1. Introduction
Global reanalysis products have contributed significantly to deepening our understanding of various aspects of the global climate system. In particular, they provide large-scale atmospheric circulation data with considerable accuracy in the tropics, where the upper air sounding network is coarse, and help elucidate the structure and dynamics of various types of tropical variability such as the Madden–Julian oscillation (MJO; Madden and Julian 1971, 1972).
MJO is the dominant mode of atmospheric variability in the tropics on intraseasonal time scales. It is characterized by a large-scale convective envelope and associated circulation field anomalies, both traveling eastward from the tropical Indian Ocean to the central Pacific at approximately 5 m s−1. The impact of MJO extends beyond the tropics to the midlatitudes (Zhang 2013). Despite decades of research progress since its original discovery, theories explaining fundamental features of MJO are still debatable, and it is difficult even for state-of-the-art climate models to represent MJO well (Lin et al. 2006; Sato et al. 2009; Kim et al. 2009, 2011; Hung et al. 2013).
Whereas MJO was discovered through analysis of upper air sounding data (Madden and Julian 1971), global long-term reanalysis products have been analyzed extensively to capture its three-dimensional structure of state variables such as wind, temperature, and humidity (Wheeler et al. 2000; Sperber 2003; Kiladis et al. 2005; Benedict and Randall 2007). The reanalysis products are further utilized to monitor the MJO amplitude and phase. Wheeler and Hendon (2004) proposed a real-time multivariate MJO index that determines the amplitude and phase for each day using 850- and 200-hPa zonal wind data of a reanalysis product, as well as satellite observations.
In addition to analysis fields of three-dimensional atmospheric state variables that are corrected by the assimilation systems, reanalysis products often include physics tendency terms of the state variables, which are calculated by parameterization schemes of the forecast models. These terms may help us examine what physical processes are responsible for temporal variation of the state variables, although we should check their accuracy beforehand, which is considered to depend strongly on the quality of the forecast models. A potential utilization of physics tendency terms for understanding MJO dynamics is to examine moist static energy (MSE) and water vapor budgets. Physical and dynamical processes that cause a vertically integrated MSE tendency, or column MSE tendency, have been studied using model simulation outputs (Maloney 2009; Andersen and Kuang 2012) and recent reanalysis products (Kiranmayi and Maloney 2011; Kim et al. 2014a) to explain MJO features. The column MSE budget equation has also been utilized as the governing equation of a conceptual model of MJO (Sobel and Maloney 2012, 2013). In the tropics, the column MSE anomalies with intraseasonal time scales are caused primarily by column water vapor (CWV) anomalies (Kiranmayi and Maloney 2011). Furthermore, these two anomalies are identical under weak temperature gradient approximation (Sobel et al. 2001), which is considered to be a good approximation when discussing MJO features.
Some of the reanalysis products further provide forecast fields of state variables, which are outputs of the forecast model and subject to the data assimilation. By subtracting the forecast fields from the analysis fields, we can obtain analysis increment fields that are the correction terms calculated by the assimilation system. The analysis increment is expected to provide information on biases in the forecast model. Mapes and Bacmeister (2012) compared the physics tendency terms and analysis tendency, which is conceptually identical to the analysis increment, of the Modern-Era Reanalysis for Research and Applications (MERRA; Rienecker et al. 2011) and indicated possible bias in the representation of cumulus convective systems. Note that the analysis increment is a major source of “residuals” that researchers frequently confront when performing budget analyses using reanalysis products.
Continuous improvements of forecast models and assimilation techniques, as well as the advent of new observation technologies, have enhanced the quality of the reanalysis data, lengthened the period of the data, enhanced space and time resolution, and increased the number of variables that have acceptable accuracy for research purposes. In recent years, several new reanalysis products were produced one after another (Saha et al. 2010; Dee et al. 2011; Rienecker et al. 2011; Compo et al. 2011; Ebita et al. 2011; Kobayashi et al. 2015). Among them, the Japan Meteorological Agency (JMA) released the Japanese 55-year Reanalysis Project (JRA-55; Ebita et al. 2011; Kobayashi et al. 2015) in 2014. JRA-55 has a number of improvements with regard to the forecast model and data assimilation system, compared with a previous Japanese reanalysis product, JRA-25 (Onogi et al. 2007). These improvements would lead to an expectation that JRA-55 represents MJO feature better than JRA-25.
The purpose of this study is to examine representation of MJO feature by JRA-55. To clarify the characteristics of JRA-55, this study will take an approach of multireanalysis comparison of JRA-55, JRA-25, and the European Centre for Medium-Range Weather Forecast (ECMWF) Interim Re-Analysis (ERA-Interim; Dee et al. 2011), the last of which is another state-of-the-art reanalysis product. In particular, a main focus is on the representation of CWV anomaly and relevant physical and dynamical processes by the reanalysis products. Furthermore, this study will examine the analysis increment of CWV to discuss bias in the forecast models. While a number of studies have performed the multireanalysis comparison of analysis fields, to the best of my knowledge, this study is the first attempt to compare the analysis increment.
The remainder of this paper is organized as follows: In section 2, I explain reanalysis products examined and analysis methods. In section 3a, the longitude–phase distribution of intraseasonal anomalies in CWV, its tendency, and its analysis increment associated with MJO is examined. The results of individual terms constituting CWV budget equation are presented in section 3b. Causes of the analysis increment anomaly are then discussed in section 3c from the perspective of biases in cloud radiative feedback strength. This section also considers potential applications of the multireanalysis comparison of the analysis increment. Finally, conclusions are presented in section 4.
2. Data and methods
This study conducts multireanalysis comparison of three sets of global reanalysis products: JRA-55 (a new Japanese reanalysis product), JRA-25 (an older Japanese product), and ERA-Interim. A comparison of these products is presented in Table 1. JRA-55 has numerous improvements over JRA-25. JRA-55 utilized an updated version of the JMA global operational forecast model with finer spatial resolution. A three-dimensional variational method (3D-Var) used in the JRA-25 data assimilation system was replaced with a four-dimensional variational method (4D-Var) in JRA-55. Dee et al. (2011) noted that 4D-Var outperforms 3D-Var, especially where observations are sparse, such as in the tropics. The ERA-Interim also adopts a 4D-Var assimilation system. The assimilation time window, which is a unit of period in which short-term weather forecasts and assimilation of the forecasts and observations are executed, is 6 h for JRA-55 and JRA-25 and 12 h for ERA-Interim. The horizontal resolution of datasets provided is different among the reanalysis products, and the results presented in this paper are derived from the reanalysis data with the original resolution, unless otherwise explained. It was confirmed that conclusions of this paper are not sensitive to interpolation of the data to, for example, 2.5° × 2.5° grids before performing the analysis.
Global reanalysis products.
For observation data, this study examines CWV and precipitation retrieved from the Special Sensor Microwave Imager (SSM/I) observations (Wentz 2013), OLR obtained by the Advanced Very High Resolution Radiometer (AVHRR) of the National Oceanic and Atmospheric Administration (NOAA) (Liebmann and Smith 1996), and TCC provided by Clouds and Earth’s Radiant Energy System (CERES; Wielicki et al. 1996). While horizontal resolution is 0.25° for CWV and precipitation, 2.5° for OLR, and 1° for TCC, I interpolated CWV, precipitation, and TCC data onto 2.5° × 2.5° grids. Note that the CWV and precipitation data of SSM/I are missing over land.
The target period for the majority of the analysis presented in this paper is 16 yr from 1989 through 2004, when all the three reanalysis products, SSM/I, and AVHRR cover. Since CERES data collection began in March 2000, TCC examination is limited to the period from this month through 2004.
Behavior of the tropical intraseasonal variability is known to exhibit considerable seasonality. In the boreal winter season, most of the events show clear eastward propagation and are recognized as canonical MJO, whereas the variability in the boreal summer season tends to have a northward propagation feature over the Indian Ocean and western Pacific (Yasunari 1979, 1980; Murakami et al. 1984; Lau and Chan 1986) in addition to eastward propagation along the equator. To focus on the canonical MJO, this study limits the target season from November through April, when the majority of intraseasonal events are classified as canonical MJO (Kikuchi et al. 2012).
While analysis CWV is constrained by a variety of observation data, satellite radiances play dominant roles on correction of CWV over the tropical ocean. Table 2 summarizes the moisture-related satellite data assimilated to the three reanalysis products over the 1989–2004 period. Data from the Television Infrared Observation Satellite Program (TIROS) Operational Vertical Sounder (TOVS) and Advanced TOVS (ATOVS) suites of instruments and data from SSM/I were assimilated into all of the three reanalysis products over the entire target period. JRA-55 and ERA-Interim used other kinds of data, although they were assimilated for only limited periods. Clear-sky radiation (CSR) from geostationary satellites such as Geostationary Meteorological Satellite-5 (GMS-5), Multifunctional Transport Satellite (MTSAT) series, the Geostationary Operational Environmental Satellite (GOES) series, and the European Organisation for the Exploitation of Meteorological Satellites (EUMETSAT) series was used by JRA-55 since 1995 and ERA-Interim since 2001. ERA-Interim also used data from Advanced Infrared Sounder (AIRS) flown on Aqua since 2003. JRA-55 used data from the Tropical Rainfall Measurement Mission (TRMM) Microwave Imager (TMI) since 1998 and data from the Advanced Microwave Scanning Radiometer for Earth Observing System (AMSR-E) flown on Aqua since 2002. Furthermore, ERA-Interim used data retrieved from radio occultation (RO) measurements of the Global Navigation Satellite Systems (GNSS) receivers on low earth orbital satellites since 2001. Note that more kinds of satellite datasets were assimilated to JRA-55 and ERA-Interim after 2004.
Satellite data used to constrain moisture field of reanalysis products over the 1989–2004 period.
To isolate the intraseasonal-scale anomaly, a Lanczos bandpass filter (Duchon 1979) with cutoff periods of 20 and 90 days and a filter length of 181 days was applied to daily mean time series of individual variables after removing the first three harmonics of the climatological annual cycle. In this paper, the intraseasonal-scale anomaly thus calculated is simply called “anomaly.” The anomaly is composited with respect to eight MJO phases determined by the real-time multivariate MJO index (Wheeler and Hendon 2004). Note that days when the amplitude of the index is less than one are excluded from the composite analysis. The composite mean of the anomaly is subject to a statistical significance test using Student’s t test. Since a typical MJO period is 30–60 days, it seems to take 4–7 days on average to move from one MJO phase to the next. Therefore, the degree of freedom is estimated at a seventh part of the number of days categorized into individual MJO phases. The estimated degree of freedom differs from phase to phase, ranging from 24 to 40. This study focuses on longitude–phase distribution of the composite mean anomalies averaged over 15°S–15°N.
3. Results and discussion
a. CWV tendency and analysis increment
Figures 1a–d present the longitude–phase distribution of the composite CWV anomaly. The analysis CWV is presented for the reanalysis products. The observation data (Fig. 1d) show a well-known eastward-propagation feature. A positive CWV anomaly located over the western Indian Ocean at around 60°E at phase 1 moves eastward toward the date line at phase 6, with four maxima around 60°E, 100°E, 150°E, and 180° at phases 1, 3, 5, and 6, respectively. All three reanalysis products represent these features. Information of statistical significance, denoted by black contours, is also similar. On the other hand, the amplitude of the anomaly, which can be estimated as root-mean-square (RMS) of the composite anomaly over 60°E–180° and phases 1–8, is underestimated by JRA-55 and JRA-25 by 18% and 20%, respectively, while it is overestimated by ERA-Interim by 14%. The analyzed tendency of CWV anomaly also has a similar longitude–phase distribution to the observations, including the information of statistical significance (Figs. 1e–h). Positive and negative tendencies are located to the east and west, respectively, of the positive CWV anomaly, representing eastward propagation. Here, the amplitude is underestimated by JRA-55 and JRA-25 and overestimated by ERA-Interim, which is consistent with the biases in CWV amplitude. The qualitative correspondence between the reanalysis products and satellite observation may primarily be due to the data assimilation of the observations.
Longitude–phase distribution of composite anomaly of analysis CWV of (a) JRA-55, (b) JRA-25, (c) and ERA-Interim, and (d) observed CWV averaged over 15°S–15°N (mm). (e)–(h) As in (a)–(d), but for the tendency of corresponding CWV anomaly (mm day−1). The vertical axis represents phases of the multivariate MJO index. Solid (dotted) black contours indicate that the composite anomaly is positive (negative) and statistically significant at a 95% confidence level. Purple contours indicate the composite CWV anomaly as a reference.
Citation: Journal of Climate 28, 2; 10.1175/JCLI-D-14-00465.1
As explained previously, the analyzed tendency of the CWV anomaly is the sum of the simulated tendency and analysis increment. Longitude–phase distribution of their composite anomaly is shown in Fig. 2. Although the simulated tendency (Figs. 2a–c) has apparently similar distribution to the analyzed tendency, there are several remarkable differences. The simulated tendency signals are generally less significant than the analyzed tendency, and this is most serious for JRA-25. For ERA-Interim, the simulated tendency distribution shifts westward compared with the analyzed tendency, and a positive (negative) simulated tendency tends to be superimposed on a positive (negative) CWV anomaly. The simulated tendency provided by JRA-55 is more similar to the analyzed tendency than the other reanalysis products, although its distribution shifts slightly eastward with respect to the analyzed tendency. In fact, pattern correlation coefficients between the composite anomaly of analyzed tendency and that of simulated tendency of JRA-55 over 60°E–180° and phases 1–8 is 0.78, which is higher than that of JRA-25 (0.71) and ERA-Interim (0.64). Furthermore, to measure the extent to which the simulated tendency is different among the reanalysis products compared with the analyzed tendency, I calculated pattern correlation coefficients of them between reanalysis products over 60°E–180° and phases 1–8, after interpolating the data into 2.5° grids. The coefficients of the simulated tendency ranges from 0.28 (JRA-55 and ERA-Interim) to 0.78 (JRA-55 and JRA-25), which are considerably lower than those of the analyzed tendency, which are as high as 0.99.
As in Figs. 1e–g, but for (a)–(c) CWV simulated tendency and (d)–(f) analysis increment (mm day−1). Data plotted are taken from (a),(d) JRA-55, (b),(e) JRA-25, and (c),(f) ERA-Interim.
Citation: Journal of Climate 28, 2; 10.1175/JCLI-D-14-00465.1
The analysis increment anomaly (Figs. 2d–f) exhibits a different longitude–phase distribution among the reanalysis products. JRA-55 produces the anomaly that correlates with the CWV anomaly; positive and negative analysis increment anomalies tend to exist in areas of positive and negative CWV anomalies, respectively, particularly over the Indian Ocean and western Maritime Continent (30°–110°E). This seems to be consistent with the underestimation of the amplitude of the CWV anomaly. In contrast, the ERA-Interim analysis increment anomaly is opposed in sign to the JRA-55 result with larger amplitude. Negative analysis increment anomalies tend to coincide with positive CWV anomalies, with the negative maximum of the former located slightly to the west of the positive maximum of the latter. These results are consistent with residuals of the budget analysis using ERA-Interim reported by Kiranmayi and Maloney (2011) and also consistent with the overestimation of the CWV anomaly amplitude. As for JRA-25, the analysis increment pattern is noisy and does not show large-scale structure. The contrast in the analysis increment among the reanalysis products described above can be quantified by calculating the regression coefficient of the composite mean of the analysis increment anomaly against the CWV anomaly over 60°E–180° and phases 1–8 (column 2 of Table 3). JRA-55 has a positive regression coefficient of +0.063 mm day−1, while ERA-Interim has a negative regression coefficient of −0.075 mm day−1.
Regression coefficients of composite anomalies of various variables against composite CWV anomaly calculated over 60°E–180° and phases 1–8 and the cloud-radiative feedback strength r. See the text for details.
Interestingly, the analysis increment anomalies of JRA-55 and ERA-Interim in areas of large CWV anomalies are statistically significant, which are considered to imply that there exist some systematic biases in the forecast models. For JRA-55, the remarkable coherence between the CWV and analysis increment anomalies with almost no phase lag suggests that, while its forecast model seems to be able to represent eastward propagation of the CWV anomaly realistically, the model tends to unrealistically weaken the amplitude and thus the assimilation system plays a role in sustaining the amplitude. This is consistent with the results reported by Matsueda and Endo (2011), which demonstrated that a version of the JMA global forecast model, which is not identical but considered to have similar characteristics to the model used for JRA-55 (H. Endo 2014, personal communication), has a bias such that MJO amplitude tends to weaken as the forecast time increases. The ERA-Interim forecast model may have the opposite bias. Further discussion of the bias implied by the analysis increment anomaly will be presented in section 3c.
One may feel from Figs. 2d–f that JRA-25 outperforms JRA-55 and ERA-Interim in representation of CWV tendency. However, it should be cautioned that shown in these figures are the composite mean of the analysis increment anomaly. In fact, RMS of raw daily-mean analysis increment of JRA-25 is larger than that of JRA-55 and ERA-Interim, as shown in Fig. 3a. Whereas JRA-25 has an RMS of 1.4–1.8 mm day−1 in most longitudes, the RMS of JRA-55 is reduced to 0.8–1.2 mm day−1, which is comparable to that of ERA-Interim. The reduction of RMS can also be recognized for the analysis interment anomaly (Fig. 3b). These results indicate that JRA-55 outperforms JRA-25 in representation of CWV tendency.
Longitudinal distribution of RMS of (a) daily-mean analysis increment and (b) its anomaly (mm day−1) averaged over 15°S–15°N for November–April period, irrespective of the MJO phase. Solid, dashed, and dotted lines indicate JRA-55, JRA-25, and ERA-Interim, respectively.
Citation: Journal of Climate 28, 2; 10.1175/JCLI-D-14-00465.1
b. CWV budget analysis
As (2) states, the simulated tendency results from the sum of vertically integrated horizontal moisture flux convergence, surface evaporation, and precipitation with sign reversed. To investigate which of them causes diversity in the simulated tendency among the reanalysis products, Fig. 4 presents longitude–phase distribution of their composite anomalies. Corresponding observations are only available for precipitation. The moisture flux convergence and precipitation have amplitudes approximately 5 times larger than surface evaporation and analyzed and simulated tendencies (note that the color-tone interval for the moisture flux convergence and precipitation is 5 times as wide as that for surface evaporation and tendencies). Broadly speaking, positive moisture flux convergence anomalies coincide with positive CWV anomalies and are largely balanced with positive precipitation anomalies. Both moisture flux convergence and precipitation anomalies have maxima at around 90°E, 135°E, and 180° at phases 3, 5, and 6, respectively. These features are shared by all three reanalysis products and observed precipitation (Fig. 4g). The pattern correlation coefficients of these two variables among the reanalysis products, calculated in the same way as those of the simulated tendency in the last section, are higher than 0.95. On the other hand, the reanalysis products generally underestimate the amplitude of the precipitation anomaly by approximately 30% (JRA-55), 34% (JRA-25), and 42% (ERA-Interim). The underestimation by ERA-Interim was also pointed out by Kim et al. (2014b). Note that the amplitude of the precipitation anomaly is underestimated to the largest degree by ERA-Interim, which is the only reanalysis product among the three that overestimates the amplitude of the CWV anomaly. Observational evidence suggests that precipitation and CWV are closely related, and the former can sometimes be considered as the latter’s exponential function (Bretherton et al. 2004; Peters and Neelin 2006). The result here suggests that precipitation simulated by the ERA-Interim forecast model is less sensitive to a CWV anomaly.
As in Fig. 1, but for (a)–(c) vertically integrated horizontal moisture flux convergence, (d)–(g) precipitation with sign reversed, and (h)–(j) surface evaporation (mm day−1). Note that color-tone intervals for (h)– (j) are the same as those in Figs. 1e–h and 2; those for (a)–(g) are extended five times. Data plotted are taken from (a),(d),(h) JRA-55, (b),(e),(i) JRA-25, (c),(f),(j) ERA-Interim, and (g) SSM/I.
Citation: Journal of Climate 28, 2; 10.1175/JCLI-D-14-00465.1
The three reanalysis products present a qualitatively similar distribution of the surface evaporation anomaly as well (Figs. 4h–j). Its longitude–phase distribution is more complicated than the moisture flux convergence and precipitation anomalies, and the phase relationship between the surface evaporation and CWV anomalies is longitude dependent. Previous studies (e.g., Lin and Johnson 1996; Zhang 1996; Shinoda et al. 1998) revealed that positive evaporation anomalies coincide with positive CWV anomalies over the western Pacific (120°E–180°), which is also represented by the three reanalysis products. Over the Indian Ocean and eastern Pacific, on the other hand, negative evaporation anomalies tend to be overlapped with positive CWV anomalies. Such longitudinal differences are probably due to differences in phase dependence of surface wind anomaly on CWV anomaly between the Indian Ocean and western Pacific, as well as differences in climatological surface wind fields. To the west of the positive CWV anomaly, a positive surface evaporation anomaly prevails. The pattern correlation coefficients among reanalysis products range from 0.89 to 0.97.
Interestingly, the pattern correlation coefficients of the three budget terms among the reanalysis products are considerably higher than those of the simulated tendency. This implies that, although the budget terms are at least qualitatively well represented, simulation of the resulting tendency is still difficult for the forecast models. This may be associated with the fact that considerable parts of the CWV tendency result from slight residuals of cancelation of horizontal moisture flux convergence and precipitation, which both have much larger amplitudes than the CWV tendency. The slight residual may be more difficult for the model to represent, as suggested by the bias in the amplitude of the precipitation anomaly. The relationship between these two terms will be discussed in detail in the next section.
c. Discussion on analysis increment
As demonstrated in section 3a, the most noticeable feature of the analysis increment of JRA-55 is statistically significant positive and negative anomalies over positive and negative CWV anomalies, respectively, while that of ERA-Interim has a nearly opposite feature with larger magnitude. These features were quantified by calculating the regression coefficients between the composite analysis increment anomaly and the composite CWV anomaly over 60°E–180° and phases 1–8 (column 2 of Table 3). To discuss causes of these features, this section also focuses on the regression coefficients between composite means of various anomalies and the composite CWV anomaly.
Figure 5 shows the longitude–phase distribution of the composite OLR anomaly. Generally, negative OLR anomalies coincide with positive CWV anomalies, with the former located slightly to the west of the latter. The reanalysis products successfully represent the distribution qualitatively; however, they tend to underestimate the amplitude by 45% (JRA-55), 35% (JRA-25), and 18% (ERA-Interim).
As in Fig. 1, but for OLR (W m−2). Data plotted are taken from (a) JRA-55, (b) JRA-25, (c) ERA-Interim, and (d) NOAA AVHRR.
Citation: Journal of Climate 28, 2; 10.1175/JCLI-D-14-00465.1
The regression coefficients of composite precipitation and OLR anomalies against the CWV anomaly are summarized in the third and fourth columns of Table 3, respectively, and are generally consistent with the amplitude described above. The cloud radiative feedback strength is shown in the fifth column of Table 3. The feedback strength calculated from the satellite observations is 0.24, which is close to the estimation reported by Bretherton and Sobel (2002). The feedback strength represented by the reanalysis products ranges from 0.18 (JRA-55) to 0.33 (ERA-Interim). Figure 6 shows that the bias in the feedback strength exhibits a nearly linear relationship with 
Scatterplot of the cloud radiative feedback strength r vs regressed analysis increment anomaly against the CWV anomaly normalized by regressed precipitation anomaly for the three reanalysis products, as well as r estimated from satellite observations (with analysis increment anomaly set to zero). The regression line of the three reanalysis plots is also shown.
Citation: Journal of Climate 28, 2; 10.1175/JCLI-D-14-00465.1
The physical interpretation of this relationship is as follows: The cloud radiative feedback enhances the diabatic heating rate of the atmospheric column per unit precipitation due to anomalous radiative heating. Therefore, over the area of positive CWV and precipitation anomalies, weaker feedback strength, as JRA-55 exhibits, leads to a smaller anomalous diabatic heating rate per unit precipitation anomaly. Under the weak temperature gradient approximation, the diabatic heating is balanced with adiabatic cooling caused by large-scale ascent. Thus, the weaker diabatic heating leads to weaker ascent and associated low-level horizontal convergence anomalies, resulting in a smaller horizontal moisture flux convergence anomaly. As a result, the anomaly of this type of moisture supply per unit precipitation anomaly becomes too small compared with the real atmosphere; thus, the simulated atmospheric column becomes too dry over the area of positive precipitation anomaly. To compensate this, the data assimilation system supplies moisture to the column over this area that corresponds to a positive analysis increment anomaly.
It should be noted that the bias in the cloud radiative feedback strength is probably a result of biases in various parameterization schemes employed in the forecast models, such as cumulus scheme, cloud microphysics scheme, and radiation scheme, and thus I do not intend to claim that the bias in the feedback strength is the root cause. However, it can be said that it is a good approach to examine the feedback strength when modifying and tuning the physics schemes, as this parameter represents characteristics of the quasi-equilibrium tropical atmosphere with deep convection represented by the forecast models.
As explained previously, active convection reduces radiative cooling primarily through extending cloud cover. Therefore, the biases in the feedback strength are expected to be consistent with those in the amplitude of the TCC anomaly. Figure 7 shows longitude–phase distribution of the TCC anomaly. Although the distribution is qualitatively similar between reanalysis products and satellite observations, JRA-55 underestimates the regressed TCC anomaly, while ERA-Interim overestimates it (column 6 of Table 3). The ratio of the regressed TCC anomaly to the regressed precipitation anomaly is also underestimated by JRA-55 and overestimated by ERA-Interim compared with the observation, which are consistent with the biases in the feedback strength.
As in Fig. 1, but for TCC (%). Data plotted are taken from (a) JRA-55, (b) JRA-25, (c) ERA-Interim, and (d) CERES.
Citation: Journal of Climate 28, 2; 10.1175/JCLI-D-14-00465.1
According to (11), the slope of the regression line of Fig. 6 may correspond to 
The analysis increment anomaly of ERA-Interim is also correlated with the analyzed tendency of CWV anomaly; positive analysis increment anomalies tend to exist over areas of positive tendency. In other words, eastward propagation of the CWV anomaly is in part achieved by the data assimilation system. Mapes and Bacmeister (2012) presented similar feature for MERRA reanalysis and argued that the forecast model may be incapable of representing shallow-to-deep convection transition within the MJO convective envelope (Kemball-Cook and Weare 2001; Kikuchi and Takayabu 2004). For further discussion, we may need to consider dependence of 
4. Conclusions
This study has conducted multireanalysis comparison of CWV tendency and analysis increment represented in a new Japanese reanalysis product, JRA-55; an older product, JRA-25; and ERA-Interim, with emphasis on tropical variability associated with boreal winter MJO. The composite mean of intraseasonal anomalies of variables with respect to eight MJO phases identified by Wheeler and Hendon (2004) was examined.
The longitude–phase distribution of the composite CWV anomaly and its analyzed tendency averaged in the tropical belt is similar among the three reanalysis products and satellite observations. In contrast, the distribution of the composite anomaly of the simulated tendency by the forecast model is qualitatively different among the reanalysis products, as well as from the analyzed tendency. However, vertically integrated horizontal moisture flux convergence, precipitation, and surface evaporation, which are calculated by the forecast models and add up to the simulated tendency, have qualitatively similar longitude–phase distribution among the reanalysis products. JRA-55 seems to exhibit the simulated tendency that is more similar to the analyzed tendency compared with the other two reanalysis products. In particular, the forecast model of JRA-55 seems to represent eastward propagation of the CWV anomaly successfully. On the other hand, the CWV analysis increment anomaly of JRA-55 is positive (negative) and statistically significant over areas of positive (negative) CWV anomaly, particularly over the Indian Ocean and Maritime Continent. This implies that the forecast model tends to weaken the amplitude of the CWV anomaly and thus the assimilation system sustains it. ERA-Interim has a nearly opposite feature to JRA-55: positive (negative) analysis increment anomalies nearly coincide with, though slightly behind, negative (positive) CWV anomalies. For JRA-25, the composite mean of analysis increment anomaly is noisy and does not exhibit large-scale distribution. It should be cautioned that this does not mean that JRA-25 outperforms JRA-55 and ERA-Interim: RMS of daily-mean analysis increment of JRA-55 is comparable to that of ERA-Interim and about 30%–40% smaller than that of JRA-25, suggesting that JRA-55 and ERA-Interim have better performance in representation of CWV tendency in the tropics than JRA-25.
With the aid of the weak temperature gradient approximation and several other assumptions, the multireanalysis comparison further reveals that the above-mentioned features of the composite analysis increment anomalies in JRA-55 and ERA-Interim are linked with the biases in cloud radiative feedback strength represented by the forecast models. In particular, the forecast model of JRA-55 represents excessively weak cloud radiative feedback. This bias means that the anomaly of moisture supply by the vertical advection term simulated by the forecast model is less sensitive to the precipitation anomaly compared with the real atmosphere, and thus the simulated atmospheric column over the areas of positive precipitation anomaly becomes too dry. The data assimilation system thus supplies moisture that corresponds to a positive analysis increment anomaly. ERA-Interim has the opposite feature: its forecast model represents excessively strong cloud radiative feedback.
These results suggest that accurate representation of cloud radiative feedback by general circulation models is necessary for realistic short-term forecast of MJO. The cloud radiative feedback has been considered an essential physical process for the existence of MJO through destabilizing tropical atmosphere to intraseasonal convective activity (Raymond 2001; Sobel and Gildor 2003; Bony and Emanuel 2005; Zurovac-Jevtic et al. 2006; Landu and Maloney 2011; Andersen and Kuang 2012; Sobel and Maloney 2012, 2013). It is fair to say that this study provides new evidence to support the importance of this feedback.
To the best of my knowledge, this study is the first attempt to perform multireanalysis comparison of the analysis increment, and demonstrates the performance of this approach. The results presented in this study suggest that this approach has the potential to provide useful information on the biases of forecast models. Furthermore, this study experimentally shows that this approach can be applicable to estimation of parameters that are difficult to estimate globally from observational data, such as normalized gross moist stability.
Acknowledgments
The author is grateful to JMA, CRIEPI, and ECMWF, which provide the reanalysis products. The SSM/I data were produced by Remote Sensing Systems and sponsored by the National Aeronautics and Space Administration (NASA) Earth Science MEaSUREs Program. The OLR data are provided by NOAA/Earth System Research Laboratory. The CERES data were obtained from the Atmospheric Science Data Center at the NASA Langley Research Center. This study is partially supported by Grant-in-Aid for Young Scientists (B-25800268) and Grant-in-Aid for Scientific Research (B-25287119) of the Japan Society for the Promotion of Science, Japan, and Global Environmental Research Fund (2A-1201) of the Ministry of Environment, Japan.
REFERENCES
Andersen, J. A., and Z. Kuang, 2012: Moist static energy budget of MJO-like disturbances in the atmosphere of a zonally symmetric aquaplanet. J. Climate, 25, 2782–2804, doi:10.1175/JCLI-D-11-00168.1.
Back, L. E., and C. S. Bretherton, 2006: Geographical variability in the export of moist static energy and vertical motion profiles in the tropical Pacific. Geophys. Res. Lett., 33, L17810, doi:10.1029/2006GL026672.
Benedict, J. J., and D. A. Randall, 2007: Observed characteristics of the MJO relative to maximum rainfall. J. Atmos. Sci., 64, 2332–2354, doi:10.1175/JAS3968.1.
Bony, S., and K. A. Emanuel, 2005: On the role of moist processes in tropical intraseasonal variability: Cloud–radiation and moist–convection feedbacks. J. Atmos. Sci., 62, 2770–2789, doi:10.1175/JAS3506.1.
Bretherton, C. S., and A. H. Sobel, 2002: A simple model of a convectively coupled Walker circulation using the weak temperature gradient approximation. J. Climate, 15, 2907–2920, doi:10.1175/1520-0442(2002)015<2907:ASMOAC>2.0.CO;2.
Bretherton, C. S., M. E. Peters, and L. E. Back, 2004: Relationships between water vapor path and precipitation over the tropical oceans. J. Climate, 17, 1517–1528, doi:10.1175/1520-0442(2004)017<1517:RBWVPA>2.0.CO;2.
Compo, G. P., and Coauthors, 2011: The Twentieth Century Reanalysis project. Quart. J. Roy. Meteor. Soc., 137, 1–28, doi:10.1002/qj.776.
Dee, D. P., and Coauthors, 2011: The ERA-Interim reanalysis: Configuration and performance of the data assimilation system. Quart. J. Roy. Meteor. Soc., 137, 553–597, doi:10.1002/qj.828.
Duchon, C. E., 1979: Lanczos filtering in one and two dimensions. J. Appl. Meteor., 18, 1016–1022, doi:10.1175/1520-0450(1979)018<1016:LFIOAT>2.0.CO;2.
Ebita, A., and Coauthors, 2011: The Japanese 55-year reanalysis “JRA-55”: An interim report. SOLA, 7, 149–152, doi:10.2151/sola.2011-038.
Hung, M.-P., J.-L. Lin, W. Wang, D. Kim, T. Shinoda, and S. J. Weaver, 2013: MJO and convectively coupled equatorial waves simulated by CMIP5 climate models. J. Climate, 26, 6185–6214, doi:10.1175/JCLI-D-12-00541.1.
Kemball-Cook, S. R., and B. C. Weare, 2001: The onset of convection in the Madden–Julian oscillation. J. Climate, 14, 780–793, doi:10.1175/1520-0442(2001)014<0780:TOOCIT>2.0.CO;2.
Kikuchi, K., and Y. N. Takayabu, 2004: The development of organized convection associated with the MJO during TOGA COARE IOP: Trimodal characteristics. Geophys. Res. Lett., 31, L10101, doi:10.1029/2004GL019601.
Kikuchi, K., B. Wang, and Y. Kajikawa, 2012: Bimodal representation of the tropical intraseasonal oscillation. Climate Dyn., 38, 1989–2000, doi:10.1007/s00382-011-1159-1.
Kiladis, G. N., K. H. Straub, and P. T. Haertel, 2005: Zonal and vertical structure of the Madden–Julian oscillation. J. Atmos. Sci., 62, 2790–2819, doi:10.1175/JAS3520.1.
Kim, D., and Coauthors, 2009: Application of MJO simulation diagnostics to climate models. J. Climate, 22, 6413–6436, doi:10.1175/2009JCLI3063.1.
Kim, D., A. H. Sobel, E. D. Maloney, D. M. W. Frierson, and I.-S. Kang, 2011: A systematic relationship between intraseasonal variability and mean state bias in AGCM simulations. J. Climate, 24, 5506–5520, doi:10.1175/2011JCLI4177.1.
Kim, D., J.-S. Kug, and A. H. Sobel, 2014a: Propagating versus nonpropagating Madden–Julian oscillation events. J. Climate, 27, 111–125, doi:10.1175/JCLI-D-13-00084.1.
Kim, D., M.-I. Lee, D. Kim, S. D. Schubert, D. E. Waliser, and B. Tian, 2014b: Representation of tropical subseasonal variability of precipitation in global reanalyses. Climate Dyn., 43, 517–534, doi:10.1007/s00382-013-1890-x.
Kiranmayi, L., and E. D. Maloney, 2011: Intraseasonal moist static energy budget in reanalysis data. J. Geophys. Res., 116, D21117, doi:10.1029/2011JD016031.
Kobayashi, S., and Coauthors, 2015: The JRA-55 Reanalysis: General specifications and basic characteristics. J. Meteor. Soc. Japan, doi:10.2151/jmsj.2015-001, in press.
Landu, K., and E. D. Maloney, 2011: Understanding intraseasonal variability in an aquaplanet GCM. J. Meteor. Soc. Japan, 89, 195–210, doi:10.2151/jmsj.2011-302.
Lau, K.-M., and P. H. Chan, 1986: Aspects of the 40–50 day oscillation during the northern summer as inferred from outgoing longwave radiation. Mon. Wea. Rev., 114, 1354–1367, doi:10.1175/1520-0493(1986)114<1354:AOTDOD>2.0.CO;2.
Liebmann, B., and C. A. Smith, 1996: Description of a complete (interpolated) outgoing longwave radiation dataset. Bull. Amer. Meteor. Soc., 77, 1275–1277.
Lin, J.-L., and B. E. Mapes, 2004: Radiation budget of the tropical intraseasonal oscillation. J. Atmos. Sci., 61, 2050–2062, doi:10.1175/1520-0469(2004)061<2050:RBOTTI>2.0.CO;2.
Lin, J.-L., and Coauthors, 2006: Tropical intraseasonal variability in 14 IPCC AR4 climate models. Part I: Convective signals. J. Climate, 19, 2665–2690, doi:10.1175/JCLI3735.1.
Lin, X., and R. H. Johnson, 1996: Kinematic and thermodynamic characteristics of the flow over the western Pacific warm pool during TOGA COARE. J. Atmos. Sci., 53, 695–715, doi:10.1175/1520-0469(1996)053<0695:KATCOT>2.0.CO;2.
Madden, R. A., and P. R. Julian, 1971: Description of a 40–50 day oscillation in the zonal wind in the tropical Pacific. J. Atmos. Sci., 28, 702–708, doi:10.1175/1520-0469(1971)028<0702:DOADOI>2.0.CO;2.
Madden, R. A., and P. R. Julian, 1972: Description of global-scale circulation cells in the tropics with a 40–50 day period. J. Atmos. Sci., 29, 1109–1123, doi:10.1175/1520-0469(1972)029<1109:DOGSCC>2.0.CO;2.
Maloney, E. D., 2009: The moist static energy budget of a composite tropical intraseasonal oscillation in a climate model. J. Climate, 22, 711–729, doi:10.1175/2008JCLI2542.1.
Mapes, B. E., and J. T. Bacmeister, 2012: Diagnosis of tropical biases and the MJO from patterns in the MERRA analysis tendency fields. J. Climate, 25, 6202–6214, doi:10.1175/JCLI-D-11-00424.1.
Matsueda, M., and H. Endo, 2011: Verification of medium-range MJO forecasts with TIGGE. Geophys. Res. Lett., 38, L11801, doi:10.1029/2011GL047480.
Murakami, T., T. Nakazawa, and J. He, 1984: On the 40-50 day oscillations during the 1979 Northern Hemisphere summer. Part I: Phase propagation. J. Meteor. Soc. Japan, 62, 440–468.
Onogi, K., and Coauthors, 2007: The JRA-25 reanalysis. J. Meteor. Soc. Japan, 85, 369–432, doi:10.2151/jmsj.85.369.
Peters, O., and J. D. Neelin, 2006: Critical phenomena in atmospheric precipitation. Nat. Phys., 2, 393–396, doi:10.1038/nphys314.
Raymond, D. J., 2001: A new model of the Madden–Julian oscillation. J. Atmos. Sci., 58, 2807–2019, doi:10.1175/1520-0469(2001)058<2807:ANMOTM>2.0.CO;2.
Raymond, D. J., S. L. Sessions, A. H. Sobel, and Z. Fuchs, 2009: The mechanics of gross moist stability. J. Adv. Model. Earth Syst., 1, 9, doi:10.3894/JAMES.2009.1.9.
Rienecker, M. M., and Coauthors, 2011: MERRA: NASA’s Modern-Era Retrospective Analysis for Research and Applications. J. Climate, 24, 3624–3648, doi:10.1175/JCLI-D-11-00015.1.
Saha, S., and Coauthors, 2010: The NCEP Climate Forecast System Reanalysis. Bull. Amer. Meteor. Soc., 91, 1015–1057, doi:10.1175/2010BAMS3001.1.
Sato, N., C. Takahashi, A. Seiki, K. Yoneyama, and R. Shirooka, 2009: An evaluation of the reproducibility of the Madden-Julian oscillation in the CMIP3 multi-models. J. Meteor. Soc. Japan, 87, 791–805, doi:10.2151/jmsj.87.791.
Shinoda, T., H. H. Hendon, and J. Glick, 1998: Intraseasonal variability of surface fluxes and sea surface temperature in the tropical western Pacific and Indian Ocean. J. Climate, 11, 1685–1702, doi:10.1175/1520-0442(1998)011<1685:IVOSFA>2.0.CO;2.
Sobel, A. H., and H. Gildor, 2003: A simple time-dependent model of SST hot spots. J. Climate, 16, 3978–3992, doi:10.1175/1520-0442(2003)016<3978:ASTMOS>2.0.CO;2.
Sobel, A. H., and E. D. Maloney, 2012: An idealized semi-empirical framework for modeling the Madden–Julian oscillation. J. Atmos. Sci., 69, 1691–1705, doi:10.1175/JAS-D-11-0118.1.
Sobel, A. H., and E. D. Maloney, 2013: Moisture modes and the eastward propagation of the MJO. J. Atmos. Sci., 70, 187–192, doi:10.1175/JAS-D-12-0189.1.
Sobel, A. H., J. Nilsson, and L. M. Polvani, 2001: The weak temperature gradient approximation and balanced tropical moisture waves. J. Atmos. Sci., 58, 3650–3665, doi:10.1175/1520-0469(2001)058<3650:TWTGAA>2.0.CO;2.
Sobel, A. H., S. Wang, and D. Kim, 2014: Moist static energy budget of the MJO during DYNAMO. J. Atmos. Sci., 71, 4276–4291, doi:10.1175/JAS-D-14-0052.1.
Sperber, K. R., 2003: Propagation and the vertical structure of the Madden–Julian oscillation. Mon. Wea. Rev., 131, 3018–3037, doi:10.1175/1520-0493(2003)131<3018:PATVSO>2.0.CO;2.
Wentz, F. J., 2013: SSM/I version-7 calibration report. Remote Sensing Systems Rep., 46 pp.
Wheeler, M. C., and H. H. Hendon, 2004: An all-season real-time multivariate MJO index: Development of an index for monitoring and prediction. Mon. Wea. Rev., 132, 1917–1932, doi:10.1175/1520-0493(2004)132<1917:AARMMI>2.0.CO;2.
Wheeler, M. C., G. N. Kiladis, and P. J. Webster, 2000: Large-scale dynamical fields associated with convectively coupled equatorial waves. J. Atmos. Sci., 57, 613–640, doi:10.1175/1520-0469(2000)057<0613:LSDFAW>2.0.CO;2.
Wielicki, B. A., B. R. Barkstrom, E. F. Harrison, R. B. Lee III, G. L. Smith, and J. E. Cooper, 1996: Clouds and the Earth’s Radiant Energy System (CERES): An Earth Observing System experiment. Bull. Amer. Meteor. Soc., 77, 853–868, doi:10.1175/1520-0477(1996)077<0853:CATERE>2.0.CO;2.
Yasunari, T., 1979: Cloudiness fluctuations associated with the Northern Hemisphere summer monsoon. J. Meteor. Soc. Japan, 57, 227–242.
Yasunari, T., 1980: A quasi-stationary appearance of 30-40 day period in the cloudiness fluctuations during the summer monsoon over India. J. Meteor. Soc. Japan, 58, 225–229.
Zhang, C., 1996: Atmospheric intraseasonal variability at the surface in the tropical western Pacific Ocean. J. Atmos. Sci., 53, 739–758, doi:10.1175/1520-0469(1996)053<0739:AIVATS>2.0.CO;2.
Zhang, C., 2013: Madden–Julian oscillation: Bridging weather and climate. Bull. Amer. Meteor. Soc., 94, 1849–1870, doi:10.1175/BAMS-D-12-00026.1.
Zurovac-Jevtic, D., S. Bony, and K. A. Emanuel, 2006: On the role of clouds and moisture in tropical waves: A two-dimensional model study. J. Atmos. Sci., 63, 2140–2155, doi:10.1175/JAS3738.1.
