Representation of Rossby wave propagation and its effect on the teleconnection between the Indian summer monsoon and extratropical rainfall in the Met Office Unified Model

Compared with Global Atmosphere 6 (GA6) of the UK Met Office Unified Model (UM), the dry bias over the Indian monsoon region in Global Atmosphere 7 (GA7) is significantly reduced. However, the physical processes controlling how this reduced dry bias in India influences rainfall teleconnections in the extratropics remain unclear. Thus, in this study, we use Rossby wave tracing in a horizontally nonuniform background flow to investigate how the improved simulation of monsoon rainfall in GA7 compared with GA6 affects extratropical rainfall teleconnections. We find that wave rays emanating from the upper troposphere in the Indian monsoon region first propagate westward, then divide into the Northern Hemisphere (NH) subtropical westerlies over Asia and the Southern Hemisphere (SH) subtropical westerlies. The wave ray trajectories in GA7 in years of strong Indian summer monsoon rainfall (ISMR) are closer to observations than those in GA6. We also find that the upper tropospheric meridional winds over the South Asian monsoon region and western Tibetan Plateau are much better simulated in GA7 than in GA6 owning to the improvement of ISMR and South Asian High (SAH), which leads to a more realistic simulation of the wave rays in GA7. The better simulated circulation teleconnections in GA7 then modulate the vertical motion and moisture transport, and hence affect extratropical rainfall anomalies in the NH and SH. This paper provides new insights for the assessment of tropical–extratropical teleconnections in models.


Introduction
The Unified Model (UM) is the atmospheric component of the numerical modelling system created by the UK Met Office (UKMO) for both weather and climate applications (https:// www. metof fice. gov. uk/ resea rch/ model ling-syste ms). It is widely used by many organizations and agencies around the world, particularly in the Australian-Asian region, including Australia, India, Korea, and the Philippines (https:// www. metoffi ce. gov. uk/ resea rch/ appro ach/ colla borat ion/ unifi ed-model/ partn ership). Two versions of the UM, namely the UM Global Atmosphere 6 (GA6) and 7 (GA7) are being used by the UK and Australia to contribute to the Intergovernmental Panel on Climate Change (IPCC) Coupled Model Intercomparison Project (CMIP6) (Hirst 2015;Walters et al. 2019) and in their operational seasonal forecast systems (MacLachlan et al. 2015;Hudson et al. 2017). As a result, assessing the performance of the UM GA in the Australian-Asian monsoon region has been an important topic of past research.
As noted in previous UM assessments (Walters et al. 2014;Walters et al. 2017;Walters et al. 2019), the UM has a climatological rainfall deficit over the Indian subcontinent. However, the simulation of Indian summer monsoon rainfall 1 3 (ISMR) within a given UM configuration was shown to improve when the model resolution was increased (Prakash et al. 2016;Jin et al. 2019). In a recent UM GA assessment study, Jin et al. (2019) showed that the area-averaged summer monsoon rainfall over the Indian subcontinent (70°-90°E, 5°-25°N) was significantly increased in GA7 compared with GA6. Furthermore, the increased ISMR in GA7 with N216 resolution improved monsoon-desert rainfall teleconnections and generated more realistic remote rainfall correlation patterns in the Australian-Asian region. Part of the teleconnection patterns showed similarity with Rossby wave propagation from the tropics into the middle and high latitudes. However, as acknowledged by the authors, the underlying physical and dynamic processes supporting these improved rainfall teleconnection patterns and the increased ISMR in the simulations was not fully explored . The major goal of this study is therefore to further investigate how the simulation of Indian monsoon rainfall in GA6 and GA7 (Walters et al. 2017(Walters et al. , 2019 affects the representation of tropical-extratropical rainfall teleconnections, and the nature of the underlying physical and dynamical processes. This analysis will also help to better understand the simulated current and future climate in these models in preparation for CMIP6. The extratropical atmospheric response to tropical localized forcing is well established in both the Northern Hemisphere (NH) (Nitta 1987;Hoskins and Rodwell 1995;Rodwell and Hoskins 1996;Kripalani et al. 1997;Wang et al. 2001;Wang 2005, 2007;Lin 2009) and the Southern Hemisphere (SH) (Wang et al. 2001;Lin 2009;Lee et al. 2013;Liu and Wang 2013;Zhao et al. 2019). Several summer teleconnection patterns in the NH associated with tropical monsoons have been investigated, including the Pacific-Japan pattern (Nitta 1987(Nitta , 1989, the East Asia-Pacific pattern (Huang and Lu 1987;Huang and Sun 1992), the circumglobal teleconnection pattern (Ding and Wang 2005;Ding et al. 2011), the ''silk road'' pattern in the 200 hPa meridional velocity Enomoto et al. 2003), the Indo-Asian-Pacific pattern Li et al. 2013a, b), and the North Atlantic-Eurasian teleconnection (Li et al. 2013a(Li et al. , b, 2019aLi and Ruan 2018). In addition, the circulation variability in the SH induced by tropical heating was the topic of several studies, including the Pacific-South America pattern (Karoly 1989), the South Africa-midlatitude pattern and the Maritime Continent-subtropical Australian pattern (Zhao et al. 2019). The mechanism proposed for these tropical-extratropical teleconnections is Rossby wave propagation and energy dispersion from localized tropical heating anomalies (Hoskins and Karoly 1981;Branstator 1983;Nathan 1994, 1997). As some theoretical studies have proved (e.g., Hoskins and Karoly 1981;Simmons 1982;Branstator 1983Branstator , 1985Lau and Lim 1984), these anomalies excite stable two-dimensional Rossby waves, thereby dispersing energy to remote regions of the globe.
These wave energy dispersion pathways can be well represented by the ''great circle'' ray trajectory (Hoskins and Karoly 1981). However, in models with a zonally varying or zonally symmetric basic flow, stationary waves can only propagate in the westerlies and cannot cross the critical latitude (i.e., the zero zonal wind speed line; Hoskins and Karoly 1981;Branstator 1983). As there is a strong easterly wind prevailing at upper levels of the atmosphere in the Indian monsoon region during boreal summer, the Rossby waves are evanescent and cannot propagate into the SH in these kinds of models. In reality, however, the Asian monsoon system has a strong meridional circulation and its meridional wind cannot be neglected, compared with the zonal wind. Schneider and Watterson (1984) and Zhang et al. (1996) proved theoretically and numerically that the Hadley circulation allows Rossby waves to propagate from one hemisphere to another via the easterly winds. Li and Li (2012) further considered the barotropic, nondivergent vorticity equation in a horizontally nonuniform basic flow, and found that steady Rossby waves can propagate in the easterlies when supported by the meridional wind. On the basis of the theory of Li and Li (2012), further research has also demonstrated that stationary waves originating from the tropical easterlies can propagate across the equator Zhao et al. 2015Zhao et al. , 2019Li et al. 2019a, b).
Another physical mechanism behind cross-equatorial easterly teleconnections was proposed by Sardeshmukh and Hoskins (1988). They suggested that the equatorial forcing in the easterly winds induces a Rossby wave source in the subtropical westerlies caused by the advection of vorticity by the perturbed divergent flow. However, as discovered by Zhao et al. (2019), the divergent flow and velocity potential over Indian Ocean and Northwest Pacific shows an evident zonal circulation which cannot simply explain the crossequatorial teleconnection over Australia-Asia monsoon region. In this study, therefore, stationary Rossby wave ray tracing is employed to investigate rainfall teleconnections simulated in the UM models.
The main focus of this study is to examine how the improved simulation of ISMR in GA7 compared with GA6 influences extratropical precipitation over the Australian-Asian monsoon region, and the nature of the underlying physical and dynamical mechanisms. We pay particular attention to exploring the signature of stationary Rossby wave energy dispersion in a horizontally nonuniform basic flow within the simulations.
The paper is organized as follows. In Sect. 2, the model, data, and methodology used in this study are introduced. Section 3 is used to assess the rainfall simulations in GA6 and GA7. Section 4 describes the circulation anomalies in the SH and NH associated with ISMR and analyzes their influence on the extratropical rainfall. Section 5 presents the trajectories obtained via Rossby wave ray tracing and discusses the role of meridional wind ducts related to ISMR and South Asian High (SAH). Section 6 contains a summary and discussion.

Model
In this paper, we use monthly precipitation, winds, and geopotential height data obtained from numerical experiments with the UM GA6 and GA7 (Walters et al. 2017;Walters et al. 2019) using a horizontal resolution of 60 km (N216 grid). We used atmosphere-only UM GA simulations by forcing the model with daily observed sea surface temperature (SST) and sea-ice conditions for the period 1982-2008, as in Walters et al. (2017), Walters et al. (2019)) and Jin et al. (2019).
Detailed descriptions of the UM GA6 and GA7 configurations have been provided in several publications (Walters et al. 2017;Walters et al. 2019;Jin et al. 2019), and here we list only some of the key features that are relevant to this study. The GA6 solves the non-hydrostatic, fully compressible, deep-atmosphere equations of motion with a semi-implicit semi-Lagrangian formulation and END-Game dynamical core (Wood et al. 2014). It uses extensively modified microphysics based on Wilson and Ballard (1999) and a revised version of the convection scheme of Gregory and Rowntree (1990) that includes downdrafts (Gregory and Allen 1991) and convective momentum transport. As pointed out by Walters et al. (2019) and Jin et al. (2019), GA7 includes further developments of the model's microphysics scheme and incremental improvements to the implementation of the dynamical core. It includes improved treatment of gaseous absorption in the radiation scheme, improvements to the treatment of warm rain and ice clouds, and revisions to the model's convection scheme to improve the fidelity of the simulation of rainfall. These developments lead to large reductions in four critical model errors: rainfall deficits over India during the South Asian monsoon, temperature and humidity biases in the tropical tropopause layer, deficiencies in the model's numerical conservation, and surface flux biases over the Southern Ocean (Walters et al. 2019).

Observational data
In order to evaluate the simulated Indian Monsoon precipitation, we use monthly precipitation from the Global Precipitation Climatology Project (GPCP; Adler et al. 2003) for the period 1982-2008. Furthermore, the horizontal winds from ERA-Interim reanalysis (Dee et al. 2011) are used for the Rossby wave ray tracing, whilst the geopotential height from ERA-Interim reanalysis data with a resolution of 2.5° longitude by 2.5° latitude for the period 1982-2008 is used to evaluate the monsoon circulation.
The indices used in this study are as follows. The Niño-3.4 index obtained from the Climate Prediction Center (http:// www. cpc. ncep. noaa. gov/ data/ indic es/), defined as the area-averaged SST anomalies over 5°S-5°N, 170°-120°W, is used to quantify the El Niño Southern Oscillation (ENSO). The Indian Ocean Dipole (IOD) Mode index (DMI) obtained from National Oceanic and Atmospheric Administration (NOAA) (http:// www. esrl. noaa. gov/ psd/ gcos_ wgsp/ Times eries/ DMI/) is defined as the difference in the SST anomaly between the tropical western Indian Ocean (10°S-10°N, 50°-70°E) and the southeastern Indian Ocean (10°S-0°N, 90°-110°E; Saji et al. 1999). To quantify the Indian summer monsoon, many indices based on the precipitation, OLR or 850 hPa wind anomalies have been used in the literature (Wang et al. 2001;Li and Zeng, 2002Ding and Wang, 2007). In this paper, in order to evaluate the ISMRdependent teleconnections in GA6 and GA7, we define the ISMR Index (ISMRI) as the normalized area-averaged rainfall anomaly over the Indian subcontinent (5°-25°N, 70°-90°E), as in Jin et al. (2019). Furthermore, we define the ISMR as being strong (weak) when the ISMRI is above (below) 0.75 (− 0.75) considering both the significance and the number of strong (weak) ISMR events. Furthermore, both the strong and weak ISMR years selected in observations and GA7 are six years, and the strong and weak ISMR years in GA6 are seven and six years, respectively. Note that by choosing a larger domain covering the whole of the south Asian monsoon region, Jin et al. (2019) showed that the agreement between GA7 simulations and observations was much improved. We define the south Asian monsoon region as the area over 5°-25°N, 30°-90°E.

Partial correlation
In our analysis, we use the first-order partial correlation coefficient (Anderson 1984) to calculate the correlation between two time series, excluding the effect of one other control variable as follows: where r ij⋅k denotes the partial correlation of variables i and j, excluding the effect of k, r ij refers to the linear correlation between variables i and j, r ik refers to the linear correlation between variables i and k, and r jk refers to the linear correlation between variables j and k. The second-order partial correlation coefficient (Anderson 1984), used to determine the correlation between two time series excluding the effect of two other control variables, is calculated as follows: where r ij⋅kh denotes the partial correlation between variables i and j, excluding the signals of k and h, and r ij⋅k , r ih⋅k , and r jh⋅k can be obtained from Eq. (1).

Partial regression
The partial regression is adopted to estimate how much of the variation of the response variable can be attributed exclusively to one set of factors, once the effect of the other set has been taken into account and controlled for. Specifically, the influences of the considered factors on the studied variables are eliminated step by step. Let's take three independent variables X, X1, X2 as an example, and Y be the dependent variable. Firstly, the effect of X1 on y is removed by subtracting the regression of Y on X1. The regressed values of Y are assumed to follow certain distribution: primes represent departure from the mean state, a is the regression coefficient, and a1 is the intercept of linear regression. Ỹ′ indicates the linear contribution of X1 ′ on Y ′ . Then Then the same way is used to remove influence of X2 can be excluded by In this case, the linear contributions of X1 and X2 on Y � (t) are removed. The Ỹ � * * (t) that is attributed exclusively to X takes the form of in which c is the partial regression coefficient, and Ỹ � * * is the partial regressed value by X ′ . (2)

Rossby wave theory in a nonuniform horizontal basic flow
Rossby wave ray tracing theory describes the pathway of wave energy dispersion (Hoskins and Karoly 1981;Li et al. 2015;Zhao et al. 2015Zhao et al. , 2019Li et al. 2019a, b) and has been widely used to explore atmospheric teleconnections. Thus, it is used in this study to reveal the dynamical link between ISMR and the extratropical climate. A linearized, spherical barotropic Rossby wave ray tracing model proposed by Li and Li (2012) and Li et al. (2015) is employed to study steady, linear Rossby wave patterns in a nonuniform horizontal basic flow. According to previous studies (Karoly 1983;Li and Nathan 1997;Li and Li 2012;Zhao et al. 2015Zhao et al. , 2019Li et al. 2019a, b), the dispersion relation of a barotropic Rossby wave is where is the frequency, ( u M , v M ) = (u, v)∕cos is the Mercator projection of the basic-state zonal and meridional winds, is the latitude, q = 2Ω sin + ∇ 2 Ψ is the basicstate absolute vorticity, Ω is the rotation rate of Earth, Ψ is the basic-state stream function, K = √ k 2 + l 2 is the total wavenumber, and k and l are the zonal and meridional wavenumbers, respectively. The local group velocity C g = (u g , v g ) obtained from Eq. (8) takes the form Zhao et al. 2015;Li et al. 2019a, b) The wave ray trajectory is tangential to the group velocity (Lighthill 1978). The wavenumbers k and l, which are determined by kinematic wave theory (Whitham 1960;Shaman et al. 2012), vary with the position of the ray, where d g ∕dt = ∕ t + C g ⋅ ∇ . For stationary waves ( = 0 ), the initial local meridional wavenumber l is determined from the dispersion relation Eq. (8) for each initial zonal wavenumber k and a given starting point. Then, the ray trajectory can be numerically integrated from Eqs. (9a, 9b) and (10a, 10b). The integration was aborted when the local meridional wavelength was calculated as < 1000 km. From Eqs. (9a,9b) and (10a, 10b), it can be seen that the barotropic stationary Rossby wave energy is dominated by the basic zonal flow, basic meridional flow, and absolute vorticity gradient. Notably, the meridional basic flow plays an important role in the dispersion of wave energy particularly over tropical monsoon region where meridional wind can't be ignored compared with zonal wind. Furthermore, considering the wave ray trajectory is sensitive to the background flow and the atmospheric circulation is subject to multiple factors, it is necessary to extract the influence of heating anomalies on the background flow by partial regression. In this paper, we considered the effects of ENSO and IOD. The basic flow is divided into climatological and abnormal parts, and the linear effect of a studied external forcing on the basic flow can be expressed by anomalies partial regressed onto the forcing. In addition, considering the large scale of Rossby wave, the basic flow is smoothed through spherical harmonics.

Rainfall simulations in GA6 and GA7
Many studies have reported that the tropical monsoons have consequences for rainfall outside the tropics (Nitta 1987;Hoskins and Rodwell 1995;Rodwell and Hoskins 1996;Kripalani et al. 1997;Wang et al. 2001;Wang 2005, 2007;Lin 2009;Lee et al. 2013;Liu and Wang 2013;Zhao et al. 2019). Since the relationship between ISMR and regional rainfall may be modulated by the influence of tropical SSTs, the impacts of some known tropical SST signals on rainfall anomalies are usually excluded first to better isolate the influence of ISMR on rainfall teleconnections. In the study of Jin et al. (2019), they eliminated the effect of ENSO when they investigated the correlation between the simulated ISMR and rainfall over the Australian-Asian monsoon region in GA6 and GA7. Although they discussed the likely influence of the IOD on rainfall anomalies in the Australian-Asian region (Ashok et al. 2001;Zhao et al. 2014;Zhao and Zhang 2016) in GA6 and GA7, their analysis did not remove the effects of the IOD. In this study, we take both the IOD and ENSO into account. Figure 1 displays the correlations and partial correlations between the ISMRI and the June-July-August (JJA) rainfall over the Australian-Asian monsoon region from GPCP, GA6, and GA7, excluding the impacts of the IOD and ENSO. As shown in Fig. 1, the rainfall anomalies in the SH particularly over southwest Australia are more evident in GPCP after removing the impacts of ENSO and IOD indicating that the influence of ENSO, IOD and ISMR on the SH rainfall teleconnections are relatively depended. This is also where the partial correlation in our study different from the results of Jin et al. (2019), suggesting that the influence of IOD on the SH rainfall teleconnections cannot be neglected. Jin et al. (2019) provided comprehensive details about the UM GA6 and GA7 rainfall simulations. In this section, we discuss only those details relevant to our wave ray analysis in the following section.
In the NH, a wave train-like rainfall teleconnection pattern, which shows positive correlations over Arabian Peninsula, Northern China and Mongolia, and negative correlations over Central Asia and the Korean Peninsula, is evident in observations and is much better captured by GA7 (Fig. 1a-c). In addition, in the NH, the anomalous rainfall pattern correlations between GA7 and observations for the full correlation and partial correlation are 0.496 and 0.431, respectively, which are better than GA6, where the correlation with observations are 0.329 and 0.255, respectively.
In the SH, negative correlations over the subtropical Indian Ocean and positive correlations over tropical western Indian Ocean and southwest Australia and the nearby Indian Ocean (Fig. 1a, d), are evident in observations. The anomalous rainfall pattern correlation in the SH between GA7 and observations for the full correlation and partial correlation are 0.251 and 0.068, respectively, but is better and worse simulated in GA6, where the correlations with observations are 0.155 and 0.26, respectively. The decrease in the partial correlation between GA7 and observations is mainly owning to the different influences of ENSO and IOD on the rainfall teleconnection magnitude in GA7 and observations. However, according to the full correlation, the wave-train-like correlation pattern is still better captured by GA7 (Fig. 1b-e). Particularly, GA6 overestimated the positive correlation over Australia and the overestimation is reduced in GA7 (Fig. 1b-e).
Overall, the rainfall correlation between GA7 and observations over the Australian-Asian domain (50°S-60°N, 30°-180°E) is still low at 0.31, but is better than GA6, where the correlation with observations is 0.251. In addition, the rainfall teleconnections in the NH are better simulated than that in the SH for both GA6 and GA7. Moreover, we still have to point out that the rainfall correlations with the ISMRI over ISM and northwest of ISM regions are poor simulated in both GA6 and GA7 which need further investigation.
We further evaluate the ISMR intensity to help understand the fidelity of rainfall teleconnections simulated in GA6 and GA7. Figure 2 shows the spatial distribution of precipitation during years of strong and weak ISMR in observations, GA7, and GA6. Rainfall deficits over the Indian subcontinent during years of strong ISMR are reduced markedly in GA7 simulations. This is accompanied by a much smaller rainfall overestimation in the tropical Indian Ocean in GA7 compared with GA6. Such results are consistent with the findings from Bush et al. (2015) and Willetts et al. (2017), which suggested that excessive rain over the equatorial Indian Ocean warm waters might have contributed to the lack of Indian monsoon rainfall. Our analysis further shows that this may be particularly true in strong monsoon years (Fig. 2h). Similarly, the opposite situation occurred over East Asia and the nearby Philippines Sea. The rainfall is overestimated over the nearby Philippian Sea and underestimated over East Asia in GA7, but is better simulated in GA6 The solid black lines represent the pathways of the rainfall teleconnection particularly during the years of strong ISMR (Fig. 2h). Thus, poor rainfall simulation in GA7 over East Asian monsoon region is also a concern for model improvement.
Overall, the rainfall pattern correlations between GA7 (GA6) and observations during years of strong and weak ISMR are 0.875 (0.811) and 0.800 (0.748) over the Fig. 2 Composites of strong/weak summer monsoon rainfall (JJA) for the period 1982-2008 (unit: mm day −1 ). a, b GPCP observations; c, d GA6; e, f GA7; and g, h difference between GA7 and GA6. The black box represents the Indian summer monsoon domain. Cross hatched areas denote significance at the 90% confidence level. Strong (weak) monsoon years are determined based on when the ISMRI (normalized area-averaged summer rainfall anomalies over 70°-90°E, 5°-25°N) is above (below) 0.75 (− 0.75) lower latitude of Australian-Asian domain (30°S-40°N, 30°-180°E). Thus, the rainfall simulation is improved in GA7 compared with GA6. Furthermore, the differences between GA7 and GA6 over the Indian monsoon domain in years of strong ISMR are much more significant than in years of weak ISMR (Fig. 2g, h). These improved rainfall simulations in GA7 during strong ISMR years may help to better understand the link between the improved ISMR and the more realistically simulated rainfall teleconnections in GA7.

Circulation anomalies
In order to further study the influence of the improvement of ISMR in GA7 on the extratropic rainfall teleconnections, circulation anomalies affecting precipitation associated with ISMR are investigated in this section. Circulation anomalies associated with the ISMR are analyzed using regression and partial regression of stream function at 250 hPa onto the ISMRI (Fig. 3). As shown in Fig. 3a, b, two distinct wave trains originated from the ISM region propagating northward and southward into the NH and SH subtropics over Australia-Asia monsoon region are observed in observations. Notably, the circulation anomalies become weaker after removing the signals (Fig. 3d), suggesting the dependent influences of ENSO, IOD and ISMR on the circulation teleconnection.
In the NH, originated from the ISM region, the wave train in observations first propagates northwestward to Central Asia, creating a region of abnormally anti-cyclonic circulation, and then eastward to Mongolia and northern China, creating a region of abnormally cyclonic circulation, and finally eastward to the northeast China and Korean Peninsula, creating a region of abnormally anti-cyclonic circulation (Fig. 3a, b), which is similar to previous results (Wu 2002(Wu , 2017Kim et al. 2002). In the SH, the wave train first propagates southward across Indian Ocean creating a region of abnormally anticyclonic circulation over the Mascarene High, then southward and northeastward creating cyclonic circulations over mid-latitude Indian Ocean and southwestern Australia (Fig. 3a, b). This is consistent with Fig. 3 Map of regression of stream function (zonal mean subtracted) (shading; units: m 2 s −1 ) at 250 hPa onto ISMRI a ERA-Interim; c GA7; e GA6. b, d, f Same as a, c, e, respectively, but for partial regression excluding the signals of both ENSO and IOD. The black box denotes the Indian summer monsoon domain (70°-90°E, 5°-25°N). The solid black lines represent the pathways of the circulation teleconnection. Dotted areas denote significance at the 90% confidence level the investigation by Zhao et al. (2019), who noted that an equivalent barotropic wave train originating from the North Indian Ocean propagates southward to extratropic Indian Ocean and Australia. This circulation teleconnection pattern over Australia-Asia monsoon region is observed in GA7, whereas the anomalous anti-cyclonic circulations over Central Asia and subtropical Indian Ocean are not captured by GA6. Furthermore, the abnormally cyclonic circulation over midlatitude Indian Ocean is underestimated in GA6. To characterize the vertical structure along the wave trains, we further present the partial regression of vertical section of geopotential height anomalies onto ISMR excluding the effect of ENSO and IOD (Fig. 4). As shown in Fig. 4, the wave trains over extratropic are barotropic, and the geopotential height anomalies generally reach the maximum at 400-100 hPa in observations and GA7, indicating that the wave propagation is more significant at upper troposphere. Compared with GA7, both the pathways and vertical structures of the wave trains are not captured by GA6.
Vertical velocity and geopotential height anomalies at 500 hPa are partial regressed onto the ISMRI removing the signals of ENSO and IOD to further examine the connection between anomalous circulation and rainfall (Fig. 5). As shown in Fig. 5, regional ascending and subsidence anomalies are closely corresponded to the rainfall increase and decrease anomalies in observations and models. In particular, the anomalous subsidence motions over Central Asia and Japanese islands which are not conducive to the formation of precipitation are better simulated in GA7 than that in GA6 (Fig. 5b, c). The subsidence anomaly over equatorial Indian Ocean and ascending anomaly over central Australia are overestimated in GA6 but significantly improved in GA7 (Fig. 5b, c). In addition, the vertical motion is opposite in the south and north ISM region, which is not well simulated in both GA6 and GA7 (Fig. 5b, c). Particularly, in the regions downstream of the troughs (cyclones) and upstream of the ridges (anti-cyclones) ascending anomalies are observed, while in the regions downstream of the ridges (anti-cyclones) and upstream of the troughs (cyclones) subsidence anomalies are observed in observations indicating that the ISMR related circulation anomalies have an influence on the vertical motions and then modulate the rainfall. (Fig. 5). Compared with GA6, the anomalous vertical motions and their correspondences with the circulations in position are better captured in GA7, which helps the better simulated rainfall teleconnections in GA7 than in GA6.
Considering the importance of moisture transport to the formation of precipitation, moisture transport at 850 hPa  Fig. 3 is also examined to gain further insight into the moisture source associated with the ISMR. Figure 6 shows the partial correlation between moist flux transports at 850 hPa and ISMR in observations and GA7, GA6 excluding the effects of ENSO and IOD. The anomalous moisture transports in observations are close to the circulation anomalies in Fig. 3 indicating the important role of advection in the moisture transports associated with ISMR. As shown in Fig. 6, the northward anomalous moisture flux transports over East Asia and anti-cyclonic moisture flux transports over subtropical Indian Ocean are better simulated in GA7 contributing to the precipitation increase over northern China and southwest Australia, respectively. Particularly, the moisture transports are underestimated over subtropical Indian Ocean and overestimated over central Australia in GA6 which is corresponded to the rainfall anomalies (Fig. 6c). Overall, the influences of ISMR-teleconnection on the vertical motions  and moisture transports lead to the formation of rainfall teleconnection. Therefore, the better simulated ISMR-teleconnection helps to improve the presentation of extratropical rainfall in the models. However, the physical mechanism behind the connection between the better simulated ISMR and the extratropic circulation and rainfall in GA7 compared with GA6 is not clear yet which will be assessed in the next section.

Rossby wave ray tracing and the role of the meridional basic flow
As mentioned above, classical Rossby wave theory cannot explain the cross-equatorial teleconnection, as the stationary Rossby wave propagation in the tropical easterly wind is impeded. Thus, in this section, Rossby wave ray tracing in a horizontally non-uniform flow is adopted to investigate the link between the improved ISMR and the associated rainfall teleconnections. Technical details about the wave ray tracing analysis can be found in Zhao et al. (2015Zhao et al. ( , 2019. Before describing the wave ray, the background flow is analyzed. Figure 7 shows the composite difference in full regressed and partial regressed wind anomalies at 250 hPa between strong and weak ISMR years. The partial regressed anomalous winds are similar to that full regressed, but with changes in the magnitude of wind anomalies in observations and models suggesting the dependent influences of ENSO, IOD and ISMR on the upper tropospheric wind and therefore the wave propagation. Particularly, we care more about the basic flow and wave rays with the isolated influence of ISMR. As shown in Fig. 7, the anti-cyclonic circulations over Central Asia and East Asia and a cyclonic circulation over subtropical Indian Ocean in observations and GA7 are in good agreement with the results of Wang et al. (2001, cf. their Fig. 8) and the anomalous circulation pattern mentioned above (Fig. 3e, f). The background flow used to calculate the stationary wave ray trajectories is the superposition of the composite of partial regressed anomalous wind and the climatology wind. Figure 8 illustrates the stationary wave ray trajectories of zonal wavenumbers 2-5 emanating from ISMR sources in observations, GA7, and GA6. The wave rays in observations first propagate westward to tropical Africa, then divide to propagate to the NH and SH subtropics (Fig. 8a) which corresponds to the circulation teleconnections in both the NH and SH observed in Fig. 3b. Evidently, the southern branch of the wave rays in years of strong ISMR is more evident than that in years of weak ISMR (Fig. 8b, c), indicating the likely diabatic heating influence of ISMR on the cross equatorial Rossby wave propagation. In the SH, the wave ray over subtropical westerly across Australia is intensive and gathering in observations during years of strong ISMR (Fig. 8b) which is better captured in GA7 (Fig. 8e) than that in GA6 (Fig. 8h). Furthermore, the wave rays in the SH subtropics are much more than those in the NH in observations (Fig. 8a-c), leading to stronger wave trains in the SH (Fig. 3a, b). This is better captured by GA7 during years of strong ISMR (Fig. 8e), so does the better presented circulation wave trains in the SH in GA7 than in GA6 (Fig. 3d,  f). On the other hand, both GA6 and GA7 simulate weaker wave propagation in the SH than that observed in years of weak ISMR (Fig. 8f, i), although in GA7, the propagation towards tropical Africa is somewhat closer to observations (Fig. 8f). The situation is similar for the northern branch of wave rays. The northern wave-ray characteristics simulated in GA7 in years of strong ISMR are much closer to observations than in GA6, with wave rays occurring in the subtropical westerlies over Asia (Fig. 8b, e), leading to more realistic circulation wave train in the NH in GA7 compared with GA6 (Fig. 3d, f). However, during years of weak ISMR, the northern branch of the wave rays in both GA7 and GA6 are poorly simulated (Fig. 8f, i), with wave rays being much stronger and further poleward than in observations. Both GA6 and GA7 perform poorly in reproducing the observed characteristics of wave rays in weak ISMR years, during which both model configurations showed a significant dry bias over the Indian monsoon domain in JJA (Fig. 2). Nevertheless, it is not clear whether we can directly associate the poor simulation of wave rays with the underestimation of ISMR. This is because during weak ISMR years, one would expect weak diabatic heating over the Indian monsoon region. However, without considering the diabatic influence of deep monsoon convection on the mean flow, the increase of isolated equatorially asymmetric heating only strengthens the atmospheric response, but not vary the atmospheric patterns (Xing et al. 2014). We need to investigate further to what extent the model's failure to reproduce wave propagation in weak monsoon years is because of the poor simulation of the atmospheric mean flow in the region, or because of the significant lack of rainfall during those years.

Meridional wind ducts in the upper troposphere
According to the studies by Zhao et al. (2015Zhao et al. ( , 2019 and Li et al. (2015), the meridional basic flow plays an important role in facilitating the propagation of stationary Rossby wave. Furthermore, the interhemispheric propagation of Rossby waves is dominated largely by the meridional flow (Lee et al. 2013;Liu and Wang 2013;Li et al. 2015;Zhao et al. 2015Zhao et al. , 2019. Figure 9 shows the 250 hPa horizontal winds from ERA-interim, GA7, and GA6 in JJA. As shown in Fig. 9a, strong easterly winds prevail at upper levels over the tropical Australian-Asian and African monsoon regions. In tropical North Africa, southerly winds prevail between 10°N and 30°N, whilst northerly winds prevail below 10°N, causing the Rossby wave to first propagate westward and then divide northward and southward over tropical North Africa and beyond. Similarly, the northerly winds over the Indian subcontinent and tropical Indian Ocean also lead the Rossby wave to propagate southward into the SH. The southerly winds prevailing over the western Tibetan Plateau drive the Rossby wave northward into the Asian subtropical westerlies. The poor simulated meridional propagation of Rossby wave is closely related to the modelling errors of the b, d, f Same as a, c, e, respectively, but for partial regression exclud-ing the liner influence of ENSO and IOD. Shaded areas denote significance at the 90% confidence level meridional wind. The significantly weak simulated northerly winds over the upper tropospheric South Asian monsoon domain in GA6 (Fig. 9e, f) are not favorable to the crossequatorial propagation of Rossby wave. Furthermore, the strength of the simulated meridional winds in Asia in GA6 are stronger than that shown in observations (Fig. 9e, f), especially for the southerly winds over the western Tibetan Plateau. This contributes to the stronger and further poleward propagation of Rossby wave in GA6 (Fig. 8g-i). In contrast, the upper tropospheric meridional winds over the western Tibetan Plateau and south Asian monsoon are more realistically simulated in GA7 (Fig. 9d), especially in years of strong ISMR (Fig. 9h). Therefore, analyzing to what extend the simulation of ISMR influence the meridional wind will help to understand the contribution of improvement of ISMR to the Rossby wave propagation. Furthermore, as the circulation over South Asia is dominated by SAH, the simulation of SAH may also play an important role in the Rossby wave propagation originated from ISM region. Moreover, SAH has an influence on the extratropical circulations (Jiang et al. 2011;Wei et al. 2015;Ning et al. 2017). Thus, the influence of SAH on the meridional wind will also be considered.
The strength of SAH is defined as the standardized areaaveraged geopotential height within the isoline of 12,500 gpm at 200 hPa ( Fig. 10g-i). To measure the liner contributions of ISMR and SAH to the meridional wind, the multiple liner regression used to model the liner relationship between explanatory variables and a response variable is obtained: in which a and b represent contributions of a unit of ISMR and SAH variation to V , respectively, c represents the climatology of V. In order to consider the separate effects of SAH and ISMR on the meridional wind, the linear effect of SAH on ISMR are excluded through partial regression. Figure 10 shows the climatological SAH and the multiple regression of meridional wind on the ISMRI and SAHI. As shown in Fig. 10, the meridional winds over South Asian monsoon region in GA6 and GA7 is closely related to ISMR. With the increase of ISMR, stronger convective activity enhances the Indian monsoon circulation, the upper northerly wind over South Asian monsoon region enhances (Fig. 9h), making stronger cross equatorial Rossby wave (Fig. 8e). Furthermore, the relationship between anomalous northerly wind over western Tibetan Plateau and ISMR is better simulated in GA7 than that in GA6 (Fig. 10b, c). Moreover, the contribution of SAH to the upper meridional wind over South Asian monsoon region in GA7 are better simulated than Difference between GA7 and GA6 of composite meridional winds from years of g weak and h strong ISMR. Dotted areas represent significance at the 90% confidence level that in GA6 (Fig. 10e, f). Therefore, both the enhancements of ISMR and SAH during years of strong ISMR in GA7 contribute to the more realistic meridional wind over south Asian monsoon and western Tibetan Plateau, and hence make more realistic propagation of Rossby wave.
What's more, the simulation of SAH in GA7 is improved significantly compared with that in GA6. Due to the dynamic relationship between wind and pressure, the simulation of wind improves with the improvement of pressure. Particularly, at midlatitudes, the pressure dominates the wind according to the geostrophic relationship. As a result, the improvement of SAH in GA7 leads to more realistic climatic mean flow over South Asia than that in GA6 (Fig. 10g-i). In particular, the much stronger southerly wind over western Tibetan Plateau and south Asian monsoon region in GA6 is mainly owning to the poor simulation of SAH (Fig. 10i). Furthermore, the improvement of ISMR intensity with more realistic convective heating in GA7 contributes to more realistic meridional wind over South Asian monsoon region. Nevertheless, it still has to point out that the inter-annual variability of ISMR in GA7 needs to be improved. The significant improvement of SAH in GA7 corresponds to the skillfully simulated ISMR, which may own to the deeper convection and more realistic diabetic heating are allowed in GA7 (Walters et al. 2019).

Summary and discussion
In this study, we have investigated the link between the improved simulation of ISMR and the associated extratropical rainfall teleconnections in two versions of the UKMO Unified Model, GA6 and GA7, using Rossby wave ray tracing theory (Li and Li 2012;Li et al. 2015;Zhao et al. 2015Zhao et al. , 2019Li et al. 2019a, b). In a previous UM assessment study  reported that the reduced Indian monsoon dry bias in UM GA7 at N216 resolution led to more realistic monsoon rainfall teleconnection patterns. However, they did not conduct detailed wave propagation analysis to support these results. Therefore, our study focused on investigating Rossby wave propagation in these two model configurations by using Rossby wave ray tracing in a horizontally nonuniform background flow, as in Zhao et al. (2015Zhao et al. ( , 2019.
Our observational analysis showed that the diabatic heating associated with ISMR can excite two distinct wave trains in the NH and SH subtropics. GA7 can better simulate the teleconnections associated with the ISMR over Australia-Asia monsoon region compared with GA6. The realistic simulated atmospheric teleconnection in GA7 plays an important role in the improvement of rainfall teleconnection by modulating the vertical motion and the moisture transport.
The teleconnection wave train coincides with the pathway of the stationary Rossby wave propagation. Driven by the upper tropospheric easterly flow, the stationary Rossby wave first propagate westward, then separate into northern and southern branches following the meridional wind ducts. The northern branch mainly propagates in the subtropical westerlies over Asia and the southern branch primarily propagates in the SH subtropical westerlies across Australia. Compared with GA6, GA7 can better capture the characteristics of Rossby wave propagation pathways in years of strong ISMR, with stronger cross-equatorial propagation and a more realistic northern branch of the wave ray tracing trajectories. This was attributed largely to the model skillfully simulating of ISMR and SAH, and their influences on the meridional basic flow over upper South Asia monsoon and western Tibetan Plateau.
Our study may also provide new insights for monsoon teleconnection evaluations by revealing the Rossby wave propagation pathway from the upper tropospheric easterlies. The upper tropospheric meridional winds associated with the monsoon system play an important role in Rossby wave propagation and hence improve the simulation of tropical monsoon teleconnections. Sakaguchi et al. (2016) detected changes in Rossby wave ray trajectories influenced by Asian monsoon rainfall and the associated basic flow using different grid refinements in the Community Atmosphere Model version 4. The teleconnection pathways revealed by Rossby wave ray trajectories provide implications for evaluating and improving the model's performance of simulating tropical monsoon teleconnections.
It is also worth noting that significant deficiencies in the modelling of ISMR remain, despite the reduced dry bias in GA7. In particular, the northerly wind ducts over the upper tropospheric South Asian monsoon region in GA7 are poorly simulated. Walters et al. (2019) indicated that the southern branch of the Hadley circulation during JJA in GA7 using an N216 grid was improved significantly compared with GA6 at the same resolution, due to the deeper convection in GA7. Thus, the simulation of convection is important to improve the simulation of circulation and tropical monsoon teleconnections.
We acknowledge that the datasets used in the current analysis come from the atmosphere-only configuration of the UM. It is important to conduct a similar analysis with globally coupled simulations (Williams et al. 2017) to better understand the rainfall teleconnections that could be modulated by air-sea interactions. This will also help us to assess whether current model deficiencies in simulating the Australian-Asian monsoon system can affect the climate and climate change outside the monsoon domain simulated by current CMIP models.