Abstract

Process-oriented diagnostics for Madden–Julian oscillation (MJO) simulations are being developed to facilitate improvements in the representation of the MJO in weather and climate models. These process-oriented diagnostics are intended to provide insights into how parameterizations of physical processes in climate models should be improved for a better MJO simulation. This paper proposes one such process-oriented diagnostic, which is designed to represent sensitivity of simulated convection to environmental moisture: composites of a relative humidity (RH) profile based on precipitation percentiles. The ability of the RH composite diagnostic to represent the diversity of MJO simulation skill is demonstrated using a group of climate model simulations participating in phases 3 and 5 of the Coupled Model Intercomparison Project (CMIP3 and CMIP5). A set of scalar process metrics that captures the key physical attributes of the RH diagnostic is derived and their statistical relationship with indices that quantify the fidelity of the MJO simulation is tested. It is found that a process metric that represents the amount of lower-tropospheric humidity increase required for a transition from weak to strong rain regimes has a robust statistical relationship with MJO simulation skill. The results herein suggest that moisture sensitivity of convection is closely related to a GCM’s ability to simulate the MJO.

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.

Table 1.

List of participating models (including complete expansion of model acronyms). Horizontal resolution of their atmospheric component models and convection schemes are also indicated.

List of participating models (including complete expansion of model acronyms). Horizontal resolution of their atmospheric component models and convection schemes are also indicated.
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.

Table 2.

MJO simulation fidelity metrics derived from observations and participating models. GPCP, TRMM, and ERA-I data include Advanced Very High Resolution Radiometer (AVHRR) products.

MJO simulation fidelity metrics derived from observations and participating models. GPCP, TRMM, and ERA-I data include Advanced Very High Resolution Radiometer (AVHRR) products.
MJO simulation fidelity metrics derived from observations and participating models. GPCP, TRMM, and ERA-I data include Advanced Very High Resolution Radiometer (AVHRR) products.
Table 3.

Correlation coefficients between measures of the fidelity of MJO simulation.

Correlation coefficients between measures of the fidelity of MJO simulation.
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.)

Fig. 1.

Precipitation amount (mm day−1) corresponding to precipitation percentiles. The lower 70th percentiles are presented.

Fig. 1.

Precipitation amount (mm day−1) corresponding to precipitation percentiles. The lower 70th percentiles are presented.

Fig. 2.

As in Fig. 1, except for the upper 30th percentiles.

Fig. 2.

As in Fig. 1, except for the upper 30th percentiles.

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.

Fig. 3.

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.

Fig. 3.

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.

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.

Fig. 4.

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.

Fig. 4.

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.

Fig. 5.

As in Fig. 4, but the RHCP diagnostics are constructed using 700-hPa RH.

Fig. 5.

As in Fig. 4, but the RHCP diagnostics are constructed using 700-hPa RH.

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 , while the latter can be the difference between and , where is an average of lower-tropospheric RH for the lower Y percent of rain rates, as illustrated in the lower part of Fig. 4a. The latter moisture sensitivity metric represents the gross gradient of mean RH between the weak and strong rain regimes. In our analysis, lower-tropospheric RH will be measured by a simple average of RH at 850- and 700-hPa levels. The 500-hPa level is excluded because inclusion of the level degrades the relationship between the moisture sensitivity metric and the MJO simulation fidelity metrics (not shown). By choosing levels in the lower-tropospheric layer (850 and 700 hPa) that exclude the planetary boundary layer, we aim to capture only the effects of environmental air on cumulus convection through entrainment to cumulus updrafts, and excluding the effects from the planetary boundary layer moisture (i.e., increasing or decreasing convective available potential energy). Therefore, RH at the 1000-hPa level is not used in the calculations below. Properly representing the effects of entrainment in the lower free troposphere has been shown to be critical for producing realistic convective sensitivity to environmental humidity in models (e.g., Sahany et al. 2012).

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 metric has a stronger relationship with the MJO simulation fidelity metrics than regardless of Y (not shown). This implies that in a GCM that simulates a relatively skillful MJO, the mean RH of the strong rain events is relatively higher than that of the weak rain events. Therefore we present later only the results based on .

Figure 6 presents the linear relationship (i.e., correlation coefficient) between and three measures of the MJO simulation fidelity as a function of X (x axis) and Y (y axis). Only model data are used in the calculation of the correlation coefficients. Although the dependence of the linear relationship on X and Y varies with the measure of the MJO simulation fidelity used, the linear relationship is statistically significant at 95% confidence level, which is 0.32,3 in a wide area for all MJO simulation fidelity metrics used. Also, Fig. 6 shows that the strongest relationship is found when the E/W power ratio is used as a measure of the MJO skill. An average of the linear relationship with the three MJO simulation fidelity metrics (Fig. 6d) suggests that the average correlation coefficient is greater than 0.7 if we choose X between 2% and 20% and Y between 15% and 30%.

Fig. 6.

Correlation coefficients between and three MJO simulation fidelity metrics: (a) E/W ratio, (b) east power, and (c) Rmax. The correlation coefficients are displayed as a function of X and Y. (d) Average of all results in (a)–(c).

Fig. 6.

Correlation coefficients between and three MJO simulation fidelity metrics: (a) E/W ratio, (b) east power, and (c) Rmax. The correlation coefficients are displayed as a function of X and Y. (d) Average of all results in (a)–(c).

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 can explain on average 50% of intermodel variability in their MJO simulation fidelity, although its skill varies with the MJO simulation fidelity metrics (Figs. 7b,d).

Fig. 7.

Sensitivity of correlation coefficients between and three MJO simulation fidelity metrics to (a) Y with X fixed at 10%, and (c) X with Y fixed at 20%. (b),(d) As in (a),(c), but percentage variance (%) of intermodel spread in MJO simulation fidelity metrics explained by the moisture sensitivity metric. Black solid line in each panel represents the average of correlation coefficients in (a),(c) or percentage variance in (b),(d) of all MJO simulation fidelity metrics.

Fig. 7.

Sensitivity of correlation coefficients between and three MJO simulation fidelity metrics to (a) Y with X fixed at 10%, and (c) X with Y fixed at 20%. (b),(d) As in (a),(c), but percentage variance (%) of intermodel spread in MJO simulation fidelity metrics explained by the moisture sensitivity metric. Black solid line in each panel represents the average of correlation coefficients in (a),(c) or percentage variance in (b),(d) of all MJO simulation fidelity metrics.

As seen in Fig. 8 for X = 10% and Y = 20%, the E/W ratio and east relationship to explains about 56% of intermodel variability, while for Rmax the explained variance is 46% (Fig. 8). Actually, explains about 65% of intermodel variability in E/W ratio when we remove two CNRM models whose E/W ratios are outliers (Table 2).

Fig. 8.

Scatterplot between with X = 10% and Y = 20% and three MJO simulation fidelity metrics: (a) E/W ratio, (b) east power, and (c) Rmax. Circles represent model simulations, while the observed values are indicated by filled triangles. The linear fit to the model data and the percentage variance of the MJO simulation fidelity metrics explained by the RH metric and the linear relationship is also displayed in each panel.

Fig. 8.

Scatterplot between with X = 10% and Y = 20% and three MJO simulation fidelity metrics: (a) E/W ratio, (b) east power, and (c) Rmax. Circles represent model simulations, while the observed values are indicated by filled triangles. The linear fit to the model data and the percentage variance of the MJO simulation fidelity metrics explained by the RH metric and the linear relationship is also displayed in each panel.

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 value that is obtained using ERA-I precipitation, while for their own values are used. This is because, as mentioned earlier, with GPCP and TRMM it is impractical to distinguish the lowest 20% percentiles exclusively from others. Although the relationship between the moisture sensitivity of convection and the MJO simulation fidelity seems robust within GCMs, the same relationship cannot explain the observations. When compared to observations, models have too strong moisture sensitivity of convection when they represent a skillful MJO, and have too weak MJO when they simulate a reasonable moisture sensitivity of convection. This is especially true when Rmax is used as a MJO simulation fidelity metric (Fig. 8c). In other words, GCMs in general underestimate the strength of the MJO for a given moisture sensitivity of convection. This suggests that processes important in MJO simulation other than moisture–convection relationship could be commonly misrepresented in GCMs.

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 could be a useful metric to look at when developing climate models and considering their capability to simulate the MJO.

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 . Sensitivity of its skill in explaining MJO simulation fidelity to adjustable parameters—X and Y—is also investigated. A robust statistical relationship with the strength of the simulated MJO was found when is used as the moisture sensitivity metric. Based on our results, we propose as a moisture sensitivity metric that can be used to assess MJO simulations. The robust statistical relationship of with the fidelity of MJO simulation found in this study suggests that a GCM’s ability to simulate the MJO is closely related to the moisture sensitivity of convection simulated in the GCM. Further studies are required to reveal effects of specific parameterization changes on the RHCP diagnostic and the moisture sensitivity metric in each model.

Observational estimates of do not uniformly lie along the linear relationship derived from GCM simulations. Models require too-strong moisture sensitivity to produce a reasonable MJO in terms of the MJO simulation fidelity metrics used, while they show too-weak MJO with reasonable moisture sensitivity. Although the robust statistical relationship between the moisture sensitivity metric and the MJO simulation fidelity among GCMs suggests the relevance of the processes that regulate moisture sensitivity of convection on MJO dynamics in those GCMs, and probably in nature, the mismatch with observations suggests that there could be processes other than moisture sensitivity of simulated convection that are relevant to the MJO dynamics. It is possible that those processes are commonly missing or misrepresented in models. Longwave cloud radiative feedback could be one such process. During an active phase of the MJO, an enhanced amount of high cloud reduces longwave radiative cooling, which means a heating in an anomaly sense. This heating from cloud–radiation interaction has been suggested as an important destabilization mechanism of the MJO in observational (Lin and Mapes 2004; Ma and Kuang 2011; Kiranmayi and Maloney 2011b; Kim et al. 2014), theoretical (Hu and Randall 1994, 1995; Raymond 2001; Sobel and Gildor 2003; Bony and Emanuel 2005; Sobel and Maloney 2012, 2013), and modeling studies (Kiranmayi and Maloney 2011a; Kim et al. 2011a; Andersen and Kuang 2012). Future work should focus on the cloud–radiation interaction as well as identifying other processes relevant to the MJO dynamics.

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 , could be due to this weakness of the data. Advances in retrieval algorithms for lower tropospheric RH and light rain rates, and in data assimilation schemes used in creating reanalysis products, will help to constrain the moisture sensitivity metric with a higher confidence on observations.

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.

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Footnotes

b

Current affiliation: Department of Atmospheric Sciences, University of Washington, Seattle, Washington.

k

Current affiliation: Climate, Atmospheric Science, and Physical Oceanography, Scripps Institute of Oceanography, University of California San Diego, La Jolla, California.

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.

2

Correlation coefficient between “east” and “west” is about 0.68, which is statistically significant at 95% confidence level.

3

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.