1. Introduction
The Madden–Julian oscillation (MJO; Madden and Julian 1972) is the dominant mode of intraseasonal variability of the tropics, characterized by a planetary spatial scale, a 30–60-day period, and eastward propagation. The MJO interacts with weather and climate phenomena globally [e.g., see reviews in Lau and Waliser (2011) and Zhang (2005)]. For example, it affects midlatitude extreme weather events (e.g., Jones 2000), modulates tropical cyclone activity over almost all basins (e.g., Maloney and Hartmann 2000), influences active and break periods of the monsoons globally (e.g., Wheeler and McBride 2005), and triggers and/or terminates some El Niño events (e.g., Takayabu et al. 1999). Considering its significant influence on high-impact weather and climate phenomena, an appropriate representation of the MJO in climate models seems necessary for an accurate estimate of future changes of those phenomena.
Historically, since the first diagnosis of intraseasonal variability simulated in the models from the Atmospheric Model Intercomparison Project (Slingo et al. 1996), the representation of the MJO in climate models has generally remained unsatisfactory (Waliser et al. 2003; Sperber et al. 2005; Lin et al. 2006; Kim et al. 2009; Hung et al. 2013). Lin et al. (2006) showed that only 2 among 14 models in phase 3 of the Coupled Model Intercomparison Project (CMIP3) had MJO variance comparable to observations, with even those lacking realism in many other MJO characteristics. Although the models participating in phase 5 of CMIP (CMIP5) simulate stronger MJO variance than that of CMIP3 models, the improvement is incremental at best (Hung et al. 2013).
Meanwhile, previous work has shown that the representation of the MJO in GCMs can be improved by changing specific aspects of their cumulus parameterization schemes. Changes that inhibit deep cumulus convection appear to be particularly effective in improving MJO activity (Tokioka et al. 1988; Wang and Schlesinger 1999; Maloney and Hartmann 2001; Lee et al. 2003; Zhang and Mu 2005; Lin et al. 2008; Kim and Kang 2012; Kim et al. 2012). Unfortunately, there is an apparent conflict between our ability to improve the MJO simulation while maintaining a realistic basic state. For example, Kim et al. (2011b) showed that mean precipitation over the warmest oceanic areas, which are the northwestern and southwestern Pacific during boreal summer and winter, respectively, becomes excessive and therefore worsens the mean state as a result of the same parameterization changes that strengthen the MJO in a number of different models. This suggests that those changes in parameterization that benefit the MJO simulation may have been rejected because of higher priority being placed on the mean state simulation compared to simulation of the MJO.
Ideally, a better parameterization must help improve both the mean state and the MJO. Toward this goal, it would be helpful if we have a diagnostic that fulfills all of the following conditions:
the diagnostic can be constructed from currently available observations;
the diagnostic is related to certain characteristics of unresolved-scale processes (i.e., parameterizations) in GCMs; and
the diagnostic represents certain features of resolved-scale processes that are important in the MJO dynamics.
If a diagnostic satisfies the first and second conditions, it can provide insight into how parameterizations should be improved to make model behavior similar to that diagnosed from observations. If that diagnostic also fulfills the third condition, it will be a useful tool that could help improve an MJO simulation for the correct physical reason. Although we expect the mean state will be improved if we improve the MJO simulation for the right physical reason, it is also possible that other processes may be missing or misrepresented that prevent a better MJO and realistic mean state at the same time. The international MJO Task Force1 has made efforts to develop diagnostics that fulfills the three conditions listed above—process-oriented MJO simulation diagnostics—with the overall goal of facilitating improvements in the representation of the MJO in weather and climate models (Wheeler and Maloney 2013).
In this paper, we present one process-oriented MJO simulation diagnostic, which is designed to better understand the relationship between moisture and convection in the tropical atmosphere, with a particular focus on the lower-tropospheric relative humidity (RH). We base the diagnostic on lower-tropospheric RH over the tropical Indian Ocean that is binned by precipitation percentiles [hereinafter RH composite based on precipitation (RHCP)].
Similar diagnostics to the RHCP diagnostic used here have been previously used to assess simulations of the MJO in different models (Thayer-Calder and Randall 2009; Zhu et al. 2009; Kim et al. 2009; Del Genio et al. 2012). Although these studies showed the usefulness of tropospheric humidity diagnostics to qualitatively distinguish relatively better MJO models from relatively worse ones, these diagnostics have previously been applied to only a limited number of models. Also, more importantly, the critical aspects and features of the tropospheric humidity distribution and its variability required for an improved simulation of the MJO have not been quantified. To demonstrate the general utility of our RHCP diagnostic, we use multimodel simulation data in the CMIP3 and CMIP5 archives. To identify the key features of the RHCP diagnostic that are related to the simulation capability of the MJO, we derive metrics from the diagnostic and test their statistical relationship with some standard measures of the fidelity of the simulated MJO. Note that although the focus here is on climate models, our findings are equally relevant to weather forecast models.
This paper is organized as follows. Section 2 describes model simulations and observations used, as well as the metrics for MJO simulation fidelity. The way to build up the RHCP diagnostic will be explained in detail in section 3. The relationship between the metrics derived from the RHCP diagnostic and the fidelity of the simulated MJO are investigated in section 4. The summary and conclusions are given in section 5.
2. Data
a. Model simulations
We use simulation data from a subset of coupled ocean–atmosphere models participating in CMIP3 and CMIP5. Table 1 contains a list of the models (with model acronym expansions) used in this study with their convection schemes and horizontal resolutions of their atmospheric component model. Readers are referred to Meehl et al. (2007) and Taylor et al. (2012) for more detailed descriptions of the CMIP3 and CMIP5 archives. Note that the selection of models was based on data availability. For each model, daily averaged precipitation and outgoing longwave radiation (OLR) during a 20-yr period from the twentieth-century simulations were obtained from the archives. For tropospheric RH, we downloaded only a 3-yr period of daily data because of limited data storage capacity. Therefore, the measures of MJO simulation fidelity are derived using 20 years of data, while the RHCP diagnostic and the metrics from it are constructed using 3 years of data. This inconsistency in data period could affect the results presented here, but evidence indicates that the effect is negligible because the observed RHCP diagnostic derived from 20 years of data is nearly identical to that from 3 years (not shown). For CMIP3 models, RH was calculated using temperature and specific humidity because RH was not available in the archive. In the case of CMIP5 models, RH was downloaded directly from the archive. The daily averaged RH profiles over the equatorial Indian Ocean (10°S–10°N, 60°–90°E) are used to construct the RHCP diagnostic. Because different models have different numbers of vertical levels, we chose four pressure levels that are common to all models used: 1000, 850, 700, and 500 hPa. Among these levels, 850 and 700 hPa are used for the RHCP diagnostic of CMIP3 and CMIP5 models. The reason for excluding 1000 and 500 hPa is given in the following sections.
List of participating models (including complete expansion of model acronyms). Horizontal resolution of their atmospheric component models and convection schemes are also indicated.
b. Observations and reanalysis
Three precipitation estimates are used to represent the uncertainty in the observations. Global Precipitation Climatology Project, version 1.1 (GPCP v1.1; Huffman et al. 2001), and the Tropical Rainfall Measuring Mission (TRMM; Huffman et al. 2007) 3B42, version 6, daily averaged data are used as observational estimates of precipitation. We also use daily averaged precipitation from the European Centre for Medium-Range Weather Forecasts (ECMWF) Interim Re-Analysis (ERA-Interim, herein ERA-I; Dee et al. 2011). We expect GPCP and TRMM precipitation to be better estimates of observations than ERA-I precipitation, because the reanalysis precipitation product is model-dependent. Nonetheless, ERA-I precipitation is also used in this study. This is because it was suggested that the satellite measurements used in this study lack capability of observing light rain events (Behrangi et al. 2012), and because the ERA-I precipitation is more physically consistent with one of the RH datasets used. Daily averaged RH profiles were obtained from two reanalysis products: ERA-I and the National Aeronautics and Space Administration (NASA)’s Modern-Era Retrospective Analysis for Research and Applications (MERRA; Rienecker et al. 2011). RH from MERRA is used only when we explore the uncertainty in the RHCP diagnostic originating from the source of RH data (Fig. 3). All simulations and observations described in this section were regridded into a 2.5° × 2.5° grid using a bilinear interpolation scheme before any calculations.
c. Fidelity of the MJO simulations
The fidelity of the MJO simulation needs to be quantified in order to make reliable inferences about relationships between the sensitivity of simulated convection to tropospheric humidity and the capability of a model to simulate the MJO. Effective metrics for the latter are needed. Because development of a method that quantifies the quality of MJO simulations in an objective manner is still an area of active research (Crueger et al. 2013), we choose three methods to reduce a possible bias caused from using only one metric.
One simple measure of the MJO is based on the space–time power spectrum of equatorial rainfall (or zonal wind). The ratio of eastward to westward power (E/W ratio) at MJO time and space scales (zonal wavenumbers 1–3 and periods of 30–60 days) reveals the prominence of the eastward propagating intraseasonal variability relative to its westward counterpart (e.g., Zhang and Hendon 1997; Lin et al. 2006; Kim et al. 2009) and is a useful indicator of how prominent the MJO is relative to the background variability. Another measure of MJO activity is the eastward power summed over eastward wavenumbers 1–3 and periods of 30–60 days. We refer to this as “east power.” The use of east power alone as a metric for MJO simulation fidelity could be inappropriate if it is unrelated with its westward counterpart (west power). Then a model A, which has a smaller E/W ratio than that of a model B, could have a greater east power than that of the model B. This is usually not the case within the group of models we use, however, as a strong linear relationship between east and west power exists.2 This allows the use of east power as an index that gives a direct indication as to whether the level of eastward power is realistic. The third measure of MJO fidelity is Rmax, which was recently proposed by Sperber and Kim (2012): Rmax is the maximum correlation between the two time series obtained by projecting model OLR anomalies onto the leading pair of empirical orthogonal functions (EOFs) of observed OLR that capture the MJO. The MJO is deemed well simulated if the correlation between the two leading principal components (PCs) is strong at a lead time of about 10–15 days, thereby demonstrating coherent eastward propagation with appropriate spatiotemporal structure.
These measures of MJO fidelity are developed using 20 yr (1979–98) of daily precipitation and OLR data from observations and from the model simulations. The wavenumber–frequency spectra, which the E/W ratio and east power measures of MJO activity are based on, are derived from 10°S–10°N averaged precipitation using the fast Fourier transforms applied to 19 segments that are 180 days long (i.e., 19 boreal winters during November–April). For Rmax, the EOF was performed over an extended Indo-Pacific warm pool area (20°S–20°N, 45°E–120°W) using OLR data during boreal winter (November–April). The values of these three measures from all of the models and the observations are presented in Table 2. In terms of Rmax, no model simulates an MJO stronger than the observed one. Regarding the E/W ratio and east power, however, there are models whose MJO is stronger than the observed MJO. For example, CNRM-CM3 and CNRM-CM5 exhibit E/W ratio values (5.91 and 4.95, respectively) that are much higher than that of observations (2.09–2.73) and of other models. Table 3 provides intercorrelation coefficients between the three measures of MJO fidelity. The correlation coefficients are all positive and statistically significant at the 95% confidence level, indicating they are consistent measures of the MJO simulation fidelity.
MJO simulation fidelity metrics derived from observations and participating models. GPCP, TRMM, and ERA-I data include Advanced Very High Resolution Radiometer (AVHRR) products.
Correlation coefficients between measures of the fidelity of MJO simulation.
3. RHCP diagnostic
In this section, we generate the RHCP diagnostic and derive a set of metrics from it. The physical insights from the diagnostic and a brief summary of previous usage of the diagnostic are also given.
a. Construction of the RHCP diagnostic
The main purpose of the RHCP diagnostic is to present RH profiles for different regimes that are distinguished from each other by the strength of precipitation. In this study, instead of absolute values of precipitation that have been used in other studies (Thayer-Calder and Randall 2009; Kim et al. 2009; Del Genio et al. 2012), we use precipitation percentiles to make this distinction. Precipitation itself is useful when analyzing a small set of models, but it could be problematic when applied to a large group of models. This is because the statistics of precipitation vary widely among models (Figs. 1 and 2). Our calculation of percentiles includes the zero precipitation rate. In fact, in GPCP and TRMM, zero precipitation occupies the lowest 60th and 55th percentiles, respectively, meaning that 60% and 55% of the time there is no rain in GPCP and TRMM (Fig. 1). When more than one percentile is occupied with zero values, it is impossible to distinguish RH profiles between those percentiles. Therefore, if this is the case, we make an average of RH profiles over all zero values and assign the mean value to all percentiles filled with zero precipitation values. (This is why in Figs. 4 and 5 TRMM and GPCP show the same RH value for the lowest 55th and 60th percentiles, respectively.)
Precipitation amount (mm day−1) corresponding to precipitation percentiles. The lower 70th percentiles are presented.
Citation: Journal of Climate 27, 14; 10.1175/JCLI-D-13-00497.1
Precipitation amount (mm day−1) corresponding to precipitation percentiles. The lower 70th percentiles are presented.
Citation: Journal of Climate 27, 14; 10.1175/JCLI-D-13-00497.1
Precipitation amount (mm day−1) corresponding to precipitation percentiles. The lower 70th percentiles are presented.
Citation: Journal of Climate 27, 14; 10.1175/JCLI-D-13-00497.1
As in Fig. 1, except for the upper 30th percentiles.
Citation: Journal of Climate 27, 14; 10.1175/JCLI-D-13-00497.1
As in Fig. 1, except for the upper 30th percentiles.
Citation: Journal of Climate 27, 14; 10.1175/JCLI-D-13-00497.1
As in Fig. 1, except for the upper 30th percentiles.
Citation: Journal of Climate 27, 14; 10.1175/JCLI-D-13-00497.1
Figures 1 and 2 display precipitation values of lower 70th and upper 30th precipitation percentiles, respectively. There is a considerable spread among models in almost all percentiles. For example, the top precipitation intensity at the 100th percentile (upper 1%) is lower than 30 mm day−1 in GISS-AOM, FGOALS-g1.0, and INM-CM3.0, while it is greater than 60 mm day−1 in CGCM3.1 (T63), CNRM-CM3, and INGV-ECHAM4. This indicates that a same precipitation rate would correspond to a different percentile in different simulations. Thus, using precipitation percentiles alleviates the influence of systematic discrepancies in the precipitation intensity among the models.
b. Physical insights
Figure 3 presents the RHCP diagnostic, which shows the averaged RH profile plotted as a function of precipitation percentiles, constructed using observations and reanalysis data over the central equatorial Indian Ocean (10°S–10°N, 60°–90°E). Three different precipitation datasets and two different RH datasets are used to demonstrate uncertainties in this diagnostic. The lack of ability in two out of three precipitation products (GPCP and TRMM) to distinguish lower percentiles from each other (Fig. 1) inhibited us from estimating the observational uncertainty for the first through 60th percentiles.
RHCP diagnostics created using (a)–(c) ERA-I and (d),(e) MERRA relative humidity (%) and precipitation (mm day−1) from GPCP (1997–2008) in (a) and (d), TRMM (1998–2008) in (b) and (e), and ERA-I (1989–2008) in (c). (f) Uncertainty of the observed RHCP diagnostic, estimated as the standard deviation of all five results divided by the average of them. Daily averaged precipitation and RH over the equatorial Indian Ocean (10°S–10°N, 60°–90°E) are used to construct the RHCP diagnostic.
Citation: Journal of Climate 27, 14; 10.1175/JCLI-D-13-00497.1
RHCP diagnostics created using (a)–(c) ERA-I and (d),(e) MERRA relative humidity (%) and precipitation (mm day−1) from GPCP (1997–2008) in (a) and (d), TRMM (1998–2008) in (b) and (e), and ERA-I (1989–2008) in (c). (f) Uncertainty of the observed RHCP diagnostic, estimated as the standard deviation of all five results divided by the average of them. Daily averaged precipitation and RH over the equatorial Indian Ocean (10°S–10°N, 60°–90°E) are used to construct the RHCP diagnostic.
Citation: Journal of Climate 27, 14; 10.1175/JCLI-D-13-00497.1
RHCP diagnostics created using (a)–(c) ERA-I and (d),(e) MERRA relative humidity (%) and precipitation (mm day−1) from GPCP (1997–2008) in (a) and (d), TRMM (1998–2008) in (b) and (e), and ERA-I (1989–2008) in (c). (f) Uncertainty of the observed RHCP diagnostic, estimated as the standard deviation of all five results divided by the average of them. Daily averaged precipitation and RH over the equatorial Indian Ocean (10°S–10°N, 60°–90°E) are used to construct the RHCP diagnostic.
Citation: Journal of Climate 27, 14; 10.1175/JCLI-D-13-00497.1
From Figs. 3a–e, which will be regarded as observations in this study, aspects of the large-scale modulation of tropical convection can be seen. For example, strongest rain events (e.g., 100th percentile), which presumably are associated with strong deep convection, occur only when the column is nearly saturated in a very deep layer (up to 200 hPa). When the precipitation rate falls below the 70th percentile, high RH (>85%) is mostly confined to a shallow layer near the surface (1000–900 hPa). The difference between weak- and strong-precipitation regimes suggests that during the transition between the two regimes, the lower troposphere above the boundary layer (850–500 hPa) experiences a significant moistening. Similar interpretation of the RHCP diagnostic (with slight variations) has been provided by earlier studies (e.g., Zhu et al. 2009).
Although the broad features of the RHCP diagnostic described above are not sensitive to the precipitation and RH data used, some details are. In particular, the gradient in ERA-I RH between weak and strong rain regimes is much greater when GPCP precipitation is used, compared to that constructed using ERA-I precipitation. Also, when MERRA RH is used instead of ERA-I RH, the depth of humid layer near the surface becomes shallower, while RH near 600 hPa becomes greater. Figure 3e displays the root-mean-square difference between the five results divided by the average of them, which is an estimate of observational uncertainty. For the 80th or higher percentile, the standard deviation is smaller than 10% of the average, while it reaches 15%–20% of the average at near 500 hPa for the 60th through 65th percentiles.
In short, the RHCP diagnostic represents physical aspects of the moisture–convection relationship over the central equatorial Indian Ocean, and those features are not sensitive to the data used to construct the diagnostic.
c. Relevant MJO dynamics
The key feature in the RHCP diagnostic concerning the relationship between tropical convection and environmental moisture is the tight coupling between them. The strong coupling between tropical convection and lower-tropospheric moisture has been shown to be an intrinsic characteristic of the tropical atmosphere (Bretherton et al. 2004; Holloway and Neelin 2009). Furthermore, Yasunaga and Mapes (2012) showed that the MJO is distinguished from other convectively coupled equatorial waves by the strong coupling between precipitable water and precipitation (see their Fig. 4). This observational evidence suggests that the tight coupling between moisture and convection should be included in theories of the MJO.
Moisture–convection coupling is a crucial ingredient in some theoretical considerations on the dynamics of the MJO (Bladé and Hartmann 1993; Raymond 2001; Bony and Emanuel 2005; Sobel and Maloney 2012, 2013). In these views, enhanced convection associated with the MJO is strongly tied to the positive moisture anomaly, and the growth or decay and propagation of the MJO can be explained by the processes regulating the moisture anomaly. In this case, growth (decay) of the MJO is controlled by the physical processes responsible for supporting (reducing) moisture anomalies in regions of enhanced convection, and propagation is regulated by the processes responsible for moistening to the east of the convective region and drying to the west. This “discharge–recharge” (Bladé and Hartmann 1993) or “moisture mode” (Raymond 2001) view has been supported by observations (e.g., Kemball-Cook and Weare 2001; Yasunaga and Mapes 2012), reanalysis (Sperber 2003), and modeling studies (e.g., Sperber et al. 2005; Thayer-Calder and Randall 2009; Zhu et al. 2009; Maloney et al. 2010).
In these views of MJO dynamics, it is argued that the time scale required for the atmosphere to build up lower-tropospheric moisture and to discharge it determines the period of the intraseasonal oscillation. A particularly critical physical process is the gradual accumulation of moisture during the recharge period, which accompanies deepening and strengthening of the cumulus clouds and takes 15–30 days to transition from a dry, nonprecipitating state to a strongly convective state. During the recharging period, strong convection, which consumes the accumulated moisture, should not be prevalent. This time scale of the recharge process determines the period of MJO, which is 30–60 days. Also, the recharge preferentially occurs to the east of the developing convective envelope, thus driving the eastward propagation. Therefore, for a climate model, an appropriate simulation of the sensitivity of cumulus convection to environmental humidity would be a necessary condition for a reasonable MJO simulation.
d. Previous usage
Moisture diagnostics related to our RHCP diagnostic have been used to distinguish a GCM with a relatively good MJO from a GCM with a relatively poor one in Thayer-Calder and Randall (2009), Zhu et al. (2009), Kim et al. (2009), Kim et al. (2011b), and Del Genio et al. (2012). In Kim et al. (2009) and Xavier (2012), the moisture diagnostic was applied to a set of models that exhibited a range of abilities to simulate the MJO. The findings in these studies support the argument that if a model better represents the relationships between the rainfall rate and environmental humidity as depicted in the RHCP diagnostic, the model tends to simulate a better MJO. A typical symptom of relatively poor MJO simulations in these studies is that they simulate too-strong rainfall rates for dry lower-tropospheric RH, meaning they lack the appropriate sensitivity to environmental moisture.
The lack of sensitivity of the parameterized convection to environmental moisture was reported in Derbyshire et al. (2004) as an issue common to a number of models. This lack of sensitivity may result in the poor simulation of the MJO in many models, in which the effect of a cumulus ensemble on the large-scale environment is represented with parameterization schemes. If a strong relationship between the sensitivity of convection to environmental moisture and the fidelity of MJO simulations is found, we could have more confidence in this argument. To investigate this further, we will derive some quantifiable metrics of the moisture–rainfall sensitivity depicted by the RHCP diagnostic and apply them to a set of models that exhibit a wide range of capabilities to simulate the MJO.
e. Derivation of moisture sensitivity metrics
To derive quantifiable metrics from the RHCP diagnostic, we constructed the RHCP diagnostic using model simulation data. We present in Figs.4 and 5 the RHCP diagnostic at 850 and 700 hPa, respectively, since as discussed in section 3b most pronounced moistening occurs above the boundary layer in the transition between the weak and strong precipitation regimes. The model results are compared to those from the ERA-I RH and the three precipitation products.
RHCP diagnostics at 850 hPa created using all participating models (color lines), and that with three different precipitation products combined with ERA-I RH (black lines) for (a) CMIP3 and (b) CMIP5. At the bottom of (a) the method to calculate the moisture sensitivity metric is illustrated.
Citation: Journal of Climate 27, 14; 10.1175/JCLI-D-13-00497.1
RHCP diagnostics at 850 hPa created using all participating models (color lines), and that with three different precipitation products combined with ERA-I RH (black lines) for (a) CMIP3 and (b) CMIP5. At the bottom of (a) the method to calculate the moisture sensitivity metric is illustrated.
Citation: Journal of Climate 27, 14; 10.1175/JCLI-D-13-00497.1
RHCP diagnostics at 850 hPa created using all participating models (color lines), and that with three different precipitation products combined with ERA-I RH (black lines) for (a) CMIP3 and (b) CMIP5. At the bottom of (a) the method to calculate the moisture sensitivity metric is illustrated.
Citation: Journal of Climate 27, 14; 10.1175/JCLI-D-13-00497.1
As in Fig. 4, but the RHCP diagnostics are constructed using 700-hPa RH.
Citation: Journal of Climate 27, 14; 10.1175/JCLI-D-13-00497.1
As in Fig. 4, but the RHCP diagnostics are constructed using 700-hPa RH.
Citation: Journal of Climate 27, 14; 10.1175/JCLI-D-13-00497.1
As in Fig. 4, but the RHCP diagnostics are constructed using 700-hPa RH.
Citation: Journal of Climate 27, 14; 10.1175/JCLI-D-13-00497.1
In Figs. 4 and 5 the lower-tropospheric RH increases with precipitation percentile in all models and observations as expected, although considerable spread exists among models for all percentiles. For example, in BCCR-BCM2.0, CNRM-CM3, and MRI-CGCM3, RH in the lower troposphere is greater than 90% for the upper 10th precipitation percentiles, while the lower-tropospheric RH hardly exceeds 80% in INM-CM3.0, MRI-CGCM2.3.2a, and CanESM2. This suggests that the former group of models requires a moister environment than the latter group to produce relatively high rainfall rates. The difference of lower-tropospheric RH between the strong and weak rain regimes also shows variability among simulations. A greater difference suggests a more sensitive convection response to lower-tropospheric RH. In this regard, ERA-I exhibits RH for the top (100th) percentile that is about 45% greater than that of the bottom (first) percentile at 850 hPa (Fig. 4). This difference is greater at 700 hPa, and is about 50% (Fig. 5). Models show a wide range of RH differences between the top and bottom percentiles. For example, at 700 hPa, MRI-CGCM3 shows a RH increase of about 65%, while FGOALS-s2 experiences about a 40% increase of RH (Fig. 5).
These results suggest that both the lower-tropospheric RH in the strong rain regime, and the difference of lower-tropospheric RH between the strong and weak rain regime can be a measure of the moisture sensitivity exhibited by model convection, and will be used as metric in the following. The former can be represented as an average of lower-tropospheric RH for the upper X percent of rain events 
4. Statistical relationship between MJO simulation fidelity and moisture–convection coupling metrics
We now explore the statistical relationship between the moisture sensitivity metrics derived from the RHCP diagnostic and the measures of the MJO simulation fidelity. Our examination revealed that the 
Figure 6 presents the linear relationship (i.e., correlation coefficient) between 
Correlation coefficients between 
Citation: Journal of Climate 27, 14; 10.1175/JCLI-D-13-00497.1
Correlation coefficients between
Citation: Journal of Climate 27, 14; 10.1175/JCLI-D-13-00497.1
Correlation coefficients between
Citation: Journal of Climate 27, 14; 10.1175/JCLI-D-13-00497.1
As seen in Fig. 7, when X is fixed at 10%, the averaged correlation coefficient is higher with Y near 20% (Fig. 7a), and when Y is fixed at 20%, the averaged linear relationship maximizes with X around 10% (Fig. 7c). In both cases, the peak is broad enough to conclude that the averaged linear relationship is not sensitive to a specific choice of X and Y. With X = 10% and Y = 20%, the moisture sensitivity metric 
Sensitivity of correlation coefficients between 
Citation: Journal of Climate 27, 14; 10.1175/JCLI-D-13-00497.1
Sensitivity of correlation coefficients between
Citation: Journal of Climate 27, 14; 10.1175/JCLI-D-13-00497.1
Sensitivity of correlation coefficients between
Citation: Journal of Climate 27, 14; 10.1175/JCLI-D-13-00497.1
As seen in Fig. 8 for X = 10% and Y = 20%, the E/W ratio and east relationship to 
Scatterplot between 
Citation: Journal of Climate 27, 14; 10.1175/JCLI-D-13-00497.1
Scatterplot between
Citation: Journal of Climate 27, 14; 10.1175/JCLI-D-13-00497.1
Scatterplot between
Citation: Journal of Climate 27, 14; 10.1175/JCLI-D-13-00497.1
Our results imply that models simulate a stronger MJO if they require a greater difference in lower-tropospheric RH between strong and weak rain percentiles. In other words, in the models that simulate stronger MJO activity, convection is more sensitive to lower-tropospheric humidity. This is consistent with the results of Hannah and Maloney (2011) and Kim et al. (2012) in which strengthening of the moisture–convection relationship caused a stronger MJO in different GCMs. Kim et al. (2012) increased the fractional entrainment rate and reevaporation of convective condensates in the convection scheme of the NASA Goddard Institute for Space Studies (GISS) GCM to make deep convection more sensitive to environmental humidity, which led the GCM to simulate an improved MJO.
In Fig. 8, results are also presented for the three observed precipitation products and ERA-I RH data. Note that in all cases we use the 
The results in this section show that the amount of moistening required for the transition from weak to strong rain regimes has a robust statistical relationship with the fidelity metrics of the simulated MJOs. In particular, the above results suggest that the RHCP diagnostic could be a useful tool as a process-oriented MJO simulation diagnostic, and that 
5. Summary and conclusions
A process-oriented MJO simulation diagnostic based on free tropospheric relative humidity is proposed and tested. The process-oriented MJO simulation diagnostic aims to give physical insight into why a GCM simulates a stronger or weaker MJO than others (cf. Wheeler and Maloney 2013). Three aspects are required of such a diagnostic: (i) currently available observations can be used to construct it, (ii) changes in parameterizations alter its behavior, and (iii) it has a tight relationship with the fidelity of the simulated MJO, meaning it has relevance to MJO dynamics, at least in models.
We propose the RH composite based on precipitation (RHCP) diagnostic as a process-oriented MJO simulation diagnostic. The RHCP diagnostic is derived by binning RH profiles into precipitation percentiles. When applied to model simulations, it represents the simulated interaction between cumulus convection and environmental humidity, and so is closely related to the moisture sensitivity of deep and shallow cumulus parameterizations in the climate model. It is also relevant to theories of the MJO in which the tight coupling between convection and environmental moisture is a crucial ingredient.
Statistical relationships between a set of moisture sensitivity metrics deduced from the RHCP diagnostic and objective measures of the simulated MJOs are investigated. The moisture sensitivity metrics are developed as the mean lower-tropospheric RH for upper X percent rain events minus that for lower Y percent rain events 
Observational estimates of 
There are uncertainties in observations. The RH data used in this study are from reanalysis products, which are model simulations constrained by observations. Because observation of RH in areas with strong convection is an extremely difficult task with current technology, the reanalysis RH in these areas is heavily influenced by model parameterizations, and therefore could be biased. The two satellite precipitation products—TRMM 3B42 and GPCP v1.1—use observations of infrared (IR) brightness temperature to estimate surface rain rate. Behrangi et al. (2012) suggested that IR-based precipitation products could underestimate the frequency of light rain (<1 mm day−1), because of the bias in the relationship they are using between IR brightness temperature and microwave precipitation measurements. We suspect that the lack of weak rain events in TRMM 3B42 and GPCP v1.1 (Figs. 1 and 2), which led us to excluding these data when estimating the mean lower-tropospheric RH for the weak rain regime 
Acknowledgments
We thank anonymous reviewers for their constructive comments. DK is supported by NASA Grant NNX13AM18G and the Korea Meteorological Administration Research and Development Program under Grant CATER 2013-3142. EDM is supported by Climate and Large-Scale Dynamics Program of the National Science Foundation under Grants ATM-0832868 and AGS-1025584 and the Science and Technology Center for Multi-Scale Modeling of Atmospheric Processes, managed by Colorado State University, under Cooperative Agreement ATM-0425247. EDM is also supported by Award NA08OAR4320893 and NA12OAR4310077 from the National Oceanic and Atmospheric Administration, U.S. Department of Commerce, and NASA Grant NNX13AQ50G. The ERA-Interim data used in this study have been provided by the ECMWF data server.
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.
Arakawa, A., and W. H. Schubert, 1974: Interaction of a cumulus cloud ensemble with the large-scale environment. Part I. J. Atmos. Sci., 31, 674–701, doi:10.1175/1520-0469(1974)031<0674:IOACCE>2.0.CO;2.
Behrangi, A., M. Lebsock, S. Wong, and B. Lambrigtsen, 2012: On the quantification of oceanic rainfall using spaceborne sensors. J. Geophys. Res., 117, D20105, doi:10.1029/2012JD017979.
Betts, A. K., 1986: A new convective adjustment scheme. Part I: Observational and theoretical basis. Quart. J. Roy. Meteor. Soc., 112, 677–691, doi:10.1002/qj.49711247307.
Bladé, I., and D. L. Hartmann, 1993: Tropical intraseasonal oscillations in a simple nonlinear model. J. Atmos. Sci., 50, 2922–2939, doi:10.1175/1520-0469(1993)050<2922:TIOIAS>2.0.CO;2.
Bony, S., and K. A. Emanuel, 2005: On the role of moist processes in tropical intraseasonal variability: Cloud–radiation and moisture–convection feedbacks. J. Atmos. Sci., 62, 2770–2789, doi:10.1175/JAS3506.1.
Bougeault, P., 1985: A simple parameterization of the large-scale effects of cumulus convection. Mon. Wea. Rev., 113, 2108–2121, doi:10.1175/1520-0493(1985)113<2108:ASPOTL>2.0.CO;2.
Bretherton, C. S., M. E. Peters, and L. E. Back, 2004: Relationship 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.
Crueger, T., B. Stevens, and R. Brokopf, 2013: The Madden–Julian oscillation in ECHAM6 and the introduction of an objective MJO metric. J. Climate, 26, 3241–3257, doi:10.1175/JCLI-D-12-00413.1.
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.
Del Genio, A. D., and M.-S. Yao, 1993: Efficient cumulus parameterization for long-term climate studies: The GISS scheme. The Representation of Cumulus Convection in Numerical Models, Meteor. Monogr., No. 46, Amer. Meteor. Soc., 181–184.
Del Genio, A. D., Y. Chen, D. Kim, and M.-S. Yao, 2012: The MJO transition from shallow to deep convection in CloudSat/CALIPSO data and GISS GCM simulations. J. Climate, 25, 3755–3770, doi:10.1175/JCLI-D-11-00384.1.
Derbyshire, S. H., I. Beau, P. Bechtold, J.-Y. Grandpeix, J.-M. Piriou, J.-L. Redelsperger, and P. M. M. Soares, 2004: Sensitivity of moist convection to environmental humidity. Quart. J. Roy. Meteor. Soc., 130, 3055–3079, doi:10.1256/qj.03.130.
Emanuel, K. A., 1991: A scheme for representing cumulus convection in large-scale models. J. Atmos. Sci., 48, 2313–2335, doi:10.1175/1520-0469(1991)048<2313:ASFRCC>2.0.CO;2.
Emori, S., T. Nozawa, A. Numaguti, and I. Uno, 2001: Importance of cumulus parameterization for precipitation simulation over East Asia in June. J. Meteor. Soc. Japan, 79, 939–947, doi:10.2151/jmsj.79.939.
Gregory, D., and P. R. Rowntree, 1990: A mass flux convection scheme with representation of cloud ensemble characteristics and stability-dependent closure. Mon. Wea. Rev., 118, 1483–1506, doi:10.1175/1520-0493(1990)118<1483:AMFCSW>2.0.CO;2.
Hannah, W. M., and E. D. Maloney, 2011: The role of moisture–convection feedbacks in simulating the Madden–Julian oscillation. J. Climate, 24, 2754–2770, doi:10.1175/2011JCLI3803.1.
Holloway, C. E., and J. D. Neelin, 2009: Moisture vertical structure, column water vapor, and tropical deep convection. J. Atmos. Sci., 66, 1665–1683, doi:10.1175/2008JAS2806.1.
Hu, Q., and D. A. Randall, 1994: Low-frequency oscillations in radiative–convective systems. J. Atmos. Sci., 51, 1089–1099, doi:10.1175/1520-0469(1994)051<1089:LFOIRC>2.0.CO;2.
Hu, Q., and D. A. Randall, 1995: Low-frequency oscillations in radiative–convective systems. Part II: An idealized model. J. Atmos. Sci., 52, 478–490, doi:10.1175/1520-0469(1995)052<0478:LFOIRC>2.0.CO;2.
Huffman, G. J., R. F. Adler, M. M. Morrissey, D. T. Bolvin, S. Curtis, R. Joyce, B. McGavock, and J. Susskind, 2001: Global precipitation at one-degree daily resolution from multisatellite observations. J. Hydrometeor., 2, 36–50, doi:10.1175/1525-7541(2001)002<0036:GPAODD>2.0.CO;2.
Huffman, G. J., and Coauthors, 2007: The TRMM Multisatellite Precipitation Analysis (TMPA): Quasi-global, multiyear, combined-sensor precipitation estimates at fine scales. J. Hydrometeor., 8, 38–55, doi:10.1175/JHM560.1.
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.
Jones, C., 2000: Occurrence of extreme precipitation events in California and relationships with the Madden–Julian oscillation. J. Climate, 13, 3576–3587, doi:10.1175/1520-0442(2000)013<3576:OOEPEI>2.0.CO;2.
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.
Kim, D., and I.-S. Kang, 2012: A bulk mass flux convection scheme for climate model: Description and moisture sensitivity. Climate Dyn., 38, 411–429, doi:10.1007/s00382-010-0972-2.
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, and I.-S. Kang, 2011a: A mechanism denial study on the Madden–Julian oscillation. J. Adv. Model. Earth Syst.,3, M12007, doi:10.1029/2011MS000081.
Kim, D., A. H. Sobel, E. D. Maloney, D. M. W. Frierson, and I.-S. Kang, 2011b: 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., A. H. Sobel, A. D. Del Genio, Y. Chen, S. J. Camargo, M.-S. Yao, M. Kelley, and L. Nazarenko, 2012: The tropical subseasonal variability simulated in the NASA GISS general circulation model. J. Climate, 25, 4641–4659, doi:10.1175/JCLI-D-11-00447.1.
Kim, D., J.-S. Kug, and A. H. Sobel, 2014: Propagating versus nonpropagating Madden–Julian oscillation events. J. Climate, 27, 111–125, doi:10.1175/JCLI-D-13-00084.1.
Kiranmayi, L., and E. D. Maloney, 2011a: Effect of SST distribution and radiative feedbacks on the simulation of intraseasonal variability in an aquaplanet GCM. J. Meteor. Soc. Japan, 89, 195–210, doi:10.2151/jmsj.2011-302.
Kiranmayi, L., and E. D. Maloney, 2011b: Intraseasonal moist static energy budget in reanalysis data. J. Geophys. Res., 116, D21117, doi:10.1029/2011JD016031.
Lau, W. K.-M., and D. E. Waliser, 2011: Intraseasonal Variability in the Atmosphere–Ocean Climate System. Springer, 648 pp.
Lee, M.-I., I.-S. Kang, and B. E. Mapes, 2003: Impacts of cumulus convection parameterization on aqua-planet AGCM simulations of tropical intraseasonal variability. J. Meteor. Soc. Japan, 81, 963–992, doi:10.2151/jmsj.81.963.
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, J.-L., M.-I. Lee, D. Kim, I.-S. Kang, and D. M. W. Frierson, 2008: The impacts of convective parameterization and moisture triggering on AGCM-simulated convectively coupled equatorial waves. J. Climate, 21, 883–909, doi:10.1175/2007JCLI1790.1.
Ma, D., and Z. Kuang, 2011: Modulation of radiative heating by the Madden–Julian oscillation and convectively coupled Kelvin waves as observed by CloudSat. Geophys. Res. Lett., 38, L21813, doi:10.1029/2011GL049734.
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., and D. L. Hartmann, 2000: Modulation of hurricane activity in the Gulf of Mexico by the Madden–Julian oscillation. Science, 287, 2002–2004, doi:10.1126/science.287.5460.2002.
Maloney, E. D., and D. L. Hartmann, 2001: The sensitivity of intraseasonal variability in the NCAR CCM3 to changes in convective parameterization. J. Climate, 14, 2015–2034, doi:10.1175/1520-0442(2001)014<2015:TSOIVI>2.0.CO;2.
Maloney, E. D., A. H. Sobel, and W. M. Hannah, 2010: Intraseasonal variability in an aquaplanet general circulation model. J. Adv. Model. Earth. Syst.,2, 5, doi:10.3894/JAMES.2010.2.5.
Meehl, G. A., C. Covey, K. E. Taylor, T. Delworth, R. J. Stouffer, M. Latif, B. McAvaney, and J. F. B. Mitchell, 2007: The WCRP CMIP3 multimodel dataset: A new era in climate change research. Bull. Amer. Meteor. Soc., 88, 1383–1394, doi:10.1175/BAMS-88-9-1383.
Moorthi, S., and M. J. Suarez, 1992: Relaxed Arakawa–Schubert. A parameterization of moist convection for general circulation models. Mon. Wea. Rev., 120, 978–1002, doi:10.1175/1520-0493(1992)120<0978:RASAPO>2.0.CO;2.
Neale, R. B., J. H. Richter, and M. Jochum, 2008: The impact of convection on ENSO: From a delayed oscillator to a series of events. J. Climate, 21, 5904–5924, doi:10.1175/2008JCLI2244.1.
Nordeng, T. E., 1994: Extended versions of the convective parametrization scheme at ECMWF and their impact on the mean and transient activity of the model in the tropics. ECMWF Tech. Memo. 206, 41 pp.
Pan, D.-M., and D. D. A. Randall, 1998: A cumulus parameterization with a prognostic closure. Quart. J. Roy. Meteor. Soc., 124, 949–981.
Raymond, D. J., 2001: A new model of the Madden–Julian oscillation. J. Atmos. Sci., 58, 2807–2819, doi:10.1175/1520-0469(2001)058<2807:ANMOTM>2.0.CO;2.
Richter, J. H., and P. J. Rasch, 2008: Effects of convective momentum transport on the atmospheric circulation in the Community Atmosphere Model, version 3. J. Climate, 21, 1487–1499, doi:10.1175/2007JCLI1789.1.
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.
Sahany, S., J. D. Neelin, K. Hales, and R. B. Neale, 2012: Temperature–moisture dependence of the deep convective transition as a constraint on entrainment in climate models. J. Atmos. Sci., 69, 1340–1358, doi:10.1175/JAS-D-11-0164.1.
Slingo, J. M., and Coauthors, 1996: Intraseasonal oscillations in 15 atmospheric general circulation models: Results from an AMIP diagnostic subproject. Climate Dyn., 12, 325–357, doi:10.1007/BF00231106.
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.
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.
Sperber, K. R., and D. Kim, 2012: Simplified metrics for the identification of the Madden–Julian oscillation in models. Atmos. Sci. Lett., 13, 187–193, doi:10.1002/asl.378.
Sperber, K. R., S. Gualdi, S. Legutke, and V. Gayler, 2005: The Madden–Julian oscillation in ECHAM4 coupled and uncoupled general circulation models. Climate Dyn., 25, 117–140, doi:10.1007/s00382-005-0026-3.
Takayabu, Y. N., T. Iguchi, M. Kachi, A. Shibata, and H. Kanzawa, 1999: Abrupt termination of the 1997–98 El Niño in response to a Madden–Julian oscillation. Nature, 402, 279–282, doi:10.1038/46254.
Taylor, K. E., R. J. Stouffer, and G. A. Meehl, 2012: An overview of CMIP5 and the experiment design. Bull. Amer. Meteor. Soc., 93, 485–498, doi:10.1175/BAMS-D-11-00094.1.
Thayer-Calder, K., and D. A. Randall, 2009: The role of convective moistening in the Madden–Julian oscillation. J. Atmos. Sci., 66, 3297–3312, doi:10.1175/2009JAS3081.1.
Tiedtke, M., 1989: A comprehensive mass flux scheme for cumulus parameterization in large-scale models. Mon. Wea. Rev., 117, 1779–1800, doi:10.1175/1520-0493(1989)117<1779:ACMFSF>2.0.CO;2.
Tokioka, T., K. Yamazaki, A. Kitoh, and T. Ose, 1988: The equatorial 30–60 day oscillation and the Arakawa–Schubert penetrative cumulus parameterization. J. Meteor. Soc. Japan, 66, 883–901.
Waliser, D. E., and Coauthors, 2003: AGCM simulations of intraseasonal variability associated with the Asian summer monsoon. Climate Dyn., 21, 423–446, doi:10.1007/s00382-003-0337-1.
Wang, W., and M. E. Schlesinger, 1999: The dependence on convection parameterization of the tropical intraseasonal oscillation simulated by the UIUC 11-layer atmospheric GCM. J. Climate, 12, 1423–1457, doi:10.1175/1520-0442(1999)012<1423:TDOCPO>2.0.CO;2.
Wheeler, M. C., and J. L. McBride, 2005: Australian–Indonesian monsoon. Intraseasonal Variability in the Atmosphere–Ocean Climate System, W. K.-M. Lau and D. E. Waliser, Eds., Springer, 125–173.
Wheeler, M. C., E. D. Maloney, and the MJO Task Force, 2013: Madden–Julian oscillation (MJO) Task Force: A joint effort of the climate and weather communities. CLIVAR Exchanges, No. 61, International CLIVAR Project Office, Southampton, United Kingdom, 9–12.
Xavier, P. K., 2012: Intraseasonal convective moistening in CMIP3 models. J. Climate, 25, 2569–2577, doi:10.1175/JCLI-D-11-00427.1.
Yasunaga, K., and B. E. Mapes, 2012: Differences between more divergent and more rotational types of convectively coupled equatorial waves. Part I: Space–time spectral analyses. J. Atmos. Sci., 69, 3–16, doi:10.1175/JAS-D-11-033.1.
Yukimoto, S., and Coauthors, 2011: Meteorological Research Institute-Earth System Model version 1 (MRI-ESM1)—Model description. Meteorological Research Institute Tech. Rep. 64, 83 pp. [Available online at http://www.mri-jma.go.jp/Publish/Technical/DATA/VOL_64/index_en.html.]
Zhang, C., 2005: Madden–Julian oscillation. Rev. Geophys., 43, RG2003, doi:10.1029/2004RG000158.
Zhang, C., and H. H. Hendon, 1997: Propagating and standing components of the intraseasonal oscillation in tropical convection. J. Atmos. Sci., 54, 741–752, doi:10.1175/1520-0469(1997)054<0741:PASCOT>2.0.CO;2.
Zhang, G. J., and N. A. McFarlane, 1995: Sensitivity of climate simulations to the parameterization of cumulus convection in the Canadian Climate Centre general circulation model. Atmos.–Ocean, 33, 407–446, doi:10.1080/07055900.1995.9649539.
Zhang, G. J., and M. Mu, 2005: Simulation of the Madden–Julian oscillation in the NCAR CCM3 using a revised Zhang–McFarlane convection parameterization scheme. J. Climate, 18, 4046–4064, doi:10.1175/JCLI3508.1.
Zhu, H., H. H. Hendon, and C. Jakob, 2009: Convection in a parameterized and superparameterized model and its role in the representation of the MJO. J. Atmos. Sci., 66, 2796–2811, doi:10.1175/2009JAS3097.1.
The international MJO Task Force had been under the World Weather Research Programme (WWRP)–The Observing System Research and Predictability Experiment (THORPEX)/World Climate Research Programme (WCRP) Year of Tropical Convection (YOTC) during 2010–12, and is currently under World Meteorological Organization (WMO) Working Group on Numerical Experimentation (WGNE) since January 2013.
Correlation coefficient between “east” and “west” is about 0.68, which is statistically significant at 95% confidence level.
Note that we count all models when estimating the degree of freedom (=28). The degree of freedom could be lower than the number of models we are using, as there are different versions of same models: GFDL CM2.0 and GFDL CM2.1; CMCC-CM and CMCC-CMS; MIROC4h, MIROC-ESM, and MIROC-ESM-CHEM; and MPI-ESM-LR and MPI-ESM-CHEM. If we consider these groups of models as one model then the degree of freedom drops to 23, and the 95% confidence level increases to 0.35.
