1. Introduction
Global reanalysis products (RAs) provide the best estimates of the true state of the atmosphere and ocean and have been widely used in weather and climate research. Since the first RA that covers a multidecade period was made available by the National Centers for Environmental Prediction and the National Center for Atmospheric Research (NCEP–NCAR; Kalnay et al. 1996), several organizations around the world, including the National Aeronautics and Space Administration (NASA), the European Centre for Medium-Range Weather Forecasts (ECMWF), and the Japan Meteorological Agency (JMA), have established their respective RAs and the subsequent upgraded versions. The refinement of the model configurations, the improvement in the assimilation scheme, and the increase in the quantity and quality of assimilated observations have significantly enhanced the data quality of the latest generation of RAs (e.g., Gelaro et al. 2017; Hersbach et al. 2019).
The research of the Madden–Julian oscillation (MJO; Madden and Julian 1971, 1972) has been greatly benefitted by the availability of RAs. As the dominant mode of intraseasonal variability in the tropical atmosphere, MJO exhibits salient features that distinguish it from other types of convectively coupled equatorial waves, including the zonal wavenumbers 1–6, the period of 30–60 days, and the eastward propagation speed of about 5 m s−1 over the Indo-Pacific warm pool (e.g., Zhang 2005). The MJO-associated convection and circulation anomalies affect global weather and climate (Zhang 2013), and thereby MJO provides a source of predictability on the subseasonal time scale (Lau and Waliser 2012) to many phenomena, including regional extreme weather events (e.g., Ren and Ren 2017; Ren et al. 2018).
Since the discovery of the MJO, various theories have been proposed to explain the salient features of MJO (e.g., Zhang 2005; Wang 2012; Zhang et al. 2020; Jiang et al. 2020). Recently, a view that considers the MJO as a “moisture mode” emerged (e.g., Raymond 2001; Raymond et al. 2009; Sobel and Maloney 2012, 2013; Adames and Kim 2016; Fuchs and Raymond 2017). Readers are referred to Adames et al. (2020), Zhang et al. (2020), and Jiang et al. (2020) for dedicated reviews of the recent developments of this particular theoretical framework. In the moisture mode theory, the maintenance and propagation of MJO are explained by those of column water vapor (CWV) anomalies. Therefore, understanding processes that are key to the maintenance and propagation of MJO requires examining the evolution of CWV anomalies.
As the moisture mode theory drew attention as a plausible explanation of the MJO, analyzing the column moist static energy (MSE) or moist entropy budget of MJO, which is analogous to the CWV budget under the strict weak temperature gradient (WTG) approximation (Charney 1963; Sobel et al. 2001), has become popular in the studies of MJO in the last decade (Table 1). Note that earlier analyses of the MJO MSE budget have been performed before the moisture mode theory was fully established (e.g., Benedict and Randall 2007; Maloney 2009), and were influenced more by the recharge–discharge paradigm (Bladé and Hartmann 1993; Kemball-Cook and Weare 2001), in which the gradual buildup of MSE anomalies in the lower troposphere before the onset of MJO convection is emphasized.
A list of published studies that examined (third column) MSE/moist entropy and (fourth column) moisture budget of the MJO. The number of studies in each year (each row) is indicated in the second column.
A comprehensive column MSE budget of MJO was first analyzed by Maloney (2009) using general circulation model (GCM) simulation data. Focusing on the time evolution of column MSE and its budget terms in the western Pacific (WP), he found that meridional advection dominated MSE recharging and discharging before and after the onset of MJO convection, respectively. Meridional advection was suggested to be the key propagation mechanism of the MJO in the model. He also showed that the modulation of synoptic eddy activity by the MJO-scale wind anomalies explained a large fraction of meridional advection. Surface latent heat flux anomalies were found to oppose the tendency by horizontal advection, slowing down the eastward movement of MJO MSE anomalies.
Kiranmayi and Maloney (2011) expanded the analysis performed by Maloney (2009) to the entire tropics. They used two RAs constructed by NCEP–Department of Energy (NCEP–DOE; Kanamitsu et al. 2002) and ECMWF [ECMWF interim reanalysis (ERA-I); Dee et al. 2011] and the results from the two products were compared with each other and to the model results of Maloney (2009). Across the Indo-Pacific warm pool, they found that horizontal advection contributed significantly to MSE tendency. Vertical advection was found to play a bigger role in the propagation of MSE anomalies, especially over the WP, in RAs than in Maloney (2009) results. Longwave radiative heating and surface latent heat flux anomalies were found to help maintain MJO MSE anomalies.
While examining the MJO MSE budget in an aquaplanet simulation, Andersen and Kuang (2012) developed a pattern projection method with which one can quantify the relative importance of individual budget terms on MSE growth and MSE propagation (see Fig. 8 for an example). The pattern projection method was adopted by many subsequent studies (e.g., Arnold et al. 2013; Adames et al. 2017; Jiang 2017). Andersen and Kuang (2012) found that horizontal MSE advection and longwave radiative heating are the essential processes for the propagation and maintenance of MJO MSE anomalies, respectively, in support of the conclusions of Maloney (2009) and Kiranmayi and Maloney (2011).
The diagnostics framework for the MJO MSE budget analysis developed by the abovementioned earlier studies (Maloney 2009; Kiranmayi and Maloney 2011; Andersen and Kuang 2012) has been widely used in the studies of MJO (Table 1). Examples of the studies that employed the MJO MSE or moisture budget analysis include examining the differences between MJO events that cross the Maritime Continent (MC) and those that do not (“MC barrier effect”; e.g., Kim et al. 2014a; Feng et al. 2015; DeMott et al. 2019), investigating processes responsible for the southward “detouring” of the MJO during austral summer (e.g., Kim et al. 2017), analyzing changes in MJO characteristics in a warmer climate (e.g., Arnold et al. 2013, 2015; Carlson and Caballero 2016; Adames et al. 2017; Wolding et al. 2017), evaluating the effect of the mean state on GCMs’ ability to simulate the MJO (e.g., Jiang 2017; Kang et al. 2020). As another example, DeMott et al. (2016) performed a thorough examination of MJO MSE budget in ERA-I with a particular focus on surface flux feedbacks to MJO.
While diagnosis of the MJO MSE budget in a model simulation can shed lights on the maintenance and propagation mechanisms of the simulated MJO, the question of whether the model simulates MJO for the right reason can be answered only by evaluating the model results against the corresponding observations. Reanalysis products have played a pivotal role as the reference dataset in this regard. Due to the necessity of the large number of atmospheric field variables as well as radiative and turbulent surface heat fluxes in an MSE budget analysis (section 2b), the MSE budgets in the observed MJOs are examined almost exclusively in the RAs (e.g., Kiranmayi and Maloney 2011; Kim et al. 2014a; Wang and Li 2020), with a few exceptions that used observations from field campaigns (Sobel et al. 2014; Yokoi and Sobel 2015; Inoue and Back 2015).
The goal of the present study is to examine the column-integrated MSE and CWV budget of the MJO in six modern RAs. While RAs are often considered as “observations,” it is well known that notable differences between RAs exist in many aspects of the weather–climate system (e.g., Kim et al. 2014b; Chen et al. 2014; Lindsay et al. 2014; Sakaeda and Roundy 2016; Gao et al. 2016, 2019). However, little attention has been paid to the question of whether and how much the MJO MSE and CWV budget is represented differently in different RAs. To our best knowledge, only Kiranmayi and Maloney (2011) and Yokoi (2015) analyzed MJO MSE or CWV budget in more than one reanalysis dataset.
Essentially, our analysis will assess the degree to which the mean state and variability of MSE and CWV are constrained in the RAs, and there are reasons to believe that there would be nonnegligible differences between RAs, especially in water vapor. Over the warm tropical oceans, where moisture variability associated with the MJO is most pronounced, water vapor in RAs is constrained mainly by satellite observations. The differences in the list of satellite datasets assimilated for constraining moisture (e.g., Table 2 in Yokoi 2015) as well as those in the data assimilation techniques can potentially lead individual RAs to have different water vapor amount at the same location and time. Moreover, there exists a large spread among satellite retrievals. As part of the Global Water and Energy Exchanges water vapor assessment project, Schröder et al. (2019) compared CWV retrievals from various instruments, including microwave and infrared sensors, ultraviolet–visible–near-infrared imagers, and GPS radio occultation measurements. They found a notable spread (10%–15%) over the tropical oceans among satellite retrievals even in the long-term mean CWV. While identifying the root cause of the inter-RA spread may be beyond the scope of our study, we aim to provide useful information to the user community by objectively quantifying the uncertainty in MSE and CWV variability associated with the MJO.
When examining inter-RA differences in the MSE budget terms, we will focus on the processes that are directly affected by model parameterization schemes. Those terms, such as vertical MSE advection, radiative fluxes, and surface turbulent fluxes, are less constrained by assimilating observations and therefore more likely to show large differences between RAs.
A special focus will also be on the budget residual. Kiranmayi and Maloney (2011) documented a large residual in the MJO MSE budget whose magnitude was comparable to that of MSE tendency in both reanalysis datasets used. Due to the existence of nonnegligible budget residual, the reanalysis-based MJO MSE budget results have been interpreted with caveats (Kiranmayi and Maloney 2011; Kim et al. 2014a). Analysis increment—correction of the field variables during the data assimilation procedure—is believed to take a large portion of the MSE budget residual (Yokoi 2015; Mapes and Bacmeister 2012), while truncation errors from the finite differencing method employed to estimate gradients and using pressure level interpolated output can also contribute to the budget residual (Hill et al. 2017).
Characterizing the evolution of analysis increment during the life cycle of MJO can offer insights into model biases. Mapes and Bacmeister (2012) analyzed moisture analysis increment in the context of MJO structure in Modern-Era Retrospective Analysis for Research and Applications, version 1 (MERRA-1), and found that moisture is added by data assimilation during the preonset phase of the MJO. They suggested that deep convection is triggered in the model too early and makes columns overly dry, which is compensated by the moisture increment. In an attempt to understand the difference in MJO CWV budget between three RAs, Yokoi (2015) found a negative correlation between the strength of cloud–radiation feedback [defined by Eq. (6) below] and MJO CWV analysis increment. While supporting the argument that cloud–radiation feedback is the dominant MJO maintenance mechanism, his results also demonstrated that analysis increment offers useful insights into model biases. Following Yokoi (2015), we will examine the relationship between MJO CWV budget residual and two parameters that characterize cloud–radiation feedback and moisture–convection coupling.
The present study is organized as follows. Section 2 introduces data and methods. Section 3 presents inter-RA comparisons of the mean state, MSE anomalies, and MSE budget analysis. The potential impacts of moisture–cloud–radiation–convection feedback on the residual in CWV budget are shown in section 4. Section 5 provides the summary and conclusions.
2. Data and methods
a. Reanalysis and observational data
We use six modern RAs, including MERRA-1, MERRA-2 (Gelaro et al. 2017), ERA-I, the fifth major global reanalysis produced by ECMWF (ERA5; Hersbach et al. 2019), NCEP Climate Forecast System Reanalysis (CFSR, Saha et al. 2010, 2014),1 and the Japanese 55-yr Reanalysis (JRA-55; Kobayashi et al. 2015). A brief description of the six RAs used in our study is presented in Table 2. To facilitate the comparison between RAs, we define the multireanalysis mean (MRM)—a simple average over all six RAs—for quantities whose corresponding observations are not available (e.g., MJO MSE anomalies). While RAs are compared to MRM, it should be noted MRM is not necessarily closer to the true state than any individual RAs used.
A brief description of the global reanalysis products used in this study.
Some observations are used to evaluate the performance of the RAs, including the outgoing longwave radiation (OLR) from NOAA satellites (Liebmann and Smith 1996) and the precipitation from Tropical Rainfall Measuring Mission (TRMM; Kummerow et al. 2000).
All data were interpolated into a uniform horizontal resolution of 2.5° longitude × 2.5° latitude to facilitate comparison between RAs. Our analysis was performed over the period that is covered by all RAs (1980–2014). It is well known that the MJO exhibits notable seasonality, with the boreal winter MJO being characterized by eastward propagation, and summer MJO activities involving significant northward-propagating component in the Indian Ocean (IO) and the WP (Yasunari 1979, 1980; Murakami et al. 1984; Lau and Chan 1986). Our analysis focuses only on the boreal winter months (November to April).
b. Column-integrated MSE and CWV budget of MJO
c. MJO life cycle composite
To characterize MJO activity, various field variables, including MSE budget terms, are composited for MJO phases that are defined using the OLR-based MJO index (OMI; Kiladis et al. 2014). For a given time, the OMI consists of two scalar values (OMI1 and OMI2) that can be located in a 2D phase diagram (e.g., Wheeler and Hendon 2004). Using the position vector that begins at the origin and ends at (OMI1, OMI2), MJO amplitude is estimated as the length of the position vector. The phase diagram can be divided into eight equal-sized spaces by x and y axes and two diagonal lines that crosses the origin. Each space corresponds to a MJO “phase.” The convention is that the space that is in the third quadrant and right beneath y axis represents phase 1 and the numeric increases counterclockwise to end at 8. MJO phase on a given day is determined by the space the end of the position vector belongs to. By MJO composite of a variable, we mean the average of the variable for each MJO phase over days with MJO amplitude greater than 1. We note that the results are almost identical with the multivariate MJO index (Wheeler and Hendon 2004, not shown).
3. Mean state and MJO MSE budget in RAs
a. Mean state
We begin by analyzing the horizontal and vertical structures of the mean MSE, DSE, and LE. As mentioned in the previous section, for each RA, anomalies are defined around its own climatological seasonal cycle. Therefore, it is worthwhile to examine the mean state and its differences between RAs. The mean state affects the MSE budget terms in various ways, in particular, through the horizontal and vertical gradient of the mean MSE. It has been reported that the ability of a model to simulate MJO is closely linked to its ability to represent the climate mean state (Zhang et al. 2006; Kim et al. 2009; Gonzalez and Jiang 2017; Jiang 2017; DeMott et al. 2019; Ahn et al. 2020a). For example, models that realistically capture the horizontal gradient of seasonal mean lower-level moisture around the MC region tend to show a more coherent propagation of the MJO (Gonzalez and Jiang 2017; Jiang 2017; DeMott et al. 2019; Ahn et al. 2020a).
The mean zonal and meridional gradient of MSE affects the horizontal MSE advection term, which has been suggested as the dominant moisture recharging and discharging process for MJO’s eastward propagation (e.g., Kim et al. 2014a) and as a damping process (e.g., Wolding et al. 2016). Figure 1 shows the horizontal distributions of the winter-mean column-integrated MSE, DSE, and LE. In Fig. 1b, the domain mean was subtracted from each variable to better compare horizontal gradient among the three variables. The horizontal gradient of the mean MSE comes mainly from that of the mean LE whereas the mean DSE is almost horizontally homogeneous. Over the Indo-Pacific warm pool, the mean MSE is relatively high in MERRA-2 and ERA-I and relatively low in JRA-55 and CFSR. As a result, the horizontal MSE gradient across the warm pool are sharper in MERRA-2 and ERA-I and smoother in JRA-55 and CFSR. MERRA-1 and ERA5 values are close to those of MRM. Figure 1 also shows that the inter-RA difference in the mean MSE originates mainly from that of LE. CFSR is an exception in this regard, in which the mean DSE is lower than the other RAs (especially in the upper and lower free troposphere, Fig. 2e).
(a) The MRM of (left) column-integrated MSE, (center) DSE, and (right) LE for boreal winter. (b) As in (a), except that the domain mean is removed. (c)–(h) Differences from MRM for (c) MERRA-1, (d) MERRA-2, (e) ERA-I, (f) ERA5, (g) CFSR, and (h) JRA-55. The contour interval in (c)–(h) is 2 × 106 J m−2.
Citation: Journal of Climate 34, 8; 10.1175/JCLI-D-20-0653.1
(left) Longitude–pressure distribution of the boreal winter mean, equatorial (10°S–10°N) (a) MSE, (d) DSE, and (g) LE in the MRM. (center) Deviation from warm-pool (10°S–10°N, 60°E–180°)-averaged MRM for each RA of (b) MSE, (e) DSE, and (h) LE. (right) Warm-pool-averaged MRM and the standard deviation for each RA of (c) MSE, (f) DSE, and (i) LE. The contour intervals in (a), (d), and (g) are 2, 5, and 4 kJ kg−1, respectively.
Citation: Journal of Climate 34, 8; 10.1175/JCLI-D-20-0653.1
Figure 2 shows the vertical structures of the MRM mean MSE, DSE, and LE. Overall, DSE and LE increases and decreases with height, respectively, resulting in MSE minima at around 700 hPa across the warm pool. Again, the longitudinal variation in MSE in the mid- to low troposphere comes from that of LE, while the mean DSE is zonally homogeneous except in the boundary layer and near 200 hPa. Also shown in Fig. 2 in the center and right panels is the warm-pool-averaged MRM, the deviation from the MRM for each RA and its standard deviation. For the mean MSE, the inter-RA differences are most pronounced in two layers: one between 950 and 800 hPa and the other between 700 and 400 hPa (Fig. 2c). In the lower one, which covers the upper part of the planetary boundary layer (PBL) and the lower part of the free troposphere, MERRA-1 is relatively dry and cold, whereas ERA-I, ERA5, and JRA-55 are relatively wet and warm. CFSR shows a transition from the warm/moist to the cold/moist condition between 950 and 800 hPa. Presumably, the difference in the representation of the boundary layer turbulence and ventilation of heat and moisture by deep convection scheme from PBL is what causes the inter-RA spread in this layer. The 700–400 hPa layer is relatively wet in MERRA-1 and MERRA-2 and dry in JRA-55. The difference in LE between MERRA-2 and JRA-55 at 600 hPa is about 4 kJ kg−1, which is 40% of the MRM value. The treatment of cumulus congestus (Johnson et al. 1999) and cloud microphysics, especially the melting process (e.g., Thayer-Calder and Randall 2009), may be caused these differences between the RAs. The vertical grid spacing near the melting level can also affect the representation of cumulus congestus (Inness et al. 2001). The substantial inter-RA spread in the mean LE shown in Fig. 2 suggests that it remains challenging to constrain moisture in the tropics through data assimilation.
b. MJO MSE budget
Figure 3a shows the longitude–phase composites of the column-integrated MSE anomaly for MRM, which well captures the coherent eastward propagation of MJO. Compared to MRM, the amplitude of MSE anomalies is larger in MERRA-2, especially in the IO. In contrast, the MJO MSE anomalies are relatively weak in JRA-55 over the entire warm pool region. Interestingly, MERRA-2 and JRA-55 exhibit climatologically wetter and drier conditions than the other RAs (Figs. 1 and 2). CFSR shows considerable deviations from MRM over the MC during the transition phases (i.e., when MSE anomalies change the sign). Overall, the MJO MSE anomalies in MERRA-1, ERA-I, and ERA5 are close to those in MRM. To quantify the degree of spread among the RAs, we calculated the standard deviation of the composite MSE anomalies using the six RAs (Fig. 3b). A large inter-RA spread appears in the eastern Indian Ocean (EIO) for MJO phases 2–3 and 6–7, and in the eastern MC to WP regions for MJO phases 1 and 5, where the MRM MSE anomalies are significant. The standard deviation is about 10% of the MRM values in those areas and phases, and the deviations in MERRA-2, and CFSR, and JRA-55 are mainly responsible for the spread.
(a) Longitude–phase composite of the MRM column-integrated MSE anomaly and (b) its standard deviation among six RAs in the equatorial region (15°S–15°N). (c)–(h) Differences (shaded, units: 106 J m−2) from MRM for (c) MERRA-1, (d) MERRA-2, (e) ERA-I, (f) ERA5, (g) CFSR, and (h) JRA-55. The contours represent MRM MSE anomaly (contour interval: 3 × 106 J m−2).
Citation: Journal of Climate 34, 8; 10.1175/JCLI-D-20-0653.1
To further examine the differences in MSE anomalies between RAs, Fig. 4 shows the horizontal distribution of the MJO MSE anomalies during MJO phase 3. In the EIO region, where positive MSE anomalies peak in the MRM, MERRA-2 and JRA-55 show substantial positive and negative differences from the MRM, respectively. In CFSR, negative difference prevails in the southern MC and WP regions while a weak positive difference appears in the EIO. The difference seems to be about 90° out of phase with the MSE anomaly, suggesting a time lag between the MRM MJO and that in CFSR MJO.
(a) MJO phase 3 composite of the MRM column-integrated MSE anomaly and (b) six-RAs’ standard deviation. (c)–(h) Differences from MRM for (c) MERRA-1, (d) MERRA-2, (e) ERA-I, (f) ERA5, (g) CFSR, and (h) JRA-55. The contours represent MRM MSE anomaly (contour interval: 4 × 106 J m−2). Note that the box in (a) covers the area of 16°–4°S, 87.5°–107.5°E.
Citation: Journal of Climate 34, 8; 10.1175/JCLI-D-20-0653.1
Figure 5 further shows MSE anomalies in longitude–pressure diagrams for MJO phase 3. The MRM MSE anomalies are tilted westward with height, with shallow MSE anomalies appearing to the east of maximum MSE anomalies. In the EIO, a large inter-RA differences appear in the low-to-middle free troposphere (800–400 hPa), especially for MERRA-2 and JRA-55. The difference in MERRA-2 is located slightly to the west of the maximum MRM MSE and shows a westward tilted structure. The deviation in JRA-55 appears mainly where the MRM MSE anomalies peak. CFSR deviations are mainly concentrated in the lower troposphere (1000–600 hPa) and show a dipole structure between the EIO and MC regions, which appears to be consistent with its slower MJO propagation speed. That the only coupled RA (CFSR) exhibits a lagged MJO may suggest that a low-frequency, unstable air–sea coupled mode (Wang and Xie 1998) is responsible for the MJO slow down.
As in Fig. 4, but for longitude–pressure composite of MSE anomaly averaged over 15°S–15°N. The contour interval is 300 J kg−1.
Citation: Journal of Climate 34, 8; 10.1175/JCLI-D-20-0653.1
In Fig. 6, the four terms that dominate the MJO MSE budget in magnitude are separately shown: horizontal advection (hAdv), vertical advection (wAdv), longwave radiative heating (LW), and surface latent heat flux (LH). In MRM, large anomalous horizontal advection of MSE appears where the MSE anomalies are changing polarity, highlighting its primary role in the propagation of the MSE anomalies. In contrast, vertical MSE advection and column longwave radiative heating show large magnitude near the positive and negative peaks of the MSE anomalies, suggesting that the two terms contribute mainly to the maintenance of the MJO MSE anomalies. The wAdv and LW terms are both directly affected by local convective activity and often tend to have the opposite signs. By slightly lagging the MSE anomalies, column LW also slows down the propagation of the MSE anomalies. Surface latent heat flux anomalies also seem to counteract the effect of horizontal MSE advection, especially over the MC.
Longitude–phase composite of (left to right) hAdv, wAdv, LW, and LH, respectively, for (a) the MRM and (b)–(g) the differences MRM for (b) MERRA-1, (c) MERRA-2, (d) ERA-I, (e) ERA5, (f) CFSR, and (g) JRA-55. The contours show the MRM MSE anomalies with the interval of 3 × 106 J m−2.
Citation: Journal of Climate 34, 8; 10.1175/JCLI-D-20-0653.1
All MSE budget terms show noticeable inter-RA spread. The difference between RAs is larger for individual budget terms than for their sum (i.e., total tendency, not shown). The role of horizontal MSE advection in moving MSE anomalies to the east seems to be stronger in ERA5 and weaker in MERRA-1. In MERRA-2 (JRA-55), horizontal MSE advection tends to dampen (amplify) MSE anomalies. Compared to MRM, the magnitude of vertical MSE advection in JRA-55 is larger, while it is smaller in CFSR. LW in the Pacific and in the Indian Ocean is relatively weak in MERRA-2 and JRA-55. LW in CFSR lags the MRM LW, exhibiting a stronger slowing effect on the MJO MSE propagation. MSE anomalies are amplified by LW more in ERA-I and ERA5 than in the other RAs. Compared to MRM, LH is represented with a much greater amplitude in CFSR. JRA-55 LH seems to damp MSE anomalies, which likely contributes to its relatively small MSE anomaly (Fig. 3).
Nonnegligible budget residual is found in all RAs (Fig. 7). In MERRA-1, MERRA-2, ERA5, and JRA-55, the budget residual tends to be in phase with the MSE anomalies, indicating that the models used to create the modern RAs need additional MSE source to maintain MJO MSE anomalies. In ERA-I and CFSR, on the other hand, budget residual appears where MSE anomalies are small, suggesting that the processes that are associated with MSE tendency are not adequately represented. Our results for ERA-I are similar to that of Wolding and Maloney (2015), who found that MSE budget residual tends to appear in the transitional phase of OLR anomalies in ERA-I.
Longitude–phase composites of MSE budget residual for (a) MRM, (b) MERRA-1, (c) MERRA-2, (d) ERA-I, (e) ERA5, (f) CFSR, and (g) JRA-55. The contours show the MRM MSE anomalies with the interval of 3 × 106 J m−2.
Citation: Journal of Climate 34, 8; 10.1175/JCLI-D-20-0653.1
Figure 8 shows Sp (top) and Sm (bottom) for each term in Eq. (2) and for two derived terms: the sum of zonal and meridional advection (hAdv) and the sum of vertical advection and radiative heating (CONV). The latter derived term represents the combined effect of MSE import/export by vertical advection and the net MSE flux into the column via longwave radiative fluxes. The numbers within parentheses indicate a measure of the inter-RA spread, which is obtained for each budget term by dividing the standard deviation of values from six RAs by the absolute value of its corresponding MRM value. The resulting number is shown in percentage.
Normalized contribution of the individual terms in the column-integrated MSE budget to the (a) propagation and (b) maintenance of MJO MSE anomalies over the domain 15°S–15°N, 60°E–180°, and MJO phases 1–8. The value for each bar is obtained using Eq. (4). The individual budget terms shown include, from left to right, MSE tendency (dmdt), zonal MSE advection (uAdv), meridional MSE advection (vAdv), vertical MSE advection (wAdv), surface sensible heat fluxes (SH), surface latent heat fluxes (LH), column longwave radiative heating (LW), column shortwave radiative heating (SW), the budget residual (res), the sum of zonal MSE advection and meridional MSE advection (hAdv), and the sum of longwave heating and vertical MSE advection (CONV). The numbers in parentheses indicate a measure of the inter-RA spread, which is obtained for each budget term by dividing the standard deviation of values from six RAs by the absolute value of its corresponding MRM value. The resulting number is shown as a percentage.
Citation: Journal of Climate 34, 8; 10.1175/JCLI-D-20-0653.1
Figure 8a indicates that, to first order, MJO MSE anomalies are moved to the east by advection processes, while surface latent heat flux and longwave radiative heating oppose the eastward propagation. Among the three advection terms, meridional advection plays a dominant role in the propagation of the MSE anomalies. Many previous studies drew similar conclusions (e.g., Kim et al. 2014a; Jiang 2017). Meridional advection is also the least uncertain process. Its inter-RA spread measured by the standard deviation is only about 4% of the MRM value. When combined with zonal advection (hAdv), its dominance becomes clearer with small differences between RAs. Vertical advection also contributes positively to MSE propagation despite relatively large inter-RA spread (about 17% of the MRM value).
While several studies have found that vertical advection serves as the dominant MSE recharging process to the east of MJO convection (e.g., Chen and Wang 2018), we found that the relative importance of vertical advection becomes comparable to that of horizontal advection only when the analysis was performed on a narrow band near the equator (e.g., 5°S–5°N, not shown). In this study, instead of focusing on the near-equatorial processes, we analyze MJO MSE budget over the latitude band between 15°S and 15°N that can account for the full meridional scale of the MJO MSE anomalies (e.g., Fig. 4). LW exhibits notable inter-RA spread (about 34% of the MRM value). The contribution of LW to MSE propagation in MERRA-2 and JRA-55 is relatively small, which is likely related to the relatively weak cloud–radiation feedback strength (Table 4).
The contribution of the budget residual to MSE propagation is not negligible and it shows substantial inter RA-spread. In CFSR and ERA-I, the budget residual gives relatively large positive contributions to MJO propagation (Fig. 7), which appears to compensate the overly active LH and LW in CFSR and the relatively weak wAdv in ERA-I. Sobel et al. (2014) also showed that the contribution of vertical advection to MJO propagation in ERA-I was underestimated compared to that in the DYNAMO sounding data. In MERRA-2, the negative budget residual suggests that the model is overproducing MSE recharging and discharging associated with MJO MSE propagation, which may be due to the weak contributions from LW.
In the maintenance of the MJO MSE anomalies (Fig. 8b), vertical MSE advection and longwave radiative heating are the two dominant processes in terms of the magnitude. Their dominance in the magnitude over other terms, however, disappears when combined (CONV), suggesting that examining the role of the other terms need to be considered together with CONV. This is especially true given that wAdv and LW tend to be negatively correlated. For example, in the area of enhanced MJO convection, MSE is exported out of the column via vertical MSE advection while anomalous LW partially compensates the loss of MSE. Both terms show notable spread among the RAs, with the standard deviation of wAdv and LW being about 25% and 18% of its MRM values, respectively. When the two terms are considered together (CONV), the effect of wAdv dominates in most RAs. Horizontal advection contributes negatively to MSE maintenance in all RAs, indicating a damping effect (e.g., Wolding et al. 2016), whereas shortwave radiative heating and surface latent heat flux has a nonnegligible positive contribution to the MSE amplitude. It is worthwhile to mention that Fig. 8b is normalized by the variance of MSE anomalies [Eq. (4b)]. The damping effect of wAdv on MSE anomalies is relatively large in JRA-55 partly because its MSE anomalies are relatively small (Fig. 3). The cause of the large inter-RA spread in wAdv will be examined further below.
Interestingly, in all RAs, the budget residual contributes positively to the maintenance of MJO MSE anomalies, indicating the common bias in the models used in RAs of underestimating the amplitude of the MJO. The budget residual plays a particularly important role in MSE maintenance in three RAs: MERRA-1, MERRA-2, and JRA-55. It appears that in these RAs the budget residual is required to compensate the overly active MSE sink from the processes that are directly affected by local convective activity (CONV). In other words, inadequate representations of convection, cloud, and radiation could be mainly responsible for the budget residual around the positive and negative MSE anomaly peaks. For MERRA-1 and JRA-55, MSE export by vertical advection is larger than the other RAs, while LW is relatively weak in MERRA-2.
To better understand the inter-RA differences in vertical MSE advection, Figs. 9a and 9b show the vertical profiles of the mean MSE and its vertical gradient over the eastern equatorial Indian Ocean, where a relatively large difference is found between RAs in MJO MSE anomalies during MJO phase 3 (black box in Fig. 4a). In the mean MSE, as seen in Fig. 2, substantial differences between the RAs occur in the upper boundary layer (900–800 hPa) and below the melting level (700–500 hPa). While ERA-I, ERA5, CFSR, and JRA-55 show the level of minimum MSE at around 650 hPa, the minimum MSE appears below 700 hPa in MERRA-1 and MERRA-2. As a result, between 850 and 600 hPa, where significant MSE anomalies appear (Fig. 5), the mean MSE vertical gradient is larger in JRA-55 and ERA5 than in MERRA-1 and MERRA-2.
Vertical profile of (a) the mean MSE (kJ kg−1) and (b) its vertical gradient (J kg−1 Pa−1) averaged over the domain of 16°–4°S, 87.5°–107.5°E (box in Fig. 4a). (c)–(e) As in (a), but for (c) anomalous vertical velocity (Pa s−1), (d) apparent heating (Q1), and (e) advection of mean MSE by anomalous vertical motion (W kg−1). The quantities plotted in (c)–(e) are normalized by the corresponding column-integrated MSE anomalies.
Citation: Journal of Climate 34, 8; 10.1175/JCLI-D-20-0653.1
The anomalous vertical motion during MJO phase 3 over EIO exhibits considerable inter-RA differences in their magnitude, especially in the layer between 600 and 200 hPa (Fig. 9c). Note that the vertical motion anomalies shown in Fig. 9c are normalized by column MSE anomalies. JRA-55, which shows a relatively large vertical velocity, has relatively small MSE anomalies (Table 3). The RAs with stronger anomalous vertical motion also exhibit stronger apparent heating (Fig. 9d), suggesting that the uncertainty in the forecast model diabatic processes is responsible for the inter-RA difference in anomalous vertical motion.
Column-integrated vertical MSE advection, MSE anomalies, and vertical MSE advection normalized by MSE anomalies over the eastern Indian Ocean (the black solid line box in Fig. 4a) during MJO phase 3. Note that vertical MSE advection is approximately estimated by the advection of mean MSE by anomalous vertical motion.
Figure 9e shows the vertical profiles of anomalous vertical MSE advection that is approximated by the advection of mean MSE by anomalous vertical motion. It can be inferred from Fig. 9e that the column-integrated vertical MSE advection is dominated by the negative MSE advection in the upper troposphere above around 600 hPa, which the result of the anomalous upward motion acting upon the mean negative MSE gradient. The magnitude of vertical MSE advection differs considerably among RAs, which is mainly due to the differences in vertical velocity. The negative vertical MSE advection above the level of minimum mean MSE is partly offset by the positive MSE vertical advection below, yielding a net MSE export in all RAs (Table 3). In JRA-55, both positive and negative MSE advections are relatively large due to the relatively stronger normalized ascent (Fig. 9e). The normalized net MSE export by vertical advection (third row in Table 3) is also largest in JRA-55, which is consistent with the largest MSE damping effect from vertical advection (Fig. 8b). In contrast, the vertical MSE advection above the minimum MSE level is weaker in CFSR and MERRA-2, yielding a smaller normalized net MSE export (Table 3). In Fig. 8b, these two RAs show relatively weaker damping effect from vertical MSE advection. The results shown in Fig. 9 and Table 3 suggest the substantial inter-RA differences in vertical MSE advection is due to the differing representation of anomalous vertical motion associated with the MJO among the RAs.
4. Relationship between cloud–radiation feedback, convective moisture adjustment time scale, and CWV budget residual
Regressed composite anomalies of (second column) budget residual, (third column) precipitation, and (fourth column) OLR variables against composite CWV anomaly calculated over 60°E–180° and MJO phases 1–8. The cloud–radiation feedback strength r and the convective adjustment time scale τc are shown in the fifth and sixth columns, respectively.
Based on Eq. (5), a hypothesis was proposed by Yokoi (2015): if NGMS is similar across the RAs, the bias in the cloud–radiation feedback strength (r − rr) would exhibit a linear relationship with the ratio of CWV analysis increment to precipitation anomalies (
We first test one of the key assumptions made in the derivation of Eq. (5): the balance between precipitation and vertical moisture advection is mainly responsible for the budget residual among the other budget terms. The relationship of the CWV budget residual with the other CWV budget terms (Fig. 10) shows that the ratio of vertical moisture advection to precipitation is most strongly associated with the budget residual normalized by precipitation (corr = −0.96, Fig. 10c), suggesting its major role in causing CWV budget residual. However, it is unlikely that vertical moisture advection is the only process that is responsible for the CWV budget residual, as the zonal advection term is also tightly correlated with the CWV budget residual (Fig. 10a), though the correlation is not statistically significant at the 95% confidence level.
Scatterplot of the normalized CWV budget residual with the normalized (a) zonal advection, (b) meridional advection, (c) vertical advection, and (d) surface latent heat flux. The quantities are obtained through regressions using values over the warm pool (15°S–15°N, 60°E–180°) and for MJO phases 1–8 (see text).
Citation: Journal of Climate 34, 8; 10.1175/JCLI-D-20-0653.1
Scatterplot of the ratio of vertical moisture advection to precipitation with (a) the cloud–radiation feedback strength (r), (b) the normalized gross moist stability, (c) alpha normalized by precipitation, and (d) apparent heating normalized by precipitation. The quantities are obtained through regressions using values over the warm pool (15°S–15°N, 60°E–180°) and for MJO phases 1–8 (see text).
Citation: Journal of Climate 34, 8; 10.1175/JCLI-D-20-0653.1
Figure 12a shows that the strength of cloud–radiation feedback quantified with r varies widely among the RAs (ERA-I is greater than MERRA-2 by a factor of 2), implying that the process is poorly constrained in RAs. Nonetheless, a nearly linear relationship between r and
Scatterplot of the normalized CWV budget residual with (a) the cloud–radiation feedback strength (r), (c) the convective moisture adjustment time scale (τc), and (d) column-integrated apparent heating normalized by precipitation. (b) Scatterplot between r and τc. The quantities are obtained through regressions using values over the warm pool (15°S–15°N, 60°E–180°) and for MJO phases 1–8 (see text).
Citation: Journal of Climate 34, 8; 10.1175/JCLI-D-20-0653.1
According to Yokoi’s (2015) interpretation of the negative linear relationship between r and
(a) Longitude–phase composites of MRM (left) precipitation (multiplied by −1), (center) vertical moisture advection, and (right) sum of the two terms. (b)–(g) Differences from MRM for (b) MERRA-1, (c) MERRA-2, (d) ERA-I, (e) ERA5, (f) CFSR, and (g) JRA-55. The contours show the MRM MSE anomalies with the interval of 3 × 106 J m−2.
Citation: Journal of Climate 34, 8; 10.1175/JCLI-D-20-0653.1
The strong correlation between the budget residual and various process-oriented metrics (Figs. 12a,c,d and 10c) provides an emergent constraint on the metrics and thereby offers the target against which the models used in the construction of RAs can be tuned. For example, the observed cloud–radiation feedback strength that can be inferred from Fig. 12a (by taking residual equal to zero) is about 0.25, which is very close to the value obtained from observations (0.24) by Yokoi (2015). Similarly, the observed τc inferred from Fig. 12c is about 1.53 days, which is close to what was obtained in previous studies (e.g., Jiang et al. 2016). Unlike r and τc, quantifying vertical moisture advection or apparent heating over large domain and for a long time is not feasible, and the vertical profiles of moisture and vertical velocity in heavily precipitation areas are not well constrained by the state-of-the-art data assimilation techniques. Figure 10c indicates that anomalous column-integrated vertical moisture advection is about 1.1 times larger than precipitation anomalies when the entire MJO life cycle is considered over the warm pool region. While ERA5 is near the inferred target value, the other five RAs are either too large (ERA-I) or too small (MERRA-1, MERRA-2, CFSR, and JRA-55). Our results also strongly suggest that, for reducing CWV budget residual in RAs, hence enhancing their quality, the errors in r, τc, Q1, and vertical moisture advection need to be reduced. Examining the effects of model parameterization schemes, including the convection, cloud, and radiation schemes, and aspects of the data assimilation system on these parameters may help improve the representation of those parameters.
5. Summary and conclusions
Recently, the diagnosis of column-integrated moist static energy (MSE) and column water vapor (CWV) budget has been performed in many studies of the MJO (Table 1). The global reanalysis products have provided unique reference datasets against which model simulations can be evaluated. While it has been recognized and documented that nonnegligible differences exist between reanalyses (RAs) in their representations of the MJO MSE or CWV budget, no detailed examinations of the budget have been conducted using more than a few RAs.
In this study, we analyzed and compared the MJO MSE and CWV budget as well as the relevant mean state in six modern RAs: MERRA-1, MERRA-2, ERA-I, ERA5, CFSR, and JRA-55. One of the main purposes of the current study is to document how similarly or differently the processes that are key to MJO propagation and maintenance are represented in the RAs. Special attention was given to the processes that are directly affected by model parameterization schemes of moist physics and also the budget residual, to which the analysis increment is believed to have large contributions.
Notable inter-RA differences were found in the horizontal and vertical gradient of the mean MSE, which affects the MSE budget through the corresponding advection terms. The differences between RAs in the mean MSE are mostly due to those in the mean latent energy (moisture). The horizontal gradient of the mean column-integrated MSE over the Indo-Pacific warm pool was relatively large in MERRA-2 and small in JRA-55. In the vertical structure of the mean MSE, considerable differences between RAs appeared in two layers: the upper planetary boundary layer and lower free troposphere (950–800 hPa) and in the midtroposphere (700–400 hPa). In the layer between 950 and 800 hPa, JRA-55 and ERA-I were found to be relatively wet, while MERRA-1 and CFSR were relatively dry. At around 600 hPa, MERRA-2 and JRA-55 were about 20% wetter and drier than the multireanalysis mean (MRM), respectively.
Column-integrated MSE anomalies associated with the MJO exhibited largest inter-RA spread in the eastern Indian Ocean, where the spread measured by standard deviation is more than 10% of the MRM value during MJO phases 3 and 7. The inter-RA spread came mostly from MERRA-2 and JRA-55, in which MJO MSE anomalies are relatively large and small, respectively, especially in the mid-to-low troposphere (400–800 hPa). In CFSR, MSE anomalies below 600 hPa tended to lag those of MRM over the MC, with maximum deviation from MRM occurring 1 phase after the MRM maximum.
The inter-RA spread was found to be greater in the individual MSE budget terms than in the MSE anomalies. In particular, the terms that are directly associated with the model parameterizations schemes, such as vertical advection, column longwave heating, and surface latent heat flux, showed particularly large inter-RA spread. The budget residual plays nonnegligible role in the MJO MSE budget. In MERRA-1, MERRA-2, ERA5, and JRA-55, the budget residual contributes to maintaining the MJO MSE anomalies. In ERA-I and CFSR, on the other hand, it mainly contributes to the recharging and discharging of MSE anomalies to the east and west of positive MSE anomalies, respectively.
In all RAs, horizontal MSE advection is found to be the dominant process for the propagation of MSE anomalies, confirming the result of many previous studies. The quantified relative contribution to MSE propagation of meridional advection was found to be most robust. Vertical MSE advection also contributes positively to the eastward movement of MSE anomalies though it is of secondary importance outside a narrow band near the equator. Surface latent heat flux and longwave radiative heating anomalies slow down the eastward propagation of the MJO MSE anomalies, among which longwave radiative heating exhibited notable inter-RA differences.
Consistent with the results of many previous studies, vertical MSE advection and longwave radiative heating were found to be the largest sink and source of MJO MSE anomalies, respectively, although both terms exhibited marked inter-RA differences. The inter-RA spread in the contribution of wAdv to the maintenance of MSE anomaly was found to be mostly due to the differences in the magnitude anomalous vertical motion. The budget residual made significant contributions to the maintenance of MJO MSE anomalies, especially in the RAs where the net effect of vertical MSE advection and longwave radiative heating is large (MERRA-2 and JRA-55), suggesting that the budget residual can be reduced by improving the two processes.
The analysis of the relationship between cloud–radiative feedback and CWV budget residual, originally performed by Yokoi (2015) with three RAs, was extended to the six RAs. We found a nearly linear relationship between them, confirming the results of Yokoi (2015). The cloud–radiation feedback parameter is also tightly correlated with vertical moisture advection. In MERRA-2 and JRA-55, cloud–radiation feedback was relatively weak and the CWV budget residual was positive. The opposite was the case in ERA-I. We also found a similar negative linear relationship between the convective adjustment time scale and CWV budget residual, and a significant positive correlation between the two parameters.
Recent reanalysis intercomparison projects (e.g., Fujiwara et al. 2017; Schröder et al. 2019) have informed the users of the processes that are robust among different RAs and those that are represented differently between RAs. The knowledge about the uncertainty in RAs could prevent the users from drawing incorrect conclusions about the uncertain aspects in the RAs. Documenting the uncertain processes in RAs can also specify the area that needs attention in the future development of the RAs. In this study, we found the processes that are directly affected by the parameterization schemes of moist physics differ notably among the RAs and emphasized the vital role of moisture–cloud–radiation feedback on the maintenance of the MJO (e.g., Raymond 2001; Bony and Emanuel 2005; Kim et al. 2011, 2015; Yokoi 2015). More works need to be done to improve the representation of deep tropical convection and its interaction with humidity, cloud, and radiation in reanalysis products.
Acknowledgments
PR and HLR were both funded by the National Science Foundation (NSF) grant of China (Grant 41775066). DK was funded by the NOAA CVP program (NA18OAR4310300), the DOE RGMA program (DE-SC0016223), the NASA MAP program (80NSSC17K0227), and the KMA R&D program (KMI2018-03110). Work of the LLNL-affiliated author (MSA) was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344 and their efforts were supported by the Regional and Global Climate Modeling Program of the United States Department of Energy’s Office of Science. We thank Dr. Brandon Wolding and two anonymous reviewers for their constructive comments, which greatly helped improve an earlier version of the manuscript.
APPENDIX
Testing the Constant NGMS Assumption Using DYNAMO Observations
We compare the mean MSE, DSE, vertical velocity, and NGMS obtained from RAs to that from the DYNAMO field campaign data. We use the time averaged fields for the northern sounding array (NSA). The data were obtained from http://johnson.atmos.colostate.edu/dynamo/products/gridded/. The version that contains only observations (v3a) is used.
Figure A1 shows the vertical profiles of the mean MSE, DSE and vertical velocity from DYNAMO data and RAs. The mean MSE in RAs exhibit negative bias in the middle and lower troposphere. In addition, the level of the minimum MSE of MERRA-2 is lower than those of other RAs, which affects the vertical gradient of MSE. In contrast, the mean DSE appears to be well constrained in RAs. Significant difference arises in the mean vertical velocity between RAs and they show a wide range of biases.
Vertical profile of (a) MSE, (b) DSE, and (c) vertical motion during the DYNAMO period averaged over the NSA region.
Citation: Journal of Climate 34, 8; 10.1175/JCLI-D-20-0653.1
Normalized gross moist stability during the dynamo period averaged around the NSA region.
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A merged dataset of CFSR (1980–2011) and CFSRv2 (2012–14) will be referred to as CFSR.
