MJO representation in the Community Earth System Model 2 Large Ensemble: detection, seasonality and amplitude

doi:10.21203/rs.3.rs-4965956/v1

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MJO representation in the Community Earth System Model 2 Large Ensemble: detection, seasonality and amplitude

https://doi.org/10.21203/rs.3.rs-4965956/v1

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The Madden-Julian Oscillation (MJO) is the leading mode of tropical intraseasonal variability in the atmosphere and impacts weather and climate, both locally in the tropics as well as globally through tropical–extratropical interactions. Various metrics have been used to classify the intensity and character of the MJO. One popular metric is the Real-time Multivariate MJO (RMM) index, which is based on an empirical orthogonal function (EOF) of zonal winds at 850 hPa and 200 hPa and outgoing longwave radiation (OLR). To date, many climate models have struggled to reproduce a realistic MJO RMM signal, due to issues associated with model tropical convective schemes and failure to capture the eastward propagation of the MJO circulation.

In this study, we assess the seasonality and amplitude of the MJO in the CESM2 Large Ensemble version 2 (CESM2-LE) experiment. We reproduce the RMM index from model output to explore the utility of OLR versus precipitation in MJO representation. Overall, we find that the model climatologies of MJO look similar to those present in the NCEP–NCAR reanalysis (for winds) and NOAA polar-orbiting satellites (for OLR). Both OLR and precipitation are found to be good indicators of MJO activity. When considering MJO amplitude over four categories (inactive, RMM < 1.0; active, RMM > 1.0; very active, RMM > 1.5; and extremely active, RMM > 2.5) the CESM2-LE model tends produce more inactive and fewer very active MJO events. Dynamically, MJO events in the CESM2-LE model are slower to propagate and weaker than observed. This is further demonstrated by model tendencies for strong MJO events to transition to weaker events faster than observed, particularly over the Indian Ocean and Maritime Continent.

Madden Julian Oscillation

Accurate representation in Earth system models of tropical convective heating produced by thunderstorms has been a challenge for the past several decades (Emanuel et al. 1994, Möbis and Stevens 2012, Bony et al. 2015, Wing et al. 2018, Tomassini 2020, Feng et al. 2023, Zheng et al. 2024). Such heating from convection, including from convection associated with the leading mode of tropical intra-seasonal variability, the Madden-Julian Oscillation (MJO, Madden and Julian, 1971, Madden and Julian, 1972, Madden and Julian, 1994), has been found to be an effective source of Rossby wave generation to the extratropics (Hoskins and Karoly, 1981, Sardeshmukh and Hoskins, 1988, Blade and Hartmann, 1995, Jin and Hoskins, 1995, Hendon and Salby, 1996, Tseng et al. 2019, Zhou et al. 2020, Yang et al. 2020, Zhang et al. 2020, Vitart et al. 2024), and even to the high latitudes (Vecchi and Bond 2004, Matthews and Meredith 2004, Yoo et al. 2012, Flatau and Kim 2013, Henderson et al. 2014, Garfinkel et al. 2014, Marín and Barrett 2017, Henderson et al. 2018, Rondandlli et al. 2019, Barrett, 2019; Kim et al. 2023). However, much debate exists regarding changes in the MJO and variability of its convection and associated extratropical teleconnections under a warming climate (Subramanian et al. 2014, Bui and Maloney 2018, Maloney et al. 2019, Jiang et al. 2020, Du et al. 2024). Without comprehensive evaluation of the MJO in Earth system models, confidence in future projections of global circulation is reduced.

Modeling the tropical atmosphere is difficult owing to its multi-scale and random nature (Wang and Li 1993, Ghil et al. 2002, Alberti et al. 2021). In terms of wavelength, the MJO is the largest intra-seasonal wave in the tropics (Wheeler and Kiladis 1999). Global climate models (GCMs) have been able to simulate the MJO with varied success (Slingo et al., 1996, Lin et al., 2006, Straub et al., 2010, Hung et al., 2013, Grabowski, 2001, Khairoutdinov et al., 2005, Khouider et al., 2011, Deng et al., 2015, Chen et al. 2022). However, models struggle to capture the basic eastward propagation, spatial structure, and variance of the convection (Kim et al., 2016, Hung et al., 2013, Jiang et al., 2015, Ahn et al., 2017, Lin et al., 2006, Heath et al. 2021, Li et al. 2021, Du et al. 2023). While many improvements in modeling the MJO have been made, the physics have remained difficult to extract (Ahn et al., 2020).

Using GCMs based on physical principles can offer information on climate in historical and future periods. There has been a concerted effort to establish extensive ensembles of climate simulations to support an investigation of climate system variability and identification of climate change patterns (Deser et al., 2014). For the MJO, these ensembles may have physics perturbations or changes in resolution that unintentionally amplify or degrade model internal variability. These could potentially distort the MJO. This issue is similar to the broader problems acknowledged in climate projections. Resolving these challenges was one of the motivations behind the creation of substantial ensembles, including the Large Ensemble Community Project (LENS, Kay et al. 2015), to more comprehensively sample natural variability (Klingaman and Demott, 2020).

One global climate model that has been used to investigate the MJO is the Community Earth System Model (CESM) (Hurrell et al., 2013). The fifth NCAR Community Atmosphere Model (CAM5, Conley et al. 2012) formed the atmospheric component of CESM. However, in CAM5 and thus in the CESM, the MJO tended to have too weak an amplitude and too fast a propagation speed (Neale et al., 2010). The model has since been updated and now the second iteration, CESM2 which uses CAM6, contains MJO amplitude, propagation speed, and even extra-tropical teleconnections that more favorably resemble observations (Danabasoglu et al., 2020). The CESM2 has a large ensemble data set, hereafter CESM2-LE, of 40 ensemble members, each of which is a fully-coupled global climate simulation that spans from 1920 to 2100 and includes both natural and anthropogenic forcings (Kay et al., 2015). The CESM2-LE output has been used to study the MJO-like convective system of CESM2. In this updated earth system model, the MJO is satisfactorily captured (Zhou et al., 2018). The CESM2-LE output has thus been used to study MJO teleconnections under increased greenhouse gas concentrations (Jenney, 2020). The MJO signal can be characterized in the CESM2-LE output through empirical orthogonal functions (EOFs) based on the wind fields. However, members of CESM2-LE do not explicitly predict OLR. Thus, EOFs based on output from CESM2-LE simulations represent the MJO as weaker than observations (Ahn et al., 2017, Li et al., 2016).

The CESM2-large ensemble (Rodgers et al., 2021) is yet another step forward in GCM prediction of the MJO. It provides finer resolution as well as more output variables than the CESM-based LENS. Indeed, CESM2-LE output has been used to study the MJO under future climate conditions (Bui and Hsu, 2023), where the MJO can be identified by analyzing the ensemble-wise standard deviation of the band-pass filtered OLR and winds. Using the Real-Time Multivariate MJO (RMM, Wheeler and Hendon 2004, hereafter WH04) index, observed amplitude and propagation characteristics of the MJO were examined by Lafleur et al. (2015). The RMM index is just one of many that can be used to characterize features of the MJO (Straub, 2013). Other indices characterize the MJO using upper-troposphere velocity potential (Ventrice et al., 2013) or filtered OLR (Kiladis et al., 2014 and Stachnik and Chrisler, 2020 and references there in). The CESM2-LE explicitly predicts more variables than its predecessor (the LENS), including net radiative flux through the top of the model. This allows for the creation of wind- and OLR-based EOFs for each ensemble, similar to the RMM. Moreover, the CESM2-LE output includes variables for precipitation, thus permitting a comparative analysis of MJO activity and timing based on EOFs from winds and both OLR and precipitation.

Here we ask the question: how well does the CESM2-LE capture MJO activity and timing at certain activity thresholds? The remainder of this article is organized as follows: data and methodology are presented in section 2, results are presented in section 3, and a summary and the conclusions are presented in section 4.

2.1. Data sources

Daily average interpolated OLR, obtained from the NOAA Office of Oceanic and Atmospheric Research (OAR) Earth System Research Laboratory (ESRL) Physical Sciences Division (PSD), Boulder, Colorado, via their website (at http://www.esrl.noaa.gov/psd/), measures the amount of terrestrial radiation released into space (Liebmann and Smith, 1996). The data are continuous in time from 01 June 1974 to 16 March 1978 and 01 January 1979 to the present. They are available at a horizontal grid spacing of 2.5° by 2.5°. Latitudes from 15°N to 15°S are retained for this study. Zonal winds at both the 200- and 850-hPa levels are taken from the NCEP–NCAR reanalysis (Kalnay et al. 1996) and are available over the same time period and horizontal grid as OLR.

Model output is taken from the CESM2-LE (Rodgers et al., 2021), and the first ten control simulation members are selected because they comprise the complete pre-industrial control simulation. Daily averages of zonal winds at the 200- and 850-hPa levels (U200 and U850), daily OLR (noted as Flux Longwave Net through Top of the model, FLNT), and total daily precipitation (noted as Precipitation Convective Total, PRECT) are analyzed from 01 January 1975 to 31 December 1977 and 01 January 1979 to 31 December 2014, with leap days removed. The year 1978 is ignored due to incomplete OLR comparison data, and 2014 is the final year of the CESM2-LE simulations.

2.2. MJO Index Calculation

To identify MJO phase, amplitude, and timing, the satellite OLR measurements, reanalysis winds, and CESM2-LE model output are analyzed in three ways (see Fig. 1 for a schematic overview; the process is described in detail in Section 2.3). 1) Anomalies of satellite OLR and reanalysis winds are used to calculate empirical orthogonal functions (EOFs), and the daily values of those two datasets are projected onto the first two principal components of the EOFs to create an RMM index that retains the structure of the MJO captured by observations. 2) Anomalies of wind and OLR (U200, U850, and FLNT) from the CESM2-LE are projected onto the first two principal components of the EOFs created from observations (as part of step 1) to create an RMM-like index that highlights the structure of the MJO captured by the model OLR and wind fields; and 3) anomalies of wind and precipitation (U200, U850, and PRECT) from the CESM2-LE are used to calculate EOFs, and those model data are projected onto the first two principal components of the model EOFs to create an RMM-like index that highlights the structure of the MJO captured by the model precipitation field.

2.3. EOF Analysis

Anomalies for all data fields are calculated using the methods of WH04. For each field, the seasonal cycle is removed by subtracting the time mean and first three harmonics of the annual cycle from each grid point using the entire time series. The data are then averaged over the tropics from 15° S to 15° N. For each field’s time series, a running mean is calculated using the previous 120 days and is subtracted from the current day of the time series to remove interannual and decadal variability (Kiladis et al., 2014).

Because the CESM2-LE output is on a finer spatial grid (1.25° longitude) than the reanalysis and OLR measurements (2.5° longitude), only those spatial points that match with the reanalysis data set are used to make direct comparisons between the observed and model data. This resolution mismatch exists for latitudes as well. However, because the anomalies are averaged over latitudes, all latitude grid points are used.

The EOF analysis is carried out similar to WH04, where the variables $\:{U}_{200}^{0}$, $\:{U}_{850}^{0}$, $\:{OLR}^{0}$ represent the time series of the 200- and 850-hPa zonal wind and OLR anomalies at each zonal point. For details of the EOF analysis, the reader is referred to Bretherton et al. (1992) and Kutz (2013), and references therein. A general outline of the EOF procedure is given here. Define the following data matrix:

$$\:{X}^{0}=\left[\begin{array}{c}{U}_{200}^{0}\\\:{U}_{850}^{0}\\\:{OLR}^{0}\end{array}\right]$$

which is dimension $\:{3·N}_{Z}\times\:{N}_{T}$, where $\:{N}_{Z}$ is the number of zonal points and $\:{N}_{T}$ is the number of time samples. For this analysis, $\:{N}_{Z}=144$ and $\:{N}_{T}=14235-120=14115$ (39 years minus 120 days at the start). Therefore, $\:{X}_{o}$ is a 432×14115 matrix. To identify the EOFs, a singular value decomposition is found for the correlation matrix $\:{X}_{o}\:{{X}_{o}}^{*}/(3{N}_{Z}-1)$ where the ^∗ denotes the matrix transpose. That is,

$$\:\frac{{{X}^{0}\left({X}^{0}\right)}^{*}}{3{N}_{z}-1}=U{\Lambda\:}{V}^{*}$$

where the $\:(3{N}_{Z}-1)$ by $\:(3{N}_{Z}-1)$ diagonal matrix Λ contains the singular values λ_i and the $\:\left(3{N}_{Z}-1\right)\:$by $\:\left(3{N}_{Z}-1\right)\:$matrix U contains the EOFs as columns. The EOF u_i explains (λ_i / $\:\sum\:_{i}{{\lambda\:}}_{i}$ )% of the variance. This procedure is repeated for the CESM2-LE output for $\:{U}_{200}^{L}$, $\:{U}_{850}^{L}$, $\:{OLR}^{L}$ (which represent the 200- and 850-hPa zonal winds and the OLR field FLNT, and the ^L represents large ensemble) from CESM2-LE, as well as for $\:{U}_{200}^{L}$, $\:{U}_{850}^{L}$, and $\:{P}^{L}\:$, where the $\:P$ field PRECT is the total convective precipitation field from CESM2-LE.

EOF1 and EOF2 are defined as the leading and second-leading modes of explained variance (13.2% and 12.1%) for observational data (Fig. 2a and d respectively). For the

CESM2-LE output (Fig. 2b and e), the EOFs are calculated for the 10 runs of the ensemble (in gray) and an average is taken (colored lines). They are labeled EOF1 and EOF2 for their appearance to the observed and not for the leading variance explained. For the $\:{U}_{200}^{L}$, $\:{U}_{850}^{L}$ and $\:{OLR}^{L}$ EOFs, EOF1 (panel (b)) is the second leading EOF for explaining variance (11.5% from the average of the ensemble) and EOF2 (panel (e)) is the first (12.3%). Together they account for a similar percentage of explained variance as observed (23.8%). For the triple$\:\:{U}_{200}^{L}$, $\:{U}_{850}^{L}$, $\:{P}^{L}$, the sign of the EOFs representing precipitation have been flipped to match the negative anomalies of OLR. Similar to the EOF produced using CESM2-LE with OLR, the PRECT EOF1 (panel c)) is the second leading EOF for explaining variance (11.1%) and EOF2 (panel f)) is the first (11.7%). Together they make up the least total explained variance (22.8%) among the three methods. All EOFs have the key characteristics of EOF1 (in shape) and OLR (and precipitation) maxima centered at the convergence zone of winds at 150° longitude. All EOF2 plots (Fig. 2d, e and f) have OLR (and precipitation) minima centered at the divergence zone of winds at 75° longitude. Also listed are the normalized magnitudes calculated from the global zonal variance, which is the anomaly that occurs for a standard deviation perturbation given the absolute maximum in each field.

2.4. MJO Indices

From WH04, the variables RMM1 and RMM2 are defined to be the first two principal components (PCs) of the EOF analysis. That is, for the observed data fields,

$$\:{X}^{o}=\left[\begin{array}{c}{U}_{200}^{0}\\\:{U}_{850}^{0}\\\:{OLR}^{0}\end{array}\right]$$

RMM1 and RMM2 are defined as the projection of this data matrix onto EOF1 ($\:{u}_{1}^{0}$) and EOF2 ($\:{u}_{2}^{0}$) respectively. The EOFs $\:{u}_{1}^{o}$ and $\:{u}_{2}^{o}$ have an $\:o$ notation to refer to the EOF analysis done using the reanalysis and OLR measurements. RMM1 and RMM2 are defined as

$$\:{RMM1}^{o}={u}_{1}^{o}{X}^{o},\:{\:RMM2}^{o}={u}_{2}^{o}{X}^{o},$$

and then they are normalized.

For the remainder of this article, there will be three RMM indices presented. The

first is the observed RMM, given by Eq. (1). The second is an RMM index for the fields $\:{U}_{200}^{L}$, $\:{U}_{850}^{L}$, $\:{OLR}^{L}$ where they are projected onto the observed EOFs. They are defined as:

$$\:{RMM1}^{Lo}={u}_{1}^{o}\left[\begin{array}{c}{U}_{200}^{L}\\\:{U}_{850}^{L}\\\:{OLR}^{L}\end{array}\right],\:{RMM2}^{Lo}={u}_{2}^{o}\left[\begin{array}{c}{U}_{200}^{L}\\\:{U}_{850}^{L}\\\:{OLR}^{L}\end{array}\right]$$

The interpretation of this index is that it compares the CESM2-LE model output to the EOF spatial structure of the observed MJO. The third RMM index is the combined fields $\:{U}_{200}^{L}$, $\:{U}_{850}^{L}$, $\:{P}^{L}\:$projected onto the CESM2-LE EOFs shown in Fig. 2 panels c) and f). That is,

$$\:{RMM1}^{Lp}={u}_{1}^{{L}_{p}}\left[\begin{array}{c}{U}_{200}^{L}\\\:{U}_{850}^{L}\\\:{P}^{L}\end{array}\right],\:{RMM2}^{{L}_{p}}={u}_{2}^{{L}_{p}}\left[\begin{array}{c}{U}_{200}^{L}\\\:{U}_{850}^{L}\\\:{P}^{L}\end{array}\right],$$

where $\:{u}_{1}^{{L}_{p}}$ is the EOF pictured in Fig. 2c and $\:{u}_{2}^{{L}_{p}}$ is the EOF pictured in Fig. 2f. The interpretation of this index is that it captures the spatial structure of the CESM2-LE output and generates an MJO index from it. To summarize, RMM1o and RMM2o is an MJO index that is from observed data, $\:{RMM1}^{{L}_{o}}$ and $\:{RMM2}^{{L}_{o}}$ combines CESM2-LE output with observed MJO structure, and $\:{RMM1}^{{L}_{p}}$ and $\:{RMM2}^{{L}_{p}}$ is generated from CESM2-LE output alone.

It is important to note that there are limitations to using EOFs to characterize the MJO. The use of a single pair of EOFs (as in the RMM index) can be helpful for simplicity, but they will not be able to capture all the subtle differences of each MJO event, which can have various structures that evolve differently or even off equatorially (Ray et al. 2009, Ray et al. 2011, Ventrice et al., 2011, Ventrice et al., 2013, Tan et al. 2020, Barrett et al. 2021). There may also be higher-frequency noise in the index because it lacks a bandpass time filter (Roundy et al., 2009). Additionally, the RMM index depends on large-scale circulation patterns to detect MJO, so it may not detect the onset of MJO if those signals are absent or weak (Straub, 2013). However, the RMM index remains a leading way to identify and characterize the MJO, and thus we use it as a tool to place our analyses in context with previous work.

Here we compare and contrast the structure, climatology, and timing of the MJO as seen in three RMM indices: one based on observations (reanalysis winds and satellite OLR) and two based on CESM2-LE model output. Model statistics are compiled from an average output from the 10 simulations chosen from the ensemble.

3.1. Structure of the MJO

The structure of the MJO is shown for boreal winter (December, January, and February (DJF)) and summer (June, July and August (JJA)) in Figs. 3 and 4. To compute the seasonal composite anomalies for phases of the observed RMM (Fig. 3a and 4a), OLR on days in which the MJO is active (RMM amplitude > 1.0) is averaged and mean seasonal OLR is subtracted. This result closely resembles the composites of WH04 (their Fig. 8). Composite anomalies for the CESM2-LE ensemble averages are created in a manner similar to the observations. This composite structure in DJF for days when the MJO is active is shown for the CESM2-LE using OLR (Fig. 3 column b) and precipitation (Fig. 3 column c).

The spatial features of the anomalies of observed OLR are well captured by the CESM2-LE in DJF. For example, N–S asymmetries are closely aligned for both observed and modeled OLR, especially during phases 6–8 (Fig. 3a and b). However, the structure of the CESM2-LE precipitation anomalies (Fig. 3c) is different than the observed OLR (Fig. 3a), particularly as the most significant precipitation anomalies seem to cluster over the maritime continent in all phases (Fig. 3c). Nevertheless, composites of model precipitation capture the eastward progression of the MJO along the equator and are similar to model results of Waliser et al. (2009, see their Figs. 11 and 12).

Comparing seasons, the composite anomalies of observed OLR (Fig. 3a and 4a) are more organized and pronounced in DJF than JJA. This relationship is mirrored in the CESM2-LE OLR composites (Fig. 3b and 4b). The spatial structure of the MJO in boreal summer (JJA, Fig. 4), is noisier than in boreal winter (Fig. 3a). For example, the observed region of negative OLR anomalies in summer is both smaller and northward displaced than in winter, especially in phases 4–6. Moreover, the region of positive OLR anomalies is also less equatorially symmetric in summer than in winter, particularly during phases 8, 1 and 2. However, the summer CESM2-LE OLR composites (Fig. 4b) resemble the observed OLR composites (Fig. 4a) during phases 1, 2, and 6–8, where the observed signal is more coherent.

Composites anomalies of precipitation (Fig. 4c) generally match the structure of modeled OLR (Fig. 4b), despite the greatest anomalies in boreal summer remaining over the maritime continent, as in boreal winter (Fig. 3c). When comparing precipitation composite anomalies between seasons (Figs. 3c and 4c), meaningful off-equatorial structure in both boreal summer and winter exists, especially for phases 3, 4, and 5 (Fig. 3c and 4c). The off-equatorial precipitation anomalies during phases 6 and 7 have pronounced seasonality, with substantial dry anomalies in the north in DJF and the south in JJA. Despite these differences, composites of observed OLR, modeled OLR, and modeled precipitation exhibit similar eastward-moving anomalies in both seasons. For the rest of this study, we present results from all three RMM indices, derived from observed OLR, CESM2-LE OLR and CESM2-LE precipitation for both the annual cycle and seasonally.

3.2. Climatology of the MJO

The first statistic considered in this study is the RMM amplitude for all days in the time series, and this and all subsequent analyses in this section follow the schematic in Fig. 1. Normalized frequencies of MJO intensity are compared between daily observed RMM amplitude (black bars), daily RMM amplitude derived from CESM2-LE composite OLR and winds (goldenrod bars), and daily RMM amplitude derived from CESM2-LE composite precipitation and winds (magenta bars) (Fig. 5). The two CESM2-LE RMMs (goldenrod and magenta bars) are almost identical (Fig. 5), and give good agreement with observations. This was confirmed using a Kolmogorov-Smirnov statistical test with 99% confidence. However, there appear to be three main differences between observed and model MJO intensity. First, the modeled MJO is too inactive (days with RMM amplitude < 1.0); second, the modeled MJO has fewer moderate-amplitude days than observations (RMM ≥ 1.0 but < 2.25) (highlighted in a black dashed box in Fig. 5); and third, the modeled MJO is too extreme (days with RMM amplitude ≥ 2.5) (highlighted in a goldenrod dashed box in Fig. 5).

To investigate these differences further, the RMM amplitudes are binned by phase and activity level (Fig. 6). The different activity levels are inactive (RMM amplitude < 1.0), active (RMM amplitude > 1.0 and < 1.5), very active (RMM amplitude > 1.5 and < 2.5), and extremely active (RMM amplitude > 2.5) (Fig. 6a-d respectively), following activity levels defined by Lafleur et al. (2015). This analysis is done for the RMM based on reanalysis wind and satellite OLR (black bars), the RMM based on model winds and OLR (goldenrod bars), and the RMM based on model winds and precipitation (magenta bars).

As highlighted above, the modeled MJO is too inactive compared with observations (Fig. 6a), and this inactivity is especially pronounced in phases 3–6. When the MJO is active, model MJO amplitude closely matches observations during most phases. Nevertheless, the model underestimates the occurrence of very active MJO in all phases (Fig. 6c), and especially during phases 1–3. Finally, the model has more extremely active MJO days than observed, a result that holds for most phases (Fig. 6d).

Next, the seasonality of MJO amplitude is explored. For each season, RMM amplitude anomalies are computed by subtracting the average frequency at different amplitudes in that season from the average frequency for the entire year (e.g., Fig. 5). These seasonal anomalies are calculated for the observed RMM (black bars) and both CESM2-LE RMMs (goldenrod and magenta bars). The dashed boxes in Fig. 7 denote the four activity levels: inactive in blue, active in green, very active in orange, and extremely active in red. In general, the CESM2-LE OLR-based RMM overestimates inactive MJO by 93% in JJA, and underestimates inactive MJO by 155% in March, April and May (MAM) (Fig. 7a and 7d). Similarly, precipitation-based RMMs overestimate inactive MJO by 44% in JJA and underestimate inactive MJO by 98% in MAM. When considering very active MJO frequency, CESM2-LE OLR-based RMM underestimates this activity level by approximately 52% in DJF, while CESM2-LE precipitation-based RMM underestimates it by 110%. Finally, when considering JJA, both model produced OLR and precipitation-based RMM active occurrence is underestimated by 205% and 186% respectively. Despite such seasonal discrepancies between CESM2-LE OLR- and precipitation- based RMMs, there is good agreement across the three datasets when considering the entire year (Fig. 5). When the MJO is more intense, the pattern reverses, where the model under predicts MJO intensity in DJF (Fig. 7c) and over predicts it in summer (JJA, Fig. 7a). Previous work has shown that the MJO is more active in winter (Madden, 1986, Knutson and Weickmann, 1987, Matthews et al., 1996, Zhang and Dong, 2004). In JJA discrepancies vary within the “very active” category, from first underestimating to then overestimating the negative anomalies in comparison to the observed (Fig. 7a). For the “extremely active” MJO cases, no significant differences between summer and winter are evident.

3.3. Dynamics and timing of the MJO

To compare MJO intensity change across the three RMMs, the probability of subsequent activity level for each intensity was calculated (Fig. 8). For example, given an inactive MJO event (“IA” or blue curve on Fig. 8a) the probability that the days following would also be inactive shifts approximately after 8 days. The resulting probabilities for both the CESM2-LE OLR-based RMM (Fig. 8 dashed), and precipitation-based RMM (Fig. 8 dotted) were similar. Key findings from this analysis include the following: first, the model tends to transition faster than observed from a weak (inactive) MJO to a stronger one (Fig. 8a), and second, the model tends to transition too quickly from a more intense MJO to an inactive one (Fig. 8b-d). This tendency for model MJOs to weaken faster than observations is even more pronounced for stronger MJO events. For example, an extremely active CESM2-LE MJO has a 24% chance of being inactive after 10 days whereas in observations the chance is only 14%.

For propagation of the MJO, counts of the time taken for the MJO to progress through RMM phase space from phase n to phase n + 8 were made for all three datasets. Defining the timing of MJO propagation has been recently studied intensely (Straub, 2013, Kiladis et al., 2014, Barrett et al. 2021). Here, an active MJO event is defined using the criteria from Jones et al. (2009) as follows: 1) the RMM amplitude is always larger than 0.35, 2) the mean RMM amplitude across all days of the event is larger than 0.9, and 3) the daily phase angle between RMM1 and RMM2 systematically rotates anticlockwise, indicating eastward propagation, until at least phase 5. Jones et al. (2009) impose a fourth criterion that the events are between 30 and 90 days long, but we do not impose that condition, as we are interested in model comparisons to observations.

Even after applying these three criteria, there are two approaches we use to count a full MJO cycle. One possible approach is to count the number and length of MJO cycles that start active and stay active as they progress anticlockwise in phase space, shown here in Fig. 9a. A second possible approach is to count the number and length of MJO cycles that start active and finish active, with the MJO still progressing anticlockwise but allowed to weaken below the active threshold (Fig. 9b). In this second approach, we only require the amplitude on the first and last days of the cycle to be greater than 0.9, similar to Lafleur et al. (2015). For both propagation approaches considered here (Fig. 9), the length of a cycle is the number of days the RMM index takes to return to the phase in which it began.

For the all-active approach, there were a total of 78 observed MJO events that propagated through all 8 phases, and there was an average of 80.9 and 68.4 MJO events in the CESM2-LE RMMs. In contrast, for the first-and-last-day-active approach, there were a total of 185 observed MJO events and an average of 194.8 and 164.1 MJO events in the CESM2-LE RMMs. While there appears to be a substantial difference in the number of MJO events in the model RMMs, an assessment of the specific physical drivers behind this disparity is beyond the scope of this work.

For both approaches, the speed of MJO propagation is faster in CESM2-LE models than observations. This is especially true for the all-active approach (Fig. 9a), where the mean circuit time for observed MJOs was 34.3 days, whereas the average circuit time for OLR-based RMMs was 27.8 days and 27.0 days for precipitation-based RMMs. Although the observed and modeled circuit times are similar for the first-and-last-day active method of defining the MJO (Fig. 9b), the CESM2-LE distribution is skewed in comparison to the observed, with the CESM2-LE events tending to persist longer in time.

The main goals of this study were to assess how well the CESM2-LE captures the structure, the climatology, and the dynamics and propagation of the MJO signal. This was done using the frequency of activity level or of consecutive days at certain activity thresholds of the WH04 RMM index. These goals were investigated by calculating three distinct RMM indices. The first index was constructed using EOFs from observed OLR and winds (closely following WH04). The second RMM index was constructed by projecting CESM2-LE OLR and winds onto the observed EOFs, which allowed us to assess how well the model captures the MJO structure seen in observations. The third RMM index was constructed by creating EOFs from CESM2-LE precipitation and winds, which allowed us, to assess the MJO using model precipitation. These contrasting approaches were designed to explore the MJO in the CESM2-LE, and also in response to previous work that highlights limitations of only using OLR to represent the MJO (Samarasinghe et al., 2021, Ahn et al., 2017, Ahn et al., 2020).

Results showed that MJO structure was well captured in both DJF and JJA by CESM2-LE, evident when comparing OLR model output to observations by phase (Figs. 3–4). The modeled precipitation field captured the MJO structure along the equator, similar to results of Waliser et al. (2009), in addition to meaningful off-equatorial structure in both boreal summer and winter, especially for phases 3, 4, and 5 (Fig. 3c and 4c).

When considering MJO climatology in the CESM2-LE output, results resemble observationsreported in Lafleur et al. (2015). Modeled MJOs were more inactive than observed (Fig. 6a), especially in phases 3–6. However, when the MJO is active, the modeled amplitudes closely match with observations in most phases. Nevertheless, the model underestimate the occurrence of very active MJO in all phases (Fig. 6c), and especially during phases 1–3. Finally, the model has more extremely active MJO days than observed, a result that holds for most phases (Fig. 6d). Seasonally, the model overestimates inactive MJO in JJA and underestimates inactive MJO in March, April and May (MAM) (Fig. 7a and d). The model tends to overestimate the frequency of active MJO in JJA and underestimate it in DJF, despite good agreement across the three datasets when considering the entire year (Fig. 5). For more intense MJO activity, the pattern reverses, where the model underestimates MJO intensity in winter DJF (Fig. 7c) and overestimates it in summer (JJA, Fig. 7a).

In terms of MJO dynamical comparison, specifically when considering the probability of an MJO event transitioning from inactive to a higher activity level or vice versa, key findings from this analysis include the following: first, a tendency of the CESM2-LE to transition too quickly from a weak (inactive) MJO to a stronger one (Fig. 8a), and second, for the model to transition too quickly from a more intense MJO to an inactive one (Fig. 8b-d). This tendency for model MJOs to weaken faster than observations is even more pronounced for stronger MJO events. For the all-active approach, there were a total of 78 observed MJO events that propagated through all 8 phases, and there were an average of 80.9 and 68.4 modeled MJO events (for OLR- and precipitation-based RMMs, respectively). In contrast, for the first-and-last-day-active approach, there were a total of 185 observed MJO events and an average of 194.8 and 164.1 modeled MJO events. These differences in number of MJO cycles per year are noteworthy. For both approaches, MJO propagation is faster in CESM2-LE models than observations.

In summary, the CESM2-LE appears to capture MJO structure, climatology, and dynamics. Nevertheless, the model has too many inactive days and too few extreme days. The model is biased toward shorter MJO events that tend to be stronger. To explore the implications of these deficiencies further, we focus briefly on the known challenge that is MJO activity across the Indian Ocean (phases 2 and 3), and eastward across the Maritime Continent (phases 4 and 5). If CESM2-LE model data favor stronger development of MJO activity over the Indian Ocean, will such events weaken faster over the Maritime continent? To answer this question, we consider the probability of subsequent activity level (as in Fig. 8) for days following activity in phases 2 and 3 (Indian Ocean) and phases 4 and 5 (Maritime Continent) (Fig. 10). From Fig. 10a, we see model data (dashed and dotted lines) transitioning to active amplitudes (including VA and EA) faster than in the observations. However, once active (Fig. 10b-c), the model data tend to capture the dynamics more accurately. For EA events however, the model displays larger variability.

Moving eastward into the Maritime Continent, we see the opposite tendency in terms of probability of subsequent MJO activity level, in that MJOs classified as being inactive are well captured in the model data (Fig. 10e), while model MJOs at the active level (Fig. 10f) tend to transition faster to inactive in comparison to observations. As MJO activity level increases to VA and EA (Fig. 10g-h), differences between model data and observations become more pronounced. For example, for MJOs of EA intensity over the MC, the model indicates a 20% chance of being inactive after seven days, whereas there is a near 0% chance based on observations.

These findings add to our growing knowledge of the unique and complex challenges associated with with the MJO in both the Indian Ocean and Maritime Continent (Zhang et al. 2020, Barrett et al. 2021). These are in addition to the overall difficulty in modeling MJO structure, climatology, and dynamics. Having a robust assessment of model capabilities and limitations when it comes to the MJO will help guide future studies seeking to use model output to extend our knowledge of impacts related to this mode of intraseasonal variability.

Competing Interests

The authors have no relevant financial or non-financial interests to disclose.

Funding

The authors gratefully acknowledge support of this research from the NSF Office of Polar Programs (OPP), award no. 1821915, in addition to the Office of Naval Research Award number: ONR N0001423WX00746.

Author Contributions

Scott Hottovy: Formal analysis, Investigation, Methodology, Visualization, Writing – original draft, Writing – review & editing. Gina Henderson: Conceptualization, Funding acquisition, Investigation, Writing – original draft, Writing – review & editing. Bradford S. Barrett: Code base programming, Writing – review & editing

Acknowledgements:

The CESM project is supported primarily by the National Science Foundation Arctic Research Program 00-144, grant no. 1203843, and the Office of Naval Research grant number ONR N0001423WX00746. Computing and data storage resources, including the Cheyenne supercomputer (doi:10.5065/D6RX99HX), were provided by the Computational and Information Systems Laboratory (CISL) at NCAR. We thank all the scientists, software engineers, and administrators who contributed to the development of CESM2.

Data Availability

The specific CESM2-LE data used in this study are available from the corresponding author upon request. Daily average interpolated OLR is obtained from the NOAA Office of Oceanic and Atmospheric Research (OAR) Earth System Research Laboratory (ESRL) Physical Sciences Division (PSD), Boulder, Colorado, via their website (at http://www.esrl.noaa.gov/psd/). Zonal winds are taken from the NCEP–NCAR reanalysis (Kalnay et al. 1996) via their website (at https://psl.noaa.gov/data/gridded/data.ncep.reanalysis.html). CESM2-LE (Rodgers et al., 2021) data is obtained from NCAR CESM2 Large Ensemble Community Project via their website (at https://www.cesm.ucar.edu/community-projects/lens2).

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MJO representation in the Community Earth System Model 2 Large Ensemble: detection, seasonality and amplitude

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Abstract

Figures

1. Introduction

2. Data & Methodology

2.1. Data sources

2.2. MJO Index Calculation

2.3. EOF Analysis

2.4. MJO Indices

3. Results

3.1. Structure of the MJO

3.2. Climatology of the MJO

3.3. Dynamics and timing of the MJO

4. Conclusions and Discussion

Declarations

Competing Interests

Funding

Author Contributions

Acknowledgements:

Data Availability

References

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