10, the difference is statistically significant. This experiment is likely to overestimate the impact of the quality of the oceanic initial conditions because climatological SSTs were used to initialize one of the experiments. This experiment therefore represents an “extreme” case of oceanic initial condition.

All the experiments described above used ERA-40 (Uppala et al. 2005) as atmospheric initial conditions. To evaluate the impact of the quality of the atmospheric initial conditions on the skill of the monthly forecasting system in predicting an MJO event, the experiment with PHYS1 and mixed layer ocean was repeated but with initial conditions taken from the 15-yr ECMWF Re-Analysis (ERA-15). The 15 December 1992–31 January 1993 MJO event is clearly visible in both ERA-15 and ERA-40 (Fig. 11), but its intensity is significantly weaker in ERA-15 than in ERA-40. Therefore, the experiment using ERA-15 initial conditions starts with a lower MJO signal than the experiment with ERA-40 initial conditions.

Results (Fig. 10) suggest that the difference in the atmospheric initial conditions has little impact on PC1, but has a surprisingly significant impact on PC2. The scores obtained with the experiment starting with ERA-15 are significantly worse than those obtained with the experiment starting from ERA-40. The anomaly correlation for PC2 decreases to 0.6 four days earlier when starting with ERA-15 than when starting with ERA-40. Those results were obtained by using ERA-40 for the verification, but using ERA-15 for verification gives very similar results. The results suggest that the atmospheric initial conditions can have a strong impact on the skill of the monthly forecasting system to predict the propagation of an MJO event and this impact is significantly larger than the impact obtained by changing the oceanic initial conditions. Calibrating the forecasts starting with ERA-15 initial conditions with ERA-40 climate gave similar results as when calibrating with ERA-15 climate. This suggests that the improvement obtained with ERA-40 is not due to an improved climate in ERA-40 over ERA-15, but it is due to a better representation of the anomalies associated with the MJO event.

b. Impact of the atmospheric perturbations

This section investigates the impact of the perturbations on the MJO forecasts. The perturbations of the oceanic and atmospheric initial conditions are not targeted at the MJO. However, while analyzing the results of the previous sections, the same ensemble members seem to perform consistently better in all the experiments. If the perturbations have a significant impact on the MJO forecasts then it is likely that the perturbation that produces the best forecast with CONTROL will also be the one producing the best forecast with the other models that have been tested in the sections above. To test if this is the case, the ensemble number that produces the best forecast is recorded along with the one producing the worst forecast for each of the 48 starting dates from 15 December 1992 to 31 January 1993. The performance of the forecast is measured by an anomaly correlation of the velocity potential at 200 hPa. The velocity potential at 200 hPa has been averaged between day 10 and 15. The anomaly correlation is applied over the tropical band 10°S–10°N. It is not always the same ensemble member that performs the best from one forecast to another. For the period of day 10–15, all the perturbation numbers are almost equally represented among the best and the worst forecasts. Figure 12 displays scatterplot diagrams of the scores of the ensemble member that produces the best day 10–15 forecast with CONTROL as a function of the score of the ensemble member that produces the worst day 10–15 forecast with CONTROL. By construction, all the 48 points are in the top left triangle with CONTROL (Fig. 12a, left). Interestingly, most of the points (42 over 48) are also in the upper triangle with CONTROL + ML and 33 over 48 are in the upper triangle with PHYS1 + ML. This represents significance above 99% for CONTROL + ML and above 95% with PHYS1 + ML according to the WMW test. This means that the perturbations that produce the best forecasts with CONTROL tend to produce the best forecasts with CONTROL + ML or PHYS1 + ML. This result is also true for PHYS2 (not shown). Therefore, the way the model is perturbed seems to have a significant impact on the prediction of the MJO. The same conclusion can be drawn for OLR (Fig. 12b) and for the zonal wind at 850 hPa (not shown).

As explained in section 2, both ocean and atmospheric initial conditions are perturbed, and stochastic perturbations are applied all along the integrations. However, the experiments with the mixed layer model do not have perturbations in the oceanic initial conditions. In addition, the results of an experiment without stochastic physics suggest that stochastic physics has little impact on the skill of the model in predicting an MJO event. Therefore, the impact of the perturbations shown in Fig. 12 are most likely due to the singular vectors applied to the atmospheric initial conditions.

8. Conclusions

The ECMWF monthly forecasting system displays some skill in predicting the evolution of the MJO up to about 13 days in advance for PC1 and 14 days in advance for PC2, which is less than the skill displayed by some statistical models (up to 20 days). In addition, the monthly forecasting system seems to have difficulties in maintaining the amplitude of an MJO event. The amplitude of the MJO is reduced by about 30% for PC1 and 50% for PC2 after 10 days of forecasts and stabilizes thereafter. This lack of variance in the MJO is likely to have a negative impact on the skill of the monthly forecast in predicting the impact of the MJO in the extratropics.

This study has examined the sensitivity of a series of MJO forecasts to different parameterizations of the atmospheric model, to changes in the horizontal resolution of the atmospheric model, and to changes in the initial conditions. The impact of the atmospheric model parameterization on the monthly forecast is quite significant and is particularly visible on PC2. The predictability of PC2 is increased by about 3 days with a different parameterization of the model physics. This improvement is even greater when coupling the atmospheric model to an ocean mixed layer model, with the model displaying skill in predicting the evolution of PC2 up to day 21.

All the experiments described in this paper have a significant impact on PC2. However, PC1 displays surprisingly very little sensitivity to the different changes. PC1 represents the phase of the MJO where the convection is either over the Maritime Continent or over Africa. PHYS1 displayed some improvement after day 10 thanks to a better propagation through the Maritime Continent. This is the phase of the MJO that seems to be the most difficult to handle by the numerical model.

A conclusion of this paper is that there is potential for improving the skill of the current monthly forecasting system in predicting an MJO event. With a different parameterization and a better representation of the ocean mixing, the monthly forecasting system displays a level of skill in predicting the evolution of an MJO event comparable to statistical models. Parts of the physical changes of PHYS2 will be operationally implemented, and this is likely to improve the skill of the ECMWF operational monthly forecasting system.

This paper also confirms the results of WVB about the importance of ocean–atmosphere coupling for the prediction of an MJO event. In the present paper, the same experiment as in WVB was repeated with three different atmospheric models, and all of them showed a significant beneficial impact in using a mixed layer ocean model rather than an ocean GCM with a coarse vertical resolution. After 18 days, the impact of mixed layer coupling is more important than the impact of the change of physical parameterization. This also shows that the impacts of the mixed layer model and the atmospheric model physics are complementary and almost additive.

The impact of the atmospheric resolution seems to be rather small compared with the impact of physical parameterization or coupling. Interestingly, the scores showed a very strong sensitivity to the quality of the atmospheric initial conditions. Starting with ERA-40 initial conditions rather than with ERA-15 initial conditions significantly improves the forecasts of the MJO propagation. The oceanic initial conditions also play a role in the propagation of the MJO. The model also shows a surprisingly high sensitivity to the perturbations of the initial conditions more than 10 days in advance, although the MJO was not directly targeted by the singular vectors. This sensitivity seems to be due to the atmospheric singular vectors that are applied to perturb the atmospheric initial conditions. Singular vectors are applied only in the extratropics (north of 30°N) except when there is a tropical cyclone, in which case tropical singular vectors are applied in a 10° × 10° box containing the initial position of the tropical cyclone. During the period from 15 December 1992 to 31 January 1993, tropical singular vectors have been applied only during the period of 20–24 December, when a tropical cyclone developed in the Arabian Sea. For all the other dates only extratropical singular vectors were applied. This suggests that perturbations in the extratropics can have a significant impact on the development of an MJO event, and this can raise the question of the importance of the extratropical circulation for the MJO. Future work will concentrate on experimenting the targeting of the Madden–Julian oscillation by singular vectors.

Acknowledgments

The authors thank Peter Webster for useful discussions and for suggesting the TOGA COARE forecasting experiments. S. J. Woolnough was supported by the Natural Environment Research Council Grant NER/A/S/2000/1283 and thanks ECMWF for additional support.

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Fig. 1.
Fig. 1.

The first two combined EOFs of OLR (dashed line), 200-hPa velocity potential (solid line), and 850-hPa zonal wind (dotted line) from 3 yr of ECMWF operational analyses.

Citation: Monthly Weather Review 135, 7; 10.1175/MWR3415.1

Fig. 2.
Fig. 2.

Equatorial Hovmoeller diagrams of the anomalies from the 1991–2003 climatology from ERA-40 of 200-hPa velocity potential (contour interval 3 × 106 m2 s−1), 850-hPa zonal wind (contour interval 2 m s−1), and OLR (contour interval 15 W m−2) for the forecast period from 15 Dec 1992 to 4 Mar 1993. In each panel the zero contour is suppressed. Negative values are contoured and shaded; positive values are shaded but not contoured.

Citation: Monthly Weather Review 135, 7; 10.1175/MWR3415.1

Fig. 3.
Fig. 3.

Correlation of the observed RMM1 and RMM2 time series with the ensemble mean forecast (solid black line), each individual ensemble member (dotted gray lines), and the persistence of the atmospheric initial conditions (solid gray line) time series, based on 48 start dates.

Citation: Monthly Weather Review 135, 7; 10.1175/MWR3415.1

Fig. 4.
Fig. 4.

Time series of the best (dotted line) and worst (solid line) anomaly correlation between the predicted 200-hPa velocity potential and observations for the period of days 10–15 for each forecast from 15 Dec 1992 to 31 Jan 1993.

Citation: Monthly Weather Review 135, 7; 10.1175/MWR3415.1

Fig. 5.
Fig. 5.

Evolution of the variance of RMM1 and RMM2 as a function of the time lag. The dotted gray line represents the analysis. The solid black, dotted black, and solid gray lines correspond to the 5 ensemble members of CONTROL, PHYS1, and PHYS2, respectively.

Citation: Monthly Weather Review 135, 7; 10.1175/MWR3415.1

Fig. 6.
Fig. 6.

Equatorial Hovmoeller diagrams of the anomalies from the 1991–2003 climatology of (left) VP200 (contour interval 3 × 106 m2 s−1), (middle) zonal wind at 850 hPa (contour interval 2 m s−1), and (right) OLR (contour interval 15 W m−2) from 24 Dec 1992 to 10 Feb 1993 of all the 48 forecasts (48 starting dates) at day 10 concatenated to produce a single time series. The forecasts at a time lag of day 10 from (top) CONTROL and (bottom) PHYS2. Negative values are contoured and shaded; positive values are shaded but not contoured.

Citation: Monthly Weather Review 135, 7; 10.1175/MWR3415.1

Fig. 7.
Fig. 7.

Correlation of the observed RMM1 and RMM2 time series with the ensemble mean forecast time series, based on 48 start dates, for the CONTROL (solid black line), PHYS1 (dotted black line), and PHYS2 (solid gray line). The results obtained when the atmospheric model is coupled to an ocean (a) GCM and (b) mixed layer model.

Citation: Monthly Weather Review 135, 7; 10.1175/MWR3415.1

Fig. 8.
Fig. 8.

(Left) Equatorial Hovmoeller diagrams of the anomalies from the 1991–2003 climatology from ERA-40 and analysis of VP200 (contour interval 3 × 106 m2 s−1) from 31 Dec 1992 to 1 Feb 1993. Hovmoeller diagrams of the ensemble mean of (middle left) CONTROL, (middle right) PHYS1, and (right) PHYS2 starting on 31 Dec 1992. Negative values are contoured and shaded; positive values are shaded but not contoured.

Citation: Monthly Weather Review 135, 7; 10.1175/MWR3415.1

Fig. 9.
Fig. 9.

Correlation of the observed RMM1 and RMM2 time series with the ensemble mean forecast time series, based on 48 start dates, for different resolutions of the atmospheric model: TL63 (solid black line), TL95 (dotted black line), TL159 (solid gray line), and TL255 (dotted gray line).

Citation: Monthly Weather Review 135, 7; 10.1175/MWR3415.1

Fig. 10.
Fig. 10.

Correlation of the observed RMM1 and RMM2 time series with the ensemble mean forecast time series, based on 48 start dates. The score of PHYS1 with mixed layer model (solid black line), the score of PHYS1 with mixed layer model starting from climatological ocean initial conditions (dotted black line), and the score of PHYS1 with mixed layer model with ERA-15 as the atmospheric initial conditions instead of ERA-40 (solid gray line) are shown.

Citation: Monthly Weather Review 135, 7; 10.1175/MWR3415.1

Fig. 11.
Fig. 11.

Equatorial Hovmoeller diagrams of the anomalies from the 1991–2003 climatology of VP200 (contour interval 3 × 106 m2 s−1) from 15 Dec 1992 to 31 Jan 1993 for (left) ERA-15 and (right) ERA-40. Negative values are contoured and shaded; positive values are shaded but not contoured.

Citation: Monthly Weather Review 135, 7; 10.1175/MWR3415.1

Fig. 12.
Fig. 12.

Impact of initial perturbations on the 10–15-day anomaly correlation of (a) VP200 and (b) OLR forecasts. We first identify the initial perturbation, which produces the best and worst CONTROL forecasts. The impacts of exactly the same perturbations are tested in the three model configurations: (left) CONTROL, (middle) CONTROL + ML, and (right) PHYS1 + ML. Shown are the scatter diagrams of best CONTROL (x axis) vs worst CONTROL (y axis). The differences between best CONTROL and worst CONTROL are maintained in the three different configurations. Each circle represents 1 forecast (there is 1 forecast per day from 15 Dec 1992 to 31 Jan 1993) and the black square represents the mean over the 48 cases.

Citation: Monthly Weather Review 135, 7; 10.1175/MWR3415.1

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