1. Introduction
South Asia has a monsoonal climate. It receives 50%–70% of its annual precipitation during the months of June, July, and August (Neelin 2007). During these months, moist static energy is abundant, fueling monsoon low pressure systems (MLPSs) that originate in the Bay of Bengal and propagate westward against the direction of the prevailing mean low-level winds, across India at speeds of around 4 m s−1 (Adames and Ming 2018a). Studies in recent years have attributed between 50% and 60% of monsoon season rainfall in central India to these lows (Hurley and Boos 2015; Praveen et al. 2015; Hunt and Fletcher 2019). For that reason, understanding what influences the propagation and structure of these transient phenomena is important for understanding what controls precipitation during the summer in South Asia.
The growth, propagation, and structure of these low pressure systems has been an area of research for several decades, dating back to Godbole (1977) and references therein. In recent years effort has been made by multiple independent research groups to compile detailed track information for monsoonal disturbances (Hurley and Boos 2015; Hunt et al. 2016a). This effort has led to new insights resulting from rigorous analysis of the composite properties of these storms (Hurley and Boos 2015; Boos et al. 2015; Ditchek et al. 2016; Hunt et al. 2016a,b; Cohen and Boos 2016; Sandeep et al. 2018). In particular, early theoretical attempts to explain the growth and propagation of monsoon depressions in terms of barotropic (Shukla 1977; Lindzen et al. 1983), baroclinic (Mishra and Salvekar 1980; Mak 1983; Moorthi and Arakawa 1985), or combined barotropic and baroclinic (Krishnamurti et al. 1976; Shukla 1978) instability mechanisms have recently been challenged by a number of alternative ideas.
An example where these early ideas were challenged is the study by Cohen and Boos (2016). They investigated composites of observed monsoon depressions in reanalysis and compared them with the canonical example of moist baroclinic instability: diabatic Rossby waves in the midlatitudes. They found that in monsoon depressions, anomalies in Ertel potential vorticity do not tilt against the mean vertical wind shear as they do in diabatic Rossby waves, which they argue is evidence against moist baroclinic instability operating as a mechanism in fueling the growth of the disturbances. In their paper Cohen and Boos (2016) also invoke results from Krishnamurti et al. (2013) to argue that barotropic instability plays a minor, if any, role in the development of MLPSs. In Krishnamurti et al. (2013) it was found that kinetic energy from the eddies in observed MLPSs was transferred to the mean zonal flow, counter to what occurs in barotropically unstable flows.
In the last five years, four (possibly overlapping) alternative explanations for monsoonal disturbance propagation have been proposed. The first is that monsoon depressions might be better described as tropical cyclone–like features propagating via adiabatic beta drift (Boos et al. 2015), although perhaps without as strong a dependence on surface fluxes, which have been shown to be important for tropical cyclones (Muller and Romps 2018). Another possible explanation, proposed in Hunt and Parker (2016), is that the Himalayan mountains may act as a rigid northern meridional boundary in the lower troposphere, leading to westward propagation of a cyclonic vortex to the south via an effective mirror-image vortex. Adames and Ming (2018b) develop a linear theory for monsoonal disturbances within a midlatitude moisture-mode like framework, where the instability depends necessarily on the inclusion of a prognostic moisture equation. Finally, Diaz and Boos (2019) revisit the potential influence of barotropic instability, and find that in the absence of convective heating, growing disturbances fueled by barotropic instability could be possible with a zonally uniform basic state; however, these disturbances did not grow at rates consistent with observed storms, motivating future study in a moist framework. These theories are still young, and their utility for explaining the properties of monsoonal disturbances and their potential sensitivity to changes in the mean state (e.g., induced by increasing greenhouse gas concentrations) has yet to be extensively investigated.
The complications of the real world, however, make monsoonal disturbances difficult to study. For instance many comprehensive general circulation models used in phase 5 of the Coupled Model Intercomparison Project (CMIP5) (Taylor et al. 2012) struggle to obtain a realistic distribution of climatological mean June, July, August, and September (JJAS) precipitation rate in the South Asian monsoon region [see the supplement of Sandeep et al. (2018)]. In addition, several models run under the Atmospheric Model Intercomparison Project (AMIP) protocol (Gates 1992) simulate unrealistic patterns of the synoptic activity index (SAI) [again, see the supplement of Sandeep et al. (2018)], a metric that quantifies an intensity-weighted frequency of MLPS days per season at each location (Ajayamohan et al. 2010). To some extent these errors are attributed to the coarse horizontal resolution of these models; indeed studies have shown that models run with higher resolution such as the Met Office Unified Model or the Geophysical Fluid Dynamics Laboratory (GFDL) HiRAM demonstrate increased skill in simulating MLPSs (Hunt and Turner 2017; Sandeep et al. 2018).
Despite sometimes having errors in the exact location of storms, however, some coarse-resolution general circulation models (GCMs) (such as GFDL’s AM4) have been shown to have the ability to reasonably simulate their general frequency statistics and structure (Adames and Ming 2018a), indicating that exact realism of precipitation location and mean winds is not necessarily required for studying the structure and propagation of these dynamical phenomena. It prompts the question of whether a simpler model, lower in the complexity hierarchy, could capture the essence of MLPSs. By a simpler model, we mean one somewhere in between an idealized aquaplanet GCM [as in Frierson et al. (2006)] and a comprehensive GCM (complete with intricate parameterizations of convection, clouds, radiation, land, chemistry, etc.). Xie and Saiki (1999), for instance, found abundant westward-propagating cyclonic vorticity anomalies, akin to MLPSs, in a simulation using a very coarse horizontal resolution GCM (T21 spectral truncation) and heavily simplified lower boundary conditions. It is worth revisiting these disturbances in a similar setup in light of recent developments (e.g., Boos et al. 2015; Cohen and Boos 2016; Hunt and Parker 2016; Adames and Ming 2018a,b; Diaz and Boos 2019).
In this study we start from a version of Frierson et al.’s (2006) idealized moist model coupled to a full radiative transfer code (Clark et al. 2018), and build up in complexity to attain an environment capable of supporting MLPS-like disturbances. We use this setup, coupled with detailed analysis of the composite anomalous budgets of Ertel potential vorticity, relative vorticity, column internal energy, and column moisture, to discuss the potential applicability of the theories for MLPS propagation described above, and touch on the importance of various boundary conditions, like topography, in the realism of the disturbances simulated.
2. Methods
a. Model description
The modeling setup we use to simulate MLPSs is heavily idealized. Our starting point is the GFDL idealized moist model as configured in Clark et al. (2018). This global model was first introduced in Frierson et al. (2006, 2007), where it consisted of a spectral dynamical core, with simplified moist physics, boundary layer, and radiation parameterizations. It has since been modified to include a simplified Betts–Miller moist convection scheme (Frierson 2007b),1 alterations to the boundary layer scheme (O’Gorman and Schneider 2008), and an option to run with full radiative transfer, rather than the original gray radiative transfer scheme (Clark et al. 2018). While the full radiative transfer scheme interacts with the active water vapor tracer in the model, there is no parameterization of cloud condensate, and therefore no cloud radiative effects or feedbacks. Slab ocean aquaplanet configurations similar to this (i.e., full radiative transfer with simplified moist physics) have been used before, such as in Merlis et al. (2013a,b), Jucker and Gerber (2017), and Vallis et al. (2018).
In this study, we examine MLPSs in the South Asia region. Due to the annual cycle in solar insolation, these primarily occur in the boreal summer months of June, July, August, and September, but can also occur during other parts of the year (Hurley and Boos 2015). To capture this seasonal variation in climate, we run all of our simulations with Earth’s current approximate obliquity and eccentricity parameters, 23.439° and 0.01671, respectively. In addition we introduce a crude parameterization of land. In prior studies, land has been added to variants of this model with varying degrees of complexity depending on the application, typically involving modification of some combination of the heat capacity, evaporation parameterization, surface roughness, surface albedo, and surface height over the land portion of the domain (e.g., Byrne and O’Gorman 2013; Merlis et al. 2013b; Maroon et al. 2016; Maroon and Frierson 2016; Voigt et al. 2016; Geen et al. 2018; Vallis et al. 2018; Zhou and Xie 2018). In other models, simplified land has been added in similar ways (e.g., Xie and Saiki 1999; Becker and Stevens 2014; Cronin et al. 2015). As a starting point in our model we choose to distinguish land from the default lower boundary, a slab ocean, in only two ways: its heat capacity and its treatment of evaporation.
The land setup maintains the slab ocean model across the entire lower boundary; however, over land grid cells we use a shallower mixed layer depth, which controls the heat capacity, and scale the potential evaporation rate as predicted by the bulk formula over a saturated surface by a fraction determined using a simple bucket hydrology model, the same as described in Vallis et al. (2018), which is similar to that in Byrne and O’Gorman (2013) or Zhou and Xie (2018), which dates back to Manabe (1969). The mixed layer depths over land and ocean are the same as those used in experiments in Geen et al. (2018), 2 m over land and 20 m over ocean, and the bucket hydrology model parameters are the same as those described in Vallis et al. (2018), a bucket depth of 150 mm and a bucket saturation fraction of 0.75. We use a surface albedo of 0.26 over land and ocean. The global mean surface albedo is greater than it might be in a comprehensive GCM as to increase the planetary albedo in the absence of clouds (Frierson et al. 2006). Finally, we prescribe zero heat flux from the ocean to the atmosphere, meaning, as a simplification, that we assume the ocean does not facilitate any horizontal energy transport. We assume the same for land regions.
In principle one could tune the mixed layer depths, surface albedo, bucket hydrology scheme parameters, and prescribed ocean heat fluxes [e.g., following the procedure outlined in Vallis et al. (2018)] to produce a mean state climate as close as possible to that in observations. However, to maintain a connection to simpler configurations we elect to use the setup described above, which produces a mean state climate that resembles that in observations, but is not an exact match (e.g., it does not contain a significant western Pacific warm pool signature, or east–west asymmetry in ocean basin SST due to warm western boundary currents). For a comparison of the mean state in our simulation to that in observations, see Fig. S1 in the online supplemental material, which compares the global pattern in JJAS mean precipitation rate and surface temperature in our idealized simulation to that in Tropical Rainfall Measuring Mission (TRMM) observations (Huffman et al. 2007) and ERA-Interim reanalysis (Dee et al. 2011).
With regard to atmospheric composition, we use approximately present-day concentrations of the well-mixed greenhouse gases (CO2 = 369.4 ppm, CH4 = 1.821 ppm), and prescribe a hemispherically symmetric pattern of ozone, based on the pattern used in the Aqua-Planet Model Intercomparison Project (Blackburn et al. 2013).
Similar to Geen et al. (2018), to improve the numerical stability of the dynamical core in the upper levels of the model, we add a Rayleigh damping tendency to the horizontal winds. The Rayleigh damping coefficient we use decreases faster than linearly from a value near 0.33 day−1 at the top of the model to near zero near the surface, following the vertical profile defined in Eqs. (13.89) and (13.90) in Jablonowski and Williamson (2011), which were first used in Boville (1986). This Rayleigh damping profile was used for several years in the European Centre for Medium-Range Weather Forecasts (ECMWF) Integrated Forecast System (IFS) model (Jablonowski and Williamson 2011).
b. Experiments
In this study we focus on a simulation with “land” as described in section 2a, with realistic continental geometry, but flat topography. We run the model for 20 years, starting from spatially uniform initial conditions (constant initial temperature and specific humidity), storing 6-hourly mean values of the relevant diagnostics. After the first 10 years, the model approximately reaches equilibrium, here defined as the moment at which the annual global mean net top of atmosphere radiative flux begins to hold steady at near zero. Accordingly, we use the final 10 years of each simulation for analysis. The model is configured with 40 unevenly spaced vertical sigma levels, with approximately three levels within the planetary boundary layer, and extends to the top of the atmosphere, with a top-level interface pressure of 0 hPa. In the horizontal, we run the model at T42 spectral resolution, which corresponds to approximately 2.8° × 2.8° horizontal resolution in grid space.
As part of this study, we ran two other simulations flanking the simulation described above in terms of the complexity of the lower boundary, although we do not show their results. On the simpler side, we ran an aquaplanet case with a uniform slab ocean mixed layer depth of 20 m, while on the more complex side, we ran a case with land and realistic topography, spectrally regularized as in Lindberg and Broccoli (1996). The aquaplanet case produced an annual cycle in precipitation significantly lagged from that on Earth’s, with monthly mean precipitation rates maximizing during September and October at the latitudes of the South Asian monsoon region. It also lacked a realistic poleward increasing meridional temperature gradient and attendant easterly vertical wind shear.2 On the other hand, the case with realistic topography produced MLPSs, but despite regularization, suffered from severe spectral ringing in the mean precipitation field near the Himalayas, compromising the quality of the climate relative to the flat topography case. Therefore the configuration with land and flat topography happened to be the best configuration of this model we tested for studying South Asian MLPSs. It is possible that one could obtain MLPS-like disturbances in a simulation with further idealized continental geometry and surface hydrology. However, we leave such experimentation to future work and choose to focus on our realistic continental geometry, flat topography simulation, which provides an important link between MLPSs in comprehensive GCMs and those in more idealized frameworks.
c. Analysis techniques
To analyze the structure of MLPSs in our model, we employ frequency–wavenumber spectral analysis and compute lag regression patterns and tracer budgets. Frequency–wavenumber spectral analysis allows us to identify the frequencies and wavenumbers of the zonally propagating waves that are most prevalent; this type of analysis is commonly used in studying equatorial waves (e.g., Wheeler and Kiladis 1999; Hendon and Wheeler 2008), although here we apply the technique in the latitudes of the South Asian monsoon region. Lag regression patterns allow us to determine the spatial structure of variable anomalies projected onto a MLPS index. Tracer budget analysis allows us to determine the leading terms governing the evolution of MLPSs in our model. We approximately follow the methods described in Adames and Ming (2018a). Here we will explain the details of these techniques, which we will employ later.
1) Spectral analysis
To compute frequency–wavenumber power spectra, we start with 6-hourly resolution model output of the precipitation rate. We then subset this dataset in time such that it only includes data points for the months of June, July, August, and September. From this time series, we construct a set of 60-day segments, which overlap by 30 days, generating a four-dimensional dataset, with dimensions of time, longitude, segment, and latitude; it follows that the segment dimension has length 242. We apply a Hanning window over the time dimension, tapering the endpoints of the segments toward zero to minimize spectral leakage (Welch 1967); in addition, we apply a Hanning window over 50°–130°E to taper data to zero outside our longitudinal region of interest. After this preparation, we compute a fast Fourier transform (FFT) in longitude and time, and compute the power as the square of the magnitude of the complex Fourier coefficients. To construct a two-dimensional frequency–wavenumber diagram, we average the power over the segments and between latitudes bounding the region of interest for the particular dataset, which correspond roughly to the latitudinal bounds of the South Asian monsoon region, and then compare it to a reference red frequency spectrum. We define the region of interest for a particular dataset as ±5° from the latitude of maximum mean JJAS precipitation rate3 along the 80°E longitude band. We compute the red spectrum as in Masunaga et al. (2006), normalizing such that the sum of the power in nonzero frequencies matches that in the power spectrum of the precipitation rate.
2) Lag regression analysis
To compute lag regression patterns we follow the methods of Adames and Wallace (2014) and Adames and Ming (2018a). This requires computing an index, which measures the intensity of MLPS activity. Adames and Ming (2018a) do this by spectrally filtering the precipitation rate to include wave activity from only MLPS-like modes (zonal wavenumbers, k, between −25 and −3 and frequencies greater than 0.067 day−1), then averaging over the spatial region of interest, here defined as ±5° latitude from the latitude of maximum JJAS mean precipitation rate, between 75° and 85°E in longitude; this results in a one-dimensional index over time, which is then standardized such that it has a mean of zero and a standard deviation of one, yielding a vector PT. Here k is the nondimensional zonal wavenumber, which can be related to a dimensional zonal wavenumber
To smooth out regression patterns, particularly in the context of the tracer budgets, we apply a regression-compositing technique similar to the one employed in Adames and Ming (2018a). This entails computing regression patterns for index regions shifted −2, −1, 0, 1, or 2 grid cells away in longitude and/or latitude from the original center of the region of interest described above, and then shifting the regression patterns back to all be centered at the same location and averaging. This results in computing and taking the mean of 25 regression patterns, producing a smoother picture.
3) Tracer budget analysis
We compute budget terms for four equations in this study: Ertel potential vorticity (EPV), relative vorticity, column-integrated internal energy, and column-integrated moisture, the equations for which are given and discussed in section 3. Anomalous terms for each budget are computed by regressing each time series against the precipitation index defined above. In the case of EPV and relative vorticity, with four-dimensional fields, the time series of each term is computed explicitly; where needed, second-order finite differences are used to estimate partial derivatives in the interior, and first-order finite differences are used to estimate partial derivatives on the boundaries. For computing horizontal derivatives on the sphere, we follow the methods of Seager and Henderson (2013). For EPV and relative vorticity, the residuals from computing the terms explicitly are small.
For the column-integrated fields of the internal energy and moisture budgets, using a purely explicit procedure does not result in an adequately closed budget. In those cases, as an objective way of partitioning the residual, we follow the methods of Hill et al. (2017).4 This entails first computing an adjusted set of horizontal winds at each vertical level using the flux-form framing of the column-integrated budget to ensure things are balanced. We then use these adjusted winds to compute the horizontal advection terms in the advective form of the budget, and compute the column-integrated vertical advection term as a residual.
3. Results
a. Mean state climate
The observed JJAS mean state climate in the South Asian monsoon region has a number of distinctive attributes (Sikka 1977). We illustrate these attributes and their counterparts in the simulation in the two columns of Fig. 1. Given the heavily idealized nature of the simulation we do not expect an exact match to the real-world climate; however, we find in our simulation that several theoretically important broad-scale features are obtained.
(a),(b) JJAS-mean precipitation rate, (c),(d) JJAS-mean column-integrated water vapor, and (e),(f) JJAS-mean temperature at 600 hPa (colors). Vectors in (e) and (f) represent the direction and magnitude of the difference in horizontal wind between 200 and 850 hPa (i.e., upper-level winds minus lower-level winds). The columns represent data from observations, in this case TRMM (Huffman et al. 2007) and ERA-Interim reanalysis (Dee et al. 2011), and the simulation, respectively. Note the differences in the color bar scales for each column.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0289.1
(a),(b) JJAS-mean precipitation rate, (c),(d) JJAS-mean column-integrated water vapor, and (e),(f) JJAS-mean temperature at 600 hPa (colors). Vectors in (e) and (f) represent the direction and magnitude of the difference in horizontal wind between 200 and 850 hPa (i.e., upper-level winds minus lower-level winds). The columns represent data from observations, in this case TRMM (Huffman et al. 2007) and ERA-Interim reanalysis (Dee et al. 2011), and the simulation, respectively. Note the differences in the color bar scales for each column.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0289.1
(a),(b) JJAS-mean precipitation rate, (c),(d) JJAS-mean column-integrated water vapor, and (e),(f) JJAS-mean temperature at 600 hPa (colors). Vectors in (e) and (f) represent the direction and magnitude of the difference in horizontal wind between 200 and 850 hPa (i.e., upper-level winds minus lower-level winds). The columns represent data from observations, in this case TRMM (Huffman et al. 2007) and ERA-Interim reanalysis (Dee et al. 2011), and the simulation, respectively. Note the differences in the color bar scales for each column.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0289.1
We first look at the JJAS-mean precipitation rate (Figs. 1a,b). Figure 1a corresponds to the 2001–16 JJAS-mean precipitation rate computed using observations from the Tropical Rainfall Measuring Mission (TRMM) (Huffman et al. 2007) and Fig. 1b corresponds with JJAS-mean precipitation from our simulation. In observations, while the detailed structure is strongly influenced by small-scale features of the topography, the large-scale structure roughly corresponds in a local shift of the intertropical convergence zone (ITCZ) northward to around 20°N. This northward shift in the area of maximum time mean precipitation is roughly captured in the simulation, albeit to a lesser extent. Figure 1b shows that JJAS-mean precipitation maximizes at roughly 12.6°N in our simulation, with a secondary maximum located near the equator.5
Another notable feature of the observed climate is that column-integrated moisture increases steadily as one moves northward from the equator through the Bay of Bengal (Adames and Ming 2018a). This is illustrated by plotting 2001–16 JJAS-mean column-integrated water vapor from the ERA-Interim reanalysis dataset (Dee et al. 2011) in Fig. 1c. This strong gradient has been theorized to play a role in the dynamics of monsoon low pressure systems (Adames and Ming 2018b). Figure 1d shows the JJAS mean column-integrated moisture in our simulation. There we can see a band of high column-integrated water vapor roughly coincident with the band of high precipitation rate, running from the Arabian Sea, across India, and over the northern Bay of Bengal and Southeast Asia. Compared with reanalysis, where the water vapor maximum is located near the land–sea boundary between Bangladesh and the Bay of Bengal, the water vapor maximum in our simulation is displaced slightly southward. In addition, column-integrated moisture magnitudes are substantially smaller than those seen in reanalysis, with maximum values of around 20 mm in our idealized simulation and around 60 mm in reanalysis (Adames and Ming 2018a).
The third salient property of the mean state South Asian monsoon climate is a meridionally increasing surface temperature field, and attendant easterly vertical wind shear, with westerly winds near the surface and easterly winds aloft (Xie and Saiki 1999; Boos et al. 2015; Cohen and Boos 2016). This is illustrated using 2001–16 JJAS-mean 600-hPa temperature, and the difference between the 200- and 850-hPa winds from the ERA-Interim reanalysis dataset (Dee et al. 2011) in Fig. 1e. The meridionally increasing temperature gradient is induced by the difference in heat capacity between the land and ocean. Because the land heats up faster than the ocean, it experiences greater seasonal variation in surface temperatures than ocean at similar latitudes, which gets communicated to the free troposphere. Through thermal wind balance, this positive meridional temperature gradient is associated with easterly vertical wind shear (Vallis 2006). The crude setup in our simulation is able to capture this, as indicated by the poleward increasing 600-hPa temperature in Fig. 1f and quiver arrows pointing from the east to the west, indicative of easterly vertical wind shear, with strongest values of about 30 m s−1 at around 12.5°N. The magnitude of the shear decreases as one moves northward over the Asian continent, which is similar to what is seen in reanalysis (e.g., in Fig. 1e).
b. The general character of South Asian monsoon low pressure systems in the idealized simulation
1) Dominant zonal wavenumber and frequency of precipitating disturbances
Despite the simplicity of the setup of the idealized simulation, notably omitting the impacts of the prominent land surface topography of southern Asia, and the impacts of ocean heat transport, we seem to obtain an adequate South Asian JJAS mean state climate to support westward-propagating, precipitating disturbances. This can be made immediately apparent by looking at a time–longitude diagram of unfiltered precipitation during an example summer season averaged between 7.6° and 17.6°N, the colors in Fig. 2. To guide one’s eye, contour lines are added, which indicate the value of the precipitation rate filtered to include data only from MLPS-like modes (i.e., with zonal wavenumbers between −25 and −3 and frequencies greater than 0.067 day−1), using the method described in section 2c(2). In the particular season shown in Fig. 2, we find active westward-propagating MLPS-like activity during July, a break in August, and reinvigorated activity in September.
Time–longitude diagram of unfiltered (colors) and filtered (contours) precipitation rate over the South Asian monsoon region during JJAS of year 0016 in the idealized simulation. Solid contour lines represent filtered anomalous precipitation rates of 1.5 mm day−1 and dashed contour lines represent filtered anomalous precipitation rates of −1.5 mm day−1. Precipitation is filtered to isolate precipitation anomalies due to MLPS-like disturbances using the spectral filtering procedure described in section 2c(2).
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0289.1
Time–longitude diagram of unfiltered (colors) and filtered (contours) precipitation rate over the South Asian monsoon region during JJAS of year 0016 in the idealized simulation. Solid contour lines represent filtered anomalous precipitation rates of 1.5 mm day−1 and dashed contour lines represent filtered anomalous precipitation rates of −1.5 mm day−1. Precipitation is filtered to isolate precipitation anomalies due to MLPS-like disturbances using the spectral filtering procedure described in section 2c(2).
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0289.1
Time–longitude diagram of unfiltered (colors) and filtered (contours) precipitation rate over the South Asian monsoon region during JJAS of year 0016 in the idealized simulation. Solid contour lines represent filtered anomalous precipitation rates of 1.5 mm day−1 and dashed contour lines represent filtered anomalous precipitation rates of −1.5 mm day−1. Precipitation is filtered to isolate precipitation anomalies due to MLPS-like disturbances using the spectral filtering procedure described in section 2c(2).
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0289.1
Frequency–wavenumber spectrum of the JJAS precipitation rate in (a) TRMM (Huffman et al. 2007) observations and (b) the simulation. All values below the 99% threshold for statistical significance (0.33 for the observations, 0.38 for the simulation) are masked.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0289.1
Frequency–wavenumber spectrum of the JJAS precipitation rate in (a) TRMM (Huffman et al. 2007) observations and (b) the simulation. All values below the 99% threshold for statistical significance (0.33 for the observations, 0.38 for the simulation) are masked.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0289.1
Frequency–wavenumber spectrum of the JJAS precipitation rate in (a) TRMM (Huffman et al. 2007) observations and (b) the simulation. All values below the 99% threshold for statistical significance (0.33 for the observations, 0.38 for the simulation) are masked.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0289.1
2) Horizontal structure of precipitation, midlevel vertical velocity, and low-level wind anomalies
The structure of the westward-propagating disturbances can be elucidated using regression analysis as described in section 2c, following the methods of Adames and Ming (2018a). We will first consider the horizontal structure of the anomalous precipitation, midlevel (500 hPa) vertical velocity, low-level (850 hPa) wind fields on days preceding, during, and following a storm event centered at 80°E and the latitude of maximum mean JJAS precipitation along 80°E in the South Asian monsoon region. In the idealized simulation, as we look at the lag sequence descending from the top of Fig. 4, we can see clear evidence of a westward-propagating cyclonic disturbance crossing the Bay of Bengal and traversing India over a span of about four days. The disturbance is flanked by dry anticyclonic circulations. Vertical velocity anomalies slightly lead precipitation anomalies, similar to the disturbances analyzed in Adames and Ming (2018b). The maximum low-level wind speed anomaly associated with the regression in the idealized experiment at lag day zero is 2.2 m s−1. This value is weaker than the observed wind perturbation, which is greater than 8.5 m s−1 (Hurley and Boos 2015). This is due in part to the implicit compositing effect of the regression analysis. Individual storms of a similar strength to the observations do occur in the idealized simulation;7 however, a more careful analysis involving tracking individual storms would be required to comprehensively compare the intensity distribution of the storms in our idealized simulation to that in observations.
Precipitation rate (colors), pressure velocity at 500 (contour lines), and 850-hPa horizontal winds (arrows) lag-regressed onto the precipitation index defined in section 2c for the idealized simulation. Only precipitation anomalies statistically significant at the 99% level are plotted. Contour levels for the vertical velocity anomalies begin at −0.0375 Pa s−1 and are evenly spaced by 0.015 Pa s−1; negative contours are dashed, while positive contours are solid. The lag day is indicated in the upper right portion of each row (time moves forward downward). In all panels, the maximum of the vorticity anomalies at 850 hPa is indicated by the filled black dot.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0289.1
Precipitation rate (colors), pressure velocity at 500 (contour lines), and 850-hPa horizontal winds (arrows) lag-regressed onto the precipitation index defined in section 2c for the idealized simulation. Only precipitation anomalies statistically significant at the 99% level are plotted. Contour levels for the vertical velocity anomalies begin at −0.0375 Pa s−1 and are evenly spaced by 0.015 Pa s−1; negative contours are dashed, while positive contours are solid. The lag day is indicated in the upper right portion of each row (time moves forward downward). In all panels, the maximum of the vorticity anomalies at 850 hPa is indicated by the filled black dot.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0289.1
Precipitation rate (colors), pressure velocity at 500 (contour lines), and 850-hPa horizontal winds (arrows) lag-regressed onto the precipitation index defined in section 2c for the idealized simulation. Only precipitation anomalies statistically significant at the 99% level are plotted. Contour levels for the vertical velocity anomalies begin at −0.0375 Pa s−1 and are evenly spaced by 0.015 Pa s−1; negative contours are dashed, while positive contours are solid. The lag day is indicated in the upper right portion of each row (time moves forward downward). In all panels, the maximum of the vorticity anomalies at 850 hPa is indicated by the filled black dot.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0289.1
In comparison to regression results from GFDL’s AM4, the disturbances are located farther south and have weaker precipitation anomalies, on the order of 4 versus 10 mm day−1, but have similar magnitude wind anomalies. The propagation direction is almost directly westward, the same direction as the climatological vertical wind shear (Fig. 1h), raising the possibility that the disturbances could be adiabatically steered by the climatological midtropospheric winds (Boos et al. 2015).
The propagation velocity of the storms can be quantified by computing the location of the maximum vorticity anomalies at 850 hPa at each lag day. This is done by interpolating the vorticity anomalies from the model native grid, spaced by roughly 2.8° in latitude and longitude, to a 0.1° × 0.1° grid, using the nonlinear “patch” interpolation method provided by the Earth System Modeling Framework (ESMF) (Collins et al. 2005; Zhuang and Jüling 2019). The maximum at each lag day plotted in Fig. 4 is marked with a filled black circle. We can compute an average zonal and meridional propagation velocity over the 4-day window plotted in Fig. 4 for each simulation by taking the difference in the position of the maximum at lag day 2 and the position of the maximum at lag day −2 and dividing by the difference in time (4 days). If we do this, we find that the average zonal propagation velocity of the maximum in the idealized simulation is −5.9 m s−1, while the average meridional propagation velocity is −0.1 m s−1. The propagation velocity in our simulation is stronger and more westward-directed than in reality (Boos et al. 2015) or in comprehensive GCMs (Adames and Ming 2018a); in both, zonal propagation velocities are typically on the order of 4 m s−1 or smaller, and at least in Boos et al. (2015) there is a more significant meridional component.
c. The dynamical properties of South Asian monsoon low pressure systems in the idealized simulation
1) Vertical structure of Ertel potential vorticity anomalies
Recent studies have illuminated the composite vertical structure of Ertel potential vorticity (EPV) anomalies of observed MLPSs in both the pressure–longitude and pressure–latitude planes (e.g., Boos et al. 2015; Cohen and Boos 2016). The structure of EPV can inform us about a disturbance’s dynamics; for example, Boos and Korty (2016) look at a zonal profile to assess whether moist baroclinic instability is occurring in observed MLPSs and Boos et al. (2015) look at a meridional profile to assess whether observed MLPSs could be steered westward by the JJAS mean zonal winds. To begin understanding the dynamics of the MLPSs in our idealized simulation, we plot such profiles as well.
If we compute EPV using 6-hourly output, regress it onto the precipitation index at lag day zero, and average the result over the latitudes of the region of interest, the result is Fig. 5a, a zonal cross section of anomalous EPV for MLPSs in our idealized simulation. Overlaid are contours representing a similarly obtained cross section of temperature anomalies. Associated with MLPSs we find a slightly westward-tilting (i.e., in the direction of the shear vector plotted in Fig. 1f) column of anomalous positive EPV centered at around 80°E and 600 hPa. The positive EPV anomalies are flanked to the west and east by weaker negative EPV anomalies, with similar tilts. Positive temperature anomalies can be found above and slightly to the east of the positive EPV anomalies, centered at around 82°E and 400 hPa, while negative temperature anomalies can be found to the west and east as well as below the central warm core. While the anomalies are weaker, the zonal profiles of temperature and EPV anomalies obtained in our idealized simulation qualitatively match those of observed MLPS shown in Cohen and Boos (2016), although they lack the characteristic bimodality of the EPV profile of MLPSs in the vertical noted by Hurley and Boos (2015) and Cohen and Boos (2016) in the ERA-Interim reanalysis dataset and Hunt and Turner (2017) in simulations using the Met Office Unified Model (MetUM). This could be due in part to the coarser vertical resolution used in our idealized simulation (40 vertical levels), when compared with the vertical resolution used in ERA-Interim (60 vertical levels) (Dee et al. 2011) or MetUM (85 vertical levels) (Hunt and Turner 2017).
(a) Zonal cross section of EPV (colors) and temperature (lines) anomalies in the idealized experiment. (b) Meridional cross section of EPV anomalies (colors) and JJAS mean zonal wind (lines). Only statistically significant anomalies at the 99% level are shown. The dashed contours represent negative values, while the solid contours represent positive values. In (b) the bold contour is the zero line. The first temperature anomaly contour in (a) greater than (less than) zero is 0.075 K (−0.075 K); with the exception of the omission of the zero contour, temperature anomaly contours are separated by 0.075 K. The zonal wind contours in (b) are separated by 2 m s−1.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0289.1
(a) Zonal cross section of EPV (colors) and temperature (lines) anomalies in the idealized experiment. (b) Meridional cross section of EPV anomalies (colors) and JJAS mean zonal wind (lines). Only statistically significant anomalies at the 99% level are shown. The dashed contours represent negative values, while the solid contours represent positive values. In (b) the bold contour is the zero line. The first temperature anomaly contour in (a) greater than (less than) zero is 0.075 K (−0.075 K); with the exception of the omission of the zero contour, temperature anomaly contours are separated by 0.075 K. The zonal wind contours in (b) are separated by 2 m s−1.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0289.1
(a) Zonal cross section of EPV (colors) and temperature (lines) anomalies in the idealized experiment. (b) Meridional cross section of EPV anomalies (colors) and JJAS mean zonal wind (lines). Only statistically significant anomalies at the 99% level are shown. The dashed contours represent negative values, while the solid contours represent positive values. In (b) the bold contour is the zero line. The first temperature anomaly contour in (a) greater than (less than) zero is 0.075 K (−0.075 K); with the exception of the omission of the zero contour, temperature anomaly contours are separated by 0.075 K. The zonal wind contours in (b) are separated by 2 m s−1.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0289.1
Taking the same EPV anomalies obtained through regression, but this time averaging between 75° and 85°E, we can obtain a profile of the composite disturbance in the pressure–latitude plane. This is shown in Fig. 5b. Following Boos et al. (2015) we also plot contour lines representing the mean JJAS zonal winds averaged over the same longitudinal region as the EPV anomalies.8 In Fig. 5 we find that the bulk of the disturbance, identified as the region of positive EPV anomalies, is located in a region of westerly winds (solid contours). At upper levels, there is some overlap between positive EPV anomalies and easterly winds; however, the magnitude of the easterly winds is fairly weak in the region of overlap.
2) Anomalous Ertel potential vorticity budget
We can learn more about the propagation mechanism of the MLPSs in our idealized simulation by computing anomalous tracer budgets. We will start with the anomalous EPV budget associated with the storms; a similar analysis was done for a single particular storm in Boos et al. (2015), though here our anomalies represent a composite obtained through regression.
Spatial patterns of the different terms in Eq. (8) at the 500- and 700-hPa levels are shown in Fig. 6. There we find that the pattern of anomalous EPV time tendency (Fig. 6a,f) is consistent with the westward propagation of the storms, with positive EPV tendencies to the west of the vortex center and negative EPV tendencies to the east at either level. As Boos et al. (2015) found in a case study of a monsoon depression, in the midtroposphere a negative diabatic tendency at the storm center (Fig. 6b) is largely compensated for by a positive vertical advection tendency in the same location (Fig. 6d). At this level in Boos et al. (2015) and in our simulation, anomalous horizontal advection of EPV (Fig. 6c) appears to project most strongly onto to the spatial pattern of the overall EPV tendency. Closer to the surface, at 700 hPa, diabatic processes appear to play a larger role in the propagation tendency (cf. Figs. 6g and 6h), with horizontal advection no longer being as significant; again this is similar to what is found in Boos et al. (2015) in reanalysis. The residual in the budget at each level, shown in Figs. 6e and 6j, is small compared to the explicitly computed terms.
Anomalous terms in the EPV budget in the idealized simulation at (top) 500 and (bottom) 700 hPa. The solid black contours represent isolines of EPV anomalies of 0.01 and 0.02 PVU, while the dashed black contours represent isolines of PV of −0.01 PVU. Only values statistically significant at the 99% level are shown.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0289.1
Anomalous terms in the EPV budget in the idealized simulation at (top) 500 and (bottom) 700 hPa. The solid black contours represent isolines of EPV anomalies of 0.01 and 0.02 PVU, while the dashed black contours represent isolines of PV of −0.01 PVU. Only values statistically significant at the 99% level are shown.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0289.1
Anomalous terms in the EPV budget in the idealized simulation at (top) 500 and (bottom) 700 hPa. The solid black contours represent isolines of EPV anomalies of 0.01 and 0.02 PVU, while the dashed black contours represent isolines of PV of −0.01 PVU. Only values statistically significant at the 99% level are shown.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0289.1
While the results plotted in Fig. 6 provide qualitative evidence of the importance of horizontal advection and diabatic processes in the propagation of EPV anomalies, we can be more quantitative about this assessment by applying projection analysis, described in section 2c, to the EPV budget. The projections for each term at each vertical level in the idealized simulation are shown in Fig. 7. Here it is quantitatively clear that anomalous horizontal advection of EPV is dominant in the mid- to upper troposphere, while diabatic processes, primarily condensation of water vapor,9 become more important in the lower troposphere (i.e., near 700 hPa). This is qualitatively consistent with the results of Boos et al. (2015). Vertical advection anomalies have a small negative contribution to the EPV tendency in the lower troposphere and a small positive contribution in the mid- to upper troposphere; in general they tend to oppose the diabatic tendency throughout the atmosphere. In doing a Reynolds decomposition, a technique described in the next paragraph, of the vertical advection term (Fig. S4), we find that at 500 hPa the product of the high-frequency vertical velocity and low-frequency vertical gradient of EPV term,
Projection of EPV budget terms on
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0289.1
Projection of EPV budget terms on
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0289.1
Projection of EPV budget terms on
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0289.1
Projecting each term onto the total EPV tendency, we find, as was qualitatively shown in Fig. 5b, that advection of high-frequency EPV by the low-frequency zonal wind tends to work against the prevailing westward-propagating tendency of EPV in the lower- to midtroposphere (solid red line in Fig. 8). Instead, the most important term is the advection of the low-frequency EPV by the high-frequency meridional winds (dashed blue line in Fig. 8). Because the high-frequency meridional winds are cyclonic, they blow southward to the west of the storm, down the low-frequency EPV gradient, bringing high mean EPV air from the north, and northward east of the storm up the low-frequency EPV gradient, bringing low mean EPV air from the south, resulting in the dipole pattern seen in Fig. 6a. This is consistent with the propagation mechanism of linear Rossby waves.
Projection of terms comprising the total horizontal advection anomaly [see Eq. (10)] on
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0289.1
Projection of terms comprising the total horizontal advection anomaly [see Eq. (10)] on
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0289.1
Projection of terms comprising the total horizontal advection anomaly [see Eq. (10)] on
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0289.1
The other terms, related to advection of low-frequency EPV by the low-frequency horizontal winds, advection of high-frequency EPV by the low-frequency meridional winds, advection of the low-frequency EPV by the high-frequency zonal winds, and advection of the high-frequency EPV by the high-frequency horizontal winds play a negligible role in the propagation of EPV anomalies in the lower troposphere, and play minor offsetting roles in the upper troposphere. The tertiary role of high-frequency EPV advection by the high-frequency horizontal winds in the budget in particular suggests that beta drift is not a primary driver of propagation for the storms in our simulation.
Further insight into the dynamics of the MLPSs in our idealized simulation can be gleaned from analysis of the budgets of vorticity, column-integrated internal energy, and column-integrated moisture. By looking at these budgets, we can approximately determine whether a simplified model, like moisture vortex instability (Adames and Ming 2018a), could be used to describe the storm systems in our simulation.
3) Anomalous vorticity budget
The terms in the anomalous budget for a level in the upper troposphere (400 hPa) and a level in the lower troposphere (850 hPa), decomposed as described above, are shown in Fig. 9. Figures 9a and 9e show the anomalous time tendency of the relative vorticity. There we can see a dipole pattern oriented along an east–west axis, similar to what we see in the anomalous EPV budget. In addition we can see that the dominant term on the right-hand side of Eq. (11) is the term involving the planetary vorticity. Terms potentially involving the low-frequency winds, such as −∇ ⋅ (ζu)′ or
Terms in the anomalous vorticity budget (colors) at (top) 400 and (bottom) 850 hPa. Only values statistically significant at the 99% level are shown. Contours represent relative vorticity anomalies, ζ′; contour levels start at ±1.0 × 10−6 s−1 and are separated by intervals of 2.0 × 10−6 s−1. Dashed contours represent negative anomalies, while solid contours represent positive anomalies.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0289.1
Terms in the anomalous vorticity budget (colors) at (top) 400 and (bottom) 850 hPa. Only values statistically significant at the 99% level are shown. Contours represent relative vorticity anomalies, ζ′; contour levels start at ±1.0 × 10−6 s−1 and are separated by intervals of 2.0 × 10−6 s−1. Dashed contours represent negative anomalies, while solid contours represent positive anomalies.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0289.1
Terms in the anomalous vorticity budget (colors) at (top) 400 and (bottom) 850 hPa. Only values statistically significant at the 99% level are shown. Contours represent relative vorticity anomalies, ζ′; contour levels start at ±1.0 × 10−6 s−1 and are separated by intervals of 2.0 × 10−6 s−1. Dashed contours represent negative anomalies, while solid contours represent positive anomalies.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0289.1
Figure 10 shows the projection of the vorticity budget terms on the time tendency of relative vorticity in the idealized simulation. There we can see that our budget closes nearly perfectly below about 500 hPa and only slightly diverges above, as evidenced by the dashed black line, representing the total of the terms on the right-hand side of Eq. (9) having a projection of about one at all pressure levels. In addition, we see quantitative evidence of the dominance of the planetary vorticity term (red line in Fig. 10), which indicates a spatial projection of over 0.5 below 300 hPa. It is only above 300 hPa that anomalous vortex stretching associated with the relative vorticity and/or anomalous relative vorticity advection, −∇ ⋅ ζu, becomes of leading-order significance in the budget. The combined effects of anomalous vertical advection and vortex tilting do not project strongly onto the time tendency of relative vorticity—in other words, they do not contribute to the propagation of vorticity anomalies anywhere in the troposphere—although they may play a role in their growth and maintenance, because of their approximate collocation with vorticity anomalies themselves.
Projection of vorticity budget terms on the time tendency of the relative vorticity.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0289.1
Projection of vorticity budget terms on the time tendency of the relative vorticity.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0289.1
Projection of vorticity budget terms on the time tendency of the relative vorticity.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0289.1
4) Anomalous column-integrated internal energy budget
Models of transient disturbances in the tropics can often be simplified by assuming a first-baroclinic mode vertical structure. This allows one to effectively remove the vertical dimension from the problem and construct a two-dimensional shallow-water-like models, where the relevant internal energy and moisture budgets are vertically integrated (e.g., Neelin and Zeng 2000; Adames and Kim 2016; Adames and Ming 2018a). To understand the importance of terms in these anomalous budgets, particularly in the context of these simplified models, we therefore look at their vertically integrated forms.
The terms in the approximate budget are plotted in Fig. 11 along with contours indicating the values of anomalous vertically integrated internal energy, Cp{T}′. In Fig. 11a we can see a negative anomaly in internal energy at the storm center, flanked by an anomalous negative internal energy tendency to the west and an anomalous positive internal energy tendency to the east; this dipole pattern in the tendency is consistent with the westward propagation of the negative internal energy anomaly at the storm center. The term on the right-hand side of the budget that projects most strongly onto the time tendency is the sum of the vertical advection of dry static energy and the column-integrated latent heating associated with precipitation (Fig. 11c); overall this has a projection value of 2.65 on the tendency over the domain plotted. Horizontal advection of internal energy serves to damp this propagation tendency (Fig. 11b). Total horizontal advection has a projection value of −1.45. Of this damping influence, horizontal advection of low-frequency internal energy by the high-frequency meridional wind,
Terms in the anomalous internal energy budget (colors) with anomalous column-integrated internal energy, Cp{T}′, overlaid (contours). Only budget values statistically significant at a 99% level are shown. Negative contours are dashed; positive contours are solid. With the exception of the omission of the zero contour, contours are separated by an interval of 2.5 × 105 J kg−1.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0289.1
Terms in the anomalous internal energy budget (colors) with anomalous column-integrated internal energy, Cp{T}′, overlaid (contours). Only budget values statistically significant at a 99% level are shown. Negative contours are dashed; positive contours are solid. With the exception of the omission of the zero contour, contours are separated by an interval of 2.5 × 105 J kg−1.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0289.1
Terms in the anomalous internal energy budget (colors) with anomalous column-integrated internal energy, Cp{T}′, overlaid (contours). Only budget values statistically significant at a 99% level are shown. Negative contours are dashed; positive contours are solid. With the exception of the omission of the zero contour, contours are separated by an interval of 2.5 × 105 J kg−1.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0289.1
Projection of the terms on the right-hand side of the column-integrated internal energy budget sorted in descending order by absolute value. The horizontal advection term is comprehensively decomposed into linear and nonlinear components. The sum of the components adds exactly to 1.0.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0289.1
Projection of the terms on the right-hand side of the column-integrated internal energy budget sorted in descending order by absolute value. The horizontal advection term is comprehensively decomposed into linear and nonlinear components. The sum of the components adds exactly to 1.0.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0289.1
Projection of the terms on the right-hand side of the column-integrated internal energy budget sorted in descending order by absolute value. The horizontal advection term is comprehensively decomposed into linear and nonlinear components. The sum of the components adds exactly to 1.0.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0289.1
5) Anomalous column-integrated moisture budget
Again, we compute the terms in the anomalous budget following the methods described in section 2c(3). The results are shown in Fig. 13. The time tendency anomaly pattern, shown in Fig. 13a, depicts an east–west-oriented dipole pattern, consistent with the westward propagation of the storms. The two largest terms on the right-hand side of the budget are the vertical advection and precipitation terms, each with maximum magnitudes on the order of 60 W m−2, with vertical advection being a net source (positive) and precipitation being a net sink (negative). Since they largely offset each other, as in Adames and Ming (2018a), we combine these into one term and refer to it as the “column moisture process.” This aggregate term projects strongly onto the time tendency, with a projection value of 0.63 over the region plotted, although it perhaps has a slightly northwestward orientation compared with the more westward orientation of the tendency itself. Horizontal advection plays a secondary role, and acts to turn the dipole orientation more toward the west (with a projection value of 0.42). In terms of propagation, the anomalous latent heat fluxes (Fig. 13d) play a minor damping role, with a projection of −0.05; however they are positive, and collocated mainly with the column moisture anomalies associated with the disturbance, and therefore more directly contribute to their in-place amplification. In the projection sense, these results are largely consistent with the results of Adames and Ming (2018a) in AM4; there the column moisture process term was dominant, with a minor positive contribution coming from horizontal advection, and a minor negative contribution coming from evaporation.
Terms in the anomalous moisture budget (colors). Only tendency anomalies statistically significant at the 99% level are shown. Contours represent column-integrated moisture anomalies scaled by the latent heat of vaporization, Lυ. Negative contours are dashed; positive contours are solid. With the exception of the omission of the zero contour, contours are separated by intervals of 4.0 × 105 J m−2.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0289.1
Terms in the anomalous moisture budget (colors). Only tendency anomalies statistically significant at the 99% level are shown. Contours represent column-integrated moisture anomalies scaled by the latent heat of vaporization, Lυ. Negative contours are dashed; positive contours are solid. With the exception of the omission of the zero contour, contours are separated by intervals of 4.0 × 105 J m−2.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0289.1
Terms in the anomalous moisture budget (colors). Only tendency anomalies statistically significant at the 99% level are shown. Contours represent column-integrated moisture anomalies scaled by the latent heat of vaporization, Lυ. Negative contours are dashed; positive contours are solid. With the exception of the omission of the zero contour, contours are separated by intervals of 4.0 × 105 J m−2.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0289.1
Similar to what we did with the EPV and internal energy budgets, we can decompose the horizontal advection term into components due to the product of the low-frequency winds and high-frequency moisture gradients, products of the high-frequency winds and the low-frequency moisture gradients, and products of the high-frequency factors. This allows us to continue to determine the feasibility of using a linear model of the column-integrated moisture equation. The spatial patterns of the terms associated with this decomposition compared with all other terms in the anomalous column-integrated moisture budget can be found in Fig. S6 of the supplemental material. For brevity, we show only the projection of each of these terms on the anomalous time tendency of column-integrated moisture in the main body of this manuscript in Fig. 14. Here we find that the primary reason for the positive contribution of the horizontal advection of moisture to the westward-propagation tendency is the component due to advection of high-frequency moisture anomalies by the low-frequency zonal winds, with a projection of 0.12. This is followed in projection magnitude by the term related to the product of the high-frequency meridional wind and high-frequency meridional moisture gradient, 0.08, and the term related to the product of the low-frequency meridional wind and high-frequency meridional moisture gradient, 0.07. We will note, however, that the term nonlinear in high-frequency factors is not statistically significant over a large portion of the South Asian monsoon region (see Fig. S6h). The term related to the product of the high-frequency meridional winds and low-frequency meridional moisture gradient has a strong spatial pattern relative to the other terms that comprise the total horizontal advection term (Fig. S6g); however, it does not project strongly onto the anomalous tendency of column-integrated moisture. This could be due to the fact that the MLPSs in our idealized simulation are centered at roughly the local maximum in the JJAS-mean column-integrated moisture field, which coupled with a cyclonic circulation leads to the quadrupole pattern seen in Fig. S6g.
Projection of the terms on the right-hand side of the column-integrated moisture budget sorted in descending order by absolute value. The horizontal advection term is comprehensively decomposed into linear and nonlinear components. The sum of the components adds exactly to 1.0.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0289.1
Projection of the terms on the right-hand side of the column-integrated moisture budget sorted in descending order by absolute value. The horizontal advection term is comprehensively decomposed into linear and nonlinear components. The sum of the components adds exactly to 1.0.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0289.1
Projection of the terms on the right-hand side of the column-integrated moisture budget sorted in descending order by absolute value. The horizontal advection term is comprehensively decomposed into linear and nonlinear components. The sum of the components adds exactly to 1.0.
Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0289.1
4. Discussion
We can assess the potential applicability of various theories that have appeared in the literature for the growth and propagation of MLPSs to the storms we find in our idealized simulation by interpreting the structure and budget analysis results presented above.
a. Advection by the mean upper-level easterly winds, modified by beta drift
We will begin by discussing one possible propagation mechanism, inspired by the notion that MLPSs could be analogous to tropical depressions (Boos et al. 2015; Cohen and Boos 2016). Here it is suggested that MLPSs could be steered westward by the low-frequency upper-level easterly winds, and have an additional northward component to their motion through beta drift (i.e., nonlinear advection of high-frequency vorticity anomalies by the high-frequency winds). Boos et al. (2015) base this hypothesis off of a composite analysis of South Asian monsoon depressions using tracks and positions from their own archive (Hurley and Boos 2015) and meteorological variables derived from the ERA-Interim reanalysis (Dee et al. 2011). In looking at the structure of EPV anomalies of the storms in our simulation in the pressure versus latitude plane, with the JJAS mean zonal winds overlaid, Fig. 5b, we find that steering by the mean upper-level easterly winds is likely not the case for our disturbances. The majority of the positive EPV anomalies are located in a region of mean westerly winds, and where there is overlap with easterly winds, the winds are too weak to propagate the vortex westward at 6 m s−1.
Beta drift is indicative of nonlinear advection of high-frequency EPV anomalies by high-frequency wind anomalies and is normally responsible for a meridional component to a storm’s path (Tamarin and Kaspi 2016), which indeed is significant for depressions seen in observations (Hurley and Boos 2015; Boos et al. 2015). In our analysis, we find that there is little nonlinear contribution to the anomalous horizontal advection term in the EPV budget, which suggests that beta drift is not playing a major role in the propagation of the storms either. This is consistent with the fact that the storms have little northward component to their propagation, which is a deviation from those in observations (Hurley and Boos 2015).
b. Baroclinic instability
Some of the original theories for MLPSs were based on the idea that they emerged out of dry or moist baroclinic instability in the presence of an easterly vertical wind shear (Mishra and Salvekar 1980; Mak 1983; Moorthi and Arakawa 1985). Indeed, this type of mechanism has been used to explain MLPS-like disturbances that occurred in a similarly idealized model roughly 20 years ago (Xie and Saiki 1999). Cohen and Boos (2016) argue, however, based on the structure of EPV anomalies in the pressure–longitude plane, that moist baroclinic instability is not occurring in observed MLPSs. They argue that in order for counterpropagating Rossby waves to interact constructively, their phasing must be such that EPV anomalies tilt against the mean vertical wind shear with height; in other words, EPV anomalies would need to tilt to the east in the South Asian monsoon region with its characteristic mean easterly shear. This is not the case in observations (Cohen and Boos 2016), and it is also not the case for the storms in our idealized simulation.
We find that the structure of EPV and temperature anomalies shown in Fig. 5a resembles that found for monsoon depressions in Cohen and Boos (2016). There, for storms midway through their lifetimes, Cohen and Boos (2016) found that monsoon depressions can be characterized by a positive column of EPV, tilting slightly westward with height (i.e., with the shear) and a warm-over-cold temperature anomaly structure. They contrast these anomaly patterns with those seen for extratropical diabatic Rossby waves, noting in particular that diabatic Rossby waves have EPV anomalies that tilt against the mean wind shear, a necessary condition for growth out of baroclinic instability. Because the positive EPV anomalies in our idealized simulation tilt with the shear,12 we take Fig. 5a as tentative evidence that baroclinic instability is not playing a role in the life cycle of the low pressure systems simulated in our idealized model.
c. Moisture vortex instability
Despite baroclinic instability appearing not to play a role in the disturbances in our idealized simulation, their propagation, at least at upper levels, appears to be consistent with the propagation mechanism of Rossby waves (i.e., advection of the planetary vorticity by the anomalous meridional winds). At lower levels, analysis of the anomalous EPV budget suggests that propagation is driven by latent heat release due to the condensation of water vapor associated with precipitation. Superficially, this is consistent with another recently proposed theory for MLPSs, called “moisture vortex instability” (MVI) (Adames and Ming 2018a).
Moisture vortex instability theory is based on using vertically truncated versions of the momentum, thermodynamic, and moisture equations; in this context “vertically truncated” means that the horizontal winds, temperature, geopotential, and specific humidity are projected onto basis functions consistent with a first-baroclinic mode vertical structure for the vertical velocity. This reduces the equations to a shallow water–like system, which is more amenable to analysis [e.g., as in Neelin and Zeng (2000), Haertel et al. (2008), or Adames and Kim (2016)]. In Adames and Ming (2018b), the truncated equations are linearized about a South Asian monsoon-season-like basic state and, through analysis of a dispersion relation, are shown to support unstable modes. The instability is associated with a partially in-phase relationship between precipitation anomalies (corresponding with upward vertical motion and convergence of low-level horizontal winds) and cyclonic (i.e., positive) vorticity anomalies. The precipitation anomalies, through their association with low-level convergence, result in a growing tendency for the vorticity anomalies through vortex stretching (Adames and Ming 2018b). Propagation of the wave in their framework is primarily due to vortex stretching from moist convection in regions of isentropic ascent and horizontal moisture advection.
In terms of the primitive equations, moisture vortex instability theory depends on the advection of planetary vorticity, vortex stretching, and meridional and vertical advection of the mean internal energy and moisture by the anomalous winds and latent heating due to precipitation. It assumes no influence by the mean state winds or terms nonlinear in anomalies (Adames and Ming 2018a). Our analysis of the anomalous vorticity, column-integrated internal energy, and column-integrated moisture budgets can shed light on whether the assumptions made in constructing the theory hold in our idealized simulation.
In the case of the vorticity budget, we find that at both 850 and 400 hPa that propagation is dominated by the terms associated with advection of planetary vorticity and vortex stretching, such as the term −∇ ⋅ (fu)′, which is consistent with MVI theory. The term related to the influence of the collective influence of vertical vorticity advection and vortex tilting,
In the case of the column-integrated internal energy budget, the picture of the storms in our simulation is largely consistent with the assumptions of MVI theory. There the anomalous radiative and sensible heating parts of the thermodynamic equation were neglected, and they are indeed found to be negligible in our simulation. The terms retained in the anomalous thermodynamic budget in Adames and Ming (2018a) were the vertical advection of mean dry static energy by the anomalous pressure velocity, the column latent heating due to precipitation, and meridional advection of mean internal energy by the anomalous meridional wind. These are indeed the leading-order terms in the anomalous thermodynamic budget in our simulation (see Fig. 12).
Finally, as assumed in Adames and Ming (2018b), the vertical advection of moisture and the loss of column moisture through precipitation play an important role in the moisture budget. That said, assumptions made regarding the horizontal advection of moisture in Adames and Ming (2018b) do not necessarily hold in our simulation. Adames and Ming (2018b) assume that advection of mean moisture by the anomalous meridional wind plays a leading-order role in the budget. We find that this does not quite hold in our simulation. While the advection of low-frequency moisture by the high-frequency meridional wind anomalies has a relatively strong magnitude relative to other terms related to horizontal advection, it does not project strongly onto the anomalous time tendency of column-integrated moisture. This is likely in part because the storms we analyze in this simulation are centered roughly at the latitude of maximum JJAS-mean column-integrated moisture, in contrast to the assumption made by Adames and Ming (2018a) that the storms form in an area of uniformly increasing column moisture in the meridional direction. A term that projects more strongly is the advection of the high-frequency moisture anomalies by the low-frequency zonal wind, which was not considered in Adames and Ming (2018a).
5. Conclusions
In this study we have completed a systematic analysis of low pressure systems in the South Asian monsoon region in a heavily idealized moist GCM, notably without impacts of clouds or topography. The low pressure systems found in our simulation share a number of characteristics with South Asian monsoon low pressure systems observed in reality and those simulated in GFDL’s AM4. For example, precipitation anomalies in the South Asian monsoon region in our simulation have a typical zonal scale of around zonal wavenumber 10, consistent with the scale seen in TRMM observations and AM4; the typical frequency of around 0.2 day−1 is consistent with that found in those datasets as well (Adames and Ming 2018a). In addition, we find that the vertical structure of potential vorticity anomalies associated with the low pressure systems simulated in our model shares an important qualitative feature with that found in reanalysis: the EPV anomalies in the troposphere tilt slightly with the JJAS mean easterly zonal wind shear (Cohen and Boos 2016).
Aspects of the low pressure systems that differ slightly from those seen in reality are their propagation speed and direction. In our simulation, the storms propagate predominantly westward at speeds of over 6 m s−1; this is faster than storms seen in GFDL’s AM4 and in reanalysis. There are several possible explanations for this difference. Two of these arise from Rossby wave theory. From inspection of Fig. 4 it is possible that these waves are of slightly larger scale, resulting in a smaller horizontal wavenumber, than the low pressure systems simulated in AM4 and observed in reanalysis. In addition, because these systems occur at a lower latitude than in the aforementioned datasets, the Rossby radius of deformation is larger, which would also cause these systems to exhibit faster westward propagation [see Eq. (22a) in Adames and Ming (2018b)]. We find little meridional component to the propagation direction, which is different than at least the reanalysis (Boos et al. 2015); in GFDL’s AM4 model, storms propagated predominantly westward as well. It is possible that the northward component of propagation is largely a result of nonlinear beta drift, which is characteristic of the stronger storms that were analyzed by Boos et al. (2015). Per the role of the meridional temperature gradient in the propagation of column-integrated moist enthalpy anomalies associated with MLPSs suggested by moisture vortex instability theory (Adames and Ming 2018a), the more equatorward location of the systems when compared with observations may be in part due to the more equatorward meridional temperature gradient in our simulation.
The movement of the weak disturbances in our simulation can largely be explained through linearized versions of the primitive equations, rather than beta drift, as was the case for monsoon depressions analyzed in reanalysis in Boos et al. (2015). A slight deviation from moisture vortex instability theory is the potential contribution of the vertical shear of the low-frequency winds to the growth and maintenance of the disturbances. Despite not being classic examples of baroclinic instability, these disturbances might still be classified as a certain form of diabatically influenced Rossby wave, like that described in Adames and Ming (2018b). A major distinguishing factor between extratropical diabatic Rossby waves and Rossby-like waves deriving from moisture vortex instability is that, while influenced by moist processes, extratropical Rossby waves can grow in the absence of precipitation (Vallis 2006); for moisture vortex instability, precipitation is necessary for growth (Adames and Ming 2018b). The possibility of an approximate explanation via a linear model could motivate further sensitivity studies in a modeling framework similar to the one used here, to test whether properties of the mean state, like the meridional temperature or moisture gradient, could influence properties of the low pressure systems, like the phase speed.
While the work we have done here demonstrates that somewhat realistic MLPS-like disturbances can be simulated with simplified model physics and boundary conditions, it does not rule out that even further idealizations could be made. We intentionally used realistic continental geometry, reduced heat capacity, and a bucket hydrology model to limit evaporation over land, in order to remove those as possible reasons for too unrealistic a mean climate to support MLPSs. In future work it could be useful to run simulations with realistic continental geometry, with only reduced heat capacity over land, or only bucket hydrology over land to see which is most important in generating a mean state climate suitable for South Asian MLPSs. For example, this could inform us whether it might be valuable to use a simpler land setup such as the “moist land” simulations with a rectangular continent in Zhou and Xie (2018) when attempting to systematically modify the mean state as suggested at the end of the previous paragraph. In those simulations in Zhou and Xie (2018), the continental geometry is significantly simplified, and the land surface is assumed to always be saturated; that is, the only thing distinguishing land from ocean is its reduced heat capacity.
Acknowledgments
We thank Steve Garner, Gan Zhang, and three anonymous reviewers for helpful comments on earlier versions of this manuscript, as well as Spencer Hill for discussions and resources regarding methods for computing closed column-integrated tracer budgets. S.K.C. was supported by a National Defense Science and Engineering Graduate Fellowship. Á.F.A. was supported by the University of Michigan’s startup package and by the National Science Foundation’s Grant ATM 1841559. The output from the simulations described in this manuscript is archived at the Geophysical Fluid Dynamics Laboratory and is available upon request.
APPENDIX
Method for Computing the Internal Energy Budget
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An important parameter in this convection scheme is the relaxation time; we use a relaxation time of 2 h, which is the typical default value used by other studies (e.g., Frierson 2007b; O’Gorman and Schneider 2008; Geen et al. 2018). While it has been shown that aspects of the climate can be sensitive to this parameter choice (e.g., Frierson 2007a; Clark et al. 2018), we find qualitatively similar results in an experiment with a larger convective relaxation time (12 h; not shown), which has been suggested by Bretherton et al. (2004) to potentially be a more appropriate convective relaxation time scale for convection parameterizations of the type used in this model.
One could potentially produce a more realistic meridional temperature gradient, and potentially MLPSs, in the aquaplanet configuration of this model by removing the seasonal cycle in solar insolation and adding a forcing to induce a warm pool at the latitudes of the South Asian monsoon region (e.g., centered at around 15°N). For instance Ajayamohan et al. (2014) find westward propagating Rossby wave–like disturbances in such a setup; however, in this study we opt to allow the natural interaction between the seasonal cycle and land–ocean contrast in heat capacity to produce such a local temperature maximum in the region.
Hurley and Boos (2015) note that MLPS activity is strongest slightly poleward of this maximum in most monsoon regions; however, we claim that as a first approximation this is a reasonable method of defining the central latitude of our region of interest.
Note in the case of the internal energy budget the methods of Hill et al. (2017) cannot be applied exactly; therefore the budget can still not be exactly closed. Instead we follow the method described in the appendix.
A similar double intertropical convergence zone (ITCZ) structure was also found in Xie and Saiki (1999). In their idealized simulation they also found latitudinal maxima in summer precipitation in the South Asian monsoon region and near the equator. To a lesser extent a double ITCZ structure is also seen after monsoon onset in the idealized “flat” simulation of Geen et al. (2018), which uses a similarly configured model to our simulation, with the single exception of additional of AMIP-derived slab ocean heat fluxes in their case. In our case, the double ITCZ structure is not a completely persistent feature. In other words, there are times when it is only raining in one rainband and not the other, but during July and August there are times when it rains in both rainbands simultaneously.
Note that the region of interest used here and in Adames and Ming (2018a) for the observations was centered at 17.5°N, rather than at 12.6°N in the case of the idealized simulation in Fig. 3b.
For instance, if we compute composite means of the anomaly patterns associated with precipitation index values greater than 2 (approximately the strongest 3%–4% of storms), we find storm-center precipitation anomalies on the order of 10 mm day−1, maximum wind speed anomalies near 8.5 m s−1, and minimum surface pressure anomalies of less than 3.6 hPa. The results of this composite analysis are shown in Fig. S2 of the supplemental material.
Note that in Boos et al. (2015) the zonal wind was smoothed with a 21-day running mean and then composited over storms; here we use the full climatological mean rather than a smoothed composite.
We conclude this by computing the component of the anomalous diabatic EPV tendency due to condensation via Eq. (5) of Tamarin and Kaspi (2016), which is based on the work of Emanuel et al. (1987) (see Fig. S3). We find that it closely resembles the anomalous pattern of the total diabatic EPV tendency over the regression index region, representing 71% of it at the 700-hPa level and 97% of it at the 500-hPa level. The dominance of condensation of water vapor in the diabatic heating component of the EPV tendency is qualitatively consistent with composites of observed MLPSs (Hunt et al. 2016b).
Consider the idealized example of two factors that can be described as a sine and cosine wave of the same frequency, ω. Their product, via the sine double angle identity, would then be a sine wave with twice the frequency, for example, sin(ωt) cos(ωt) = (1/2)sin(2ωt), which could project onto a higher-frequency index.
Note that since we high-pass filter all quantities before regressing, as described in section 2c, any low-frequency component of u will be filtered out.
Above the 200-hPa pressure level there is a strong positive EPV anomaly slightly east of the midtropospheric EPV anomalies, and a negative anomaly directly above the midtroposphere maximum. It is possible one could interpret these as evidence of tilting against the shear, and thus possible baroclinic instability, following the argument of Cohen and Boos (2016). However, while not apparent in Fig. 5a due to the statistical significance mask, these anomalies appear rather to be components of a more organized packet of gravity waves propagating upward from the monsoon low pressure system, similar to those seen emanating from convectively coupled waves near the equator (Kiladis et al. 2009), and not part of the low pressure system itself.